tanhf (example 3.4)

Time bar (total: 3.8s)

start0.0ms (0%)

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

analyze153.0ms (4.1%)

Memory
-14.4MiB live, 86.4MiB allocated; 52ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
37.5%37.5%62.5%0%0%0%0%4
43.8%43.7%56.2%0%0%0%0%5
46.9%46.9%53.1%0%0%0%0%6
48.4%48.4%51.5%0%0%0%0%7
49.2%49.2%50.8%0%0%0%0%8
49.6%49.6%50.4%0%0%0%0%9
49.8%49.8%50.2%0%0%0%0%10
49.9%49.9%50.1%0%0%0%0%11
50%49.9%50%0%0%0%0%12
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample2.2s (57.8%)

Memory
67.5MiB live, 1 743.2MiB allocated; 1.1s collecting garbage
Samples
942.0ms2 250×2valid
505.0ms4 104×0valid
292.0ms734×3valid
112.0ms1 165×1valid
3.0ms3×4valid
Precisions
Click to see histograms. Total time spent on operations: 1.2s
ival-cos: 775.0ms (63% of total)
ival-sin: 183.0ms (14.9% of total)
adjust: 147.0ms (12% of total)
ival-div!: 76.0ms (6.2% of total)
ival-sub!: 48.0ms (3.9% of total)
Bogosity

preprocess42.0ms (1.1%)

Memory
-18.4MiB live, 26.5MiB allocated; 12ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01213
15512
223412
3133712
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶52.7%
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Symmetry

(negabs x)

Compiler

Compiled 12 to 12 computations (0% saved)

series3.0ms (0.1%)

Memory
4.2MiB live, 4.2MiB allocated; 0ms collecting garbage
Counts
6 → 20
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#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 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 (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) x (sin x))
1.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) x (sin x))
1.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) x (sin x))

rewrite189.0ms (5%)

Memory
41.2MiB live, 86.9MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0103316
0109295
1648295
25699295
08023271
124133271
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
26 → 89
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#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 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 (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 #s(literal 1 binary64) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(neg.f64 (tan.f64 (*.f64 #s(literal -1/2 binary64) x)))
(neg.f64 (tan.f64 (*.f64 x #s(literal -1/2 binary64))))
(neg.f64 (*.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(neg.f64 (tan.f64 (/.f64 (neg.f64 x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (sin.f64 x)))
(neg.f64 (-.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(tan.f64 (/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64)))
(tan.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)) (PI.f64)))
(tan.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64)))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (/.f64 (cos.f64 x) (sin.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (neg.f64 (cos.f64 x)) (sin.f64 x)))
(neg.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (cos.f64 x))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x)))
#s(literal 1 binary64)
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 x))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x) (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (neg.f64 (cos.f64 x))) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) #s(literal 2 binary64))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (neg.f64 (fabs.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (fabs.f64 (fabs.f64 x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (+.f64 (fabs.f64 x) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 (PI.f64) #s(literal 1/2 binary64) x))
(fma.f64 (sin.f64 (fabs.f64 x)) #s(literal 0 binary64) (cos.f64 x))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (cos.f64 x))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (cos.f64 x))
(fma.f64 (cos.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(-.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (*.f64 (cos.f64 x) (sin.f64 (neg.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 (fabs.f64 x))))
(cos.f64 (neg.f64 (fabs.f64 (fabs.f64 x))))
(cos.f64 (fabs.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (fabs.f64 (neg.f64 (fabs.f64 x))))
(cos.f64 (fabs.f64 (fabs.f64 (fabs.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 (fabs.f64 x)))
(cos.f64 (fabs.f64 (fabs.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 (fabs.f64 x))
(cos.f64 x)
(+.f64 (*.f64 (sin.f64 (fabs.f64 x)) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (*.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (*.f64 (sin.f64 x) #s(literal 0 binary64)) (cos.f64 x))
(+.f64 (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
x
(sin.f64 x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (*.f64 x x) #s(literal 1/720 binary64)) (*.f64 x x) #s(literal -1/24 binary64)) x) x #s(literal 1/2 binary64)) x) x))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64)))
#s(approx x x)
#s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal 1 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))

eval47.0ms (1.2%)

Memory
-35.1MiB live, 11.8MiB allocated; 3ms collecting garbage
Compiler

Compiled 548 to 315 computations (42.5% saved)

prune5.0ms (0.1%)

Memory
8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New76783
Fresh000
Picked101
Done000
Total77784
Accuracy
100.0%
Counts
84 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
4.4%
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
99.7%
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
▶100.0%
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶51.7%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
▶51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 146 to 142 computations (2.7% saved)

series12.0ms (0.3%)

Memory
16.1MiB live, 16.1MiB allocated; 0ms collecting garbage
Counts
22 → 52
Calls
Call 1
Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64))
(*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x)
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
Outputs
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 1/240))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 (+ 1/240 (* 17/40320 (pow x 2)))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* 17/40320 (pow x 7))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* 17/40320 (pow x 6))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* 17/40320 (pow x 5))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* (pow x 5) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* (pow x 5) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (* 17/40320 (pow x 4))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 (* 17/40320 (pow x 2))))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))))
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((tan (* 1/2 x)) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) 1/240 (/ (- 1 (cos x)) (sin x)) (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240) 17/40320)
3.0ms
x
@inf
((tan (* 1/2 x)) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) 1/240 (/ (- 1 (cos x)) (sin x)) (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240) 17/40320)
3.0ms
x
@0
((tan (* 1/2 x)) (* 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) 1/24 (/ (- 1 (cos x)) (sin x)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) 1/240 (/ (- 1 (cos x)) (sin x)) (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (+ (* 17/40320 (* x x)) 1/240) 17/40320)

rewrite295.0ms (7.9%)

Memory
-5.5MiB live, 134.7MiB allocated; 19ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01921399
02191299
110491291
276491291
081221260
1268071260
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
74 → 352
Calls
Call 1
Inputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x)
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64))
(*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x)
(fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
#s(literal 17/40320 binary64)
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/240 (pow x 2))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* x (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2)))))))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 1/240))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 (+ 1/240 (* 17/40320 (pow x 2)))))
#s(approx (tan (* 1/2 x)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* 1/240 (pow x 4))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) #s(hole binary64 (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* 17/40320 (pow x 7))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* (pow x 7) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* 17/40320 (pow x 6))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) #s(hole binary64 (* (pow x 6) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (+ (* 1/240 (/ 1 (pow x 2))) (* 1/2 (/ 1 (pow x 6)))))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* 17/40320 (pow x 5))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* (pow x 5) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* (pow x 5) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (* 17/40320 (pow x 4))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) #s(hole binary64 (* (pow x 4) (+ 17/40320 (+ (/ 1/24 (pow x 4)) (* 1/240 (/ 1 (pow x 2))))))))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 (* 17/40320 (pow x 2))))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(hole binary64 (* (pow x 2) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 4))) (+ 17/40320 (* 1/240 (/ 1 (pow x 2)))))))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/240 (* 1/24 (/ 1 (pow x 2)))) (pow x 2))) 17/40320)))))
Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) x))) (sin.f64 (*.f64 x #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (-.f64 (cos.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 x))))
(*.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) x))))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 #s(literal 1 binary64) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (sin.f64 (+.f64 (fma.f64 x #s(literal 1/2 binary64) (PI.f64)) (PI.f64))) (cos.f64 (+.f64 (fma.f64 x #s(literal 1/2 binary64) (PI.f64)) (PI.f64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (sin.f64 x))
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(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1/240 binary64)) (-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)) #s(literal -1/24 binary64)))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))) #s(literal 1/24 binary64))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) (fma.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) (-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)) #s(literal -1/24 binary64)))
(fma.f64 (*.f64 (*.f64 #s(literal 1/240 binary64) x) x) #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
(fma.f64 (*.f64 (*.f64 #s(literal 1/240 binary64) x) x) #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)) #s(literal -1/24 binary64)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)) #s(literal -1/24 binary64)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) (fma.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) (-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)) #s(literal -1/24 binary64)))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) (fma.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
(fma.f64 x (*.f64 #s(literal 1/240 binary64) x) (-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)) #s(literal -1/24 binary64)))
(fma.f64 x (*.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) #s(literal 1/24 binary64))
(-.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x) #s(literal -1/24 binary64))
(-.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) (neg.f64 x)))
(+.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)))
(+.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x) #s(literal 1/24 binary64))
(+.f64 (*.f64 (*.f64 #s(literal 1/240 binary64) x) x) (fma.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
(+.f64 (*.f64 (*.f64 #s(literal 1/240 binary64) x) x) (-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) (*.f64 (*.f64 x x) x)) #s(literal -1/24 binary64)))
(+.f64 #s(literal 1/24 binary64) (neg.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) (neg.f64 x))))
(+.f64 #s(literal 1/24 binary64) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) x) x))
(neg.f64 (-.f64 #s(literal -1/240 binary64) (*.f64 (*.f64 #s(literal 17/40320 binary64) x) x)))
(neg.f64 (-.f64 (*.f64 #s(literal -17/40320 binary64) (*.f64 x x)) #s(literal 1/240 binary64)))
(fma.f64 (*.f64 #s(literal 17/40320 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1/240 binary64))
(fma.f64 (*.f64 #s(literal 17/40320 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1/240 binary64))
(fma.f64 (*.f64 #s(literal 17/40320 binary64) x) x #s(literal 1/240 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 17/40320 binary64)) #s(literal 1/240 binary64))
(fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64))
(fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64))
(fma.f64 x (*.f64 #s(literal 17/40320 binary64) x) #s(literal 1/240 binary64))
(-.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) x) #s(literal -1/240 binary64))
(-.f64 #s(literal 1/240 binary64) (*.f64 #s(literal -17/40320 binary64) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 #s(literal 17/40320 binary64) x) x) #s(literal 1/240 binary64))
(+.f64 #s(literal 1/240 binary64) (neg.f64 (*.f64 #s(literal -17/40320 binary64) (*.f64 x x))))
(+.f64 #s(literal 1/240 binary64) (*.f64 (*.f64 #s(literal 17/40320 binary64) x) x))
#s(literal 17/40320 binary64)
#s(approx (tan (* 1/2 x)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (tan (* 1/2 x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (tan (* 1/2 x)) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (* 1/2 x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
#s(approx x x)
#s(approx (+ (* (* x x) 1/24) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* (* x x) 1/24) 1/2) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (+ (* 1/240 (* x x)) 1/24) #s(literal 1/24 binary64))
#s(approx (+ (* 1/240 (* x x)) 1/24) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (fma.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (*.f64 #s(literal 1/24 binary64) x))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) x))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (+ (* 17/40320 (* x x)) 1/240) #s(literal 1/240 binary64))
#s(approx (+ (* 17/40320 (* x x)) 1/240) (fma.f64 (*.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)))
#s(approx (tan (* 1/2 x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
#s(approx (tan (* 1/2 x)) (tan.f64 (*.f64 x #s(literal 1/2 binary64))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) (*.f64 x x)))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64)))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/240 binary64)))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64))))
#s(approx (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ (* 1/240 (* x x)) 1/24) (*.f64 (*.f64 #s(literal 1/240 binary64) x) x))
#s(approx (+ (* 1/240 (* x x)) 1/24) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64)) x) x))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (*.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 17/40320 binary64)))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (*.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64) (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (*.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64) #s(literal 17/40320 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 17/40320 binary64)))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (*.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (*.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64) (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64)))))
#s(approx (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) (*.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64) #s(literal 17/40320 binary64)) (fma.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -6 binary64)) (/.f64 #s(literal -1/240 binary64) (*.f64 x x)))) (pow.f64 x #s(literal 6 binary64))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 17/40320 binary64)))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (*.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64) (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 17/40320 binary64)))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (*.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64)) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) (*.f64 (fma.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64) (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ (* 17/40320 (* x x)) 1/240) (*.f64 (*.f64 #s(literal 17/40320 binary64) x) x))
#s(approx (+ (* 17/40320 (* x x)) 1/240) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64)) x) x))
#s(approx (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (*.f64 (-.f64 #s(literal 1/240 binary64) (/.f64 (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (*.f64 (-.f64 #s(literal 17/40320 binary64) (/.f64 (-.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x x))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ (* (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) x) 1/2) x) (*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/240 binary64) (*.f64 x x)) #s(literal -17/40320 binary64)) (*.f64 (-.f64 #s(literal -1/24 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (pow.f64 x #s(literal -4 binary64)))) (pow.f64 x #s(literal 7 binary64))))
#s(approx (* (+ (* (+ (* 17/40320 (* x x)) 1/240) (* x x)) 1/24) x) (*.f64 (-.f64 #s(literal 17/40320 binary64) (/.f64 (-.f64 #s(literal -1/240 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64))))

eval45.0ms (1.2%)

Memory
26.1MiB live, 69.1MiB allocated; 7ms collecting garbage
Compiler

Compiled 3 424 to 1 465 computations (57.2% saved)

prune21.0ms (0.6%)

Memory
-25.1MiB live, 27.6MiB allocated; 10ms collecting garbage
Pruning

10 alts after pruning (5 fresh and 5 done)

PrunedKeptTotal
New3744378
Fresh112
Picked055
Done000
Total37510385
Accuracy
100.0%
Counts
385 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶4.4%
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
▶99.7%
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
✓100.0%
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
▶51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
▶51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓51.7%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
✓51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶26.9%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 188 to 184 computations (2.1% saved)

series11.0ms (0.3%)

Memory
17.9MiB live, 17.9MiB allocated; 0ms collecting garbage
Counts
30 → 53
Calls
Call 1
Inputs
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(cos.f64 (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) x)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x)
(-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
#s(literal -1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(sin.f64 x)
Outputs
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx x #s(hole binary64 x))
#s(approx (cos (* -1/2 x)) #s(hole binary64 1))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) x)))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#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 (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 (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* -1/2 x)))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (cos (* -1/2 x))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (+ (* (* (* x x) x) 1/24) (* x 1/2)) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (+ (* (* (* x x) x) 1/24) (* x 1/2)) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (+ 1/24 (* 1/2 (/ 1 (pow x 2))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))
Calls

3 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
((/ (sin (* x 1/2)) (cos (* -1/2 x))) (sin (* x 1/2)) (* x 1/2) x 1/2 (cos (* -1/2 x)) (* -1/2 x) -1/2 (/ (- 1 (cos x)) (sin x)) (+ (* (* (* x x) x) 1/24) (* x 1/2)) (* (* x x) x) (* x x) 1/24 (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (- (/ 1/2 (* x x)) -1/24) (/ 1/2 (* x x)) -1/24 (/ (- 1 (cos x)) (sin x)) (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) (+ (* (* x x) 1/240) 1/24) 1/240 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x))
3.0ms
x
@inf
((/ (sin (* x 1/2)) (cos (* -1/2 x))) (sin (* x 1/2)) (* x 1/2) x 1/2 (cos (* -1/2 x)) (* -1/2 x) -1/2 (/ (- 1 (cos x)) (sin x)) (+ (* (* (* x x) x) 1/24) (* x 1/2)) (* (* x x) x) (* x x) 1/24 (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (- (/ 1/2 (* x x)) -1/24) (/ 1/2 (* x x)) -1/24 (/ (- 1 (cos x)) (sin x)) (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) (+ (* (* x x) 1/240) 1/24) 1/240 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x))
3.0ms
x
@0
((/ (sin (* x 1/2)) (cos (* -1/2 x))) (sin (* x 1/2)) (* x 1/2) x 1/2 (cos (* -1/2 x)) (* -1/2 x) -1/2 (/ (- 1 (cos x)) (sin x)) (+ (* (* (* x x) x) 1/24) (* x 1/2)) (* (* x x) x) (* x x) 1/24 (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (- (/ 1/2 (* x x)) -1/24) (/ 1/2 (* x x)) -1/24 (/ (- 1 (cos x)) (sin x)) (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) (+ (* (* x x) 1/240) 1/24) 1/240 (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x))

rewrite247.0ms (6.6%)

Memory
-18.8MiB live, 117.5MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02431106
02741046
114021046
08375980
126977980
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
83 → 247
Calls
Call 1
Inputs
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
(sin.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(cos.f64 (*.f64 #s(literal -1/2 binary64) x))
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 (*.f64 x x) x)
(*.f64 x x)
#s(literal 1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x)
(-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
#s(literal -1/24 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64))
#s(literal 1/240 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
(sin.f64 x)
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx x #s(hole binary64 x))
#s(approx (cos (* -1/2 x)) #s(hole binary64 1))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (* -1/2 x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) x)))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 1/24))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (+ 1/24 (* 1/240 (pow x 2)))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#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 (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 (/ (sin (* x 1/2)) (cos (* -1/2 x))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* -1/2 x)))))
#s(approx (sin (* x 1/2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (* -1/2 x)) #s(hole binary64 (cos (* -1/2 x))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (+ (* (* (* x x) x) 1/24) (* x 1/2)) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (+ (* (* (* x x) x) 1/24) (* x 1/2)) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (+ 1/24 (* 1/2 (/ 1 (pow x 2))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* 1/240 (pow x 5))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* 1/240 (pow x 2))))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(hole binary64 (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))))
Outputs
(*.f64 (sin.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))))
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal -1/2 binary64) x))))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (sin.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x)))) (neg.f64 (neg.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))))
(/.f64 (sin.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x))))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 1/2 binary64)
(sin.f64 (+.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 (fabs.f64 x) #s(literal 1/2 binary64) (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(sin.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) x)) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x)) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(cos.f64 (neg.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x))))
(cos.f64 (neg.f64 (*.f64 (fabs.f64 x) #s(literal 1/2 binary64))))
(cos.f64 (fabs.f64 (*.f64 (fabs.f64 x) #s(literal 1/2 binary64))))
(cos.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) x)))
(cos.f64 (*.f64 (fabs.f64 x) #s(literal 1/2 binary64)))
(cos.f64 (*.f64 #s(literal -1/2 binary64) x))
(+.f64 (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) x)) (cos.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))) (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) x)) (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 x #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(neg.f64 (-.f64 (*.f64 (neg.f64 x) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x))))
(neg.f64 (-.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x)) (*.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x))))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (*.f64 (neg.f64 (neg.f64 x)) #s(literal 1/2 binary64)))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (neg.f64 (*.f64 (neg.f64 x) #s(literal 1/2 binary64))))
(fma.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x) (neg.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x))))
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(sin.f64 x)
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) (*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (* x 1/2)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (* x 1/2)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 x x) #s(literal -1/48 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (* x 1/2)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 x x) #s(literal 1/3840 binary64)) (*.f64 x x) #s(literal -1/48 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx x x)
#s(approx (cos (* -1/2 x)) #s(literal 1 binary64))
#s(approx (cos (* -1/2 x)) (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (* -1/2 x)) (fma.f64 (fma.f64 #s(literal 1/384 binary64) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (* -1/2 x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/46080 binary64) (*.f64 x x) #s(literal 1/384 binary64)) (*.f64 x x) #s(literal -1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (* -1/2 x) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* (* x x) x) (*.f64 (*.f64 x x) x))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* (* x x) 1/24) 1/2) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
#s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ (* (* x x) 1/240) 1/24) #s(literal 1/24 binary64))
#s(approx (+ (* (* x x) 1/240) 1/24) (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (*.f64 x x) #s(literal 1/720 binary64)) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (/ (sin (* x 1/2)) (cos (* -1/2 x))) (/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x))))
#s(approx (sin (* x 1/2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (cos (* -1/2 x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (* (* (* x x) x) 1/24) (* x 1/2)) (*.f64 (*.f64 x x) (*.f64 #s(literal 1/24 binary64) x)))
#s(approx (+ (* (* (* x x) x) 1/24) (* x 1/2)) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) (*.f64 (*.f64 x x) x)))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) (*.f64 x x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (*.f64 #s(literal 1/24 binary64) x))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x))
#s(approx (- (/ 1/2 (* x x)) -1/24) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/240 binary64)))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) (*.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -4 binary64)) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))) #s(literal -1/240 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (* x x) 1/240) 1/24) (*.f64 (*.f64 x x) #s(literal 1/240 binary64)))
#s(approx (+ (* (* x x) 1/240) 1/24) (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal -1/240 binary64)) (*.f64 x x)))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))
#s(approx (+ (* (+ (* (* x x) 1/240) 1/24) (* (* x x) x)) (* x 1/2)) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) (*.f64 x x))) #s(literal 1/240 binary64)) (pow.f64 x #s(literal 5 binary64)))))

eval50.0ms (1.3%)

Memory
-1.5MiB live, 52.5MiB allocated; 26ms collecting garbage
Compiler

Compiled 2 219 to 1 083 computations (51.2% saved)

prune17.0ms (0.4%)

Memory
22.3MiB live, 22.3MiB allocated; 0ms collecting garbage
Pruning

12 alts after pruning (3 fresh and 9 done)

PrunedKeptTotal
New2653268
Fresh000
Picked145
Done055
Total26612278
Accuracy
100.0%
Counts
278 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶4.4%
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
✓99.7%
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
✓100.0%
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
✓51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓51.7%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
✓51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓26.9%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
▶27.1%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x))
▶51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 175 to 170 computations (2.9% saved)

series13.0ms (0.3%)

Memory
-30.3MiB live, 13.0MiB allocated; 6ms collecting garbage
Counts
24 → 41
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x))
(*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)
(*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
#s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(*.f64 x x)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/6 binary64)
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#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 (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 (+ (* -1/6 (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 1/24))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (+ 1/24 (* 1/2 (/ 1 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) #s(hole binary64 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (+ (* -1/6 (* x x)) 1) #s(hole binary64 (* -1/6 (pow x 2))))
#s(approx (+ (* -1/6 (* x x)) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))))
Calls

3 calls:

TimeVariablePointExpression
7.0ms
x
@0
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (/ 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (- (/ 1/2 (* x x)) -1/24) (/ 1/2 (* x x)) (* x x) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (* (+ (* -1/6 (* x x)) 1) x) (+ (* -1/6 (* x x)) 1) -1/6)
2.0ms
x
@-inf
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (/ 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (- (/ 1/2 (* x x)) -1/24) (/ 1/2 (* x x)) (* x x) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (* (+ (* -1/6 (* x x)) 1) x) (+ (* -1/6 (* x x)) 1) -1/6)
2.0ms
x
@inf
((/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (/ 1/2 x) 1/2 x (/ (- 1 (cos x)) (sin x)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* (* (- (/ 1/2 (* x x)) -1/24) x) x) (* (- (/ 1/2 (* x x)) -1/24) x) (- (/ 1/2 (* x x)) -1/24) (/ 1/2 (* x x)) (* x x) (/ (- 1 (cos x)) (sin x)) (- 1 (cos x)) 1 (cos x) (sin x) (* (+ (* -1/6 (* x x)) 1) x) (+ (* -1/6 (* x x)) 1) -1/6)

rewrite231.0ms (6.1%)

Memory
0.2MiB live, 146.6MiB allocated; 17ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0171935
0184893
1943882
27789882
08074814
126272814
Stop Event
1×saturated
1×node-limit
1×iter-limit
Counts
65 → 169
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x)
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x))
(*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)
(*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
#s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(*.f64 x x)
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/6 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 1/2))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (+ 1/2 (* 1/24 (pow x 2)))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ 1/2 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ 1/2 (pow x 2))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (/ (+ 1/2 (* 1/24 (pow x 2))) (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#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 (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 (+ (* -1/6 (* x x)) 1) #s(hole binary64 (+ 1 (* -1/6 (pow x 2)))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* 1/24 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) #s(hole binary64 (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(hole binary64 (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* 1/24 x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) #s(hole binary64 (* x (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 1/24))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(hole binary64 (+ 1/24 (* 1/2 (/ 1 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) #s(hole binary64 (* -1/6 (pow x 3))))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) #s(hole binary64 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (+ (* -1/6 (* x x)) 1) #s(hole binary64 (* -1/6 (pow x 2))))
#s(approx (+ (* -1/6 (* x x)) 1) #s(hole binary64 (* (pow x 2) (- (/ 1 (pow x 2)) 1/6))))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x)
(*.f64 x #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)
(*.f64 x #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 x))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1/2 binary64) x)
(neg.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 #s(literal -1/2 binary64) x))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 x)))
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x))
(*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x)
(*.f64 x #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (neg.f64 x)) (neg.f64 x))
(*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (fabs.f64 x)) (fabs.f64 x))
(*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)
(*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (*.f64 x x))
(*.f64 x (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x))
(*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x)
(*.f64 x #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
#s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (fabs.f64 x)) (/.f64 #s(literal 1 binary64) (fabs.f64 x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1/2 binary64) (fabs.f64 x)) (fabs.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 x))
(/.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 x) x))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) x)
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (fabs.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (*.f64 (*.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(*.f64 (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))))
(*.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))))
(*.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (cos x) #s(literal 1 binary64)))) (*.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(/.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (neg.f64 (neg.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))
(neg.f64 (*.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (neg.f64 #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))))
(neg.f64 (/.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(neg.f64 (-.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (neg.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (/.f64 (neg.f64 #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(-.f64 (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(+.f64 (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (neg.f64 (/.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)))))
(+.f64 (/.f64 #s(literal 1 binary64) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))) (/.f64 (neg.f64 #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))))
(neg.f64 (-.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 #s(approx (cos x) #s(literal 1 binary64)))))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
(+.f64 (neg.f64 #s(approx (cos x) #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 #s(approx (cos x) #s(literal 1 binary64))))
#s(literal 1 binary64)
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal 2 binary64))
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/6 binary64) x) (*.f64 x x) x)
(fma.f64 (*.f64 (*.f64 x x) x) #s(literal -1/6 binary64) x)
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/6 binary64)) x x)
(fma.f64 (*.f64 x x) (*.f64 #s(literal -1/6 binary64) x) x)
(fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) x) x)
(fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/6 binary64)) x)
(-.f64 x (*.f64 (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))
(-.f64 x (*.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) x))
(-.f64 x (neg.f64 (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/6 binary64))))
(+.f64 (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/6 binary64)) x)
(+.f64 x (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/6 binary64)))
(neg.f64 (-.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))))
(neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (neg.f64 x)) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/6 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/6 binary64) x)) x #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/6 binary64) x) x #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(-.f64 (*.f64 (*.f64 x x) #s(literal -1/6 binary64)) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))
#s(literal -1/6 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
#s(approx (+ (* (* x x) 1/24) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (* (* x x) 1/24) 1/2) (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx x x)
#s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
#s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal -1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/40320 binary64) (*.f64 x x) #s(literal 1/720 binary64)) (*.f64 x x) #s(literal -1/24 binary64)) x) x #s(literal 1/2 binary64)) x) x))
(*.f64 #s(approx (cos x) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64)))
#s(approx (cos x) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(literal 2 binary64))
#s(approx (cos x) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) x) x #s(literal 1 binary64)))
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal 1 binary64)) x))
#s(approx (+ (* -1/6 (* x x)) 1) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (tan.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) (*.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64)))
#s(approx (* (+ (* (* x x) 1/24) 1/2) x) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) (*.f64 (*.f64 x x) x)))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(literal 1/24 binary64)))
#s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) (*.f64 x x)))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (*.f64 #s(literal 1/24 binary64) x))
#s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x))
#s(approx (- (/ 1/2 (* x x)) -1/24) #s(literal 1/24 binary64))
#s(approx (- (/ 1/2 (* x x)) -1/24) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) (*.f64 (*.f64 (*.f64 x x) x) #s(literal -1/6 binary64)))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x) (*.f64 x x)))
#s(approx (+ (* -1/6 (* x x)) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64)))
#s(approx (+ (* -1/6 (* x x)) 1) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x) x))
#s(approx (* (+ (* -1/6 (* x x)) 1) x) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) x) (*.f64 x x)))

eval15.0ms (0.4%)

Memory
17.8MiB live, 17.8MiB allocated; 0ms collecting garbage
Compiler

Compiled 1 437 to 786 computations (45.3% saved)

prune13.0ms (0.4%)

Memory
13.0MiB live, 13.0MiB allocated; 0ms collecting garbage
Pruning

17 alts after pruning (6 fresh and 11 done)

PrunedKeptTotal
New1516157
Fresh000
Picked123
Done099
Total15217169
Accuracy
100.0%
Counts
169 → 17
Alt Table
Click to see full alt table
StatusAccuracyProgram
4.3%
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
2.2%
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 #s(approx (+ (* -1/6 (* x x)) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))
✓99.7%
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
27.9%
(/.f64 #s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x)) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
27.9%
(/.f64 #s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
✓100.0%
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
✓51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓51.7%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
✓51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓26.9%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
✓27.1%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x))
27.0%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))) x) x)) x))
26.0%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x))
✓51.5%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
✓51.6%
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Compiler

Compiled 462 to 388 computations (16% saved)

regimes44.0ms (1.2%)

Memory
-33.1MiB live, 13.1MiB allocated; 3ms collecting garbage
Counts
21 → 1
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 #s(approx (+ (* -1/6 (* x x)) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x)) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) x)) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 (sin.f64 (*.f64 x #s(literal 1/2 binary64))) (cos.f64 (*.f64 #s(literal -1/2 binary64) x)))
Outputs
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
Calls

2 calls:

37.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
5.0ms
x
Results
AccuracySegmentsBranch
100.0%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
100.0%1x
Compiler

Compiled 7 to 7 computations (0% saved)

regimes10.0ms (0.3%)

Memory
14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Counts
17 → 1
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 #s(approx (+ (* -1/6 (* x x)) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (*.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64)) x) x)) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) (sin.f64 x))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (*.f64 x x) #s(literal 1/240 binary64)) (*.f64 x x) #s(literal 1/24 binary64)) x) x #s(literal 1/2 binary64)) x))
Calls

2 calls:

5.0ms
x
4.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
51.7%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
51.7%1x
Compiler

Compiled 7 to 7 computations (0% saved)

regimes8.0ms (0.2%)

Memory
12.5MiB live, 12.5MiB allocated; 0ms collecting garbage
Accuracy

Total -32.4b remaining (-104.5%)

Threshold costs -32.4b (-104.5%)

Counts
13 → 1
Calls
Call 1
Inputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 #s(approx (* (- (/ 1/2 (* x x)) -1/24) x) (/.f64 #s(literal 1/2 binary64) x)) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (*.f64 (*.f64 x x) x) #s(literal 1/24 binary64) (*.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 #s(approx (+ (* -1/6 (* x x)) 1) (*.f64 (*.f64 x x) #s(literal -1/6 binary64))) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 x x) #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) x) x)) x))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (cos x) #s(literal 1 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1/24 binary64)) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(approx (+ (* (* x x) 1/24) 1/2) (*.f64 (*.f64 #s(approx (- (/ 1/2 (* x x)) -1/24) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))) x) x)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
(/.f64 #s(approx (- 1 (cos x)) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) #s(approx (sin x) (*.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64)) x)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/240 binary64) #s(literal 1/24 binary64)) (*.f64 (*.f64 x x) x) (*.f64 x #s(literal 1/2 binary64))))
Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
Calls

2 calls:

4.0ms
x
3.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
51.6%1(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
51.6%1x
Compiler

Compiled 7 to 7 computations (0% saved)

derivations75.0ms (2%)

Memory
-27.9MiB live, 63.3MiB allocated; 7ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 26 to 20 computations (23.1% saved)

preprocess40.0ms (1.1%)

Memory
13.2MiB live, 65.1MiB allocated; 8ms collecting garbage
Remove

(negabs x)

Compiler

Compiled 98 to 90 computations (8.2% saved)

end0.0ms (0%)

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

Profiling

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