2tan (problem 3.3.2)

Time bar (total: 9.1s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze645.0ms (7.1%)

Memory
-314.3MiB live, 57.1MiB allocated; 796ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%50.6%49.4%0%0%0%0
0%0%50.6%49.4%0%0%0%1
0%0%50.6%49.4%0%0%0%2
0%0%25.3%49.4%0%25.3%0%3
0%0%25.3%49.4%0%25.3%0%4
0%0%19%49.4%0%31.6%0%5
0%0%15.8%49.4%0%34.8%0%6
0%0%11.1%49.4%0%39.5%0%7
0%0%8.7%49.4%0%41.9%0%8
0%0%5.9%49.4%0%44.6%0%9
0%0%4.5%49.4%0%46%0%10
0%0%3.1%49.4%0%47.5%0%11
0%0%2.7%49.4%0%47.9%0%12
Compiler

Compiled 27 to 19 computations (29.6% saved)

sample4.5s (49.4%)

Memory
124.5MiB live, 6 449.3MiB allocated; 1.1s collecting garbage
Samples
2.2s26 352×0invalid
813.0ms5 546×1valid
224.0ms2 710×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.0s
ival-tan: 750.0ms (38% of total)
ival-fabs: 271.0ms (13.7% of total)
ival-<: 241.0ms (12.2% of total)
ival-add!: 214.0ms (10.8% of total)
adjust: 186.0ms (9.4% of total)
ival-mult!: 144.0ms (7.3% of total)
ival-sub!: 91.0ms (4.6% of total)
ival-and: 64.0ms (3.2% of total)
ival-assert: 14.0ms (0.7% of total)
Bogosity

explain107.0ms (1.2%)

Memory
7.0MiB live, 192.7MiB allocated; 27ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2313(-1.850409177714507e-304 3.8644703780191705e-307)5(5.9602954035502565e-36 9.21258888489744e-38)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10-1(-54.89339948577615 2.2208188317139637e-8)(tan.f64 (+.f64 x eps))
00-0-eps
00-0-(+.f64 x eps)
00-0-(tan.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))cancellation2297
Confusion
Predicted +Predicted -
+2265
-322
Precision
0.9868995633187773
Recall
0.9783549783549783
Confusion?
Predicted +Predicted MaybePredicted -
+22650
-3220
Precision?
0.9788135593220338
Recall?
1.0
Freqs
test
numberfreq
027
1229
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
52.0ms378×1valid
6.0ms134×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
adjust: 22.0ms (52.2% of total)
ival-tan: 16.0ms (38% of total)
ival-sub!: 2.0ms (4.7% of total)
ival-add!: 2.0ms (4.7% of total)

preprocess68.0ms (0.7%)

Memory
-16.8MiB live, 33.4MiB allocated; 19ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02150
14050
26750
311450
418950
533050
666050
7151350
8290350
9433450
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶59.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 14 to 12 computations (14.3% saved)

series12.0ms (0.1%)

Memory
13.5MiB live, 13.5MiB allocated; 0ms collecting garbage
Counts
6 → 36
Calls
Call 1
Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
eps
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
x
@0
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
eps
@inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))
2.0ms
eps
@-inf
((- (tan (+ x eps)) (tan x)) (tan (+ x eps)) (+ x eps) x eps (tan x))

rewrite156.0ms (1.7%)

Memory
29.4MiB live, 163.6MiB allocated; 13ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02011262
02061117
11269904
08326874
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
42 → 87
Calls
Call 1
Inputs
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))))
(/.f64 (neg.f64 (sin.f64 (-.f64 (+.f64 eps x) x))) (neg.f64 (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (cos.f64 x))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (cos.f64 x)) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (cos.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (sin.f64 x)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 eps x)) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))))
(-.f64 (/.f64 (*.f64 (sin.f64 (+.f64 eps x)) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (/.f64 (*.f64 (cos.f64 (+.f64 eps x)) (sin.f64 x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
(-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))
(/.f64 (neg.f64 (sin.f64 (neg.f64 (+.f64 eps x)))) (neg.f64 (neg.f64 (cos.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(/.f64 (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 (PI.f64)))))
(/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 eps) (tan.f64 x))))
(/.f64 (sin.f64 (neg.f64 (+.f64 eps x))) (neg.f64 (cos.f64 (+.f64 eps x))))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 (+.f64 x (PI.f64)) eps))
(tan.f64 (+.f64 (+.f64 eps x) (PI.f64)))
(tan.f64 (+.f64 eps x))
(+.f64 (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (tan.f64 eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(+.f64 (/.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))) (/.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (cos.f64 (+.f64 eps x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 eps eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (*.f64 x x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 eps eps) eps))) (neg.f64 (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 x eps)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x))) (neg.f64 (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 eps eps)) (-.f64 x eps))
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x x)) (-.f64 eps x))
(/.f64 (fma.f64 (*.f64 x x) x (*.f64 (*.f64 eps eps) eps)) (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 x eps))))
(/.f64 (fma.f64 (*.f64 eps eps) eps (*.f64 (*.f64 x x) x)) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x eps)) (/.f64 (*.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (*.f64 eps eps) (-.f64 eps x)) (/.f64 (*.f64 x x) (-.f64 eps x)))
(+.f64 (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 x eps)))) (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 x x (-.f64 (*.f64 eps eps) (*.f64 x eps)))))
(+.f64 (/.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))) (/.f64 (*.f64 (*.f64 x x) x) (fma.f64 eps eps (-.f64 (*.f64 x x) (*.f64 eps x)))))
(+.f64 eps x)
(+.f64 x eps)
x
eps
(/.f64 (neg.f64 (neg.f64 (sin.f64 x))) (neg.f64 (neg.f64 (cos.f64 x))))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 (PI.f64)))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (cos.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 x (PI.f64)))
(tan.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 x (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (*.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (*.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))))))) #s(literal 1/2 binary64)) x)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (tan (+ x eps)) (tan.f64 eps))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 x (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (*.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))))))) #s(literal 1/6 binary64)) x)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (tan x) x)
#s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x))
#s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (tan x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (tan x) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 eps (neg.f64 x))) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (-.f64 eps (neg.f64 x))))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (tan (+ x eps)) (tan.f64 x))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x)))
#s(approx (tan (+ x eps)) (fma.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x)))
#s(approx eps eps)
#s(approx (+ x eps) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 x (neg.f64 eps))) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (-.f64 x (neg.f64 eps))))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval12.0ms (0.1%)

Memory
-37.0MiB live, 14.3MiB allocated; 9ms collecting garbage
Compiler

Compiled 1 962 to 415 computations (78.8% saved)

prune17.0ms (0.2%)

Memory
20.9MiB live, 20.9MiB allocated; 0ms collecting garbage
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New671784
Fresh000
Picked011
Done000
Total671885
Accuracy
99.9%
Counts
85 → 18
Alt Table
Click to see full alt table
StatusAccuracyProgram
23.1%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
35.7%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
59.1%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
35.6%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
▶59.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 eps x) (PI.f64))) (tan.f64 x))
✓59.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
57.5%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶57.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
57.2%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
56.5%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
5.4%
(-.f64 (tan.f64 #s(approx (+ x eps) x)) (tan.f64 x))
▶99.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶96.5%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
Compiler

Compiled 1 021 to 520 computations (49.1% saved)

series135.0ms (1.5%)

Memory
13.9MiB live, 149.3MiB allocated; 12ms collecting garbage
Counts
64 → 341
Calls
Call 1
Inputs
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(*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64))
(-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))))
(*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps)
(-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
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(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x))))
(neg.f64 eps)
eps
(fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
(sin.f64 x)
(cos.f64 x)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x))
(fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))))
(+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64))
(+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))
(neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 eps)
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(tan.f64 (+.f64 x eps))
(+.f64 x eps)
#s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
(*.f64 x x)
#s(literal 1/3 binary64)
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(tan.f64 (+.f64 (+.f64 x (PI.f64)) eps))
(+.f64 (+.f64 x (PI.f64)) eps)
(+.f64 x (PI.f64))
(PI.f64)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(+.f64 (tan.f64 x) (tan.f64 eps))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 x) (tan.f64 eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
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#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))))
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#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))))))
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#s(approx (tan x) #s(hole binary64 x))
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#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
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#s(approx (cos x) #s(hole binary64 1))
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#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
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#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
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#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
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#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
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#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
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#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
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#s(approx (+ x eps) #s(hole binary64 eps))
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#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
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#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 1/3))
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#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
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#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (PI))))
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#s(approx (* (tan x) (tan eps)) #s(hole binary64 (/ (* x (sin eps)) (cos eps))))
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#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (tan eps) #s(hole binary64 eps))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
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Calls

6 calls:

TimeVariablePointExpression
28.0ms
x
@-inf
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22.0ms
x
@inf
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17.0ms
x
@0
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16.0ms
eps
@inf
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15.0ms
eps
@-inf
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rewrite320.0ms (3.5%)

Memory
-4.7MiB live, 256.3MiB allocated; 133ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0156830063
0168626782
0815226402
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
405 → 529
Calls
Call 1
Inputs
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#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
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#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
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#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
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#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
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#s(approx (tan x) #s(hole binary64 x))
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#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
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#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
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#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
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#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
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#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
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#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (pow x 2))))
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#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
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#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (pow x 2)))
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#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (pow x 2)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 1))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (tan (+ x eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (tan (+ x eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (* (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* 2/15 (* x x)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (* x (pow (sin (+ eps (PI))) 2)) (pow (cos (+ eps (PI))) 2)))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI)))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (PI))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (+ x (PI)))))
#s(approx (+ x (PI)) #s(hole binary64 (PI)))
#s(approx (+ x (PI)) #s(hole binary64 (+ x (PI))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ x (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))))
#s(approx (+ (tan x) (tan eps)) #s(hole binary64 (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 1))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* -1 (/ (* x (sin eps)) (cos eps))))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* x (- (* -1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps)))))))
#s(approx (- 1 (* (tan x) (tan eps))) #s(hole binary64 (+ 1 (* x (- (* (pow x 2) (- (* -2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps)))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (/ (* x (sin eps)) (cos eps))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* 1/3 (/ (* (pow x 2) (sin eps)) (cos eps))) (/ (sin eps) (cos eps))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* (pow x 2) (+ (* 2/15 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 1/3 (/ (sin eps) (cos eps))))) (/ (sin eps) (cos eps))))))
#s(approx (* (tan x) (tan eps)) #s(hole binary64 (* x (+ (* (pow x 2) (+ (* 1/3 (/ (sin eps) (cos eps))) (* (pow x 2) (+ (* 17/315 (/ (* (pow x 2) (sin eps)) (cos eps))) (* 2/15 (/ (sin eps) (cos eps))))))) (/ (sin eps) (cos eps))))))
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#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#s(approx eps #s(hole binary64 eps))
#s(approx (tan eps) #s(hole binary64 eps))
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Outputs
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#s(approx (tan x) (tan.f64 x))
#s(approx (sin x) (sin.f64 x))
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#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan.f64 x))
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#s(approx (+ (+ x (PI)) eps) eps)
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (-.f64 (tan.f64 (-.f64 (+.f64 x (PI.f64)) (*.f64 #s(literal -1 binary64) eps))) (tan.f64 x)))
#s(approx (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan.f64 (-.f64 (+.f64 x (PI.f64)) (*.f64 #s(literal -1 binary64) eps))))
#s(approx (+ (+ x (PI)) eps) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (PI.f64)) eps)) #s(literal 1 binary64)))))

eval213.0ms (2.3%)

Memory
7.9MiB live, 328.6MiB allocated; 50ms collecting garbage
Compiler

Compiled 143 474 to 8 903 computations (93.8% saved)

prune55.0ms (0.6%)

Memory
-0.4MiB live, 96.4MiB allocated; 8ms collecting garbage
Pruning

34 alts after pruning (31 fresh and 3 done)

PrunedKeptTotal
New91224936
Fresh5712
Picked325
Done011
Total92034954
Accuracy
100.0%
Counts
954 → 34
Alt Table
Click to see full alt table
StatusAccuracyProgram
23.1%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
35.7%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
59.1%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
35.6%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
58.4%
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
4.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
▶7.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
✓4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 eps x) (PI.f64))) (tan.f64 x))
✓59.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
57.5%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
✓57.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
▶98.9%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 #s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -5/6 binary64) (*.f64 x x))))) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+.f64 #s(literal 1/3 binary64) (*.f64 x (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 #s(literal 4/3 binary64) eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))))) eps))
96.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 eps (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) eps))
3.5%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
96.6%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))
▶97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
25.3%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) eps))) eps))))))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
▶96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
Compiler

Compiled 7 397 to 2 624 computations (64.5% saved)

series163.0ms (1.8%)

Memory
-24.1MiB live, 169.8MiB allocated; 63ms collecting garbage
Counts
79 → 397
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64))
(-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))))
(*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps)
(-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
(-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x)))
(*.f64 #s(literal 2/3 binary64) (*.f64 eps x))
#s(literal 2/3 binary64)
(*.f64 eps x)
eps
x
#s(literal 1/6 binary64)
(+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
(fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
(neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))
(cos.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(sin.f64 x)
(cos.f64 x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (tan eps) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))
(fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))
(*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))
#s(literal -1/3 binary64)
(*.f64 eps eps)
(*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))
(fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))
(*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))
(*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))
#s(literal -4/3 binary64)
(*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))
(*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))
#s(literal -2/3 binary64)
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
(tan.f64 (+.f64 (+.f64 x (PI.f64)) eps))
(+.f64 (+.f64 x (PI.f64)) eps)
(+.f64 x (PI.f64))
(PI.f64)
(tan.f64 (+.f64 x (PI.f64)))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
(*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))
(-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))
(*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
(fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
#s(literal -1 binary64)
(*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
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#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (pow x 2)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 1))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (* eps (- 1 (* -1/3 (pow eps 2))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* x (- 1 (* -4/3 (pow eps 2))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (+ (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* x (- (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (PI))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (+ x (PI)))))
#s(approx (+ x (PI)) #s(hole binary64 (PI)))
#s(approx (+ x (PI)) #s(hole binary64 (+ x (PI))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (/ (sin (PI)) (cos (PI)))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))) (cos (PI)))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ x (PI))) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2)))))))) (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI))))))) (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (* -1 (/ (pow (sin eps) 4) (pow (cos eps) 4))) (* -1/3 (/ (pow (sin eps) 2) (pow (cos eps) 2))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 eps))
#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2))))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 1))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1 (* x (- x (* -1 eps))))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1 eps))))))
#s(approx (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) #s(hole binary64 1))
#s(approx (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) #s(hole binary64 (+ 1 (* x (- (* 4/3 (* eps (pow x 2))) (* -1 eps))))))
#s(approx (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) #s(hole binary64 (+ 1 (* x (- (* (pow x 2) (- (* 17/15 (* eps (pow x 2))) (* -4/3 eps))) (* -1 eps))))))
#s(approx (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))))) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))))) #s(hole binary64 (* x (+ (* -4/3 (* eps (pow x 2))) (* -1 eps)))))
#s(approx (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))))) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -4/3 eps) (* -17/15 (* eps (pow x 2)))))))))
#s(approx (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))))) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -4/3 eps) (* (pow x 2) (+ (* -17/15 eps) (* -248/315 (* eps (pow x 2)))))))))))
#s(approx (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* -1 (* eps x))))
#s(approx (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* x (+ (* -4/3 (* eps (pow x 2))) (* -1 eps)))))
#s(approx (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -4/3 eps) (* -17/15 (* eps (pow x 2)))))))))
#s(approx (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* x (+ (* -1 eps) (* (pow x 2) (+ (* -4/3 eps) (* (pow x 2) (+ (* -17/15 eps) (* -248/315 (* eps (pow x 2)))))))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx eps #s(hole binary64 eps))
#s(approx (tan eps) #s(hole binary64 eps))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
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#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
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Calls

6 calls:

TimeVariablePointExpression
38.0ms
eps
@inf
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37.0ms
x
@-inf
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17.0ms
x
@0
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(tan x)) (* -1 (pow (tan x) 3)))) (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) -1 (* -1 (pow (tan x) 3)) (pow (tan x) 3) 3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))) (- 1/2 (* -1/2 (cos (* 2 x)))) (* -1/2 (cos (* 2 x))))
16.0ms
x
@inf
((- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) 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x))))))))) eps) (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (* 2/3 (* eps x)) 2/3 (* eps x) eps x 1/6 (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) 2 -1/2 (* (pow (tan x) 2) 1/6) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) (- 1/2 (* 1/2 (cos (* 2 x)))) 1/2 (* 1/2 (cos (* 2 x))) (cos (* 2 x)) (* 2 x) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) (+ 1/2 (* 1/2 (cos (* 2 x)))) (neg (/ (* (- 1 (neg (pow (tan x) 2))) 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eps eps)) -1/3 (* eps eps) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (* x (- 1 (* -4/3 (* eps eps)))) (- 1 (* -4/3 (* eps eps))) (* -4/3 (* eps eps)) -4/3 (* (* eps eps) (- 1 (* -2/3 (* eps eps)))) (- 1 (* -2/3 (* eps eps))) (* -2/3 (* eps eps)) -2/3 (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) (tan (+ (+ x (PI)) eps)) (+ (+ x (PI)) eps) (+ x (PI)) (PI) (tan (+ x (PI))) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))))) (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))) (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) -1 (* -1 (pow (tan x) 3)) (pow (tan x) 3) 3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))) (- 1/2 (* -1/2 (cos (* 2 x)))) (* -1/2 (cos (* 2 x))))
15.0ms
eps
@-inf
((- (tan (+ x eps)) (tan x)) (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) 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x))))))))) eps) (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) 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eps eps)) -1/3 (* eps eps) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (* x (- 1 (* -4/3 (* eps eps)))) (- 1 (* -4/3 (* eps eps))) (* -4/3 (* eps eps)) -4/3 (* (* eps eps) (- 1 (* -2/3 (* eps eps)))) (- 1 (* -2/3 (* eps eps))) (* -2/3 (* eps eps)) -2/3 (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) (tan (+ (+ x (PI)) eps)) (+ (+ x (PI)) eps) (+ x (PI)) (PI) (tan (+ x (PI))) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))))) (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))) (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) -1 (* -1 (pow (tan x) 3)) (pow (tan x) 3) 3 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))) (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))) (- 1/2 (* -1/2 (cos (* 2 x)))) (* -1/2 (cos (* 2 x))))

rewrite266.0ms (2.9%)

Memory
22.2MiB live, 299.0MiB allocated; 25ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0177532842
0190029129
0874328508
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
476 → 603
Calls
Call 1
Inputs
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#s(literal 2/3 binary64)
(*.f64 eps x)
eps
x
#s(literal 1/6 binary64)
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#s(literal 1 binary64)
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(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
#s(literal 2 binary64)
#s(literal -1/2 binary64)
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#s(literal 1/2 binary64)
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#s(approx (tan eps) eps)
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* 2/3 (* eps x)) 1/6)))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* x (+ (* 2/3 eps) (* 17/9 (* eps (pow x 2))))) 1/6)))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2))))))) 1/6)))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* 2/3 (* eps x))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* 17/9 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2)))))))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* (pow x 2) (+ (* 124/45 eps) (* 2764/945 (* eps (pow x 2)))))))))))
#s(approx (* 2/3 (* eps x)) #s(hole binary64 (* 2/3 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 -1/2))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -1/2))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (pow x 2)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 1))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (* eps (- 1 (* -1/3 (pow eps 2))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) #s(hole binary64 (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* x (- 1 (* -4/3 (pow eps 2))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan (+ x (PI)))) #s(hole binary64 (- (+ (* x (- (+ (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))) (* x (- (+ (* -1 (/ (* (sin (PI)) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (cos (PI)))) (* x (- (+ (* -1 (/ (* (pow (sin (PI)) 2) (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (pow (cos (PI)) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (* 1/6 (/ (pow (sin (PI)) 2) (pow (cos (PI)) 2))))) (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI))))) (/ (sin (PI)) (cos (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
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Outputs
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#s(approx (tan eps) (tan.f64 eps))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) x (fma.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps) (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) x (fma.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps) (fma.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) eps) (/.f64 x (*.f64 eps eps)))))))
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#s(approx (- 1 (* -1/3 (* eps eps))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
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#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))
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#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) x (fma.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps) (/.f64 x (*.f64 eps eps))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal 2/3 binary64) x (fma.f64 #s(literal 4/3 binary64) (/.f64 (*.f64 x x) eps) (+.f64 (/.f64 x (*.f64 eps eps)) (/.f64 (*.f64 x x) (*.f64 (*.f64 eps eps) eps)))))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal -4/3 binary64) (/.f64 x eps)))))
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#s(approx (+ (+ x (PI)) eps) eps)
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -4/3 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 x eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 x eps))) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) eps))) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -4/3 binary64) x) (/.f64 #s(literal 1 binary64) eps)) eps)))))
#s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 x eps)) eps))) eps)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (-.f64 (tan.f64 (-.f64 (+.f64 x (PI.f64)) (*.f64 #s(literal -1 binary64) eps))) (tan.f64 x)))
#s(approx (tan (+ (+ x (PI)) eps)) (tan.f64 (-.f64 (+.f64 x (PI.f64)) (*.f64 #s(literal -1 binary64) eps))))
#s(approx (+ (+ x (PI)) eps) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (PI.f64)) eps)) #s(literal 1 binary64)))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) eps)) (*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))
#s(approx (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) eps))))

eval172.0ms (1.9%)

Memory
15.7MiB live, 256.1MiB allocated; 37ms collecting garbage
Compiler

Compiled 120 028 to 6 168 computations (94.9% saved)

prune78.0ms (0.9%)

Memory
12.8MiB live, 105.1MiB allocated; 6ms collecting garbage
Pruning

55 alts after pruning (50 fresh and 5 done)

PrunedKeptTotal
New69831729
Fresh71926
Picked325
Done033
Total70855763
Accuracy
100.0%
Counts
763 → 55
Alt Table
Click to see full alt table
StatusAccuracyProgram
23.1%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
35.7%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
59.1%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
35.6%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
58.4%
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
4.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓7.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
✓4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
▶4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 eps x) (PI.f64))) (tan.f64 x))
✓59.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
57.5%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
✓57.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
98.9%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))))
98.2%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -248/315 binary64) (*.f64 x x)) #s(literal 17/15 binary64))) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
98.4%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/15 binary64) (*.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
98.9%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
96.5%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
▶98.7%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
96.5%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
97.2%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 x (-.f64 eps (*.f64 #s(literal -4/3 binary64) (*.f64 (*.f64 eps eps) x))) (*.f64 eps eps))))))
97.1%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
98.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 #s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -5/6 binary64) (*.f64 x x))))) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) #s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -88/63 binary64) (*.f64 x x)) #s(literal 77/45 binary64))) #s(literal 5/3 binary64))) #s(literal 1 binary64)))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -17/270 binary64) (*.f64 x x)))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 17/270 binary64) (*.f64 #s(literal -31/945 binary64) (*.f64 x x)))))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/135 binary64) (*.f64 x x)) #s(literal 2/9 binary64))) #s(literal 1/3 binary64))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(literal -1/2 binary64)) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) #s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -248/135 binary64) (*.f64 x x)) #s(literal 17/9 binary64))) #s(literal 4/3 binary64))) #s(literal 1/2 binary64)))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) #s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/9 binary64) (*.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1/2 binary64)))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 #s(literal 4/3 binary64) eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))))) eps))
3.5%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal -4/3 binary64) (/.f64 x eps)))))))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 x (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
97.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
▶97.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) #s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))))))))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps #s(approx (- 1 (* -1/3 (* eps eps))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
55.4%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (/.f64 (-.f64 (*.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))))) (*.f64 (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) (-.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))))
25.3%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) eps))) eps))))))
23.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 x x) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))) x))))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) (*.f64 x x)))))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps x) (*.f64 #s(literal 4/3 binary64) (*.f64 x x)))))) (*.f64 x x)))))))
▶97.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
5.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
✓96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
Compiler

Compiled 14 436 to 5 571 computations (61.4% saved)

series138.0ms (1.5%)

Memory
-2.2MiB live, 141.6MiB allocated; 34ms collecting garbage
Counts
76 → 387
Calls
Call 1
Inputs
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#s(literal -1/6 binary64)
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(tan.f64 x)
x
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
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(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
#s(literal 1/2 binary64)
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eps
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(sin.f64 x)
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
(*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
(*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))
(-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) eps)
(fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
#s(literal -1 binary64)
(fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
(*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))
(*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
#s(literal 3 binary64)
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))
#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) #s(hole binary64 (* 1/3 eps)))
#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) #s(hole binary64 (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))))
#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) #s(hole binary64 (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))))
#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) #s(hole binary64 (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))))
#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) #s(hole binary64 1/3))
#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) #s(hole binary64 (+ 1/3 (* 2/3 (* eps x)))))
#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))))
#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 -1/6))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* 2/3 (* eps x)) 1/6)))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* x (+ (* 2/3 eps) (* 17/9 (* eps (pow x 2))))) 1/6)))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2))))))) 1/6)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 -1/2))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -1/2))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (pow x 2)))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 1/2))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* -1 (pow x 2)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (* 1/2 (cos (* 2 x))) #s(hole binary64 (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (cos (* 2 x)) #s(hole binary64 1))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 2/3 (pow x 2)) 2)))))
#s(approx (cos (* 2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/3 (* -4/45 (pow x 2)))) 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 1))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* 2 (pow x 2)))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* 7/3 (pow x 2)))))))
#s(approx (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 2 (* (pow x 2) (+ 7/3 (* 94/45 (pow x 2)))))))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* -4/3 (pow x 2)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* (pow x 2) (+ 61/120 (* 277/1008 (pow x 2))))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (* eps (- 1 (* -1/3 (pow eps 2))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))))
#s(approx (* eps (+ 1 (* x x))) #s(hole binary64 eps))
#s(approx (* eps (+ 1 (* x x))) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ 1 (* x x)) #s(hole binary64 1))
#s(approx (+ 1 (* x x)) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2)))))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (* eps (* (* x x) (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* eps (* (pow x 2) (- 1 (* -4/3 (pow eps 2)))))))
#s(approx (* (* x x) (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* (pow x 2) (- 1 (* -4/3 (pow eps 2))))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (+ (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (* x (pow (sin (+ eps (PI))) 2)) (pow (cos (+ eps (PI))) 2)))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI)))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
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Calls

6 calls:

TimeVariablePointExpression
17.0ms
eps
@-inf
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16.0ms
x
@-inf
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15.0ms
x
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14.0ms
eps
@inf
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11.0ms
eps
@0
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rewrite359.0ms (4%)

Memory
-20.3MiB live, 352.1MiB allocated; 44ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0173933144
0185329291
0835328583
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
463 → 577
Calls
Call 1
Inputs
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#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* -1 x)))
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#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -17/15 (pow x 2)) 4/3)) 1))))
#s(approx (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/315 (pow x 2)) 17/15)) 4/3)) 1))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
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#s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
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#s(approx (sin x) #s(hole binary64 x))
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#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (cos x) #s(hole binary64 1))
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#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
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#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (* eps (- 1 (* -1/3 (pow eps 2))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* (pow eps 2) (* x (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(hole binary64 (+ (* eps (- 1 (* -1/3 (pow eps 2)))) (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2)))))))))
#s(approx (* eps (+ 1 (* x x))) #s(hole binary64 eps))
#s(approx (* eps (+ 1 (* x x))) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (+ 1 (* x x)) #s(hole binary64 1))
#s(approx (+ 1 (* x x)) #s(hole binary64 (+ 1 (pow x 2))))
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#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* x (+ (* eps (* x (- 1 (* -4/3 (pow eps 2))))) (* (pow eps 2) (- 1 (* -2/3 (pow eps 2))))))))
#s(approx (* eps (* (* x x) (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* eps (* (pow x 2) (- 1 (* -4/3 (pow eps 2)))))))
#s(approx (* (* x x) (- 1 (* -4/3 (* eps eps)))) #s(hole binary64 (* (pow x 2) (- 1 (* -4/3 (pow eps 2))))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (+ (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (* x (pow (sin (+ eps (PI))) 2)) (pow (cos (+ eps (PI))) 2)))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI)))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ eps x) (PI))) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (tan (+ (+ eps x) (PI))) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ eps x) (PI))) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
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#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 eps))
#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* 4/3 (* (pow eps 2) x)))) (pow eps 2))))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 1))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1 (* x (- x (* -1 eps))))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (+ 1 (* x (- (* x (+ 1 (* 4/3 (* eps x)))) (* -1 eps))))))
#s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) #s(hole binary64 1))
#s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* 4/3 (* eps x)))))))))
#s(approx (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))))) #s(hole binary64 (/ 1 eps)))
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#s(approx (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))))) #s(hole binary64 (+ (* x (+ 1 (/ x eps))) (/ 1 eps))))
#s(approx (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))))) #s(hole binary64 (+ (* x (+ 1 (* x (+ (* 4/3 x) (/ 1 eps))))) (/ 1 eps))))
#s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* -1 x)))
#s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* x (- (* -1 (/ x eps)) 1))))
#s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* x (- (* x (- (* -4/3 x) (/ 1 eps))) 1))))
#s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) #s(hole binary64 (* x (- (* x (- (* x (- (* -2/3 (/ x eps)) 4/3)) (/ 1 eps))) 1))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) #s(hole binary64 (* -1 (/ (pow x 2) eps))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) #s(hole binary64 (* (pow x 2) (- (* -1 x) (/ 1 eps)))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) #s(hole binary64 (* (pow x 2) (- (* x (- (* -2/3 (/ x eps)) 1)) (/ 1 eps)))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) #s(hole binary64 (* (pow x 2) (- (* x (- (* x (- (* -1 x) (* 2/3 (/ 1 eps)))) 1)) (/ 1 eps)))))
#s(approx (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (/ (pow x 2) eps)))
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#s(approx (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ (* (pow x 2) (+ (* 17/45 (/ (pow x 2) eps)) (* 2/3 (/ 1 eps)))) (/ 1 eps)))))
#s(approx (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x)))))) #s(hole binary64 (* (pow x 2) (+ (* (pow x 2) (+ (* (pow x 2) (+ (* 62/315 (/ (pow x 2) eps)) (* 17/45 (/ 1 eps)))) (* 2/3 (/ 1 eps)))) (/ 1 eps)))))
#s(approx (* eps (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 eps))
#s(approx (* eps (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* -1 (* eps (pow x 2))))))
#s(approx (* eps (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1 eps) (* 1/3 (* eps (pow x 2))))))))
#s(approx (* eps (- 1/2 (* -1/2 (cos (* 2 x))))) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1 eps) (* (pow x 2) (+ (* -2/45 (* eps (pow x 2))) (* 1/3 eps))))))))
#s(approx (- 1/2 (* -1/2 (cos (* 2 x)))) #s(hole binary64 1))
#s(approx (- 1/2 (* -1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (- 1/2 (* -1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (- 1/2 (* -1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 -1/2))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (pow x 2) 1/2)))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) 1/2)))
#s(approx (* -1/2 (cos (* 2 x))) #s(hole binary64 (- (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3)))) 1/2)))
#s(approx (* -1 (pow (tan x) 3)) #s(hole binary64 (* -1 (pow x 3))))
#s(approx (* -1 (pow (tan x) 3)) #s(hole binary64 (* (pow x 3) (- (* -1 (pow x 2)) 1))))
#s(approx (* -1 (pow (tan x) 3)) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* -11/15 (pow x 2)) 1)) 1))))
#s(approx (* -1 (pow (tan x) 3)) #s(hole binary64 (* (pow x 3) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/189 (pow x 2)) 11/15)) 1)) 1))))
#s(approx (pow (tan x) 3) #s(hole binary64 (pow x 3)))
#s(approx (pow (tan x) 3) #s(hole binary64 (* (pow x 3) (+ 1 (pow x 2)))))
#s(approx (pow (tan x) 3) #s(hole binary64 (* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* 11/15 (pow x 2))))))))
#s(approx (pow (tan x) 3) #s(hole binary64 (* (pow x 3) (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 11/15 (* 88/189 (pow x 2))))))))))
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#s(approx eps #s(hole binary64 eps))
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#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ x eps))) eps)) (* 2/3 x)))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (/ (+ (* -4/3 (pow x 2)) (* -1 (/ (+ x (/ (pow x 2) eps)) eps))) eps)) (* 2/3 x)))))
#s(approx (* eps (* (* x x) (- 1 (* -4/3 (* eps eps))))) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -4/3 (pow x 2)) (* -1 (/ (pow x 2) (pow eps 2))))))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) #s(hole binary64 (- (/ (sin (- (+ x (PI)) (* -1 eps))) (cos (- (+ x (PI)) (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ (+ eps x) (PI))) #s(hole binary64 (/ (sin (- (+ x (PI)) (* -1 eps))) (cos (- (+ x (PI)) (* -1 eps))))))
#s(approx (+ (+ eps x) (PI)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (PI)) eps)) 1)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (- 1 (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) eps)) (* -1 (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))))))
#s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (sin x) (cos x))) (+ (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))) (* 1/2 (/ (cos (* 2 x)) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))))) (+ (/ 1/2 (* eps (- 1/2 (* -1/2 (cos (* 2 x)))))) (/ 1 eps)))))))
#s(approx (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))))) #s(hole binary64 (- (* -1 (/ (- (* 1/2 (/ (cos (* 2 x)) (- 1/2 (* -1/2 (cos (* 2 x)))))) (+ 1 (* 1/2 (/ 1 (- 1/2 (* -1/2 (cos (* 2 x)))))))) eps)) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3)))))))
#s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) #s(hole binary64 (+ (* -1 (/ (sin x) (cos x))) (+ (* -1 (/ (- (* 1/2 (/ 1 (- 1/2 (* -1/2 (cos (* 2 x)))))) (* 1/2 (/ (cos (* 2 x)) (- 1/2 (* -1/2 (cos (* 2 x))))))) eps)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3)))))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) #s(hole binary64 (+ (* -1 (/ (- (* 1/2 (/ 1 (- 1/2 (* -1/2 (cos (* 2 x)))))) (* 1/2 (/ (cos (* 2 x)) (- 1/2 (* -1/2 (cos (* 2 x))))))) eps)) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))
Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
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#s(literal 3 binary64)
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (tan.f64 eps))
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#s(approx (tan x) (tan.f64 x))
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#s(approx (* 1/2 (cos (* 2 x))) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
#s(approx (cos (* 2 x)) (cos.f64 (*.f64 #s(literal 2 binary64) x)))
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#s(approx (cos x) (cos.f64 x))
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#s(approx (* eps (- 1/2 (* -1/2 (cos (* 2 x))))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
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#s(approx (* -1/2 (cos (* 2 x))) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
#s(approx (* -1 (pow (tan x) 3)) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
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#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) (-.f64 (tan.f64 (-.f64 (+.f64 eps (PI.f64)) (*.f64 #s(literal -1 binary64) x))) (tan.f64 x)))
#s(approx (tan (+ (+ eps x) (PI))) (tan.f64 (-.f64 (+.f64 eps (PI.f64)) (*.f64 #s(literal -1 binary64) x))))
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#s(approx eps eps)
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#s(approx (* eps eps) (*.f64 eps eps))
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x))))))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -4/3 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 x eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 x eps))) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (/.f64 (*.f64 x x) eps)) eps))) eps) (*.f64 #s(literal 2/3 binary64) x))))
#s(approx (* eps (* (* x x) (- 1 (* -4/3 (* eps eps))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (*.f64 eps eps)))))))
#s(approx (- (tan (+ (+ eps x) (PI))) (tan x)) (-.f64 (tan.f64 (-.f64 (+.f64 x (PI.f64)) (*.f64 #s(literal -1 binary64) eps))) (tan.f64 x)))
#s(approx (tan (+ (+ eps x) (PI))) (tan.f64 (-.f64 (+.f64 x (PI.f64)) (*.f64 #s(literal -1 binary64) eps))))
#s(approx (+ (+ eps x) (PI)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (PI.f64)) eps)) #s(literal 1 binary64)))))
#s(approx (+ eps x) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64)))))
#s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) eps)) (*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))
#s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (/.f64 #s(literal 1 binary64) eps))))))
#s(approx (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))))) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) eps)) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
#s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) eps) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))
#s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) eps) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))

eval141.0ms (1.6%)

Memory
31.0MiB live, 269.5MiB allocated; 29ms collecting garbage
Compiler

Compiled 117 521 to 6 004 computations (94.9% saved)

prune180.0ms (2%)

Memory
-27.0MiB live, 207.4MiB allocated; 36ms collecting garbage
Pruning

63 alts after pruning (55 fresh and 8 done)

PrunedKeptTotal
New67220692
Fresh103545
Picked235
Done055
Total68463747
Accuracy
100.0%
Counts
747 → 63
Alt Table
Click to see full alt table
StatusAccuracyProgram
23.1%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))))
35.7%
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
59.1%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
35.6%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
58.4%
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
4.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓7.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
✓4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓4.8%
(-.f64 (tan.f64 (+.f64 (+.f64 eps x) (PI.f64))) (tan.f64 x))
✓59.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
57.5%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
✓57.4%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
99.3%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.9%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))))
98.2%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -248/315 binary64) (*.f64 x x)) #s(literal 17/15 binary64))) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
98.4%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/15 binary64) (*.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
98.9%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
96.5%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
✓98.7%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
98.0%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -88/189 binary64) (*.f64 x x)) #s(literal 11/15 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)))))))))))
98.1%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))))))))))
98.4%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) #s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))))))))
96.9%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 #s(literal -2/3 binary64) (/.f64 x eps)) #s(literal 4/3 binary64))) (/.f64 #s(literal 1 binary64) eps))) #s(literal 1 binary64)))))))))
98.2%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))))))
97.2%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
97.1%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
96.5%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
97.1%
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
98.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 #s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -5/6 binary64) (*.f64 x x))))) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) #s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/9 binary64) (*.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1/2 binary64)))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))) #s(literal 1 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) #s(approx (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -88/63 binary64) (*.f64 x x)) #s(literal 77/45 binary64))) #s(literal 5/3 binary64))) #s(literal 1 binary64)))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -17/270 binary64) (*.f64 x x)))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 17/270 binary64) (*.f64 #s(literal -31/945 binary64) (*.f64 x x)))))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/135 binary64) (*.f64 x x)) #s(literal 2/9 binary64))) #s(literal 1/3 binary64))) #s(literal 1/2 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(literal -1/2 binary64)) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) #s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -248/135 binary64) (*.f64 x x)) #s(literal 17/9 binary64))) #s(literal 4/3 binary64))) #s(literal 1/2 binary64)))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) #s(approx (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/9 binary64) (*.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1/2 binary64)))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 #s(literal 4/3 binary64) eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
98.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))))) eps))
3.5%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 x (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
97.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
✓97.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) #s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))))))))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) #s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 eps (*.f64 (*.f64 x x) #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps)))))))))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps #s(approx (- 1 (* -1/3 (* eps eps))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
25.3%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) eps))) eps))))))
23.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 x x) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))) x))))))
97.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) (*.f64 x x)))))))
97.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps x) (*.f64 #s(literal 4/3 binary64) (*.f64 x x)))))) (*.f64 x x)))))))
6.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
5.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
97.0%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
✓96.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
Compiler

Compiled 20 882 to 4 185 computations (80% saved)

regimes77.0ms (0.9%)

Memory
13.1MiB live, 111.0MiB allocated; 13ms collecting garbage
Counts
93 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)))) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (-.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) eps))) eps))))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

26.0ms
eps
22.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
20.0ms
x
Results
AccuracySegmentsBranch
99.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.5%1x
99.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes76.0ms (0.8%)

Memory
-3.8MiB live, 88.4MiB allocated; 4ms collecting garbage
Counts
91 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

25.0ms
eps
21.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
20.0ms
x
Results
AccuracySegmentsBranch
99.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes68.0ms (0.7%)

Memory
16.5MiB live, 71.4MiB allocated; 4ms collecting garbage
Counts
88 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -17/270 binary64) (*.f64 x x)))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 17/270 binary64) (*.f64 #s(literal -31/945 binary64) (*.f64 x x)))))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 17/270 binary64) (*.f64 #s(literal -31/945 binary64) (*.f64 x x)))))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (neg.f64 (*.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))) #s(literal 1/6 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

21.0ms
eps
19.0ms
x
19.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.3%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.3%1x
99.3%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes72.0ms (0.8%)

Memory
-26.6MiB live, 111.3MiB allocated; 12ms collecting garbage
Counts
85 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 #s(approx (* (- 1 (neg (pow (tan x) 2))) (sin x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -5/6 binary64) (*.f64 x x))))) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -17/270 binary64) (*.f64 x x)))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (neg (pow (tan x) 2)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/45 binary64) (*.f64 x x)) #s(literal 2/3 binary64))) #s(literal 1 binary64))))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 1/9 binary64) (*.f64 #s(literal -17/270 binary64) (*.f64 x x)))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(literal -1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 17/270 binary64) (*.f64 #s(literal -31/945 binary64) (*.f64 x x)))))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 #s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps x))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(approx (* (pow (tan x) 2) 1/6) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/6 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 1/9 binary64) (*.f64 (*.f64 x x) (-.f64 #s(literal 17/270 binary64) (*.f64 #s(literal -31/945 binary64) (*.f64 x x)))))))))) (neg.f64 (*.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) (+.f64 #s(literal 1/3 binary64) (*.f64 x (fma.f64 #s(literal 2/3 binary64) eps (*.f64 #s(literal 4/3 binary64) x))))) eps) (neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

22.0ms
x
18.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms
eps
Results
AccuracySegmentsBranch
99.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.2%1x
99.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes53.0ms (0.6%)

Memory
19.3MiB live, 116.3MiB allocated; 8ms collecting garbage
Counts
65 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))))
Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))))
Calls

3 calls:

17.0ms
eps
16.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
14.0ms
x
Results
AccuracySegmentsBranch
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.9%1x
98.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes66.0ms (0.7%)

Memory
-17.8MiB live, 75.3MiB allocated; 6ms collecting garbage
Counts
64 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 x (-.f64 eps (*.f64 #s(literal -4/3 binary64) (*.f64 (*.f64 eps eps) x))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/15 binary64) (*.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -248/315 binary64) (*.f64 x x)) #s(literal 17/15 binary64))) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) #s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (/.f64 (-.f64 (*.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))))) (*.f64 (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) (-.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -88/189 binary64) (*.f64 x x)) #s(literal 11/15 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)))))))))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (-.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 eps (fma.f64 #s(literal -1 binary64) (tan.f64 x) (*.f64 #s(literal -1 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))
Calls

3 calls:

30.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
16.0ms
eps
14.0ms
x
Results
AccuracySegmentsBranch
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.9%1x
98.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes86.0ms (0.9%)

Memory
-12.2MiB live, 61.3MiB allocated; 79ms collecting garbage
Counts
61 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
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(-.f64 (tan.f64 #s(approx (+ x eps) x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 eps x) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 #s(literal 4/3 binary64) eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))))))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -17/15 binary64) (*.f64 x x)) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (*.f64 eps #s(approx (+ (* -1 (tan x)) (* -1 (pow (tan x) 3))) (*.f64 x (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -248/315 binary64) (*.f64 x x)) #s(literal 17/15 binary64))) #s(literal 4/3 binary64))) #s(literal 1 binary64))))))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) #s(approx (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3))) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (/.f64 (-.f64 (*.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))))) (*.f64 (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) (-.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -88/189 binary64) (*.f64 x x)) #s(literal 11/15 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)))))))))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

53.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms
x
13.0ms
eps
Results
AccuracySegmentsBranch
98.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.9%1x
98.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes50.0ms (0.5%)

Memory
9.9MiB live, 58.1MiB allocated; 4ms collecting garbage
Counts
59 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
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#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (/.f64 (-.f64 (*.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))))) (*.f64 (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) (-.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)))))))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) (fma.f64 #s(literal -1 binary64) (tan.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))) #s(approx (* -1 (pow (tan x) 3)) (*.f64 (*.f64 (*.f64 x x) x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -88/189 binary64) (*.f64 x x)) #s(literal 11/15 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)))))))))))
(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 #s(literal 4/3 binary64) eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

18.0ms
x
13.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms
eps
Results
AccuracySegmentsBranch
98.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.8%1x
98.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes47.0ms (0.5%)

Memory
-18.7MiB live, 71.9MiB allocated; 8ms collecting garbage
Counts
47 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
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(-.f64 (tan.f64 (+.f64 (+.f64 eps x) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 (+.f64 x (PI.f64))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (fma.f64 #s(literal 1/3 binary64) eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

17.0ms
eps
15.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms
x
Results
AccuracySegmentsBranch
98.6%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.6%1x
98.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes40.0ms (0.4%)

Memory
33.1MiB live, 84.5MiB allocated; 8ms collecting garbage
Counts
45 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 x (-.f64 eps (*.f64 #s(literal -4/3 binary64) (*.f64 (*.f64 eps eps) x))) (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (*.f64 eps (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) (*.f64 x x)))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) #s(approx (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps)))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 (*.f64 eps eps) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 x (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps x) (*.f64 #s(literal 4/3 binary64) (*.f64 x x)))))) (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 x x) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))) (/.f64 (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))) x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal -4/3 binary64) (/.f64 x eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 #s(literal -2/3 binary64) (/.f64 x eps)) #s(literal 4/3 binary64))) (/.f64 #s(literal 1 binary64) eps))) #s(literal 1 binary64)))))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps #s(approx (- 1 (* -1/3 (* eps eps))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal -4/3 binary64) (*.f64 x x) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) eps))) eps))) #s(literal 1/3 binary64)) eps) (*.f64 #s(literal 2/3 binary64) x))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 4/3 binary64) (*.f64 #s(literal -17/9 binary64) (*.f64 eps eps))))))))))))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 #s(literal 2/15 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 #s(literal 1/3 binary64) eps)) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 (tan.f64 #s(approx (+ x eps) x)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 eps x) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

15.0ms
x
10.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms
eps
Results
AccuracySegmentsBranch
98.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.4%1x
98.4%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes34.0ms (0.4%)

Memory
-14.1MiB live, 77.3MiB allocated; 14ms collecting garbage
Counts
34 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) (-.f64 #s(literal 2/3 binary64) (*.f64 #s(literal -4/3 binary64) (/.f64 x eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 eps (PI.f64))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (*.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) eps) #s(approx (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))) (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 x (-.f64 (*.f64 #s(literal -2/3 binary64) (/.f64 x eps)) #s(literal 4/3 binary64))) (/.f64 #s(literal 1 binary64) eps))) #s(literal 1 binary64)))))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps #s(approx (- 1 (* -1/3 (* eps eps))) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x (fma.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps x)))))))))))
Calls

3 calls:

11.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms
x
8.0ms
eps
Results
AccuracySegmentsBranch
97.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.2%1x
97.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.2%)

Memory
-1.0MiB live, 45.8MiB allocated; 3ms collecting garbage
Counts
14 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps (+.f64 eps x)))))))
Calls

3 calls:

6.0ms
eps
4.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms
x
Results
AccuracySegmentsBranch
97.2%1x
97.2%1eps
97.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.2%)

Memory
-6.3MiB live, 46.2MiB allocated; 6ms collecting garbage
Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 #s(literal 2/3 binary64) (*.f64 (*.f64 (*.f64 eps eps) (*.f64 eps eps)) x)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))) (*.f64 eps x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
Calls

3 calls:

7.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
x
3.0ms
eps
Results
AccuracySegmentsBranch
97.1%1eps
97.1%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.1%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes8.0ms (0.1%)

Memory
23.0MiB live, 23.0MiB allocated; 0ms collecting garbage
Counts
8 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
Outputs
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) #s(approx (* eps (- (/ 1 eps) (+ (* -1 (tan x)) (+ (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (* eps (- 1/2 (* -1/2 (cos (* 2 x))))))) (* -1 (pow (tan x) 3)))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))))))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
2.0ms
eps
Results
AccuracySegmentsBranch
97.1%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.1%1x
97.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory
-25.9MiB live, 20.8MiB allocated; 4ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 x x))))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) #s(approx (* eps (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x)))))))) (+.f64 eps (*.f64 (*.f64 eps eps) x))))
#s(approx (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (*.f64 eps #s(approx (- (- 1 (* 1 (* eps (+ (* -1 (tan x)) (* -1 (pow (tan x) 3)))))) (* -1 (/ (- 1/2 (* 1/2 (cos (* 2 x)))) (- 1/2 (* -1/2 (cos (* 2 x))))))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) #s(approx (* eps (+ 1 (* x x))) (+.f64 eps (*.f64 eps (*.f64 x x)))))))
Calls

3 calls:

4.0ms
x
2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
eps
Results
AccuracySegmentsBranch
97.0%1eps
97.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.0%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0%)

Memory
11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Accuracy

Total -57.6b remaining (-2553.1%)

Threshold costs -57.6b (-2553.1%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(approx (+ (* eps (- 1 (* -1/3 (* eps eps)))) (* x (+ (* eps (* x (- 1 (* -4/3 (* eps eps))))) (* (* eps eps) (- 1 (* -2/3 (* eps eps))))))) (*.f64 eps #s(approx (+ 1 (* x x)) (*.f64 x x))))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) eps))
Calls

3 calls:

1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
96.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
96.5%1x
96.5%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations454.0ms (5%)

Memory
14.9MiB live, 543.3MiB allocated; 37ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 1 969 to 275 computations (86% saved)

preprocess176.0ms (1.9%)

Memory
-22.4MiB live, 403.3MiB allocated; 32ms collecting garbage
Compiler

Compiled 4 022 to 610 computations (84.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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