Metrics for tanhf (example 3.4)

analyze179.0ms (2.8%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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 16 to 11 computations (31.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 103.0ms

Operation ival-<=, time spent: 24.0ms, 23.0% of total-time

Operation ival-sin, time spent: 20.0ms, 19.0% of total-time

Operation ival-sub, time spent: 15.0ms, 15.0% of total-time

Operation ival-cos, time spent: 13.0ms, 13.0% of total-time

Operation ival-neg, time spent: 10.0ms, 10.0% of total-time

Operation ...c/syntax/syntax.rkt:191:8, time spent: 10.0ms, 10.0% of total-time

Operation ival-div, time spent: 7.0ms, 7.0% of total-time

Operation ival-and, time spent: 3.0ms, 3.0% of total-time

Operation const, time spent: 1.0ms, 1.0% of total-time

sample5.1s (78.7%)

Results

1.2s	4385×	128	valid
2.4s	2012×	2048	valid
582.0ms	1054×	1024	valid
209.0ms	493×	512	valid
60.0ms	254×	256	valid
65.0ms	57×	4096	valid
0.0ms	1×	512	valid

Precisions

Click to see histograms. Total time spent on operations: 3.4s

Operation ival-sin, time spent: 1.6s, 48.0% of total-time

Operation ival-cos, time spent: 1.0s, 30.0% of total-time

Operation ival-<=, time spent: 190.0ms, 6.0% of total-time

Operation ival-div, time spent: 187.0ms, 6.0% of total-time

Operation ival-sub, time spent: 161.0ms, 5.0% of total-time

Operation ival-neg, time spent: 113.0ms, 3.0% of total-time

Operation ...c/syntax/syntax.rkt:191:8, time spent: 84.0ms, 2.0% of total-time

Operation ival-and, time spent: 28.0ms, 1.0% of total-time

Operation const, time spent: 12.0ms, 0.0% of total-time

Bogosity

preprocess403.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-def`
410×	`div-sub`
196×	`associate-/r*`
176×	`associate-/l*`
118×	`sub-neg`

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
69	1	(3.891289419655604e+73)	1	(2.9826949956398787e+141)	`(-.f64 1 (cos.f64 x))`
68	0	-	4	(9.700756053361986e-161)	`(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`x`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	60
1	44	60
2	69	56
3	143	56
4	326	56
5	734	56
6	1393	56
7	1777	56
8	1858	56
9	1935	56
10	1986	56
11	1998	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))

Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))
(/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x)))
(tan.f64 (/.f64 (neg.f64 x) 2))
(tan.f64 (*.f64 -1/2 x))
(tan.f64 (*.f64 x -1/2))
(neg.f64 (/.f64 (-.f64 1 (cos.f64 (neg.f64 x))) (sin.f64 (neg.f64 x))))
(tan.f64 (/.f64 x 2))
(tan.f64 (*.f64 x 1/2))

Symmetry

(negabs x)

Compiler

Compiled 46 to 26 computations (43.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

Operation ival-sin, time spent: 94.0ms, 42.0% of total-time

Operation ival-cos, time spent: 94.0ms, 42.0% of total-time

Operation ival-sub, time spent: 20.0ms, 9.0% of total-time

Operation ival-div, time spent: 11.0ms, 5.0% of total-time

Operation const, time spent: 4.0ms, 2.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tan.f64 (/.f64 x 2))

Compiler

Compiled 5 to 4 computations (20% saved)

localize31.0ms (0.5%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(tan.f64 (/.f64 x 2))

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

Operation ival-tan, time spent: 6.0ms, 59.0% of total-time

Operation ival-div, time spent: 4.0ms, 39.0% of total-time

Operation const, time spent: 1.0ms, 10.0% of total-time

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(tan.f64 (/.f64 x 2))
1.0ms	x	@	-inf	(tan.f64 (/.f64 x 2))
1.0ms	x	@	0	(tan.f64 (/.f64 x 2))

rewrite173.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1294×	`frac-times`
400×	`unpow-prod-down`
328×	`cbrt-prod`
324×	`log-prod`
313×	`log1p-expm1-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	76	14
2	870	14

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

Inputs
(tan.f64 (/.f64 x 2))

Outputs
(+.f64 0 (tan.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 (tan.f64 (.f64 x 1/2)) (log.f64 (E.f64)))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 1/4) (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)))
(.f64 (pow.f64 1 1/3) (tan.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2) 1/3) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 5)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(/.f64 (cbrt.f64 (.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 2) (sin.f64 (.f64 x 1/2)))) (cbrt.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sqrt.f64 (.f64 (tan.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))) (sqrt.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 x 1/2)) (tan.f64 (.f64 x 1/2)))) (sqrt.f64 (cos.f64 (.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(pow.f64 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(neg.f64 (tan.f64 (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(fabs.f64 (tan.f64 (*.f64 x 1/2)))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2)))) 2))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

928×	`associate-r`
804×	`associate-l`
734×	`associate-+r+`
734×	`associate-+l+`
676×	`fma-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1671
1	294	1608
2	830	1586
3	4357	1586

Stop Event

1×	node limit

Counts

58 → 78

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))
(+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (.f64 17/40320 (pow.f64 x 7)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(+.f64 0 (tan.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 (tan.f64 (.f64 x 1/2)) (log.f64 (E.f64)))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 1/4) (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)))
(.f64 (pow.f64 1 1/3) (tan.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2) 1/3) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 5)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(/.f64 (cbrt.f64 (.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 2) (sin.f64 (.f64 x 1/2)))) (cbrt.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sqrt.f64 (.f64 (tan.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))) (sqrt.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 x 1/2)) (tan.f64 (.f64 x 1/2)))) (sqrt.f64 (cos.f64 (.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(pow.f64 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(neg.f64 (tan.f64 (*.f64 x 1/2)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(fabs.f64 (tan.f64 (*.f64 x 1/2)))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2)))) 2))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/2 x)))
(+.f64 (.f64 17/40320 (pow.f64 x 7)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(+.f64 0 (tan.f64 (*.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 1/2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 1/2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(tan.f64 (*.f64 1/2 x))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(tan.f64 (*.f64 1/2 x))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(.f64 (tan.f64 (.f64 x 1/2)) (log.f64 (E.f64)))
(tan.f64 (*.f64 1/2 x))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 1/4) (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3/2)))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 1 1/3) (tan.f64 (.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (.f64 1/2 x)) (cbrt.f64 (tan.f64 (.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 8)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2) 1/3) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 5/2)) (pow.f64 (tan.f64 (*.f64 1/2 x)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (tan.f64 (.f64 1/2 x)) (cbrt.f64 (tan.f64 (.f64 1/2 x)))) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 8)) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 5/2)) (pow.f64 (tan.f64 (*.f64 1/2 x)) 1/6))
(.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3/2)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/4))
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 5)) (pow.f64 (tan.f64 (*.f64 x 1/2)) 1/6))
(.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 5)))
(.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 1/6) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 5/2))
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (neg.f64 (cos.f64 (.f64 1/2 x))))
(/.f64 (neg.f64 (sin.f64 (.f64 1/2 x))) (cos.f64 (.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (-.f64 (sin.f64 (+.f64 1 x)) (sin.f64 1)) (+.f64 (cos.f64 (+.f64 1 x)) (cos.f64 1)))
(tan.f64 (/.f64 (-.f64 (+.f64 x 1) 1) 2))
(tan.f64 (/.f64 (+.f64 x 0) 2))
(tan.f64 (/.f64 x 2))
(/.f64 (cbrt.f64 (.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 2) (sin.f64 (.f64 x 1/2)))) (cbrt.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (pow.f64 (tan.f64 (.f64 1/2 x)) 2))) (cbrt.f64 (cos.f64 (.f64 1/2 x))))
(/.f64 (sqrt.f64 (.f64 (tan.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2)))) (sqrt.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sqrt.f64 (.f64 (tan.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))) (sqrt.f64 (cos.f64 (.f64 1/2 x))))
(/.f64 (sqrt.f64 (.f64 (sin.f64 (.f64 x 1/2)) (tan.f64 (.f64 x 1/2)))) (sqrt.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sqrt.f64 (.f64 (tan.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))) (sqrt.f64 (cos.f64 (.f64 1/2 x))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))) -1)
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (.f64 1/2 x)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (.f64 1/2 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (.f64 1/2 x))))) (sqrt.f64 (log.f64 (tan.f64 (.f64 1/2 x)))))
(neg.f64 (tan.f64 (*.f64 x 1/2)))
(neg.f64 (tan.f64 (*.f64 1/2 x)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(tan.f64 (*.f64 1/2 x))
(fabs.f64 (tan.f64 (*.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 3))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2)))) 2))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))

eval33.0ms (0.5%)

Compiler: Compiled 888 to 741 computations (16.6% saved)

prune9.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Accuracy

100.0%

Counts

79 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
▶	52.7%	(*.f64 1/2 x)
✓	100.0%	(tan.f64 (/.f64 x 2))

Compiler

Compiled 19 to 15 computations (21.1% saved)

localize71.0ms (1.1%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(sin.f64 (*.f64 x 1/2))
✓	99.7%	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

Compiler

Compiled 29 to 21 computations (27.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

Operation ival-cos, time spent: 12.0ms, 30.0% of total-time

Operation ival-sin, time spent: 12.0ms, 30.0% of total-time

Operation ival-mult, time spent: 10.0ms, 25.0% of total-time

Operation ival-div, time spent: 4.0ms, 10.0% of total-time

Operation const, time spent: 2.0ms, 5.0% of total-time

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(sin.f64 (*.f64 x 1/2))
0.0ms	x	@	0	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
0.0ms	x	@	inf	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
0.0ms	x	@	-inf	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
0.0ms	x	@	inf	(sin.f64 (*.f64 x 1/2))

rewrite82.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

808×	`unpow-prod-down`
576×	`log-prod`
519×	`log1p-expm1-u`
519×	`expm1-log1p-u`
491×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	111	28
2	1385	28

Stop Event

1×	node limit

Counts

2 → 97

Calls

Call 1

Inputs
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(sin.f64 (*.f64 x 1/2))

Outputs
(+.f64 0 (tan.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 (tan.f64 (.f64 x 1/2)) (log.f64 (E.f64)))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (neg.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 1 (cos.f64 (.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))
(.f64 (/.f64 1 (cos.f64 (.f64 x 1/2))) (pow.f64 (/.f64 1 (sin.f64 (*.f64 x 1/2))) -1))
(.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) -2) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (cos.f64 (.f64 x 1/2)))))
(.f64 (pow.f64 (cos.f64 (.f64 x 1/2)) -1/2) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (cos.f64 (.f64 x 1/2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (.f64 x 1/2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 1 1/3) (tan.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 3) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 2) (sin.f64 (.f64 x 1/2))) 1/3) (cbrt.f64 (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 1 (tan.f64 (.f64 x 1/2)))) 2) -1) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) -2) -1) (pow.f64 (/.f64 (cos.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) -1))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) -1/2) -1) (pow.f64 (/.f64 (cos.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 (.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2) 1) -1) (pow.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) -1))
(.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2)) -1) (pow.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2) (sqrt.f64 (sin.f64 (.f64 x 1/2)))) -1) (pow.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) 1) -1) (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) -1))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2)) -1) (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (.f64 x 1/2)))) -1) (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(pow.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(neg.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2)))))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2)))) 2))
(exp.f64 (.f64 (neg.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) -1))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 x 1/2))
(+.f64 0 (sin.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2))))))
(-.f64 (+.f64 1 (sin.f64 (*.f64 x 1/2))) 1)
(-.f64 (.f64 (sin.f64 (+.f64 1 (.f64 x 1/2))) (cos.f64 1)) (.f64 (cos.f64 (+.f64 1 (.f64 x 1/2))) (sin.f64 1)))
(.f64 (sin.f64 (.f64 x 1/2)) 1)
(.f64 (sin.f64 (.f64 x 1/2)) (log.f64 (E.f64)))
(.f64 1 (sin.f64 (.f64 x 1/2)))
(.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 1 1/3) (sin.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 2) 3) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) 3))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3)) 1/3))
(.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2)))))
(pow.f64 (sin.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 3)
(pow.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 1/2)
(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (sin.f64 (*.f64 x 1/2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))))
(sqrt.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
(log.f64 (exp.f64 (sin.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3))
(expm1.f64 (log1p.f64 (sin.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (sin.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2)))) 2))
(log1p.f64 (expm1.f64 (sin.f64 (*.f64 x 1/2))))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1634×	`fma-def`
1252×	`times-frac`
1136×	`associate-/l*`
576×	`distribute-lft-in`
574×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	3788
1	720	3554
2	2348	3454

Stop Event

1×	node limit

Counts

121 → 162

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))
(+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (.f64 17/40320 (pow.f64 x 7)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(*.f64 1/2 x)
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (.f64 1/2 x))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 1/3840 (pow.f64 x 5)) (*.f64 1/2 x)))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 -1/645120 (pow.f64 x 7)) (+.f64 (.f64 1/3840 (pow.f64 x 5)) (.f64 1/2 x))))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
(+.f64 0 (tan.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 (tan.f64 (.f64 x 1/2)) (log.f64 (E.f64)))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (neg.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 1 (cos.f64 (.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))
(.f64 (/.f64 1 (cos.f64 (.f64 x 1/2))) (pow.f64 (/.f64 1 (sin.f64 (*.f64 x 1/2))) -1))
(.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) -2) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (cos.f64 (.f64 x 1/2)))))
(.f64 (pow.f64 (cos.f64 (.f64 x 1/2)) -1/2) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (cos.f64 (.f64 x 1/2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (.f64 x 1/2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 1 1/3) (tan.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 3) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3)) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 2) (sin.f64 (.f64 x 1/2))) 1/3) (cbrt.f64 (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 (.f64 x 1/2)) (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 1 (tan.f64 (.f64 x 1/2)))) 2) -1) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) -2) -1) (pow.f64 (/.f64 (cos.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) -1))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) -1/2) -1) (pow.f64 (/.f64 (cos.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 (.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2) 1) -1) (pow.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) -1))
(.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2)) -1) (pow.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2) (sqrt.f64 (sin.f64 (.f64 x 1/2)))) -1) (pow.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) 1) -1) (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2))) -1))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2)) -1) (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(.f64 (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (.f64 x 1/2)))) -1) (pow.f64 (/.f64 (sqrt.f64 (cos.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (*.f64 x 1/2)))) -1))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2) 1/2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(pow.f64 (E.f64) (log.f64 (tan.f64 (*.f64 x 1/2))))
(pow.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)) 1/3)
(pow.f64 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (tan.f64 (.f64 x 1/2)))))
(neg.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2)))))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (tan.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2)))) 2))
(exp.f64 (.f64 (neg.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) -1))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 x 1/2))
(+.f64 0 (sin.f64 (*.f64 x 1/2)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 x 1/2))))))
(-.f64 (+.f64 1 (sin.f64 (*.f64 x 1/2))) 1)
(-.f64 (.f64 (sin.f64 (+.f64 1 (.f64 x 1/2))) (cos.f64 1)) (.f64 (cos.f64 (+.f64 1 (.f64 x 1/2))) (sin.f64 1)))
(.f64 (sin.f64 (.f64 x 1/2)) 1)
(.f64 (sin.f64 (.f64 x 1/2)) (log.f64 (E.f64)))
(.f64 1 (sin.f64 (.f64 x 1/2)))
(.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 1 1/3) (sin.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 2) 3) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) 3))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3)) 1/3))
(.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2)))))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2)))))
(pow.f64 (sin.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 3)
(pow.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 1/2)
(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (sin.f64 (*.f64 x 1/2))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))))
(sqrt.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
(log.f64 (exp.f64 (sin.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3))
(expm1.f64 (log1p.f64 (sin.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (sin.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2)))) 2))
(log1p.f64 (expm1.f64 (sin.f64 (*.f64 x 1/2))))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (.f64 17/40320 (pow.f64 x 7)) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 1/24 (pow.f64 x 3)) (.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))))
(fma.f64 17/40320 (pow.f64 x 7) (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(*.f64 1/2 x)
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (.f64 1/2 x))
(fma.f64 -1/48 (pow.f64 x 3) (*.f64 1/2 x))
(fma.f64 (pow.f64 x 3) -1/48 (*.f64 1/2 x))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 1/3840 (pow.f64 x 5)) (*.f64 1/2 x)))
(fma.f64 -1/48 (pow.f64 x 3) (fma.f64 1/3840 (pow.f64 x 5) (*.f64 1/2 x)))
(fma.f64 (pow.f64 x 3) -1/48 (fma.f64 1/2 x (*.f64 (pow.f64 x 5) 1/3840)))
(fma.f64 1/2 x (fma.f64 (pow.f64 x 3) -1/48 (*.f64 (pow.f64 x 5) 1/3840)))
(+.f64 (.f64 -1/48 (pow.f64 x 3)) (+.f64 (.f64 -1/645120 (pow.f64 x 7)) (+.f64 (.f64 1/3840 (pow.f64 x 5)) (.f64 1/2 x))))
(fma.f64 -1/48 (pow.f64 x 3) (fma.f64 -1/645120 (pow.f64 x 7) (fma.f64 1/3840 (pow.f64 x 5) (*.f64 1/2 x))))
(fma.f64 (pow.f64 x 3) -1/48 (fma.f64 (pow.f64 x 7) -1/645120 (fma.f64 1/2 x (*.f64 (pow.f64 x 5) 1/3840))))
(fma.f64 (pow.f64 x 3) -1/48 (fma.f64 (pow.f64 x 7) -1/645120 (fma.f64 (pow.f64 x 5) 1/3840 (*.f64 1/2 x))))
(sin.f64 (*.f64 1/2 x))
(sin.f64 (*.f64 1/2 x))
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(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))
(.f64 (pow.f64 1 1/3) (sin.f64 (.f64 x 1/2)))
(sin.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 2) 3) (cbrt.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2)))) 3))
(sin.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (sqrt.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3)) 1/3))
(.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3))))
(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3/2)) (cbrt.f64 (pow.f64 (sin.f64 (*.f64 1/2 x)) 3/2)))
(.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x)))) (cbrt.f64 (pow.f64 (.f64 (sin.f64 (.f64 1/2 x)) (cbrt.f64 (sin.f64 (*.f64 1/2 x)))) 2)))
(.f64 (cbrt.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x)))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 1/2 x))) 4) 2)))
(.f64 (cbrt.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x)))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 1/2 x))) 8)))
(.f64 (pow.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 5/2)) (cbrt.f64 (sqrt.f64 (sin.f64 (*.f64 1/2 x)))))
(pow.f64 (sin.f64 (*.f64 x 1/2)) 1)
(sin.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 3)
(sin.f64 (*.f64 1/2 x))
(pow.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))) 1/2)
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))))
(sqrt.f64 (fma.f64 -1/2 (cos.f64 x) 1/2))
(pow.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) 1/3)
(sin.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 2)
(sin.f64 (*.f64 1/2 x))
(pow.f64 (E.f64) (log.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))) 2)) (cbrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sin.f64 (.f64 1/2 x)))) 2)) (cbrt.f64 (log.f64 (sin.f64 (.f64 1/2 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 (.f64 x 1/2))))) (sqrt.f64 (log.f64 (sin.f64 (.f64 x 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sin.f64 (.f64 1/2 x))))) (sqrt.f64 (log.f64 (sin.f64 (.f64 1/2 x)))))
(sqrt.f64 (-.f64 1/2 (*.f64 1/2 (cos.f64 x))))
(sqrt.f64 (+.f64 1/2 (*.f64 -1/2 (cos.f64 x))))
(sqrt.f64 (fma.f64 -1/2 (cos.f64 x) 1/2))
(log.f64 (exp.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3))
(sin.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2)))) 3))
(sin.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (.f64 3 (log.f64 (sin.f64 (*.f64 x 1/2)))) 1/3))
(sin.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2)))) 2))
(sin.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (sin.f64 (*.f64 x 1/2))))
(sin.f64 (*.f64 1/2 x))

eval61.0ms (0.9%)

Compiler: Compiled 2489 to 2091 computations (16% saved)

prune21.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	162	3	165

Accuracy

100.0%

Counts

165 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
✓	52.7%	(*.f64 1/2 x)
✓	100.0%	(tan.f64 (/.f64 x 2))

Compiler

Compiled 43 to 33 computations (23.3% saved)

regimes9.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(tan.f64 (/.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

Outputs
(tan.f64 (/.f64 x 2))

Calls

2 calls:

5.0ms	x
3.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)

Outputs
(*.f64 1/2 x)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
52.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	12	24

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)

Outputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)
(*.f64 x 1/2)

Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness118.0ms (1.8%)

Rules

750×	`fma-def`
410×	`div-sub`
196×	`associate-/r*`
176×	`associate-/l*`
118×	`sub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	60
1	44	60
2	69	56
3	143	56
4	326	56
5	734	56
6	1393	56
7	1777	56
8	1858	56
9	1935	56
10	1986	56
11	1998	56

Stop Event

1×

saturated

Compiler

Compiled 12 to 9 computations (25% saved)

end0.0ms (0%)

preprocess36.0ms (0.6%)

Remove: (negabs x)
Compiler: Compiled 72 to 56 computations (22.2% saved)

analyze179.0ms (2.8%)

sample5.1s (78.7%)

preprocess403.0ms (6.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize31.0ms (0.5%)

series2.0ms (0%)

rewrite173.0ms (2.7%)

simplify58.0ms (0.9%)

eval33.0ms (0.5%)

prune9.0ms (0.1%)

localize71.0ms (1.1%)

series1.0ms (0%)

rewrite82.0ms (1.3%)

simplify88.0ms (1.4%)

eval61.0ms (0.9%)

prune21.0ms (0.3%)

regimes9.0ms (0.1%)

regimes3.0ms (0%)

simplify3.0ms (0.1%)

soundness118.0ms (1.8%)

end0.0ms (0%)

preprocess36.0ms (0.6%)

Profiling