2tan (problem 3.3.2)

Time bar (total: 6.8s)

start0.0ms (0%)

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

analyze81.0ms (1.2%)

Memory
-49.7MiB live, 67.0MiB allocated; 60ms 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)

sample4.1s (60.5%)

Memory
86.8MiB live, 5 202.2MiB allocated; 800ms collecting garbage
Samples
2.0s26 282×0invalid
841.0ms5 566×1valid
200.0ms2 690×0valid
Precisions
Click to see histograms. Total time spent on operations: 1.9s
ival-tan: 644.0ms (34.7% of total)
ival-fabs: 266.0ms (14.3% of total)
adjust: 247.0ms (13.3% of total)
ival-mult!: 189.0ms (10.2% of total)
ival-add!: 163.0ms (8.8% of total)
ival-<: 148.0ms (8% of total)
ival-sub!: 120.0ms (6.5% of total)
ival-and: 66.0ms (3.6% of total)
ival-assert: 14.0ms (0.8% of total)
Bogosity

explain92.0ms (1.4%)

Memory
16.5MiB live, 111.1MiB allocated; 5ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2373(5.771636815668268e-269 4.3981893004906006e-271)5(-4.341299336118073e-255 6.934219090358582e-257)(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
30-1(-28.536006434126797 0.0003530805701196077)(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))cancellation2358
tan.f64(tan.f64 (+.f64 x eps))sensitivity20
Confusion
Predicted +Predicted -
+2325
-316
Precision
0.9872340425531915
Recall
0.9789029535864979
Confusion?
Predicted +Predicted MaybePredicted -
+23250
-3313
Precision?
0.9753086419753086
Recall?
1.0
Freqs
test
numberfreq
021
1233
22
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
34.0ms360×1valid
7.0ms150×0valid
0.0ms2×2valid
Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 25.0ms
ival-tan: 12.0ms (48.1% of total)
adjust: 9.0ms (36.1% of total)
ival-sub!: 2.0ms (8% of total)
ival-add!: 2.0ms (8% of total)

preprocess55.0ms (0.8%)

Memory
-44.6MiB live, 8.5MiB 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
▶58.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 14 to 12 computations (14.3% saved)

series12.0ms (0.2%)

Memory
13.9MiB live, 13.9MiB 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))

rewrite154.0ms (2.3%)

Memory
29.0MiB live, 168.4MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

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

eval17.0ms (0.3%)

Memory
-30.3MiB live, 20.9MiB allocated; 3ms collecting garbage
Compiler

Compiled 1 894 to 399 computations (78.9% saved)

prune10.0ms (0.2%)

Memory
16.2MiB live, 16.1MiB allocated; 0ms collecting garbage
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New701484
Fresh000
Picked011
Done000
Total701585
Accuracy
100.0%
Counts
85 → 15
Alt Table
Click to see full alt table
StatusAccuracyProgram
59.1%
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
▶58.8%
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
59.1%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶3.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
6.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
6.9%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓58.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
57.9%
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
58.7%
(-.f64 #s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x))) (tan.f64 x))
98.2%
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
▶99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶97.8%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
Compiler

Compiled 875 to 446 computations (49% saved)

series158.0ms (2.3%)

Memory
28.2MiB live, 204.4MiB allocated; 58ms collecting garbage
Counts
53 → 305
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))))
(-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x))))
(neg.f64 eps)
eps
(fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
(sin.f64 x)
(cos.f64 x)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x))
(fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))))
(+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))
(fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (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))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
#s(literal -1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
#s(literal 1/6 binary64)
(*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
(tan.f64 eps)
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(tan.f64 (+.f64 (+.f64 x (PI.f64)) eps))
(+.f64 (+.f64 x (PI.f64)) eps)
(+.f64 x (PI.f64))
(PI.f64)
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(sin.f64 (-.f64 (+.f64 eps x) x))
(-.f64 (+.f64 eps x) x)
(+.f64 eps x)
(*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos.f64 (+.f64 eps x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64))
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)))))
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#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* -2/3 (pow x 2)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* -1/6 x)))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* -11/9 (pow x 2)) 1/6))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* -41/36 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (- 1 (neg (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 (neg (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 (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -1/2))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 x))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (* x (pow (sin (+ eps (PI))) 2)) (pow (cos (+ eps (PI))) 2)))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI)))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (PI))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (+ x (PI)))))
#s(approx (+ x (PI)) #s(hole binary64 (PI)))
#s(approx (+ x (PI)) #s(hole binary64 (+ x (PI))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* 5/6 eps) (* -1/2 eps))))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 1))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (* 5/6 eps) (* -1/2 eps))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (+ (* 5/6 eps) (* (pow x 2) (- (* 61/120 eps) (+ (* -1/2 (- (* 5/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (* eps (+ (* -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)))))) (+ 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
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#s(approx (+ (+ x (PI)) eps) #s(hole binary64 x))
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#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (- (+ x (PI)) (* -1 eps))) (cos (- (+ x (PI)) (* -1 eps))))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (PI)) eps)) 1)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
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Calls

6 calls:

TimeVariablePointExpression
36.0ms
eps
@-inf
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(tan x) 2))) (sin x)))) (cos x)))) (neg eps) eps (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (* (- 1 (neg (pow (tan x) 2))) (sin x)) (- 1 (neg (pow (tan x) 2))) 1 (neg (pow (tan x) 2)) (pow (tan x) 2) (tan x) x 2 (sin x) (cos x) -1/2 (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (sin x) 2) (pow (cos x) 2) -1 (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (* (pow (tan x) 2) 1/6) 1/6 (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) (- (tan (+ x eps)) (tan x)) (tan eps) (- (tan (+ (+ x (PI)) eps)) (tan x)) (tan (+ (+ x (PI)) eps)) (+ (+ x (PI)) eps) (+ x (PI)) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (sin (- (+ eps x) x)) (- (+ eps x) x) (+ eps x) (* (cos (+ eps x)) (cos x)) (cos (+ eps x)) (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1))
30.0ms
eps
@inf
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(cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 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x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1))
26.0ms
x
@-inf
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x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1))
17.0ms
x
@inf
((- (tan (+ x eps)) (tan x)) (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow 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16.0ms
x
@0
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x))) 1) (neg (pow (tan x) 2))) eps) (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1))

rewrite215.0ms (3.2%)

Memory
-18.0MiB live, 118.6MiB allocated; 16ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0141825539
0152323871
0830823428
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
358 → 493
Calls
Call 1
Inputs
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#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* -1/6 x)))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* -11/9 (pow x 2)) 1/6))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* -41/36 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (- 1 (neg (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 (neg (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 (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -1/2))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 x))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (/ (sin (+ eps (PI))) (cos (+ eps (PI)))) (/ (* x (pow (sin (+ eps (PI))) 2)) (pow (cos (+ eps (PI))) 2)))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (* x (- (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI)))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (+ eps (PI))) (cos (+ eps (PI))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (/ (* x (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))) (cos (+ eps (PI))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin (+ eps (PI))) 2) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (pow (cos (+ eps (PI))) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (* 1/6 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2)))))))) (* -1 (/ (* (sin (+ eps (PI))) (- 1 (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (cos (+ eps (PI)))))))) (* -1 (/ (pow (sin (+ eps (PI))) 2) (pow (cos (+ eps (PI))) 2))))) (/ (sin (+ eps (PI))) (cos (+ eps (PI)))))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (PI))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (+ eps (+ x (PI)))))
#s(approx (+ x (PI)) #s(hole binary64 (PI)))
#s(approx (+ x (PI)) #s(hole binary64 (+ x (PI))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin eps)))
#s(approx (- (+ eps x) x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (cos eps)))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* -1 (* x (cos eps))))))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (+ (cos eps) (* x (+ (* -1 (sin eps)) (* x (+ (* -1 (cos eps)) (* x (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))))))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos eps)))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 1))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* 5/6 eps) (* -1/2 eps))))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 1))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (* 5/6 eps) (* -1/2 eps))))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (+ 1 (* x (+ eps (* (pow x 2) (- (+ (* 5/6 eps) (* (pow x 2) (- (* 61/120 eps) (+ (* -1/2 (- (* 5/6 eps) (* -1/2 eps))) (* 1/24 eps))))) (* -1/2 eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (* eps (+ (* -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)))))) (+ 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
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#s(approx (+ (+ x (PI)) eps) #s(hole binary64 x))
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#s(approx (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (+ (* -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))))) (* -1 (/ (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -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))))))) eps))))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/2 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* 1/6 (/ 1 eps)) (/ (* (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))))))))))))
#s(approx (- (tan (+ (+ x (PI)) eps)) (tan x)) #s(hole binary64 (- (/ (sin (- (+ x (PI)) (* -1 eps))) (cos (- (+ x (PI)) (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (tan (+ (+ x (PI)) eps)) #s(hole binary64 (/ (sin (- (+ x (PI)) (* -1 eps))) (cos (- (+ x (PI)) (* -1 eps))))))
#s(approx (+ (+ x (PI)) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (+ x (PI)) eps)) 1)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (sin (- (+ eps x) x)) #s(hole binary64 (sin (neg (* -1 eps)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (* (cos (+ eps x)) (cos x)) #s(hole binary64 (* (cos x) (cos (- x (* -1 eps))))))
#s(approx (cos (+ eps x)) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (* -1 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps))))))
Outputs
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(*.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x))) eps (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) eps)
(/.f64 (-.f64 (*.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x))) eps #s(literal 1 binary64)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x))) eps #s(literal 1 binary64))) (*.f64 (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
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#s(approx (tan (+ (+ x (PI)) eps)) (tan.f64 (+.f64 eps x)))
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#s(approx (tan eps) (tan.f64 eps))
#s(approx (+ (+ x (PI)) eps) eps)
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#s(approx (+ eps x) (*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64))))
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#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (cos.f64 x)) (/.f64 #s(literal 1/6 binary64) eps))))))))))
#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (neg.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)))) eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (cos.f64 x)))))))
#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x))) (pow.f64 eps #s(literal -1 binary64))) eps) (neg.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)))) eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (cos.f64 x)))))))
#s(approx (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1 binary64) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (cos.f64 x))) (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 eps (cos.f64 x))) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) #s(literal 1/6 binary64)) eps)))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (cos.f64 x)) (/.f64 #s(literal 1/6 binary64) eps)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (-.f64 (tan.f64 (-.f64 (+.f64 (PI.f64) x) (neg.f64 eps))) (tan.f64 x)))
#s(approx (tan (+ (+ x (PI)) eps)) (tan.f64 (-.f64 (+.f64 (PI.f64) x) (neg.f64 eps))))
#s(approx (+ (+ x (PI)) eps) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (+.f64 (PI.f64) x) eps)) #s(literal 1 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 (*.f64 #s(literal 1 binary64) eps)) (cos.f64 x)) (cos.f64 (-.f64 x (neg.f64 eps)))))
#s(approx (sin (- (+ eps x) x)) (sin.f64 (*.f64 #s(literal 1 binary64) eps)))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (* (cos (+ eps x)) (cos x)) (*.f64 (cos.f64 x) (cos.f64 (-.f64 x (neg.f64 eps)))))
#s(approx (cos (+ eps x)) (cos.f64 (-.f64 x (neg.f64 eps))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (*.f64 (neg.f64 eps) (*.f64 #s(literal -1 binary64) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x))) (pow.f64 eps #s(literal -1 binary64)))))

eval193.0ms (2.8%)

Memory
1.9MiB live, 144.7MiB allocated; 32ms collecting garbage
Compiler

Compiled 121 064 to 7 399 computations (93.9% saved)

prune29.0ms (0.4%)

Memory
-14.5MiB live, 33.1MiB allocated; 1ms collecting garbage
Pruning

24 alts after pruning (21 fresh and 3 done)

PrunedKeptTotal
New93119950
Fresh729
Picked325
Done011
Total94124965
Accuracy
100.0%
Counts
965 → 24
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
99.6%
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
✓3.9%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
6.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
6.9%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓58.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
▶99.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
▶99.9%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
▶99.7%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (-.f64 (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (neg.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 #s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) x) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
97.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
98.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
97.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
3.2%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
✓97.8%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
98.2%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
▶97.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
▶97.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
Compiler

Compiled 2 660 to 1 172 computations (55.9% saved)

series79.0ms (1.2%)

Memory
40.4MiB live, 40.4MiB allocated; 0ms collecting garbage
Counts
49 → 218
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64))))
eps
(fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))
(fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))
(neg.f64 eps)
(fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x))))
(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
(sin.f64 x)
x
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
(cos.f64 x)
#s(literal 3 binary64)
#s(literal -1/3 binary64)
(neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))
(/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x))
(*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))))
(-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))
#s(literal 1/2 binary64)
(pow.f64 (cos.f64 x) #s(literal -2 binary64))
#s(literal -2 binary64)
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))
#s(literal 1/6 binary64)
(neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
#s(literal 4 binary64)
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64))))
(*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))
(fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64))
(*.f64 eps eps)
(fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64))
#s(literal 2/15 binary64)
#s(literal 1/3 binary64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
(*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64))))
(fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* eps (* x (+ 1 (* 4/3 (pow eps 2))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #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 (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 1/3))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (+ 1/3 (* 2/3 (* eps x)))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* 4/3 x))))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (+ 1/3 (* x (+ (* 2/3 eps) (* x (+ 4/3 (* 17/9 (* eps x)))))))))
#s(approx (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) #s(hole binary64 (* -2/3 x)))
#s(approx (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) #s(hole binary64 (* x (- (* -17/9 (pow x 2)) 2/3))))
#s(approx (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))))
#s(approx (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (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 (/ (sin x) (pow (cos x) 3)) #s(hole binary64 x))
#s(approx (/ (sin x) (pow (cos x) 3)) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (/ (sin x) (pow (cos x) 3)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (/ (sin x) (pow (cos x) 3)) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx x #s(hole binary64 x))
#s(approx (pow (cos x) 3) #s(hole binary64 1))
#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* -3/2 (pow x 2)))))
#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 7/8 (pow x 2)) 3/2)))))
#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))))
#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 (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* -1/3 x)))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* x (- (* -13/9 (pow x 2)) 1/3))))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* 1/3 x)))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* x (+ 1/3 (* 13/9 (pow x 2))))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 13/9 (* 107/45 (pow x 2))))))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 13/9 (* (pow x 2) (+ 107/45 (* 2516/945 (pow x 2))))))))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* 1/3 x)))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* x (+ 1/3 (* 23/18 (pow x 2))))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 23/18 (* 601/360 (pow x 2))))))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 23/18 (* (pow x 2) (+ 601/360 (* 23183/15120 (pow x 2))))))))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 1/3))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (+ 1/3 (* 4/3 (pow x 2)))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 1/2))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (+ 1/2 (* 1/2 (pow x 2)))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/2 (* 1/3 (pow x 2)))))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/3 (* 17/90 (pow x 2)))))))))
#s(approx (pow (cos x) -2) #s(hole binary64 1))
#s(approx (pow (cos x) -2) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (pow (cos x) -2) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (pow (cos x) -2) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 1/6))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (+ 1/6 (* -5/6 (pow x 2)))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (+ 1/6 (* (pow x 2) (- (* -14/9 (pow x 2)) 5/6)))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (+ 1/6 (* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6)))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (pow x 2)))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (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 (pow (cos x) 4) #s(hole binary64 1))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 5/3 (pow x 2)) 2)))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/3 (* -34/45 (pow x 2)))) 2)))))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 x))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#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 (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 eps))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* -1/6 eps) (* -3/2 eps)))))) (pow eps 2))))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 1))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* -1/6 eps) (* -3/2 eps))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ (* eps (+ (* eps (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2)))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (+ (* eps (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))))
#s(approx (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) #s(hole binary64 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (sin x) (pow (cos x) 3)) #s(hole binary64 (/ (sin x) (pow (cos x) 3))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (pow (cos x) 3) #s(hole binary64 (pow (cos x) 3)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* -1 (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (/ 1/2 (pow (cos x) 2))))
#s(approx (pow (cos x) -2) #s(hole binary64 (/ 1 (pow (cos x) 2))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (- (* 1/6 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 4)))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 4))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (pow (cos x) 4) #s(hole binary64 (pow (cos x) 4)))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (/ (sin x) (pow (cos x) 3))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (+ (* -1 (* eps (+ (* -1 (/ (* (sin x) (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (cos x))) (+ (* -1/2 (/ (sin x) (pow (cos x) 3))) (* 1/6 (/ (sin x) (pow (cos x) 3))))))) (* 1/2 (/ 1 (pow (cos x) 2)))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (/ 1 (pow (cos x) 2))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ (* eps (+ (* eps (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2)))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (/ (sin x) (pow (cos x) 3))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (+ (* eps (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#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 (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 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 (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 eps))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 1))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow eps 2)))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (/ 1 (pow (cos x) 2))))
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#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (* -1 (* (pow eps 2) (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
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#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/2 (* eps (pow (cos x) 2))) (+ (/ (sin x) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4)))))) (/ 1/6 (* eps (pow (cos x) 2)))))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* eps (- (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/2 (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))) (/ 1/6 (* eps (pow (cos x) 2)))))))
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#s(approx (tan eps) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* 2/15 (pow eps 5))))
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#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(hole binary64 (* 2/15 (pow eps 2))))
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#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (/ (* (pow eps 2) (sin x)) (pow (cos x) 3))))
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#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (/ (* eps (sin x)) (pow (cos x) 3))))
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Calls

6 calls:

TimeVariablePointExpression
27.0ms
x
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) (/ (sin x) (pow (cos x) 3)) (sin x) x (pow (cos x) 3) (cos x) 3 -1/3 (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) (* 1/2 (pow (cos x) -2)) 1/2 (pow (cos x) -2) -2 (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) 1/6 (neg (/ (pow (sin x) 2) (pow (cos x) 4))) (/ (pow (sin x) 2) (pow (cos x) 4)) (pow (sin x) 2) 2 (pow (cos x) 4) 4 (* 1 (/ (sin x) (pow (cos x) 3))) 1 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) (* eps eps) (+ (* 2/15 (* eps eps)) 1/3) 2/15 1/3 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)))
12.0ms
x
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) (/ (sin x) (pow (cos x) 3)) (sin x) x (pow (cos x) 3) (cos x) 3 -1/3 (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) (* 1/2 (pow (cos x) -2)) 1/2 (pow (cos x) -2) -2 (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) 1/6 (neg (/ (pow (sin x) 2) (pow (cos x) 4))) (/ (pow (sin x) 2) (pow (cos x) 4)) (pow (sin x) 2) 2 (pow (cos x) 4) 4 (* 1 (/ (sin x) (pow (cos x) 3))) 1 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) (* eps eps) (+ (* 2/15 (* eps eps)) 1/3) 2/15 1/3 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)))
8.0ms
eps
@inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) (/ (sin x) (pow (cos x) 3)) (sin x) x (pow (cos x) 3) (cos x) 3 -1/3 (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) (* 1/2 (pow (cos x) -2)) 1/2 (pow (cos x) -2) -2 (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) 1/6 (neg (/ (pow (sin x) 2) (pow (cos x) 4))) (/ (pow (sin x) 2) (pow (cos x) 4)) (pow (sin x) 2) 2 (pow (cos x) 4) 4 (* 1 (/ (sin x) (pow (cos x) 3))) 1 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) (* eps eps) (+ (* 2/15 (* eps eps)) 1/3) 2/15 1/3 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)))
8.0ms
eps
@-inf
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) (/ (sin x) (pow (cos x) 3)) (sin x) x (pow (cos x) 3) (cos x) 3 -1/3 (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) (* 1/2 (pow (cos x) -2)) 1/2 (pow (cos x) -2) -2 (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) 1/6 (neg (/ (pow (sin x) 2) (pow (cos x) 4))) (/ (pow (sin x) 2) (pow (cos x) 4)) (pow (sin x) 2) 2 (pow (cos x) 4) 4 (* 1 (/ (sin x) (pow (cos x) 3))) 1 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) (* eps eps) (+ (* 2/15 (* eps eps)) 1/3) 2/15 1/3 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)))
7.0ms
eps
@0
((/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) (/ (sin x) (pow (cos x) 3)) (sin x) x (pow (cos x) 3) (cos x) 3 -1/3 (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) (* 1/2 (pow (cos x) -2)) 1/2 (pow (cos x) -2) -2 (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) 1/6 (neg (/ (pow (sin x) 2) (pow (cos x) 4))) (/ (pow (sin x) 2) (pow (cos x) 4)) (pow (sin x) 2) 2 (pow (cos x) 4) 4 (* 1 (/ (sin x) (pow (cos x) 3))) 1 (- (tan (+ x eps)) (tan x)) (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (- (tan (+ x eps)) (tan x)) (tan eps) (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) (* eps eps) (+ (* 2/15 (* eps eps)) 1/3) 2/15 1/3 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (pow (cos x) 2) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)))

rewrite210.0ms (3.1%)

Memory
-8.6MiB live, 86.5MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105312247
0113411532
1655911532
0841111291
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
267 → 446
Calls
Call 1
Inputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
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eps
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(sin.f64 x)
x
(pow.f64 (cos.f64 x) #s(literal 3 binary64))
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#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 x #s(hole binary64 x))
#s(approx (pow (cos x) 3) #s(hole binary64 1))
#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* -3/2 (pow x 2)))))
#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 7/8 (pow x 2)) 3/2)))))
#s(approx (pow (cos x) 3) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 7/8 (* -61/240 (pow x 2)))) 3/2)))))
#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 (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* -1/3 x)))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* x (- (* -13/9 (pow x 2)) 1/3))))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* 1/3 x)))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* x (+ 1/3 (* 13/9 (pow x 2))))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 13/9 (* 107/45 (pow x 2))))))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 13/9 (* (pow x 2) (+ 107/45 (* 2516/945 (pow x 2))))))))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* 1/3 x)))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* x (+ 1/3 (* 23/18 (pow x 2))))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 23/18 (* 601/360 (pow x 2))))))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* x (+ 1/3 (* (pow x 2) (+ 23/18 (* (pow x 2) (+ 601/360 (* 23183/15120 (pow x 2))))))))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 1/3))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (+ 1/3 (* 4/3 (pow x 2)))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 1/2))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (+ 1/2 (* 1/2 (pow x 2)))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/2 (* 1/3 (pow x 2)))))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/3 (* 17/90 (pow x 2)))))))))
#s(approx (pow (cos x) -2) #s(hole binary64 1))
#s(approx (pow (cos x) -2) #s(hole binary64 (+ 1 (pow x 2))))
#s(approx (pow (cos x) -2) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))))
#s(approx (pow (cos x) -2) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 1/6))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (+ 1/6 (* -5/6 (pow x 2)))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (+ 1/6 (* (pow x 2) (- (* -14/9 (pow x 2)) 5/6)))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (+ 1/6 (* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6)))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* -1 (pow x 2))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* (pow x 2) (- (* -5/3 (pow x 2)) 1))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -77/45 (pow x 2)) 5/3)) 1))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -88/63 (pow x 2)) 77/45)) 5/3)) 1))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (pow x 2)))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (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 (pow (cos x) 4) #s(hole binary64 1))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* -2 (pow x 2)))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 5/3 (pow x 2)) 2)))))
#s(approx (pow (cos x) 4) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 5/3 (* -34/45 (pow x 2)))) 2)))))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 x))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#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 (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 eps))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* -1/6 eps) (* -3/2 eps)))))) (pow eps 2))))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 1))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (* x (+ eps x)))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ 1 (* x (+ eps (* x (+ 1 (* x (- (* -1/6 eps) (* -3/2 eps))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (+ eps x))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ (* eps (+ (* eps (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2)))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (+ (* eps (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (- (+ (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2))))))
#s(approx (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) #s(hole binary64 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (sin x) (pow (cos x) 3)) #s(hole binary64 (/ (sin x) (pow (cos x) 3))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (pow (cos x) 3) #s(hole binary64 (pow (cos x) 3)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) #s(hole binary64 (* -1 (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) #s(hole binary64 (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x))))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) #s(hole binary64 (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))))
#s(approx (* 1/2 (pow (cos x) -2)) #s(hole binary64 (/ 1/2 (pow (cos x) 2))))
#s(approx (pow (cos x) -2) #s(hole binary64 (/ 1 (pow (cos x) 2))))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) #s(hole binary64 (- (* 1/6 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) #s(hole binary64 (* -1 (/ (pow (sin x) 2) (pow (cos x) 4)))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 4))))
#s(approx (pow (sin x) 2) #s(hole binary64 (pow (sin x) 2)))
#s(approx (pow (cos x) 4) #s(hole binary64 (pow (cos x) 4)))
#s(approx (* 1 (/ (sin x) (pow (cos x) 3))) #s(hole binary64 (/ (sin x) (pow (cos x) 3))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (pow (cos x) 2) #s(hole binary64 (pow (cos x) 2)))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- eps (* -1 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 (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (* eps (+ (* eps (- (* eps (- (* 1/2 (/ 1 (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))))) (* -1 (/ (sin x) (pow (cos x) 3))))) (/ 1 (pow (cos x) 2))))))
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#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* eps (+ (* eps (+ (* eps (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (/ 1 (pow (cos x) 2))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ (/ 1 (pow (cos x) 2)) (/ (* eps (sin x)) (pow (cos x) 3)))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (+ (* eps (+ (* eps (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))) (/ 1 (pow (cos x) 2)))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (/ (sin x) (pow (cos x) 3))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (+ (* eps (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (/ (sin x) (pow (cos x) 3)))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))))
#s(approx (neg eps) #s(hole binary64 (* -1 eps)))
#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 (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 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 (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 eps))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 1))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(hole binary64 1/3))
#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(hole binary64 (+ 1/3 (* 2/15 (pow eps 2)))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (/ eps (pow (cos x) 2))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (/ 1 (pow (cos x) 2))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* -1 (* (pow eps 4) (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/3 (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/3 (* eps (pow (cos x) 2))) (+ (/ (sin x) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4)))))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/3 (* eps (pow (cos x) 2))) (+ (/ 1 (* (pow eps 3) (pow (cos x) 2))) (+ (/ (sin x) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (* -1 (* (pow eps 3) (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/3 (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/3 (* eps (pow (cos x) 2))) (+ (/ (sin x) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4)))))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (* (pow eps 3) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/3 (* eps (pow (cos x) 2))) (+ (/ 1 (* (pow eps 3) (pow (cos x) 2))) (+ (/ (sin x) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))))))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (* -1 (* (pow eps 2) (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/2 (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))) (/ 1/6 (* eps (pow (cos x) 2)))))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (* (pow eps 2) (- (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/2 (* eps (pow (cos x) 2))) (+ (/ (sin x) (* (pow eps 2) (pow (cos x) 3))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4)))))) (/ 1/6 (* eps (pow (cos x) 2)))))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* -1 (* eps (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* eps (- (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/2 (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))) (/ 1/6 (* eps (pow (cos x) 2)))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (/ (* (pow eps 2) (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))))
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#s(approx (tan eps) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* 2/15 (pow eps 5))))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* (pow eps 5) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* (pow eps 5) (+ 2/15 (+ (* 1/3 (/ 1 (pow eps 2))) (/ 1 (pow eps 4)))))))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 (* 2/15 (pow eps 4))))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 (* (pow eps 4) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(hole binary64 (* (pow eps 4) (+ 2/15 (+ (* 1/3 (/ 1 (pow eps 2))) (/ 1 (pow eps 4)))))))
#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(hole binary64 (* 2/15 (pow eps 2))))
#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(hole binary64 (* (pow eps 2) (+ 2/15 (* 1/3 (/ 1 (pow eps 2)))))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (/ (* (pow eps 2) (sin x)) (pow (cos x) 3))))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) #s(hole binary64 (* (pow eps 2) (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (/ (* eps (sin x)) (pow (cos x) 3))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (* eps (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* (pow eps 4) (- (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (+ (/ 1/2 (* eps (pow (cos x) 2))) (/ (pow (sin x) 2) (* eps (pow (cos x) 4))))) (/ 1/6 (* eps (pow (cos x) 2)))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (* -1 (/ (sin x) (* eps (pow (cos x) 3))))) eps))))))
#s(approx (* eps (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2))) #s(hole binary64 (* (pow eps 4) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (* -1 (/ (+ (/ 1 (* eps (pow (cos x) 2))) (/ (sin x) (pow (cos x) 3))) eps))) eps))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1 (/ (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))) eps)) (* -1/3 (/ (sin x) (pow (cos x) 3)))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1 (/ (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (+ (/ (sin x) (* eps (pow (cos x) 3))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2)))) eps)) (* -1/3 (/ (sin x) (pow (cos x) 3)))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) #s(hole binary64 (* -1 (* (pow eps 3) (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2)))) eps)) (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4)))) (* 1/6 (/ 1 (pow (cos x) 2)))) eps)) (* -1/3 (/ (sin x) (pow (cos x) 3)))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (- (* -1/3 (/ (sin x) (pow (cos x) 3))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))) (* -1 (/ (+ (* -1 (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (* -1 (/ (sin x) (* eps (pow (cos x) 3))))) eps))))))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) #s(hole binary64 (* -1 (* eps (- (+ (* -1 (/ (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2)))) eps)) (* -1/3 (/ (sin x) (pow (cos x) 3)))) (/ (* (sin x) (- (+ (* 1/2 (/ 1 (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 4))) (* 1/6 (/ 1 (pow (cos x) 2))))) (cos x)))))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) #s(hole binary64 (* -1 (* (pow eps 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow eps 2))) (pow eps 2))) 2/15)))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (sin x) (pow (cos x) 3))) (/ 1 (* eps (pow (cos x) 2))))))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (sin.f64 x)) (neg.f64 (cos.f64 x)))) (neg.f64 eps) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (cos.f64 x) #s(literal -2 binary64))) eps))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (sin.f64 x)) (neg.f64 (cos.f64 x)))) (neg.f64 eps) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (cos.f64 x) #s(literal -2 binary64))) eps)
(*.f64 eps (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (sin.f64 x)) (neg.f64 (cos.f64 x)))) (neg.f64 eps) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps (pow.f64 (cos.f64 x) #s(literal -2 binary64))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (sin.f64 x)) (neg.f64 (cos.f64 x)))) (neg.f64 eps) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) eps))
(fma.f64 eps (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (sin.f64 x)) (neg.f64 (cos.f64 x)))) (neg.f64 eps) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal -2 binary64))))
(+.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (sin.f64 x)) (neg.f64 (cos.f64 x)))) (neg.f64 eps) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps) eps) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) eps))
(+.f64 (*.f64 eps (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (*.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))) (sin.f64 x)) (neg.f64 (cos.f64 x)))) (neg.f64 eps) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) eps)) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal -2 binary64))))
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#s(literal 1/2 binary64)
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#s(literal -2 binary64)
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#s(literal 1/6 binary64)
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(*.f64 (sin.f64 x) (sin.f64 x))
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
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(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))
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#s(literal 2 binary64)
(*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow.f64 (cos.f64 x) #s(literal 4 binary64))
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#s(literal 4 binary64)
(*.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
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(/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
#s(literal 1 binary64)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps)
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#s(approx (tan eps) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
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(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (*.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64))))
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(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (fabs.f64 eps) (fabs.f64 eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 eps #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))))
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#s(approx (sin x) x)
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#s(approx x x)
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#s(approx (pow (cos x) -2) #s(literal 1 binary64))
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#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) (*.f64 x x))
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#s(approx (pow (sin x) 2) (*.f64 x x))
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#s(approx (pow (cos x) 4) #s(literal 1 binary64))
#s(approx (pow (cos x) 4) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal 1 binary64)))
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#s(approx (/ (sin x) (pow (cos x) 3)) x)
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#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
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#s(approx (/ eps (pow (cos x) 2)) eps)
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#s(approx (pow (cos x) 2) #s(literal 1 binary64))
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#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) eps)
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#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps))
#s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 x eps) #s(literal 4/3 binary64)) eps eps) x (*.f64 eps eps)) x eps))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) #s(literal 1 binary64))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 x eps #s(literal 1 binary64)))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 4/3 binary64) eps) x #s(literal 1 binary64)) x eps) x #s(literal 1 binary64)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
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#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (fma.f64 (neg.f64 eps) (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)) (cos.f64 x))) (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64)))))
#s(approx (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)))) (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)) (cos.f64 x))))
#s(approx (/ (sin x) (pow (cos x) 3)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
#s(approx (sin x) (sin.f64 x))
#s(approx (pow (cos x) 3) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))
#s(approx (cos x) (cos.f64 x))
#s(approx (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))) (neg.f64 (/.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)) (cos.f64 x))))
#s(approx (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x)) (/.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)) (cos.f64 x)))
#s(approx (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)))
#s(approx (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))) (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))))
#s(approx (* 1/2 (pow (cos x) -2)) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64)))
#s(approx (pow (cos x) -2) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))
#s(approx (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))) (-.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))))
#s(approx (neg (/ (pow (sin x) 2) (pow (cos x) 4))) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))
#s(approx (/ (pow (sin x) 2) (pow (cos x) 4)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))
#s(approx (pow (sin x) 2) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))
#s(approx (pow (cos x) 4) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
#s(approx (/ (sin x) (pow (cos x) 3)) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
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#s(approx (/ eps (pow (cos x) 2)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
#s(approx (pow (cos x) 2) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
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#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) eps (pow.f64 (cos.f64 x) #s(literal -2 binary64))))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 eps (neg.f64 x))) (tan.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
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#s(approx eps eps)
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#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (fma.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
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#s(approx (neg eps) (neg.f64 eps))
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#s(approx (tan eps) eps)
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#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) eps)
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#s(approx (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1) #s(literal 1 binary64))
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#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (+ (* 2/15 (* eps eps)) 1/3) #s(literal 1/3 binary64))
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#s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (neg.f64 (*.f64 (-.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1 binary64))) eps) #s(literal -1 binary64) (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64)))) eps))) (/.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)) (cos.f64 x))) (pow.f64 eps #s(literal 3 binary64)))))
#s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (*.f64 (*.f64 #s(literal -1 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (sin.f64 x) #s(literal -1/3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)) (cos.f64 x))) (/.f64 (fma.f64 (/.f64 (/.f64 (sin.f64 x) eps) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64) (neg.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))))) eps))) (*.f64 eps eps)))
#s(approx (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (*.f64 (neg.f64 eps) (-.f64 (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (/.f64 (neg.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64)))) eps)) (/.f64 (*.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x)) (cos.f64 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (-.f64 (tan.f64 (-.f64 x (neg.f64 eps))) (tan.f64 x)))
#s(approx (* eps (+ (* (* eps eps) (+ (* 2/15 (* eps eps)) 1/3)) 1)) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/3 binary64)) (*.f64 eps eps))) #s(literal 2/15 binary64)) (pow.f64 eps #s(literal 5 binary64)))))
#s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (pow.f64 (*.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) eps) #s(literal -1 binary64)))))

eval129.0ms (1.9%)

Memory
8.6MiB live, 99.2MiB allocated; 8ms collecting garbage
Compiler

Compiled 68 437 to 5 202 computations (92.4% saved)

prune38.0ms (0.6%)

Memory
-22.8MiB live, 30.4MiB allocated; 5ms collecting garbage
Pruning

25 alts after pruning (21 fresh and 4 done)

PrunedKeptTotal
New74613759
Fresh8816
Picked235
Done213
Total75825783
Accuracy
100.0%
Counts
783 → 25
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
99.6%
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
6.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
6.9%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓58.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
▶99.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
99.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
97.9%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 #s(approx (sin x) x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 #s(approx (/ (sin x) (pow (cos x) 3)) x) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
✓99.7%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (fma.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
97.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
▶98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
▶99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
3.2%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
✓97.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
▶97.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
✓97.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
Compiler

Compiled 2 172 to 1 128 computations (48.1% saved)

series76.0ms (1.1%)

Memory
6.6MiB live, 53.2MiB allocated; 3ms collecting garbage
Counts
69 → 315
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps)
(-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64))
(fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))))
(-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x))))
(neg.f64 eps)
eps
(fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan.f64 x)
x
#s(literal 2 binary64)
(sin.f64 x)
(cos.f64 x)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x))
(fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x))))
(+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(literal -1/2 binary64))) #s(literal 1/6 binary64))
(fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(literal -1/2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (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))
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
#s(literal -1 binary64)
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(literal -1/2 binary64))
#s(literal 1/6 binary64)
(*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))
(+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))
(fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))))
(fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps))
(fma.f64 (*.f64 x x) eps eps)
(*.f64 x x)
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps)))
(fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps))
(fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64))
(*.f64 eps eps)
#s(literal 2/15 binary64)
#s(literal 1/3 binary64)
(*.f64 #s(literal 1 binary64) eps)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
(/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))
(cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI.f64)
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
(/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x))))
(/.f64 (sin.f64 eps) (cos.f64 x))
(sin.f64 eps)
(cos.f64 (-.f64 eps (neg.f64 x)))
(-.f64 eps (neg.f64 x))
(neg.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)))))
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#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* -1/6 x)))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* -11/9 (pow x 2)) 1/6))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* -41/36 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (- 1 (neg (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 (neg (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 (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -1/2))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 x))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (/ eps (- 1/2 (* 1/2 (cos (PI)))))))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (+ (* -1 (/ (* eps (* x (sin (PI)))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))) (/ eps (- 1/2 (* 1/2 (cos (PI))))))))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (* eps (pow (sin (PI)) 2)) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (/ (* eps (cos (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))))) (/ (* eps (sin (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2)))) (/ eps (- 1/2 (* 1/2 (cos (PI))))))))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* eps (* (cos (PI)) (sin (PI)))) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (+ (* -1 (/ (* (sin (PI)) (+ (* -1 (/ (* eps (pow (sin (PI)) 2)) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (/ (* eps (cos (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2)))) (- 1/2 (* 1/2 (cos (PI)))))) (* -2/3 (/ (* eps (sin (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))))))) (+ (* -1 (/ (* eps (pow (sin (PI)) 2)) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (/ (* eps (cos (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))))) (/ (* eps (sin (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2)))) (/ eps (- 1/2 (* 1/2 (cos (PI))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (PI))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- (+ 1/2 (* x (sin (PI)))) (* 1/2 (cos (PI))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (cos (PI))) (* -1 (sin (PI)))))) (* 1/2 (cos (PI))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (PI)))) (* -1 (cos (PI))))) (* -1 (sin (PI)))))) (* 1/2 (cos (PI))))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (* 1/2 (cos (PI)))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1 (* x (sin (PI)))) (* 1/2 (cos (PI))))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* 1/2 (cos (PI))) (* x (+ (* -1 (sin (PI))) (* -1 (* x (cos (PI)))))))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* 1/2 (cos (PI))) (* x (+ (* -1 (sin (PI))) (* x (+ (* -1 (cos (PI))) (* 2/3 (* x (sin (PI)))))))))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (cos (PI))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (+ (cos (PI)) (* -2 (* x (sin (PI)))))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (+ (cos (PI)) (* x (- (* -2 (* x (cos (PI)))) (* 2 (sin (PI))))))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (+ (cos (PI)) (* x (- (* x (+ (* -2 (cos (PI))) (* 4/3 (* x (sin (PI)))))) (* 2 (sin (PI))))))))
#s(approx (* 2 (+ x (/ (PI) 2))) #s(hole binary64 (PI)))
#s(approx (* 2 (+ x (/ (PI) 2))) #s(hole binary64 (+ (PI) (* 2 x))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (sin eps)))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (cos eps)))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (- eps (neg x)) #s(hole binary64 eps))
#s(approx (- eps (neg x)) #s(hole binary64 (+ eps x)))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (* eps (+ (* -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)))))) (+ 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
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Calls

6 calls:

TimeVariablePointExpression
12.0ms
eps
@inf
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10.0ms
eps
@-inf
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10.0ms
x
@inf
((- (tan (+ x eps)) (tan x)) (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow 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(neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow 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eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (- (tan (+ x eps)) (tan x)) (tan eps) (+ (* (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) eps) (* 1 eps)) (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) (+ (* (* eps eps) 2/15) 1/3) (* eps eps) 2/15 1/3 (* 1 eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) (cos (* 2 (+ x (/ (PI) 2)))) (* 2 (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) (/ (sin eps) (cos x)) (sin eps) (cos (- eps (neg x))) (- eps (neg x)) (neg x))
10.0ms
x
@-inf
((- (tan (+ x eps)) (tan x)) (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow 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eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (- (tan (+ x eps)) (tan x)) (tan eps) (+ (* (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) eps) (* 1 eps)) (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) (+ (* (* eps eps) 2/15) 1/3) (* eps eps) 2/15 1/3 (* 1 eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) (cos (* 2 (+ x (/ (PI) 2)))) (* 2 (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) (/ (sin eps) (cos x)) (sin eps) (cos (- eps (neg x))) (- eps (neg x)) (neg x))
9.0ms
eps
@0
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eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (pow (cos x) 2)) (+ (* (* x x) eps) eps) (* x x) (- (tan (+ x eps)) (tan x)) (tan eps) (+ (* (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) eps) (* 1 eps)) (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) (+ (* (* eps eps) 2/15) 1/3) (* eps eps) 2/15 1/3 (* 1 eps) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) (cos (* 2 (+ x (/ (PI) 2)))) (* 2 (+ x (/ (PI) 2))) (+ x (/ (PI) 2)) (/ (PI) 2) (PI) (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) (/ (sin eps) (cos x)) (sin eps) (cos (- eps (neg x))) (- eps (neg x)) (neg x))

rewrite206.0ms (3%)

Memory
24.6MiB live, 112.8MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0145625569
0155923852
0855423116
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
384 → 542
Calls
Call 1
Inputs
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(neg.f64 eps)
eps
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(tan.f64 x)
x
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#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* -17/45 (pow x 2)) 2/3)) 1))))
#s(approx (neg (pow (tan x) 2)) #s(hole binary64 (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/315 (pow x 2)) 17/45)) 2/3)) 1))))
#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))))
#s(approx (pow (tan x) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))))
#s(approx (tan x) #s(hole binary64 x))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* 1/3 (pow x 2))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))))
#s(approx (tan x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* -1/6 x)))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* -11/9 (pow x 2)) 1/6))))
#s(approx (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* -1/6 x)))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* -41/36 (pow x 2)) 1/6))))
#s(approx (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 -1/3))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)))
#s(approx (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 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 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 -1/2))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* -4/3 (pow x 2)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/2)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 5/3 (pow x 2))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* 77/45 (pow x 2))))))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* (pow x 2) (+ 5/3 (* (pow x 2) (+ 77/45 (* 88/63 (pow x 2))))))))))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (pow x 2)))
#s(approx (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) #s(hole binary64 (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))))
#s(approx (* (- 1 (neg (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 (neg (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 (pow (cos x) 2) #s(hole binary64 1))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* -1 (pow x 2)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))))
#s(approx (pow (cos x) 2) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -2/45 (pow x 2)))) 1)))))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 -1/2))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* -1/3 (pow x 2)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3)) 1/2)))
#s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(hole binary64 (- (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3)) 1/2)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* 1/6 (pow x 2))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* 1/9 (pow x 2))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* 17/270 (pow x 2))))))))
#s(approx (* (pow (tan x) 2) 1/6) #s(hole binary64 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/9 (* (pow x 2) (+ 17/270 (* 31/945 (pow x 2))))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 x))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* 4/3 (pow x 2))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* 17/15 (pow x 2))))))))
#s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/15 (* 248/315 (pow x 2))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 eps))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (/ eps (pow (cos x) 2)) #s(hole binary64 (+ eps (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 eps) (+ (* -2/45 eps) (* 2/3 eps))))) (+ (* -1 eps) (* 1/3 eps)))) (* -1 eps))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 eps))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (+ eps (* eps (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (/ eps (- 1/2 (* 1/2 (cos (PI)))))))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (+ (* -1 (/ (* eps (* x (sin (PI)))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))) (/ eps (- 1/2 (* 1/2 (cos (PI))))))))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (* eps (pow (sin (PI)) 2)) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (/ (* eps (cos (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))))) (/ (* eps (sin (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2)))) (/ eps (- 1/2 (* 1/2 (cos (PI))))))))
#s(approx (/ eps (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* eps (* (cos (PI)) (sin (PI)))) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (+ (* -1 (/ (* (sin (PI)) (+ (* -1 (/ (* eps (pow (sin (PI)) 2)) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (/ (* eps (cos (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2)))) (- 1/2 (* 1/2 (cos (PI)))))) (* -2/3 (/ (* eps (sin (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))))))) (+ (* -1 (/ (* eps (pow (sin (PI)) 2)) (pow (- 1/2 (* 1/2 (cos (PI)))) 3))) (/ (* eps (cos (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2))))) (/ (* eps (sin (PI))) (pow (- 1/2 (* 1/2 (cos (PI)))) 2)))) (/ eps (- 1/2 (* 1/2 (cos (PI))))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- 1/2 (* 1/2 (cos (PI))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- (+ 1/2 (* x (sin (PI)))) (* 1/2 (cos (PI))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (cos (PI))) (* -1 (sin (PI)))))) (* 1/2 (cos (PI))))))
#s(approx (- 1/2 (* 1/2 (cos (* 2 (+ x (/ (PI) 2)))))) #s(hole binary64 (- (+ 1/2 (* x (- (* x (- (* -2/3 (* x (sin (PI)))) (* -1 (cos (PI))))) (* -1 (sin (PI)))))) (* 1/2 (cos (PI))))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (* 1/2 (cos (PI)))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* -1 (* x (sin (PI)))) (* 1/2 (cos (PI))))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* 1/2 (cos (PI))) (* x (+ (* -1 (sin (PI))) (* -1 (* x (cos (PI)))))))))
#s(approx (* 1/2 (cos (* 2 (+ x (/ (PI) 2))))) #s(hole binary64 (+ (* 1/2 (cos (PI))) (* x (+ (* -1 (sin (PI))) (* x (+ (* -1 (cos (PI))) (* 2/3 (* x (sin (PI)))))))))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (cos (PI))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (+ (cos (PI)) (* -2 (* x (sin (PI)))))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (+ (cos (PI)) (* x (- (* -2 (* x (cos (PI)))) (* 2 (sin (PI))))))))
#s(approx (cos (* 2 (+ x (/ (PI) 2)))) #s(hole binary64 (+ (cos (PI)) (* x (- (* x (+ (* -2 (cos (PI))) (* 4/3 (* x (sin (PI)))))) (* 2 (sin (PI))))))))
#s(approx (* 2 (+ x (/ (PI) 2))) #s(hole binary64 (PI)))
#s(approx (* 2 (+ x (/ (PI) 2))) #s(hole binary64 (+ (PI) (* 2 x))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (* 1/2 (PI))))
#s(approx (+ x (/ (PI) 2)) #s(hole binary64 (+ x (* 1/2 (PI)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (/ (sin eps) (cos eps))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (+ (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (+ (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (+ (/ (* (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3))))) (cos eps)) (/ (* (sin eps) (+ (* 1/6 (sin eps)) (* 1/2 (sin eps)))) (pow (cos eps) 2)))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 3)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (sin eps)))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (+ (sin eps) (* 1/2 (* (pow x 2) (sin eps))))))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (/ (sin eps) (cos x)) #s(hole binary64 (+ (sin eps) (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/720 (sin eps)) (+ (* 1/48 (sin eps)) (* 1/2 (+ (* -1/4 (sin eps)) (* 1/24 (sin eps)))))))) (+ (* -1/4 (sin eps)) (* 1/24 (sin eps))))) (* -1/2 (sin eps)))))))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (cos eps)))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (+ (cos eps) (* -1 (* x (sin eps))))))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))))
#s(approx (- eps (neg x)) #s(hole binary64 eps))
#s(approx (- eps (neg x)) #s(hole binary64 (+ eps x)))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))))
#s(approx (* (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* eps (+ 1 (+ (* eps (+ (* eps (- (* -1 (* eps (+ (* -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)))))) (+ 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)))))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (pow (tan x) 2) #s(hole binary64 (/ (pow (sin x) 2) (pow (cos x) 2))))
#s(approx (tan x) #s(hole binary64 (/ (sin x) (cos x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
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#s(approx (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (+ (* -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))))) (* -1 (/ (+ 1/6 (+ (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x)))) (+ (* -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))))))) eps))))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2)))) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* -1/2 (/ (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) eps)) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (+ (* 1/6 (/ 1 eps)) (/ (* (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))))))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(hole binary64 (/ (sin (neg (* -1 eps))) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (+ (* (* x x) eps) eps) #s(hole binary64 (* -1 (* eps (- (* -1 (pow x 2)) 1)))))
#s(approx (+ (* (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) eps) (* 1 eps)) #s(hole binary64 (* -1 (* (pow eps 5) (- (* -1 (/ (+ 1/3 (/ 1 (pow eps 2))) (pow eps 2))) 2/15)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) #s(hole binary64 (/ (sin eps) (* (cos x) (cos (- x (* -1 eps)))))))
#s(approx (cos (- eps (neg x))) #s(hole binary64 (cos (- x (* -1 eps)))))
#s(approx (- eps (neg x)) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
Outputs
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(/.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (tan.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (sin.f64 x) (*.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (+.f64 #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #s(literal -1/2 binary64)) #s(literal 1/6 binary64))) (sin.f64 x))) (cos.f64 x)))) (+.f64 (fma.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.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)))) #s(literal -1 binary64) (fma.f64 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#s(approx (tan eps) (tan.f64 eps))
#s(approx (+ (* (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) eps) (* 1 eps)) (*.f64 #s(literal 2/15 binary64) (pow.f64 eps #s(literal 5 binary64))))
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#s(approx (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) (*.f64 #s(literal 2/15 binary64) (pow.f64 eps #s(literal 4 binary64))))
#s(approx (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) (*.f64 (pow.f64 eps #s(literal 4 binary64)) (fma.f64 #s(literal 1/3 binary64) (pow.f64 eps #s(literal -2 binary64)) #s(literal 2/15 binary64))))
#s(approx (+ (* (* eps eps) 2/15) 1/3) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))
#s(approx (+ (* (* eps eps) 2/15) 1/3) (*.f64 (*.f64 eps eps) (fma.f64 #s(literal 1/3 binary64) (pow.f64 eps #s(literal -2 binary64)) #s(literal 2/15 binary64))))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (- eps (neg x)) (*.f64 eps (+.f64 (/.f64 x eps) #s(literal 1 binary64))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (-.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x)))
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#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (cos.f64 x)) (/.f64 #s(literal 1/6 binary64) eps))))))))))
#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (/.f64 (sin.f64 x) eps) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (cos.f64 x)) (neg.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)))) eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (cos.f64 x)))))))
#s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x))) (pow.f64 eps #s(literal -1 binary64))) eps) (neg.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)))) eps) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (cos.f64 x)))))))
#s(approx (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) (*.f64 (*.f64 eps eps) (*.f64 #s(literal -1 binary64) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (/.f64 (fma.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (*.f64 (*.f64 #s(literal 1/6 binary64) (sin.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))) (cos.f64 x))) (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 eps (cos.f64 x))) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) #s(literal 1/6 binary64)) eps)))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (*.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (sin.f64 x) (/.f64 (+.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal 1/6 binary64)) (cos.f64 x)) (/.f64 #s(literal 1/6 binary64) eps)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
#s(approx (+ (* (* x x) eps) eps) (*.f64 (neg.f64 eps) (-.f64 (neg.f64 (*.f64 x x)) #s(literal 1 binary64))))
#s(approx (+ (* (* (+ (* (* eps eps) 2/15) 1/3) (* eps eps)) eps) (* 1 eps)) (neg.f64 (*.f64 (pow.f64 eps #s(literal 5 binary64)) (-.f64 (neg.f64 (/.f64 (+.f64 (pow.f64 eps #s(literal -2 binary64)) #s(literal 1/3 binary64)) (*.f64 eps eps))) #s(literal 2/15 binary64)))))
#s(approx (/ (/ (sin eps) (cos x)) (cos (- eps (neg x)))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (+.f64 eps x))))
#s(approx (cos (- eps (neg x))) (cos.f64 (+.f64 eps x)))
#s(approx (- eps (neg x)) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval215.0ms (3.2%)

Memory
-52.2MiB live, 123.4MiB allocated; 109ms collecting garbage
Compiler

Compiled 108 972 to 6 840 computations (93.7% saved)

prune37.0ms (0.5%)

Memory
-9.1MiB live, 38.4MiB allocated; 1ms collecting garbage
Pruning

26 alts after pruning (22 fresh and 4 done)

PrunedKeptTotal
New78712799
Fresh61016
Picked415
Done134
Total79826824
Accuracy
100.0%
Counts
824 → 26
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.8%
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
99.6%
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
6.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
6.9%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
✓58.8%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (-.f64 eps (neg.f64 x)))))
99.7%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
99.9%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)) (cos.f64 x)))))
99.6%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 #s(approx (sin eps) eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
99.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
99.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
99.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
99.1%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
97.9%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
✓99.7%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
97.8%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
✓98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
6.3%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
98.2%
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
3.2%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
✓97.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
97.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
Compiler

Compiled 3 720 to 950 computations (74.5% saved)

regimes43.0ms (0.6%)

Memory
24.7MiB live, 24.7MiB allocated; 0ms collecting garbage
Counts
59 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 #s(approx (sin eps) eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (-.f64 eps (neg.f64 x)))))
(-.f64 #s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x))) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)) (cos.f64 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (fma.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (-.f64 (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (neg.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 #s(approx (/ (sin x) (pow (cos x) 3)) x) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 #s(approx (sin x) x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 #s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) x) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

13.0ms
x
13.0ms
eps
13.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes47.0ms (0.7%)

Memory
-27.2MiB live, 24.6MiB allocated; 5ms collecting garbage
Counts
58 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 #s(approx (sin eps) eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (-.f64 eps (neg.f64 x)))))
(-.f64 #s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x))) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)) (cos.f64 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (fma.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (-.f64 (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (neg.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 #s(approx (/ (sin x) (pow (cos x) 3)) x) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 #s(approx (sin x) x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 #s(approx (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) x) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) #s(approx (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) #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) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64))) eps (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
Calls

3 calls:

17.0ms
x
13.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms
eps
Results
AccuracySegmentsBranch
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes39.0ms (0.6%)

Memory
23.2MiB live, 23.2MiB allocated; 0ms collecting garbage
Counts
55 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 #s(approx (sin eps) eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (-.f64 eps (neg.f64 x)))))
(-.f64 #s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x))) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)) (cos.f64 x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (sin.f64 eps)) (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (cos.f64 eps)) (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) x (tan.f64 eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 #s(approx (pow (tan x) 2) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) eps))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps #s(approx (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3)))) (fma.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/2 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (cos.f64 x) #s(literal -2 binary64)) #s(literal 1/6 binary64))) eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (-.f64 (*.f64 eps (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (neg.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (fma.f64 (neg.f64 eps) (+.f64 (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)))) #s(literal 1/6 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 #s(approx (/ (sin x) (pow (cos x) 3)) x) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 #s(approx (sin x) x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64) (neg.f64 (/.f64 (*.f64 (sin.f64 x) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (cos.f64 x)))) (-.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64))) (fma.f64 #s(literal 1/6 binary64) (pow.f64 (cos.f64 x) #s(literal -2 binary64)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 eps (-.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)) (cos.f64 x)))))
Calls

3 calls:

12.0ms
x
12.0ms
eps
12.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.9%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.9%1x
99.9%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes33.0ms (0.5%)

Memory
-27.5MiB live, 19.6MiB allocated; 2ms collecting garbage
Counts
45 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 #s(approx (sin eps) eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (-.f64 eps (neg.f64 x)))))
(-.f64 #s(approx (tan (+ x eps)) (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps (tan.f64 x))) (tan.f64 x))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) #s(approx (cos (- eps (neg x))) (fma.f64 (neg.f64 eps) (sin.f64 x) (cos.f64 x)))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps (fma.f64 eps (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (pow.f64 (cos.f64 x) #s(literal -2 binary64)))))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) (cos.f64 (-.f64 eps (neg.f64 x)))))
Calls

3 calls:

11.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
10.0ms
eps
10.0ms
x
Results
AccuracySegmentsBranch
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.8%1x
99.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes29.0ms (0.4%)

Memory
18.0MiB live, 18.0MiB allocated; 0ms collecting garbage
Counts
40 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 #s(approx (sin eps) eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
(/.f64 (sin.f64 (-.f64 (+.f64 eps x) x)) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) (*.f64 eps (fma.f64 #s(literal -1/6 binary64) (*.f64 eps eps) #s(literal 1 binary64)))) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
Calls

3 calls:

9.0ms
eps
9.0ms
x
9.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.8%1x
99.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.4%)

Memory
16.9MiB live, 16.9MiB allocated; 0ms collecting garbage
Counts
37 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 (/.f64 #s(approx (sin eps) eps) (cos.f64 x)) (cos.f64 (-.f64 eps (neg.f64 x)))))
Outputs
(/.f64 #s(approx (sin (- (+ eps x) x)) eps) (*.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))
Calls

3 calls:

9.0ms
eps
9.0ms
x
8.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.6%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.6%1x
99.6%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes27.0ms (0.4%)

Memory
-31.0MiB live, 16.1MiB allocated; 0ms collecting garbage
Counts
35 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x (PI.f64))))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 #s(approx (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64))))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (/.f64 (-.f64 (*.f64 x x) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (-.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))))))))
Calls

3 calls:

9.0ms
x
8.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms
eps
Results
AccuracySegmentsBranch
99.1%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.1%1x
99.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.3%)

Memory
13.3MiB live, 13.3MiB allocated; 0ms collecting garbage
Counts
27 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(approx (* 2 (+ x (/ (PI) 2))) (fma.f64 #s(literal 2 binary64) x (PI.f64))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64)))))))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (sin.f64 (fma.f64 #s(literal 2 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x) (/.f64 (PI.f64) #s(literal 2 binary64))))))))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
Calls

3 calls:

6.0ms
eps
6.0ms
x
6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
99.1%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.1%1x
99.1%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes18.0ms (0.3%)

Memory
12.1MiB live, 12.1MiB allocated; 0ms collecting garbage
Counts
23 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (* eps (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2))) (fma.f64 (fma.f64 x eps (*.f64 eps eps)) x eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (/.f64 eps #s(approx (pow (cos x) 2) (fma.f64 (*.f64 x x) #s(literal -1 binary64) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 #s(literal 2/15 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)) #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) eps) eps) eps eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) eps) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (fma.f64 (*.f64 (fma.f64 (*.f64 eps eps) #s(literal 2/15 binary64) #s(literal 1/3 binary64)) (*.f64 eps eps)) eps (*.f64 #s(literal 1 binary64) eps))))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (neg.f64 (*.f64 x x)) (*.f64 eps #s(literal -2/3 binary64)) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) eps) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (fma.f64 (-.f64 (*.f64 (neg.f64 (*.f64 x x)) (fma.f64 eps #s(literal 28/45 binary64) (neg.f64 eps))) (*.f64 eps #s(literal -2/3 binary64))) (*.f64 x x) (*.f64 #s(literal 1 binary64) eps)) (*.f64 x x) eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (fma.f64 #s(literal 2/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 4/3 binary64) (*.f64 eps eps) #s(literal 1 binary64)))))) #s(literal 1 binary64))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 (+.f64 (PI.f64) eps)))
(-.f64 (tan.f64 (+.f64 x eps)) #s(approx (tan x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 1 binary64)) x)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (fma.f64 x (fma.f64 eps eps (*.f64 eps x)) eps)))
Calls

3 calls:

6.0ms
eps
6.0ms
x
6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
98.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.2%1x
98.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes9.0ms (0.1%)

Memory
7.2MiB live, 7.2MiB allocated; 0ms collecting garbage
Counts
9 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (/ (sin x) (pow (cos x) 3))) (pow (cos x) -2)) (fma.f64 (+.f64 x eps) x #s(literal 1 binary64)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (+ (* (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) (+ (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (pow (sin x) 2)) (pow (cos x) 2)) -1) (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6))) 1/6)) eps) (* 1 (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) (*.f64 eps #s(approx (+ (* eps (+ (* eps (+ (* (neg eps) (+ (* (/ (sin x) (pow (cos x) 3)) -1/3) (neg (/ (* (sin x) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4)))))) (cos x))))) (- (* 1/2 (pow (cos x) -2)) (+ (* 1/6 (pow (cos x) -2)) (neg (/ (pow (sin x) 2) (pow (cos x) 4))))))) (* 1 (/ (sin x) (pow (cos x) 3))))) (pow (cos x) -2)) (fma.f64 (*.f64 eps eps) #s(literal 1/3 binary64) #s(literal 1 binary64)))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 x (+.f64 eps x) #s(literal 1 binary64))) eps))
Calls

3 calls:

3.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
eps
3.0ms
x
Results
AccuracySegmentsBranch
98.2%1x
98.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory
6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (fma.f64 (*.f64 x x) eps eps)))
Calls

3 calls:

2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
eps
2.0ms
x
Results
AccuracySegmentsBranch
98.2%1x
98.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.2%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory
-41.9MiB live, 5.7MiB allocated; 1ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
Outputs
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) eps)))
Calls

3 calls:

2.0ms
eps
2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
Results
AccuracySegmentsBranch
98.2%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.2%1eps
98.2%1x
Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0.1%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Accuracy

Total -58.6b remaining (-4184.3%)

Threshold costs -58.6b (-4184.3%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (/ (sin (- (+ eps x) x)) (* (cos (+ eps x)) (cos x))) #s(approx (/ eps (pow (cos x) 2)) #s(approx (+ (* (* x x) eps) eps) (*.f64 eps (*.f64 x x)))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (fma.f64 eps x #s(literal 1 binary64))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
Calls

3 calls:

1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
eps
1.0ms
x
Results
AccuracySegmentsBranch
97.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
97.8%1x
97.8%1eps
Compiler

Compiled 9 to 10 computations (-11.1% saved)

derivations291.0ms (4.3%)

Memory
36.2MiB live, 36.2MiB allocated; 0ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 593 to 153 computations (74.2% saved)

preprocess78.0ms (1.1%)

Memory
-37.3MiB live, 57.1MiB allocated; 8ms collecting garbage
Compiler

Compiled 635 to 183 computations (71.2% saved)

end0.0ms (0%)

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

Profiling

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