Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample150.0ms (1.7%)

Algorithm

1×

intervals

Results

37.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 63 to 33 computations (47.6% saved)

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/l/_binary32`
455×	`associate-/l*_binary32`
281×	`times-frac_binary32`
257×	`associate-/r/_binary32`
154×	`associate-*l/_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	24	36
2	80	36
3	299	36
4	822	36
5	1265	36
6	1211	36
7	1239	36
8	1247	36
9	1251	36
10	1253	36
11	1219	36
12	1217	36

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 69 to 30 computations (56.5% saved)

localize35.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	0.4b	(*.f32 x (PI.f32))
✓	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series56.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

32.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
11.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
10.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
2.0ms	(*.f32 x (PI.f32))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary32`
20×	`add-exp-log_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
10×	`add-cube-cbrt_binary32`

Counts

4 → 77

Calls

4 calls:

5.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
4.0ms	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
3.0ms	(*.f32 x (PI.f32))
1.0ms	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))

simplify132.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

805×	`associate-/l*_binary32`
347×	`fma-def_binary32`
320×	`cancel-sign-sub-inv_binary32`
307×	`associate-/l/_binary32`
235×	`unswap-sqr_binary32`

Counts

149 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2890
1	484	2546
2	1854	2521
3	4970	2521

prune331.0ms (3.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	217	20	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	20	238

Error

0.1b

Counts

238 → 20

Alt Table

Status	Error	Program
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32)))) (*.f32 x (PI.f32))))
	4.8b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (.f32 1/5040 (.f32 (pow.f32 tau 6) (pow.f32 (.f32 (PI.f32) x) 6))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.3b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32))))) (*.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	3.2b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))
▶	0.8b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	3.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 1)))
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (exp.f32 (-.f32 (log.f32 (sin.f32 (.f32 x (PI.f32)))) (log.f32 (*.f32 x (PI.f32))))))

Compiler

Compiled 7707 to 1760 computations (77.2% saved)

localize47.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
	0.4b	(*.f32 x (PI.f32))
✓	0.4b	(/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))

series47.0ms (0.5%)

Counts

2 → 32

Calls

2 calls:

37.0ms	(/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))
10.0ms	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary32`
33×	`times-frac_binary32`
18×	`*-un-lft-identity_binary32`
18×	`add-sqr-sqrt_binary32`
18×	`add-cube-cbrt_binary32`

Counts

2 → 71

Calls

2 calls:

13.0ms	(/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))
2.0ms	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

818×	`associate-/r*_binary32`
419×	`fma-def_binary32`
312×	`associate-/r/_binary32`
292×	`cancel-sign-sub-inv_binary32`
266×	`associate-/l/_binary32`

Counts

103 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	3057
1	378	2675
2	1511	2615
3	4685	2615
4	5005	2615

prune284.0ms (3.3%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	203	5	208
Fresh	4	15	19
Picked	0	1	1
Done	0	0	0
Total	207	21	228

Error

0.1b

Counts

228 → 21

Alt Table

Status	Error	Program
	3.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 1)))
	1.2b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	3.2b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
✓	0.8b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))
	0.9b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	0.8b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	1.2b	(.f32 (/.f32 (/.f32 1 (.f32 (cbrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))))) (cbrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.8b	(.f32 (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))) 1) (fma.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x))) (.f32 1/5040 (.f32 (pow.f32 tau 6) (pow.f32 (.f32 (PI.f32) x) 6))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x)))) (.f32 x (PI.f32))))

Compiler

Compiled 7707 to 2158 computations (72% saved)

localize50.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
✓	0.4b	(/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
	0.4b	(*.f32 x (PI.f32))
	0.4b	(/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))

series11.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

11.0ms

(/.f32 1 (/.f32 (*.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`times-frac_binary32`
22×	`add-exp-log_binary32`
17×	`*-un-lft-identity_binary32`
17×	`add-sqr-sqrt_binary32`
17×	`add-cube-cbrt_binary32`

Counts

1 → 58

Calls

1 calls:

5.0ms

(/.f32 1 (/.f32 (*.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))))

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary32`
604×	`unswap-sqr_binary32`
443×	`associate-/l*_binary32`
398×	`associate-l_binary32`
360×	`associate-r_binary32`

Counts

70 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1611
1	224	1406
2	750	1357
3	3377	1349
4	5340	1349

prune373.0ms (4.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	4	15	19
Picked	1	0	1
Done	0	1	1
Total	254	20	274

Error

0.1b

Counts

274 → 20

Alt Table

Status	Error	Program
	3.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) (fma.f32 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x)) -1/6 1)))
	1.2b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	3.2b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 x (PI.f32))) (cbrt.f32 (.f32 x (PI.f32)))) (cbrt.f32 (.f32 x (PI.f32)))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
	0.9b	(.f32 (/.f32 (/.f32 1 (.f32 (PI.f32) (.f32 tau x))) (/.f32 1 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
▶	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))
✓	0.8b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.5b	(.f32 (/.f32 (/.f32 1 (sqrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (sqrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (/.f32 1 (.f32 (cbrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))))) (cbrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (.f32 (cbrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	1.2b	(.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (.f32 (PI.f32) (.f32 tau x)) (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.4b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x)))) (.f32 x (PI.f32))))

Compiler

Compiled 9560 to 2889 computations (69.8% saved)

localize46.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(*.f32 x (PI.f32))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
✓	0.5b	(.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))

series26.0ms (0.3%)

Counts

1 → 8

Calls

1 calls:

26.0ms

(*.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`sqrt-prod_binary32`
29×	`add-sqr-sqrt_binary32`
16×	`pow1_binary32`
13×	`*-un-lft-identity_binary32`
13×	`add-cube-cbrt_binary32`

Counts

1 → 68

Calls

1 calls:

13.0ms

(*.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32)))))

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary32`
484×	`associate-l_binary32`
477×	`cancel-sign-sub-inv_binary32`
424×	`associate-r_binary32`
284×	`fma-neg_binary32`

Counts

76 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	111	1801
1	196	1597
2	637	1515
3	2960	1458
4	4710	1432
5	4969	1432
6	4952	1432

prune609.0ms (7.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	409	8	417
Fresh	7	11	18
Picked	1	0	1
Done	1	0	1
Total	418	19	437

Error

0.1b

Counts

437 → 19

Alt Table

Status	Error	Program
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) (sqrt.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))) (.f32 (sqrt.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))) (sqrt.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))))
	1.0b	(.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	0.8b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 x) (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	3.2b	(.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (PI.f32) (sqrt.f32 x)))) (*.f32 x (PI.f32))))))
	1.0b	(.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (cbrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))
	0.9b	(.f32 (/.f32 (/.f32 1 (.f32 (PI.f32) (.f32 tau x))) (/.f32 1 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	3.5b	(.f32 (/.f32 (/.f32 1 (sqrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (sqrt.f32 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32)))) (.f32 x (PI.f32))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))) 4) (pow.f32 (cbrt.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))) 2)))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (.f32 x (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
	1.4b	(.f32 (/.f32 1 (/.f32 (.f32 (PI.f32) (.f32 tau x)) (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (/.f32 1 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	0.9b	(.f32 (.f32 (/.f32 1 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (.f32 (/.f32 (.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 x (PI.f32))) (/.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	1.5b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (sqrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))))

Compiler

Compiled 16289 to 2322 computations (85.7% saved)

regimes4.0s (46%)

Accuracy

Total 0.6b remaining (82%)

Threshold costs 0.6b (82%)

Counts

584 → 1

Compiler

Compiled 75672 to 38520 computations (49.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	70
1	21	70
2	21	70

end1.0ms (0%)

Compiler: Compiled 42 to 15 computations (64.3% saved)

sample2.0s (23.6%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
222.0ms	8000×	pre	128	true

Compiler

Compiled 776 to 336 computations (56.7% saved)

Details

analyze5.0ms (0.1%)

sample150.0ms (1.7%)

simplify45.0ms (0.5%)

prune2.0ms (0%)

localize35.0ms (0.4%)

series56.0ms (0.7%)

rewrite22.0ms (0.3%)

simplify132.0ms (1.5%)

prune331.0ms (3.9%)

localize47.0ms (0.5%)

series47.0ms (0.5%)

rewrite21.0ms (0.2%)

simplify101.0ms (1.2%)

prune284.0ms (3.3%)

localize50.0ms (0.6%)

series11.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify72.0ms (0.8%)

prune373.0ms (4.3%)

localize46.0ms (0.5%)

series26.0ms (0.3%)

rewrite20.0ms (0.2%)

simplify115.0ms (1.3%)

prune609.0ms (7.1%)

regimes4.0s (46%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.0s (23.6%)

Profiling