2tan (problem 3.3.2)

Time bar (total: 2.5min)

start0.0ms (0%)

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

analyze41.0ms (0%)

Memory
-9.7MiB live, 33.7MiB allocated; 12ms 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)

sample4.6s (3%)

Memory
-179.7MiB live, 5 081.8MiB allocated; 1.6s collecting garbage
Samples
2.4s26 303×0invalid
745.0ms5 555×1valid
179.0ms2 701×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.2s
ival-mult!: 656.0ms (29.8% of total)
ival-tan: 589.0ms (26.8% of total)
ival-fabs: 225.0ms (10.2% of total)
ival-<: 224.0ms (10.2% of total)
ival-add!: 164.0ms (7.5% of total)
adjust: 155.0ms (7% of total)
ival-sub!: 101.0ms (4.6% of total)
ival-and: 71.0ms (3.2% of total)
ival-assert: 15.0ms (0.7% of total)
Bogosity

explain117.0ms (0.1%)

Memory
-6.7MiB live, 142.6MiB allocated; 9ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2250-4(4.4498555222472154e-85 5.965643538873561e-87)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
41(-3761.8017651054197 1942.1292520713973)2(-15.759348112389198 5.463676594966092e-11)(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))cancellation22110
tan.f64(tan.f64 (+.f64 x eps))sensitivity30
Confusion
Predicted +Predicted -
+2214
-130
Precision
0.9954954954954955
Recall
0.9822222222222222
Confusion?
Predicted +Predicted MaybePredicted -
+22140
-1624
Precision?
0.9698275862068966
Recall?
1.0
Freqs
test
numberfreq
034
1220
22
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
62.0ms362×1valid
7.0ms150×0valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-tan: 13.0ms (45.3% of total)
adjust: 8.0ms (27.9% of total)
ival-add!: 5.0ms (17.4% of total)
ival-sub!: 2.0ms (7% of total)

preprocess56.0ms (0%)

Memory
1.6MiB live, 49.0MiB allocated; 2ms 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
▶61.2%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 14 to 12 computations (14.3% saved)

series12.0ms (0%)

Memory
12.7MiB live, 12.7MiB 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))

rewrite188.0ms (0.1%)

Memory
33.4MiB live, 268.5MiB allocated; 34ms 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 (*.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)))) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x)))) (-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x)))) (neg.f64 (fma.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (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 (+.f64 (+.f64 eps x) (PI.f64))) (neg.f64 (cos.f64 x))) (*.f64 (cos.f64 (+.f64 (+.f64 eps x) (PI.f64))) (neg.f64 (sin.f64 x)))) (*.f64 (cos.f64 (+.f64 (+.f64 eps x) (PI.f64))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (sin.f64 (+.f64 (+.f64 eps x) (PI.f64))) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 (+.f64 eps x) (PI.f64))) (sin.f64 x))) (*.f64 (cos.f64 (+.f64 (+.f64 eps x) (PI.f64))) (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))))
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(tan.f64 (+.f64 (+.f64 x (PI.f64)) eps))
(tan.f64 (+.f64 (+.f64 eps x) (PI.f64)))
(tan.f64 (+.f64 eps x))
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(+.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)))
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#s(approx (tan (+ x eps)) (fma.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
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#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 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))))
#s(approx (+ x eps) x)
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#s(approx (tan (+ x eps)) (tan.f64 x))
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#s(approx eps eps)
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1 binary64) #s(literal 1 binary64)) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps)) (PI.f64))) (tan.f64 x)))
#s(approx (tan (+ x eps)) (tan.f64 (+.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps)) (PI.f64))))
#s(approx (+ x eps) (*.f64 (*.f64 (-.f64 (*.f64 (/.f64 x eps) #s(literal -1 binary64)) #s(literal 1 binary64)) eps) #s(literal -1 binary64)))

eval14.0ms (0%)

Memory
-15.4MiB live, 29.2MiB allocated; 4ms collecting garbage
Compiler

Compiled 2 284 to 417 computations (81.7% saved)

prune12.0ms (0%)

Memory
-20.5MiB live, 25.2MiB allocated; 4ms collecting garbage
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New87289
Fresh000
Picked011
Done000
Total87390
Accuracy
100.0%
Counts
90 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓61.2%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶97.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1 binary64) x) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
▶99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))) eps))
Compiler

Compiled 260 to 85 computations (67.3% saved)

series161.0ms (0.1%)

Memory
8.4MiB live, 292.8MiB allocated; 41ms collecting garbage
Counts
64 → 338
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))) eps))
(*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))) eps)
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(*.f64 #s(literal -1 binary64) eps)
#s(literal -1 binary64)
eps
(fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))
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(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(*.f64 #s(literal 1 binary64) (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)
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(fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))))
(+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (cos.f64 x))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1/6 binary64) (cos.f64 x))
#s(literal 1/6 binary64)
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1 binary64) x) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1 binary64) x) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps))
(fma.f64 (fma.f64 (*.f64 #s(literal -1 binary64) x) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(fma.f64 (*.f64 #s(literal -1 binary64) x) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))))
(*.f64 #s(literal -1 binary64) x)
(+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (cos.f64 eps))
(cos.f64 eps)
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))
(pow.f64 (tan.f64 eps) #s(literal 2 binary64))
(tan.f64 eps)
(pow.f64 (sin.f64 eps) #s(literal 2 binary64))
(sin.f64 eps)
(fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(/.f64 #s(literal 1/6 binary64) (cos.f64 eps))
(/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))
(*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.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 (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))))
#s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) 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 (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) 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 (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) #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 (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) #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 (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (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)))))))))
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#s(approx (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* 2/3 (* eps x))))
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#s(approx (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
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#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
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#s(approx (+ 1 (* 1 (pow (tan x) 2))) #s(hole binary64 1))
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#s(approx (+ 1 (* 1 (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (+ 1 (* 1 (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (* 1 (pow (tan x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* 1 (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
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#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 (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)))))
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#s(approx (+ (* (+ (* (* -1 x) (+ (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) 1/2)) (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)))) x) (* 1 (pow (tan eps) 2))) #s(hole binary64 (* eps (+ x (* eps (+ 1 (+ (* 4/3 (pow x 2)) (* eps (+ (* 4/3 x) (* eps (+ 2/3 (* 17/9 (pow x 2)))))))))))))
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#s(approx (+ (* (* -1 x) (+ (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) 1/2)) (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)))) #s(hole binary64 (* eps (+ 1 (* eps (+ (* 4/3 eps) (* 4/3 x)))))))
#s(approx (+ (* (* -1 x) (+ (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) 1/2)) (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)))) #s(hole binary64 (* eps (+ 1 (* eps (+ (* 4/3 x) (* eps (+ 4/3 (* 17/9 (* eps x))))))))))
#s(approx (+ (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) 1/2) #s(hole binary64 (* -4/3 (pow eps 2))))
#s(approx (+ (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) 1/2) #s(hole binary64 (* (pow eps 2) (- (* -17/9 (pow eps 2)) 4/3))))
#s(approx (+ (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) 1/2) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (- (* -248/135 (pow eps 2)) 17/9)) 4/3))))
#s(approx (+ (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) 1/2) #s(hole binary64 (* (pow eps 2) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -1382/945 (pow eps 2)) 248/135)) 17/9)) 4/3))))
#s(approx (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) #s(hole binary64 (- (* -4/3 (pow eps 2)) 1/2)))
#s(approx (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) #s(hole binary64 (- (* (pow eps 2) (- (* -17/9 (pow eps 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ -1 (cos eps)) (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps))) (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))))) #s(hole binary64 (- (* (pow eps 2) (- (* (pow eps 2) (- (* -248/135 (pow eps 2)) 17/9)) 4/3)) 1/2)))
#s(approx (/ -1 (cos eps)) #s(hole binary64 -1))
#s(approx (/ -1 (cos eps)) #s(hole binary64 (- (* -1/2 (pow eps 2)) 1)))
#s(approx (/ -1 (cos eps)) #s(hole binary64 (- (* (pow eps 2) (- (* -5/24 (pow eps 2)) 1/2)) 1)))
#s(approx (/ -1 (cos eps)) #s(hole binary64 (- (* (pow eps 2) (- (* (pow eps 2) (- (* -61/720 (pow eps 2)) 5/24)) 1/2)) 1)))
#s(approx (cos eps) #s(hole binary64 1))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* -1/2 (pow eps 2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
#s(approx (cos eps) #s(hole binary64 (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps)) #s(hole binary64 (pow eps 2)))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 7/6 (pow eps 2))))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 7/6 (* 331/360 (pow eps 2))))))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) (cos eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 7/6 (* (pow eps 2) (+ 331/360 (* 3071/5040 (pow eps 2))))))))))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* 17/45 (pow eps 2))))))))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (pow (sin eps) 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* (pow eps 2) (+ 17/45 (* 62/315 (pow eps 2))))))))))
#s(approx (+ 1 (* 1 (pow (tan eps) 2))) #s(hole binary64 1))
#s(approx (+ 1 (* 1 (pow (tan eps) 2))) #s(hole binary64 (+ 1 (pow eps 2))))
#s(approx (+ 1 (* 1 (pow (tan eps) 2))) #s(hole binary64 (+ 1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))
#s(approx (+ 1 (* 1 (pow (tan eps) 2))) #s(hole binary64 (+ 1 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* 17/45 (pow eps 2)))))))))
#s(approx (* 1 (pow (tan eps) 2)) #s(hole binary64 (pow eps 2)))
#s(approx (* 1 (pow (tan eps) 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
#s(approx (* 1 (pow (tan eps) 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* 17/45 (pow eps 2))))))))
#s(approx (* 1 (pow (tan eps) 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* (pow eps 2) (+ 17/45 (* 62/315 (pow eps 2))))))))))
#s(approx (pow (tan eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (tan eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
#s(approx (pow (tan eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* 17/45 (pow eps 2))))))))
#s(approx (pow (tan eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* (pow eps 2) (+ 17/45 (* 62/315 (pow eps 2))))))))))
#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))))))))
#s(approx (tan eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))))
#s(approx (pow (sin eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (sin eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1/3 (pow eps 2))))))
#s(approx (pow (sin eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (- (* 2/45 (pow eps 2)) 1/3))))))
#s(approx (pow (sin eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 2/45 (* -1/315 (pow eps 2)))) 1/3))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2))))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2))))) #s(hole binary64 (- (* -1/3 (pow eps 2)) 1/2)))
#s(approx (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2))))) #s(hole binary64 (- (* (pow eps 2) (- (* -2/9 (pow eps 2)) 1/3)) 1/2)))
#s(approx (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2))))) #s(hole binary64 (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/135 (pow eps 2)) 2/9)) 1/3)) 1/2)))
#s(approx (/ 1/6 (cos eps)) #s(hole binary64 1/6))
#s(approx (/ 1/6 (cos eps)) #s(hole binary64 (+ 1/6 (* 1/12 (pow eps 2)))))
#s(approx (/ 1/6 (cos eps)) #s(hole binary64 (+ 1/6 (* (pow eps 2) (+ 1/12 (* 5/144 (pow eps 2)))))))
#s(approx (/ 1/6 (cos eps)) #s(hole binary64 (+ 1/6 (* (pow eps 2) (+ 1/12 (* (pow eps 2) (+ 5/144 (* 61/4320 (pow eps 2)))))))))
#s(approx (/ (pow (sin eps) 2) (cos eps)) #s(hole binary64 (pow eps 2)))
#s(approx (/ (pow (sin eps) 2) (cos eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 1/6 (pow eps 2))))))
#s(approx (/ (pow (sin eps) 2) (cos eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 1/6 (* 31/360 (pow eps 2))))))))
#s(approx (/ (pow (sin eps) 2) (cos eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 1/6 (* (pow eps 2) (+ 31/360 (* 173/5040 (pow eps 2))))))))))
#s(approx (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))) #s(hole binary64 -1/2))
#s(approx (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))) #s(hole binary64 (- (* -1/2 (pow eps 2)) 1/2)))
#s(approx (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))) #s(hole binary64 (- (* (pow eps 2) (- (* -1/3 (pow eps 2)) 1/2)) 1/2)))
#s(approx (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))) #s(hole binary64 (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/90 (pow eps 2)) 1/3)) 1/2)) 1/2)))
#s(approx (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps))) #s(hole binary64 eps))
#s(approx (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps))) #s(hole binary64 (* eps (+ 1 (* 4/3 (pow eps 2))))))
#s(approx (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 4/3 (* 17/15 (pow eps 2))))))))
#s(approx (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 4/3 (* (pow eps 2) (+ 17/15 (* 248/315 (pow eps 2))))))))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)) #s(hole binary64 eps))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)) #s(hole binary64 (* eps (+ 1 (* 4/3 (pow eps 2))))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 4/3 (* 17/15 (pow eps 2))))))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 4/3 (* (pow eps 2) (+ 17/15 (* 248/315 (pow eps 2))))))))))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) #s(hole binary64 eps))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) #s(hole binary64 (* eps (+ 1 (* 5/6 (pow eps 2))))))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 5/6 (* 61/120 (pow eps 2))))))))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 5/6 (* (pow eps 2) (+ 61/120 (* 277/1008 (pow eps 2))))))))))
#s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) #s(hole binary64 (* -1 (* (pow eps 4) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))))))
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Calls

6 calls:

TimeVariablePointExpression
29.0ms
x
@-inf
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27.0ms
x
@inf
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21.0ms
eps
@-inf
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19.0ms
x
@0
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rewrite270.0ms (0.2%)

Memory
26.1MiB live, 304.1MiB allocated; 23ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147831415
0161928819
0813428309
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
402 → 532
Calls
Call 1
Inputs
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#s(approx (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) #s(hole binary64 1/3))
#s(approx (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) #s(hole binary64 (+ 1/3 (* 2/3 (* eps x)))))
#s(approx (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))))
#s(approx (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))))
#s(approx (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* 2/3 (* eps x))))
#s(approx (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* 17/9 (* eps (pow x 2)))))))
#s(approx (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (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 (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (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 (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* -2/3 x)))
#s(approx (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* -17/9 (pow x 2)) 2/3))))
#s(approx (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))))
#s(approx (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
#s(approx (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (* (+ 1 (* 1 (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 (* 1 (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 (* 1 (pow (tan x) 2))) (sin x)) #s(hole binary64 x))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* 5/6 (pow x 2))))))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 5/6 (* 61/120 (pow x 2))))))))
#s(approx (* (+ 1 (* 1 (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 (+ 1 (* 1 (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (+ 1 (* 1 (pow (tan x) 2))) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (+ 1 (* 1 (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (+ 1 (* 1 (pow (tan x) 2))) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (* 1 (pow (tan x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* 1 (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* 1 (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (* 1 (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 (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 (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 (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* -1/6 x)))
#s(approx (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* -11/9 (pow x 2)) 1/6))))
#s(approx (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* (pow x 2) (- (* -197/90 (pow x 2)) 11/9)) 1/6))))
#s(approx (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2392/945 (pow x 2)) 197/90)) 11/9)) 1/6))))
#s(approx (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* -41/36 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -1141/720 (pow x 2)) 41/36)) 1/6))))
#s(approx (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -44981/30240 (pow x 2)) 1141/720)) 41/36)) 1/6))))
#s(approx (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)))
#s(approx (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (/ -1 (cos x)) #s(hole binary64 -1))
#s(approx (/ -1 (cos x)) #s(hole binary64 (- (* -1/2 (pow x 2)) 1)))
#s(approx (/ -1 (cos x)) #s(hole binary64 (- (* (pow x 2) (- (* -5/24 (pow x 2)) 1/2)) 1)))
#s(approx (/ -1 (cos x)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -61/720 (pow x 2)) 5/24)) 1/2)) 1)))
#s(approx (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x)) #s(hole binary64 (pow x 2)))
#s(approx (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x)) #s(hole binary64 (* (pow x 2) (+ 1 (* 7/6 (pow x 2))))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 7/6 (* 331/360 (pow x 2))))))))
#s(approx (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 7/6 (* (pow x 2) (+ 331/360 (* 3071/5040 (pow x 2))))))))))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin 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 (pow (sin x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))))
#s(approx (pow (sin x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))))
#s(approx (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2)) #s(hole binary64 -1/2))
#s(approx (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (/ 1/6 (cos x)) #s(hole binary64 1/6))
#s(approx (/ 1/6 (cos x)) #s(hole binary64 (+ 1/6 (* 1/12 (pow x 2)))))
#s(approx (/ 1/6 (cos x)) #s(hole binary64 (+ 1/6 (* (pow x 2) (+ 1/12 (* 5/144 (pow x 2)))))))
#s(approx (/ 1/6 (cos x)) #s(hole binary64 (+ 1/6 (* (pow x 2) (+ 1/12 (* (pow x 2) (+ 5/144 (* 61/4320 (pow x 2)))))))))
#s(approx (/ (pow (sin x) 2) (cos x)) #s(hole binary64 (pow x 2)))
#s(approx (/ (pow (sin x) 2) (cos x)) #s(hole binary64 (* (pow x 2) (+ 1 (* 1/6 (pow x 2))))))
#s(approx (/ (pow (sin x) 2) (cos x)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* 31/360 (pow x 2))))))))
#s(approx (/ (pow (sin x) 2) (cos x)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 31/360 (* 173/5040 (pow x 2))))))))))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) -1/2) #s(hole binary64 -1/2))
#s(approx (* (+ 1 (* 1 (pow (tan x) 2))) -1/2) #s(hole binary64 (- (* -1/2 (pow x 2)) 1/2)))
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#s(approx (+ 1 (* 1 (pow (tan eps) 2))) #s(hole binary64 (+ 1 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* 17/45 (pow eps 2)))))))))
#s(approx (* 1 (pow (tan eps) 2)) #s(hole binary64 (pow eps 2)))
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#s(approx (pow (tan eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (tan eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))))
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#s(approx (pow (tan eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (+ 2/3 (* (pow eps 2) (+ 17/45 (* 62/315 (pow eps 2))))))))))
#s(approx (tan eps) #s(hole binary64 eps))
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#s(approx (pow (sin eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (- (* 2/45 (pow eps 2)) 1/3))))))
#s(approx (pow (sin eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 2/45 (* -1/315 (pow eps 2)))) 1/3))))))
#s(approx (sin eps) #s(hole binary64 eps))
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#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx (+ (* (/ 1/6 (cos eps)) (/ (pow (sin eps) 2) (cos eps))) (* -1/2 (+ 1 (* 1 (pow (tan eps) 2))))) #s(hole binary64 -1/2))
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#s(approx (/ 1/6 (cos eps)) #s(hole binary64 1/6))
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#s(approx (/ 1/6 (cos eps)) #s(hole binary64 (+ 1/6 (* (pow eps 2) (+ 1/12 (* (pow eps 2) (+ 5/144 (* 61/4320 (pow eps 2)))))))))
#s(approx (/ (pow (sin eps) 2) (cos eps)) #s(hole binary64 (pow eps 2)))
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#s(approx (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))) #s(hole binary64 -1/2))
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#s(approx (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))) #s(hole binary64 (- (* (pow eps 2) (- (* -1/3 (pow eps 2)) 1/2)) 1/2)))
#s(approx (* -1/2 (+ 1 (* 1 (pow (tan eps) 2)))) #s(hole binary64 (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/90 (pow eps 2)) 1/3)) 1/2)) 1/2)))
#s(approx (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps))) #s(hole binary64 eps))
#s(approx (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps))) #s(hole binary64 (* eps (+ 1 (* 4/3 (pow eps 2))))))
#s(approx (* 1 (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps))) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 4/3 (* 17/15 (pow eps 2))))))))
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#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)) #s(hole binary64 eps))
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#s(approx (/ (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) (cos eps)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 4/3 (* (pow eps 2) (+ 17/15 (* 248/315 (pow eps 2))))))))))
#s(approx (* (+ 1 (* 1 (pow (tan eps) 2))) (sin eps)) #s(hole binary64 eps))
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Outputs
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#s(approx (tan eps) (tan.f64 eps))
#s(approx (pow (sin eps) 2) (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))
#s(approx (sin eps) (sin.f64 eps))
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#s(approx (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) (*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps))) eps))) eps) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))))))
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#s(approx (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) eps)) (+.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (cos.f64 x)))) eps)) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))))))
#s(approx (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal -1 binary64) (+.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (pow.f64 eps #s(literal -1 binary64))) eps))) eps) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))))))
#s(approx (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1 binary64) (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))) (/.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (cos.f64 x))) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) eps)))))
#s(approx (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) (*.f64 (*.f64 #s(literal -1 binary64) eps) (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (fma.f64 #s(literal 1/6 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (pow.f64 eps #s(literal -1 binary64))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x)))))))

eval321.0ms (0.2%)

Memory
0.2MiB live, 573.6MiB allocated; 74ms collecting garbage
Compiler

Compiled 190 525 to 9 006 computations (95.3% saved)

prune23.3s (15.5%)

Memory
135.6MiB live, 26 386.4MiB allocated; 4.4s collecting garbage
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1 19021 192
Fresh000
Picked112
Done011
Total1 19141 195
Accuracy
100.0%
Counts
1 195 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓61.2%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓97.4%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1 binary64) x) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (cos.f64 eps)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (*.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))) #s(literal 1/2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (sin.f64 eps)) (cos.f64 eps)))) x (*.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
▶99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) eps) (+.f64 (*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 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2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64))) eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))))) eps))
▶32.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal -1 binary64) (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))) (/.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) eps))))))
Compiler

Compiled 1 065 to 187 computations (82.4% saved)

series358.0ms (0.2%)

Memory
-27.0MiB live, 495.4MiB allocated; 31ms collecting garbage
Counts
84 → 545
Calls
Call 1
Inputs
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(pow.f64 eps #s(literal 4 binary64))
eps
#s(literal 4 binary64)
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#s(literal -1 binary64)
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#s(literal -1/2 binary64)
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(sin.f64 x)
x
#s(literal 1 binary64)
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(pow.f64 (sin.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
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#s(literal 1/6 binary64)
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(fma.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)) (*.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) eps) (+.f64 (*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64))) eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(*.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal -1 binary64) eps) (+.f64 (*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 x)) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (cos.f64 x)) (fma.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal -1/2 binary64)))) #s(literal 1/6 binary64))) eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1 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 (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))))
#s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) 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 (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) 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 (* (pow eps 4) (* -1 (+ (+ (+ (* -1/2 (/ (+ (* (sin x) 1) (* (sin x) (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* 1/6 (/ (+ (* (sin x) 1) (* (sin x) (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (+ (* (pow (sin x) 2) 1) (* (pow (sin x) 2) (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))))))) (cos x))) (/ (+ (+ 1/6 (* -1 (/ (+ (* (pow (sin x) 2) 1) (* (pow (sin x) 2) (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1 (/ (- (+ (pow eps -1) (/ (+ (* (sin x) 1) (* (sin x) (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* -1 (pow (sin x) 2)) (* eps (pow (cos x) 2)))) eps)) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x)))))) eps)))) #s(hole binary64 (* (pow eps 4) (+ (* 1/3 (/ 1 eps)) (/ 1 (pow eps 3))))))
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Calls

6 calls:

TimeVariablePointExpression
45.0ms
x
@inf
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45.0ms
x
@-inf
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45.0ms
x
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37.0ms
eps
@-inf
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33.0ms
eps
@0
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rewrite497.0ms (0.3%)

Memory
50.3MiB live, 757.9MiB allocated; 35ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02594128754
02802118495
08153115870
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
629 → 718
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal -1 binary64) (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))) (/.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) eps))))))
#s(approx (* (- (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6) (sin x)) (* 1/6 (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (* 1 (pow (tan x) 2))) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (* 1 (pow (tan x) 2))) -1/2))) 1/6)) eps) (* 1 (/ (* (+ 1 (* 1 (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (* (pow (tan x) 2) -1)) eps) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal -1 binary64) (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))) (/.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) eps)))))
(*.f64 (pow.f64 eps #s(literal 4 binary64)) (*.f64 #s(literal -1 binary64) (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))) (/.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) eps))))
(pow.f64 eps #s(literal 4 binary64))
eps
#s(literal 4 binary64)
(*.f64 #s(literal -1 binary64) (+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))) (/.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) eps)))
#s(literal -1 binary64)
(+.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))) (/.f64 (+.f64 (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (+.f64 (pow.f64 eps #s(literal -1 binary64)) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))) (/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) eps) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x)))))) eps))
(+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)) (*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))))
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x))
(fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(sin.f64 x)
x
#s(literal 1 binary64)
(*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos.f64 x)
(*.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (sin.f64 x) #s(literal 1 binary64) (*.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (cos.f64 x)))
#s(literal 1/6 binary64)
(/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (*.f64 (/.f64 #s(literal 1/6 binary64) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (cos.f64 x))))))) (cos.f64 x))
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#s(approx (* (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (pow (tan x) 2)) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (pow (tan x) 2)) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (pow (tan x) 2)) -1/2))) 1/6) (sin x)) (* (* 1/6 (+ 1 (pow (tan x) 2))) (sin x))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (pow (tan x) 2)) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (pow (tan x) 2)) -1/2))) 1/6)) eps) (/ (* (+ 1 (pow (tan x) 2)) (sin x)) (cos x))) eps) 1) (* (pow (tan x) 2) -1)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (* (pow (sin x) 2) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))) (pow (cos x) 2))) (* -1 (/ (+ (* -1 (/ (* (pow (sin x) 3) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 3)))) (/ (* (pow (sin x) 2) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (pow (cos x) 2))) eps)))))))
#s(approx (* (+ (* (+ (* (- (* (* -1 eps) (+ (* (/ (* (+ 1 (pow (tan x) 2)) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (pow (tan x) 2)) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (pow (tan x) 2)) -1/2))) 1/6) (sin x)) (* (* 1/6 (+ 1 (pow (tan x) 2))) (sin x))) (cos x)))) (+ (+ (* (/ -1 (cos x)) (/ (* (+ 1 (pow (tan x) 2)) (pow (sin x) 2)) (cos x))) (+ (* (/ 1/6 (cos x)) (/ (pow (sin x) 2) (cos x))) (* (+ 1 (pow (tan x) 2)) -1/2))) 1/6)) eps) (/ (* (+ 1 (pow (tan x) 2)) (sin x)) (cos x))) eps) 1) (* (pow (tan x) 2) -1)) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (* (pow (sin x) 2) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))))) (pow (cos x) 2))) (* -1 (/ (+ (* -1 (/ (+ (/ (* (pow (sin x) 3) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 3)) (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) eps)) (/ (* (pow (sin x) 2) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (pow (cos x) 2))) eps)))))))
Outputs
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(pow.f64 eps #s(literal 4 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 4 binary64)))
eps
#s(literal 4 binary64)
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eval1.9s (1.3%)

Memory
-5.4MiB live, 3 229.5MiB allocated; 222ms collecting garbage
Compiler

Compiled 2 256 132 to 25 780 computations (98.9% saved)

prune2.0min (78.8%)

Memory
314.2MiB live, 191 425.1MiB allocated; 7.7s collecting garbage

end0.0ms (0%)

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

Profiling

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