Details

analyze116.0ms (0.7%)

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)

sample2.5s (15.2%)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 111 to 85 computations (23.4% saved)

simplify46.0ms (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
	0.6b	(/.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)))))
▶	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))))))

Status

Error

Program

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)))))

▶

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))))))

Compiler

Compiled 148 to 113 computations (23.6% saved)

localize63.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f32 (fma.f32 cosTheta -2 1))
✓	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)))

series107.0ms (0.6%)

Counts

4 → 38

Calls

4 calls:

60.0ms	(/.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))))))
21.0ms	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
15.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))
11.0ms	(.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary32`
32×	`add-exp-log_binary32`
22×	`add-sqr-sqrt_binary32`
21×	`times-frac_binary32`
21×	`add-cube-cbrt_binary32`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/.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)))
1.0ms	(sqrt.f32 (fma.f32 cosTheta -2 1))

simplify141.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

449×	`cancel-sign-sub-inv_binary32`
348×	`associate-r_binary32`
306×	`associate-l_binary32`
287×	`unswap-sqr_binary32`
281×	`fma-def_binary32`

Counts

155 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	364	5718
1	1029	5271
2	3838	5255
3	5406	5255

prune402.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	191	9	200
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	193	9	202

Error

0.0b

Counts

202 → 9

Alt Table

Status	Error	Program
	0.5b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (fma.f32 cosTheta -2 1)))) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sqrt.f32 (cbrt.f32 (fma.f32 cosTheta -2 1))) (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))))))))
	0.8b	(/.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)))))))
▶	0.4b	(/.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)))))))
	0.8b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (.f32 (cbrt.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))) (cbrt.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))) (cbrt.f32 (.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)))))))
	1.1b	(-.f32 (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (+.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 2)) (+.f32 (.f32 5/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3))) (+.f32 (.f32 (.f32 (pow.f32 c 2) (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3))) (+.f32 (.f32 2 (.f32 (.f32 c (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3)))) (.f32 (sqrt.f32 (pow.f32 (PI.f32) 3)) (pow.f32 cosTheta 3))))))) (+.f32 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 2))) (+.f32 (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))) (+.f32 (.f32 2 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 3)))) (.f32 (PI.f32) (pow.f32 cosTheta 2))))))
	13.3b	(.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 (sqrt.f32 (fma.f32 cosTheta -2 1)) (/.f32 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))
	0.7b	(.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))))))))

Compiler

Compiled 8159 to 4654 computations (43% saved)

localize79.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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)))))
✓	0.3b	(/.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 (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))))
✓	0.5b	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series234.0ms (1.4%)

Counts

4 → 46

Calls

4 calls:

138.0ms	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))
64.0ms	(/.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)))))))
21.0ms	(/.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)))))
11.0ms	(.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))))

rewrite60.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary32`
42×	`*-un-lft-identity_binary32`
34×	`add-cbrt-cube_binary32`
31×	`prod-exp_binary32`
22×	`add-sqr-sqrt_binary32`

Counts

4 → 132

Calls

4 calls:

15.0ms	(/.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)))))
13.0ms	(.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))))
10.0ms	(/.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)))))))
7.0ms	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

simplify162.0ms (1%)

Algorithm

1×	egg-herbie

Rules

445×	`associate-r_binary32`
372×	`associate-l_binary32`
300×	`unswap-sqr_binary32`
298×	`fma-def_binary32`
258×	`*-commutative_binary32`

Counts

178 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	404	7630
1	1128	6450
2	4163	6415
3	5227	6415

prune361.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	234	8	242

Error

0.0b

Counts

242 → 8

Alt Table

Status	Error	Program
	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)))))))
	0.5b	(/.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 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))))) (.f32 (sqrt.f32 (cbrt.f32 (cbrt.f32 (PI.f32)))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
	0.4b	(.f32 (/.f32 1 (+.f32 (.f32 (-.f32 (.f32 1 1) (.f32 c c)) (.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))))) (.f32 (-.f32 1 c) (sqrt.f32 (fma.f32 cosTheta -2 1))))) (.f32 (-.f32 1 c) (.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))))))
	13.3b	(.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))))))
	0.8b	(/.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)))))))
	1.1b	(-.f32 (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (+.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 2)) (+.f32 (.f32 5/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3))) (+.f32 (.f32 (.f32 (pow.f32 c 2) (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3))) (+.f32 (.f32 2 (.f32 (.f32 c (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3)))) (.f32 (sqrt.f32 (pow.f32 (PI.f32) 3)) (pow.f32 cosTheta 3))))))) (+.f32 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 2))) (+.f32 (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))) (+.f32 (.f32 2 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 3)))) (.f32 (PI.f32) (pow.f32 cosTheta 2))))))
▶	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.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 (/.f32 (exp.f32 (neg.f32 (.f32 cosTheta cosTheta))) cosTheta) (sqrt.f32 (PI.f32))))))

Compiler

Compiled 10873 to 5282 computations (51.4% saved)

localize73.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32)))
✓	0.3b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
✓	0.4b	(/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))
	0.5b	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series127.0ms (0.8%)

Counts

3 → 26

Calls

3 calls:

58.0ms

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

43.0ms

(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32)))

26.0ms

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

rewrite64.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`times-frac_binary32`
111×	`*-un-lft-identity_binary32`
91×	`add-sqr-sqrt_binary32`
91×	`add-cube-cbrt_binary32`
57×	`sqrt-prod_binary32`

Counts

3 → 217

Calls

3 calls:

19.0ms

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

16.0ms

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

3.0ms

(/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32)))

simplify315.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

337×	`associate-r_binary32`
319×	`associate-/r*_binary32`
307×	`associate-l_binary32`
258×	`fma-def_binary32`
226×	`*-commutative_binary32`

Counts

243 → 328

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	454	10444
1	1243	9629
2	4597	9598
3	4978	9598
4	4980	9598

prune1.8s (11%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	374	4	378
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	379	7	386

Error

0.0b

Counts

386 → 7

Alt Table

Status	Error	Program
	0.8b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))) (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))) (/.f32 1 (cbrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))))
▶	0.4b	(.f32 (/.f32 1 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (.f32 c c))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (fma.f32 cosTheta -2 1)))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (/.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (cbrt.f32 (fma.f32 cosTheta -2 1))) (cbrt.f32 (PI.f32)))))))
✓	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	13.3b	(.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))))))
	1.1b	(-.f32 (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (+.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 2)) (+.f32 (.f32 5/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3))) (+.f32 (.f32 (.f32 (pow.f32 c 2) (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3))) (+.f32 (.f32 2 (.f32 (.f32 c (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3)))) (.f32 (sqrt.f32 (pow.f32 (PI.f32) 3)) (pow.f32 cosTheta 3))))))) (+.f32 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 2))) (+.f32 (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))) (+.f32 (.f32 2 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 3)))) (.f32 (PI.f32) (pow.f32 cosTheta 2))))))

Compiler

Compiled 15618 to 8352 computations (46.5% saved)

localize117.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (*.f32 c c))))
✓	0.3b	(.f32 (/.f32 1 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (.f32 c c))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
✓	0.5b	(.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32))))
	0.5b	(.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))

series814.0ms (4.9%)

Counts

3 → 48

Calls

3 calls:

620.0ms

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

125.0ms

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

69.0ms

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

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-exp-log_binary32`
75×	`prod-exp_binary32`
40×	`add-cbrt-cube_binary32`
23×	`cbrt-unprod_binary32`
17×	`pow1_binary32`

Counts

3 → 100

Calls

3 calls:

16.0ms

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

8.0ms

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

0.0ms

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

simplify223.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary32`
391×	`times-frac_binary32`
352×	`associate-/r*_binary32`
338×	`associate-/l*_binary32`
260×	`*-commutative_binary32`

Counts

148 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	686	15244
1	2250	13352
2	5224	13352

prune627.0ms (3.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	243	8	251

Error

Counts

251 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (fma.f32 cosTheta -2 1)))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (/.f32 (.f32 cosTheta (exp.f32 (*.f32 cosTheta cosTheta))) (/.f32 (sqrt.f32 (cbrt.f32 (fma.f32 cosTheta -2 1))) (cbrt.f32 (PI.f32)))))))
✓	0.4b	(/.f32 1 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	0.7b	(/.f32 (/.f32 1 (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))) (sqrt.f32 (+.f32 (+.f32 1 c) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))))
	13.3b	(.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))))))
✓	0.4b	(.f32 (/.f32 1 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (.f32 c c))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta)))))
	0.5b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (.f32 c c))))) (cbrt.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (.f32 c c))))))) (.f32 (/.f32 1 (cbrt.f32 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (.f32 c c)))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (cbrt.f32 (PI.f32))) (*.f32 cosTheta (pow.f32 (exp.f32 cosTheta) cosTheta))))))
	1.1b	(-.f32 (+.f32 (.f32 (sqrt.f32 (PI.f32)) cosTheta) (+.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 2)) (+.f32 (.f32 5/2 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 cosTheta 3))) (+.f32 (.f32 (.f32 (pow.f32 c 2) (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3))) (+.f32 (.f32 2 (.f32 (.f32 c (pow.f32 cosTheta 3)) (sqrt.f32 (pow.f32 (PI.f32) 3)))) (.f32 (sqrt.f32 (pow.f32 (PI.f32) 3)) (pow.f32 cosTheta 3))))))) (+.f32 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 2))) (+.f32 (.f32 2 (.f32 (PI.f32) (pow.f32 cosTheta 3))) (+.f32 (.f32 2 (.f32 c (.f32 (PI.f32) (pow.f32 cosTheta 3)))) (.f32 (PI.f32) (pow.f32 cosTheta 2))))))
	0.4b	(.f32 (/.f32 1 (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (cbrt.f32 (PI.f32))) (-.f32 1 c) (.f32 (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (PI.f32)))) (-.f32 1 (.f32 c c))))) (.f32 (-.f32 1 c) (.f32 (sqrt.f32 (cbrt.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))))) (.f32 (.f32 cosTheta (exp.f32 (.f32 cosTheta cosTheta))) (sqrt.f32 (cbrt.f32 (cbrt.f32 (PI.f32))))))))

Compiler

Compiled 21596 to 11687 computations (45.9% saved)

regimes7.8s (46.8%)

Accuracy

Total 0.4b remaining (93.5%)

Threshold costs 0.4b (93.5%)

Counts

610 → 1

Compiler

Compiled 162796 to 115823 computations (28.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	70
1	36	70
2	43	70
3	47	70
4	49	70
5	48	70

end263.0ms (1.6%)

Compiler: Compiled 576 to 359 computations (37.7% saved)

Details

analyze116.0ms (0.7%)

sample2.5s (15.2%)

simplify46.0ms (0.3%)

prune5.0ms (0%)

localize63.0ms (0.4%)

series107.0ms (0.6%)

rewrite36.0ms (0.2%)

simplify141.0ms (0.8%)

prune402.0ms (2.4%)

localize79.0ms (0.5%)

series234.0ms (1.4%)

rewrite60.0ms (0.4%)

simplify162.0ms (1%)

prune361.0ms (2.2%)

localize73.0ms (0.4%)

series127.0ms (0.8%)

rewrite64.0ms (0.4%)

simplify315.0ms (1.9%)

prune1.8s (11%)

localize117.0ms (0.7%)

series814.0ms (4.9%)

rewrite46.0ms (0.3%)

simplify223.0ms (1.3%)

prune627.0ms (3.8%)

regimes7.8s (46.8%)

simplify5.0ms (0%)

end263.0ms (1.6%)

Profiling