Details

analyze101.0ms (0.8%)

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)

sample2.0s (14.9%)

Results

1.9s	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 111 to 85 computations (23.4% saved)

simplify44.0ms (0.3%)

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
▶	0.4b	(/.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 (.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

▶

0.4b

(/.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 (*.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)

localize61.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.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))))
✓	0.3b	(/.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 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series122.0ms (0.9%)

Counts

4 → 46

Calls

4 calls:

79.0ms	(/.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))))))
25.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
11.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
6.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))

rewrite36.0ms (0.3%)

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:

10.0ms	(/.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 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
5.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
4.0ms	(*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))

simplify132.0ms (1%)

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

prune336.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	215	13	228
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	217	13	230

Error

0.0b

Counts

230 → 13

Alt Table

Status	Error	Program
	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)))))))
	3.1b	(exp.f32 (neg.f32 (log1p.f32 (+.f32 c (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))))))))
	1.3b	(fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (-.f32 -1 c) (.f32 (PI.f32) (.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 (sqrt.f32 cosTheta) (*.f32 (sqrt.f32 cosTheta) (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	20.5b	(.f32 (/.f32 1 (+.f32 (pow.f32 (+.f32 1 c) 3) (pow.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) 3))) (+.f32 (.f32 (+.f32 1 c) (+.f32 1 c)) (-.f32 (.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))))))))
▶	0.4b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.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))))))))
	0.4b	(/.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))))))))
	0.9b	(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (cbrt.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (cbrt.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (/.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)))))))
	0.6b	(-.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)))))))))
	14.2b	(.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))))))
	1.0b	(.f32 (.f32 (cbrt.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))))))) (cbrt.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)))))))) (cbrt.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))))))))

Compiler

Compiled 9466 to 5399 computations (43% saved)

localize128.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
✓	0.1b	(/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))
✓	0.3b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
	0.3b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series2.6s (19.5%)

Counts

3 → 48

Calls

3 calls:

2.1s

(*.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

508.0ms

(/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))

9.0ms

(*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))

rewrite77.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-exp-log_binary32`
75×	`prod-exp_binary32`
42×	`add-cbrt-cube_binary32`
23×	`cbrt-unprod_binary32`
20×	`*-un-lft-identity_binary32`

Counts

3 → 120

Calls

3 calls:

16.0ms

(*.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))) (*.f32 (+.f32 (*.f32 1 1) (-.f32 (*.f32 c c) (*.f32 1 c))) (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

5.0ms

(*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))

2.0ms

(/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))

simplify327.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

407×	`*-commutative_binary32`
346×	`+-commutative_binary32`
309×	`associate-+r+_binary32`
249×	`fma-def_binary32`
178×	`associate-r_binary32`

Counts

168 → 228

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1125	21034
1	3736	18886
2	4959	18886
3	4962	18886

prune855.0ms (6.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	277	7	284

Error

Counts

284 → 7

Alt Table

Status	Error	Program
	0.4b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))
	1.3b	(fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (-.f32 -1 c) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))
	0.6b	(-.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 (expm1.f32 (log1p.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.4b	(/.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))))))))
	0.5b	(/.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)))))))
	0.7b	(.f32 (log.f32 (exp.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 30862 to 18459 computations (40.2% saved)

localize133.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f32 (log1p.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))))
	0.1b	(/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))
	0.3b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
	0.3b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series503.0ms (3.8%)

Counts

1 → 18

Calls

1 calls:

502.0ms

(expm1.f32 (log1p.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f32 (log1p.f32 (/.f32 1 (fma.f32 (*.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (*.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))))

simplify107.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

430×	`fma-def_binary32`
367×	`times-frac_binary32`
346×	`associate-r_binary32`
323×	`associate-/r*_binary32`
279×	`associate-l_binary32`

Counts

29 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	418	5490
1	1388	5003
2	4999	5003
3	5057	5003

prune590.0ms (4.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	198	7	205

Error

Counts

205 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))
	1.3b	(fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (-.f32 -1 c) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))
	0.6b	(-.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 (expm1.f32 (log1p.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.4b	(/.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))))))))
	0.5b	(/.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)))))))
	0.7b	(.f32 (log.f32 (exp.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 22063 to 13368 computations (39.4% saved)

localize126.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1))))
	0.3b	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))
✓	0.3b	(.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))
✓	0.4b	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))

series154.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

142.0ms

(*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))

12.0ms

(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`pow1_binary32`
14×	`add-exp-log_binary32`
10×	`associate-r_binary32`
9×	`cbrt-unprod_binary32`

Counts

2 → 50

Calls

2 calls:

11.0ms

(*.f32 (sqrt.f32 (*.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))

6.0ms

(*.f32 (*.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary32`
540×	`distribute-rgt-in_binary32`
510×	`unswap-sqr_binary32`
441×	`*-commutative_binary32`
230×	`sqr-pow_binary32`

Counts

74 → 80

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1736
1	318	1387
2	1009	1358
3	1877	1321
4	3790	1235
5	4983	1235

prune481.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	190	7	197

Error

Counts

197 → 7

Alt Table

Status	Error	Program
✓	0.4b	(.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))))))
	1.3b	(fma.f32 (sqrt.f32 (PI.f32)) (+.f32 cosTheta (.f32 cosTheta cosTheta)) (.f32 (-.f32 -1 c) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))
	0.6b	(-.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 (expm1.f32 (log1p.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.4b	(/.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))))))))
	0.5b	(/.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)))))))
	0.7b	(.f32 (log.f32 (exp.f32 (/.f32 1 (fma.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (pow.f32 c 3)) (.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (fma.f32 c (+.f32 c -1) 1)))))) (.f32 (+.f32 (.f32 1 1) (-.f32 (.f32 c c) (.f32 1 c))) (.f32 (sqrt.f32 (PI.f32)) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))

Compiler

Compiled 17811 to 9423 computations (47.1% saved)

regimes4.0s (30.4%)

Accuracy

Total 0.4b remaining (91.4%)

Threshold costs 0.4b (91.4%)

Counts

378 → 1

Compiler

Compiled 129588 to 88138 computations (32% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
2×	`+-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	72
1	33	72
2	32	72

end239.0ms (1.8%)

Compiler: Compiled 504 to 338 computations (32.9% saved)

Details

analyze101.0ms (0.8%)

sample2.0s (14.9%)

simplify44.0ms (0.3%)

prune5.0ms (0%)

localize61.0ms (0.5%)

series122.0ms (0.9%)

rewrite36.0ms (0.3%)

simplify132.0ms (1%)

prune336.0ms (2.5%)

localize128.0ms (1%)

series2.6s (19.5%)

rewrite77.0ms (0.6%)

simplify327.0ms (2.5%)

prune855.0ms (6.5%)

localize133.0ms (1%)

series503.0ms (3.8%)

rewrite1.0ms (0%)

simplify107.0ms (0.8%)

prune590.0ms (4.5%)

localize126.0ms (1%)

series154.0ms (1.2%)

rewrite20.0ms (0.2%)

simplify78.0ms (0.6%)

prune481.0ms (3.6%)

regimes4.0s (30.4%)

simplify2.0ms (0%)

end239.0ms (1.8%)

Profiling