Details

analyze95.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.3%	87.7%	0
0%	12.3%	87.7%	1
6.2%	6.2%	87.7%	2
6.2%	6.2%	87.7%	3
9.2%	3.1%	87.7%	4
9.2%	3.1%	87.7%	5
10.8%	1.5%	87.7%	6
10.8%	1.5%	87.7%	7
11.5%	0.8%	87.7%	8
11.5%	0.8%	87.7%	9
11.9%	0.4%	87.7%	10
11.9%	0.4%	87.7%	11
12.1%	0.2%	87.7%	12
12.1%	0.2%	87.7%	13
12.1%	0.1%	87.8%	14

Compiler

Compiled 42 to 32 computations (23.8% saved)

sample115.0ms (0.5%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 71 to 55 computations (22.5% saved)

simplify46.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-neg_binary32`
929×	`fma-def_binary32`
740×	`times-frac_binary32`
329×	`div-sub_binary32`
317×	`associate-l_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	45	35
2	107	35
3	264	33
4	605	33
5	2500	33
6	3754	33
7	5049	33

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Status

Error

Program

▶

0.5b

(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))

0.6b

(/.f32 1 (+.f32 (+.f32 1 c) (*.f32 (*.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))

Compiler

Compiled 148 to 113 computations (23.6% saved)

localize57.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
✓	0.3b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
✓	0.4b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series126.0ms (0.6%)

Counts

4 → 46

Calls

4 calls:

84.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
26.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
10.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
5.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary32`
36×	`add-exp-log_binary32`
28×	`add-sqr-sqrt_binary32`
23×	`add-cube-cbrt_binary32`
22×	`add-cbrt-cube_binary32`

Counts

4 → 129

Calls

4 calls:

9.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
7.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
7.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
6.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))

simplify133.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-r_binary32`
336×	`associate-l_binary32`
295×	`fma-def_binary32`
272×	`unswap-sqr_binary32`
226×	`*-commutative_binary32`

Counts

175 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	6018
1	1072	5539
2	4023	5523
3	4986	5523

prune353.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	217	11	228
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	11	230

Error

0.0b

Counts

230 → 11

Alt Table

Status	Error	Program
	13.8b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 1 (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))))))))
	0.8b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
▶	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
	13.7b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (.f32 (.f32 cosTheta cosTheta) (pow.f32 (exp.f32 (.f32 cosTheta cosTheta)) 2)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.7b	(-.f32 (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3)) 5/2 (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 cosTheta 3) c)) (fma.f32 3 (.f32 (pow.f32 (PI.f32) 3/2) (pow.f32 cosTheta 4)) (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta) (fma.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2)) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 cosTheta 4))) (.f32 6 (.f32 c (pow.f32 cosTheta 4))))))))))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (fma.f32 3 (.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2))) (fma.f32 6 (.f32 (PI.f32) (.f32 c (pow.f32 cosTheta 4))) (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 3)) (+.f32 2 (.f32 2 c)))) (+.f32 (.f32 (pow.f32 cosTheta 4) (+.f32 (pow.f32 (PI.f32) 2) (.f32 (PI.f32) 6))) (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (*.f32 3 c)))))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 cosTheta) (pow.f32 (sqrt.f32 (exp.f32 cosTheta)) cosTheta)) (.f32 (sqrt.f32 cosTheta) (pow.f32 (sqrt.f32 (exp.f32 cosTheta)) cosTheta)))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (sqrt.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))

Compiler

Compiled 9208 to 5239 computations (43.1% saved)

localize54.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f32 (fma.f32 cosTheta -2 1))
✓	0.0b	(.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
✓	0.3b	(/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))

series148.0ms (0.7%)

Counts

4 → 38

Calls

4 calls:

90.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
33.0ms	(.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))
16.0ms	(/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))
7.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))

rewrite72.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary32`
194×	`add-sqr-sqrt_binary32`
161×	`*-un-lft-identity_binary32`
161×	`add-cube-cbrt_binary32`
96×	`sqrt-prod_binary32`

Counts

4 → 282

Calls

4 calls:

22.0ms	(.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))
9.0ms	(/.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))
6.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
1.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))

simplify255.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

363×	`associate-r_binary32`
343×	`associate-l_binary32`
274×	`fma-def_binary32`
234×	`associate-/l/_binary32`
201×	`associate-/r*_binary32`

Counts

320 → 422

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	522	12066
1	1421	11441
2	4913	11441
3	5043	11441

prune622.0ms (2.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	417	5	422
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	423	10	433

Error

0.0b

Counts

433 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 1 (+.f32 (.f32 (-.f32 (.f32 1 1) (.f32 c c)) (sqrt.f32 (PI.f32))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta))))) (.f32 (-.f32 1 c) (sqrt.f32 (PI.f32))))
	0.8b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 1 (sqrt.f32 cosTheta)) (.f32 (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 cosTheta))))))
	0.7b	(-.f32 (fma.f32 (sqrt.f32 (PI.f32)) cosTheta (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3)) 5/2 (fma.f32 7/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 2 (.f32 (pow.f32 (PI.f32) 3/2) (.f32 (pow.f32 cosTheta 3) c)) (fma.f32 3 (.f32 (pow.f32 (PI.f32) 3/2) (pow.f32 cosTheta 4)) (fma.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2) (fma.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta cosTheta) (fma.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 3) (pow.f32 (PI.f32) 3/2)) (.f32 (pow.f32 (PI.f32) 3/2) (+.f32 (.f32 3 (.f32 (.f32 c c) (pow.f32 cosTheta 4))) (.f32 6 (.f32 c (pow.f32 cosTheta 4))))))))))))) (fma.f32 c (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (fma.f32 3 (.f32 (.f32 c c) (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2))) (fma.f32 6 (.f32 (PI.f32) (.f32 c (pow.f32 cosTheta 4))) (+.f32 (+.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 3)) (+.f32 2 (.f32 2 c)))) (+.f32 (.f32 (pow.f32 cosTheta 4) (+.f32 (pow.f32 (PI.f32) 2) (.f32 (PI.f32) 6))) (.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (PI.f32) 2)) (+.f32 (pow.f32 c 3) (*.f32 3 c)))))))))
	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (log1p.f32 (expm1.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)))) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
	0.8b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32)))))))) (cbrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))))
	13.7b	(.f32 (/.f32 1 (-.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (/.f32 (fma.f32 cosTheta -2 1) (.f32 (PI.f32) (.f32 (.f32 cosTheta cosTheta) (pow.f32 (exp.f32 (.f32 cosTheta cosTheta)) 2)))))) (-.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.7b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 cosTheta) (pow.f32 (sqrt.f32 (exp.f32 cosTheta)) cosTheta)) (.f32 (sqrt.f32 cosTheta) (pow.f32 (sqrt.f32 (exp.f32 cosTheta)) cosTheta)))))))
▶	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))))))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))

Compiler

Compiled 17035 to 7723 computations (54.7% saved)

localize69.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))))))
✓	0.3b	(.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32)))))
✓	0.4b	(/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))

series701.0ms (3.1%)

Counts

4 → 46

Calls

4 calls:

284.0ms	(/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))
197.0ms	(.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32)))))
170.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))))))
49.0ms	(.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))))

rewrite180.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

587×	`times-frac_binary32`
498×	`add-sqr-sqrt_binary32`
268×	`*-un-lft-identity_binary32`
250×	`add-cube-cbrt_binary32`
201×	`sqrt-prod_binary32`

Counts

4 → 487

Calls

4 calls:

62.0ms	(.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32)))))
23.0ms	(.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))))
7.0ms	(/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))
7.0ms	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 1 cosTheta) (sqrt.f32 (cbrt.f32 (PI.f32))))))))

simplify432.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

564×	`associate-*r/_binary32`
492×	`associate-*l/_binary32`
378×	`fma-def_binary32`
306×	`associate-/l*_binary32`
244×	`*-commutative_binary32`

Counts

533 → 672

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	660	22298
1	2009	19484
2	4972	19484
3	4977	19484

prune1.1s (4.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	668	4	672
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	675	7	682

Error

0.0b

Counts

682 → 7

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 1 (+.f32 (.f32 (-.f32 (.f32 1 1) (.f32 c c)) (sqrt.f32 (PI.f32))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta))))) (.f32 (-.f32 1 c) (sqrt.f32 (PI.f32))))
	0.8b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	1.1b	(-.f32 (.f32 (pow.f32 (PI.f32) 1/6) (.f32 (cbrt.f32 (PI.f32)) (+.f32 (.f32 cosTheta cosTheta) cosTheta))) (.f32 (+.f32 1 c) (.f32 (cbrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta cosTheta) (pow.f32 (PI.f32) 2/3)))))
	0.6b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 (/.f32 1 cosTheta) (fabs.f32 (cbrt.f32 (cbrt.f32 (PI.f32))))) (sqrt.f32 (cbrt.f32 (cbrt.f32 (PI.f32)))))))))
	0.5b	(.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (sqrt.f32 (cbrt.f32 (PI.f32)))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 1 cosTheta)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (*.f32 1 c))) (sqrt.f32 (cbrt.f32 (PI.f32)))))
▶	0.4b	(/.f32 1 (fma.f32 (/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (*.f32 cosTheta 2))) 1))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))

Compiler

Compiled 31479 to 15641 computations (50.3% saved)

localize59.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (*.f32 cosTheta cosTheta)))
✓	0.2b	(*.f32 cosTheta (cbrt.f32 (PI.f32)))
✓	0.3b	(/.f32 1 (fma.f32 (/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (*.f32 cosTheta 2))) 1))
✓	0.3b	(/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32))))

series503.0ms (2.3%)

Counts

4 → 42

Calls

4 calls:

257.0ms	(*.f32 cosTheta (cbrt.f32 (PI.f32)))
183.0ms	(/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (*.f32 cosTheta cosTheta)))
33.0ms	(/.f32 1 (fma.f32 (/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (*.f32 cosTheta 2))) 1))
30.0ms	(/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32))))

rewrite66.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

307×	`times-frac_binary32`
153×	`add-sqr-sqrt_binary32`
149×	`*-un-lft-identity_binary32`
149×	`add-cube-cbrt_binary32`
130×	`unpow-prod-down_binary32`

Counts

4 → 289

Calls

4 calls:

12.0ms	(/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32))))
10.0ms	(/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (*.f32 cosTheta cosTheta)))
3.0ms	(*.f32 cosTheta (cbrt.f32 (PI.f32)))
2.0ms	(/.f32 1 (fma.f32 (/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (*.f32 cosTheta 2))) 1))

simplify313.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary32`
407×	`fma-neg_binary32`
324×	`cancel-sign-sub-inv_binary32`
253×	`associate-/l*_binary32`
209×	`associate-/r*_binary32`

Counts

331 → 417

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	375	10802
1	812	10044
2	2953	9804
3	4313	9790
4	4880	9790
5	4941	9790

prune814.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	415	2	417
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	417	7	424

Error

0.0b

Counts

424 → 7

Alt Table

Status	Error	Program
	0.8b	(.f32 (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	1.1b	(-.f32 (.f32 (pow.f32 (PI.f32) 1/6) (.f32 (cbrt.f32 (PI.f32)) (+.f32 (.f32 cosTheta cosTheta) cosTheta))) (.f32 (+.f32 1 c) (.f32 (cbrt.f32 (PI.f32)) (.f32 (*.f32 cosTheta cosTheta) (pow.f32 (PI.f32) 2/3)))))
	0.4b	(/.f32 1 (fma.f32 (.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) cosTheta) (/.f32 (pow.f32 (exp.f32 cosTheta) (neg.f32 cosTheta)) (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 cosTheta 2))) 1))
	0.9b	(-.f32 (+.f32 (.f32 5/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3))) (+.f32 (.f32 (sqrt.f32 (pow.f32 (PI.f32) 3)) (pow.f32 cosTheta 3)) (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 2))))) (+.f32 (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))) (.f32 (PI.f32) (pow.f32 cosTheta 2))))
	0.5b	(.f32 (/.f32 1 (+.f32 (.f32 (+.f32 (pow.f32 1 3) (pow.f32 c 3)) (sqrt.f32 (cbrt.f32 (PI.f32)))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) (fabs.f32 (cbrt.f32 (PI.f32)))) (/.f32 1 cosTheta)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (*.f32 1 c))) (sqrt.f32 (cbrt.f32 (PI.f32)))))
✓	0.4b	(/.f32 1 (fma.f32 (/.f32 (/.f32 (pow.f32 (/.f32 1 (PI.f32)) 1/6) (exp.f32 (.f32 cosTheta cosTheta))) (.f32 cosTheta (cbrt.f32 (PI.f32)))) (sqrt.f32 (-.f32 1 (*.f32 cosTheta 2))) 1))
	0.9b	(/.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))

Compiler

Compiled 16174 to 9723 computations (39.9% saved)

regimes14.3s (64.1%)

Accuracy

Total 0.4b remaining (91.8%)

Threshold costs 0.4b (91.8%)

Counts

1188 → 1

Compiler

Compiled 279090 to 198326 computations (28.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary32`
4×	`*-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	35	47
2	39	47
3	42	47
4	43	47
5	42	47

end1.0ms (0%)

Compiler: Compiled 31 to 25 computations (19.4% saved)

sample1.7s (7.5%)

Algorithm

1×

intervals

Results

896.0ms	8000×	body	128	valid
188.0ms	8000×	pre	128	true

Compiler

Compiled 380 to 270 computations (28.9% saved)

Details

analyze95.0ms (0.4%)

sample115.0ms (0.5%)

simplify46.0ms (0.2%)

prune5.0ms (0%)

localize57.0ms (0.3%)

series126.0ms (0.6%)

rewrite37.0ms (0.2%)

simplify133.0ms (0.6%)

prune353.0ms (1.6%)

localize54.0ms (0.2%)

series148.0ms (0.7%)

rewrite72.0ms (0.3%)

simplify255.0ms (1.1%)

prune622.0ms (2.8%)

localize69.0ms (0.3%)

series701.0ms (3.1%)

rewrite180.0ms (0.8%)

simplify432.0ms (1.9%)

prune1.1s (4.8%)

localize59.0ms (0.3%)

series503.0ms (2.3%)

rewrite66.0ms (0.3%)

simplify313.0ms (1.4%)

prune814.0ms (3.7%)

regimes14.3s (64.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.7s (7.5%)

Profiling