Metrics for tanhf (example 3.4)

analyze215.0ms (3.4%)

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)

sample4.7s (73.5%)

Results

961.0ms	4545×	256	valid
3.1s	2074×	2048	valid
461.0ms	1054×	1024	valid
109.0ms	511×	512	valid
58.0ms	72×	4096	valid

Bogosity

preprocess317.0ms (5%)

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	Example	Underpredictions	Example	Subexpression
91	-	1	(1.0080298158638024e+241)	`(-.f64 1 (cos.f64 x))`
51	-	4	(9.038181831305531e-159)	`(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))`
0	-	0	-	`x`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`(cos.f64 x)`
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)

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)

localize27.0ms (0.4%)

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)

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))

rewrite266.0ms (4.2%)

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))))

simplify210.0ms (3.3%)

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)

prune10.0ms (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
▶	99.8%	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
▶	52.4%	(*.f64 1/2 x)
✓	100.0%	(tan.f64 (/.f64 x 2))

Compiler

Compiled 19 to 15 computations (21.1% saved)

localize63.0ms (1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.8%	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

Compiler

Compiled 29 to 21 computations (27.6% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
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)))

rewrite76.0ms (1.2%)

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	14
1	111	14
2	1385	14

Stop Event

1×	node limit

Counts

1 → 63

Calls

Call 1

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

simplify199.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

760×	`unswap-sqr`
606×	`fma-def`
602×	`sqr-pow`
504×	`log-prod`
440×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	2314
1	526	2264
2	1472	2234
3	5247	2160

Stop Event

1×	node limit

Counts

75 → 103

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 (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))

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 1/24 (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 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 (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 (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 1 (tan.f64 (.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(.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 (sin.f64 (.f64 1/2 x)) (cos.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 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.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 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (neg.f64 (cos.f64 (*.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 1 (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 1 (cos.f64 (.f64 x 1/2))) (pow.f64 (/.f64 1 (sin.f64 (*.f64 x 1/2))) -1))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (pow.f64 (cos.f64 (.f64 1/2 x)) -1/2) (/.f64 (sin.f64 (.f64 1/2 x)) (sqrt.f64 (cos.f64 (.f64 1/2 x)))))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (pow.f64 (cos.f64 (.f64 1/2 x)) -1/2)) (sqrt.f64 (cos.f64 (.f64 1/2 x))))
(.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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)))
(/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (/.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) (cbrt.f64 (sin.f64 (.f64 1/2 x)))) -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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (sin.f64 (.f64 1/2 x)) (cos.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 (cbrt.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) 2) 3) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(.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))
(tan.f64 (*.f64 1/2 x))
(.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))
(tan.f64 (*.f64 1/2 x))
(.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 (cbrt.f64 (.f64 (sin.f64 (.f64 1/2 x)) (pow.f64 (tan.f64 (.f64 1/2 x)) 2))) (cbrt.f64 (/.f64 1 (cos.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 (cbrt.f64 (tan.f64 (.f64 1/2 x)))) (cbrt.f64 (pow.f64 (.f64 (tan.f64 (.f64 1/2 x)) (cbrt.f64 (tan.f64 (*.f64 1/2 x)))) 2)))
(.f64 (cbrt.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x)))) (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 4) 2)))
(.f64 (cbrt.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x)))) (cbrt.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 8)))
(.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 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 5/2)) (cbrt.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x)))))
(.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 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 1 (tan.f64 (*.f64 1/2 x)))) 2)))
(/.f64 (.f64 1 (cbrt.f64 (tan.f64 (.f64 1/2 x)))) (pow.f64 (cbrt.f64 (/.f64 1 (tan.f64 (*.f64 1/2 x)))) 2))
(/.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (/.f64 1 (tan.f64 (.f64 1/2 x)))) 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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (/.f64 1 (pow.f64 (sin.f64 (.f64 1/2 x)) -1/2)) (/.f64 1 (/.f64 (cos.f64 (.f64 1/2 x)) (sqrt.f64 (sin.f64 (.f64 1/2 x))))))
(.f64 (/.f64 1 (pow.f64 (sin.f64 (.f64 1/2 x)) -1/2)) (/.f64 (sqrt.f64 (sin.f64 (.f64 1/2 x))) (cos.f64 (.f64 1/2 x))))
(/.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 1/2 x))) (cos.f64 (.f64 1/2 x))) (pow.f64 (sin.f64 (*.f64 1/2 x)) -1/2))
(.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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (/.f64 1 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2) (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2))) (/.f64 1 (/.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) (cbrt.f64 (sin.f64 (*.f64 1/2 x))))))
(.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)) (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2)) (.f64 (/.f64 1 (cbrt.f64 (cos.f64 (.f64 1/2 x)))) (cbrt.f64 (sin.f64 (*.f64 1/2 x)))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) -2)) (/.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) (cbrt.f64 (cos.f64 (.f64 1/2 x)))))
(pow.f64 (/.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) (cbrt.f64 (cos.f64 (.f64 1/2 x)))) 3)
(.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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.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 (/.f64 (sqrt.f64 (cos.f64 (.f64 1/2 x))) (sqrt.f64 (sin.f64 (.f64 1/2 x)))) -2)
(.f64 (sin.f64 (.f64 1/2 x)) (pow.f64 (sqrt.f64 (cos.f64 (*.f64 1/2 x))) -2))
(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 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(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 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)) 1/3)
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (.f64 1/2 x)) 3)))
(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 3))
(pow.f64 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1) -1)
(tan.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 (/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 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))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (.f64 1/2 x)) 3)))
(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 3))
(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))
(exp.f64 (.f64 (neg.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) -1))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(tan.f64 (*.f64 x 1/2))
(tan.f64 (*.f64 1/2 x))

eval39.0ms (0.6%)

Compiler: Compiled 1519 to 1290 computations (15.1% saved)

prune13.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	103	3	106

Accuracy

100.0%

Counts

106 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
✓	52.4%	(*.f64 1/2 x)
✓	100.0%	(tan.f64 (/.f64 x 2))

Compiler

Compiled 43 to 33 computations (23.3% saved)

regimes7.0ms (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:

4.0ms	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)

regimes40.0ms (0.6%)

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:

40.0ms

Results

Accuracy	Segments	Branch
52.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

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)

soundness129.0ms (2%)

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%)

preprocess35.0ms (0.6%)

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

analyze215.0ms (3.4%)

sample4.7s (73.5%)

preprocess317.0ms (5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize27.0ms (0.4%)

series2.0ms (0%)

rewrite266.0ms (4.2%)

simplify210.0ms (3.3%)

eval33.0ms (0.5%)

prune10.0ms (0.1%)

localize63.0ms (1%)

series1.0ms (0%)

rewrite76.0ms (1.2%)

simplify199.0ms (3.1%)

eval39.0ms (0.6%)

prune13.0ms (0.2%)

regimes7.0ms (0.1%)

regimes40.0ms (0.6%)

simplify2.0ms (0%)

soundness129.0ms (2%)

end0.0ms (0%)

preprocess35.0ms (0.6%)

Profiling