Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample2.6s (18.6%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.5s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

913×	`times-frac_binary32`
551×	`associate-/l*_binary32`
460×	`associate-/l/_binary32`
362×	`associate-*l/_binary32`
312×	`associate-/r/_binary32`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	54	34
2	171	32
3	710	32
4	3631	32
5	4627	32
6	5261	32

prune4.0ms (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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Status

Error

Program

0.5b

(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

▶

0.5b

(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Compiler

Compiled 154 to 104 computations (32.5% saved)

localize53.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
✓	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.4b	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
✓	0.8b	(sinh.f32 (/.f32 1 v))

series532.0ms (3.8%)

Counts

4 → 96

Calls

4 calls:

444.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
69.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-cbrt-cube_binary32`
44×	`add-exp-log_binary32`
34×	`times-frac_binary32`
21×	`*-un-lft-identity_binary32`
21×	`add-sqr-sqrt_binary32`

Counts

4 → 114

Calls

4 calls:

13.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
8.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

simplify132.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

584×	`times-frac_binary32`
466×	`associate-/r*_binary32`
456×	`associate-/l*_binary32`
371×	`associate-l_binary32`
150×	`fma-def_binary32`

Counts

210 → 218

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	419	9291
1	1297	8518
2	5043	8518

prune462.0ms (3.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	204	14	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	205	15	220

Error

0.1b

Counts

220 → 15

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) v) (/.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (cbrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	22.4b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (cbrt.f32 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (.f32 (cbrt.f32 v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.f32 v (/.f32 (cbrt.f32 cosTheta_i) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (sqrt.f32 v)) v) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
▶	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 (.f32 v v) (exp.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 v (/.f32 (exp.f32 (-.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) v))))))

Compiler

Compiled 9274 to 5035 computations (45.7% saved)

localize57.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.4b	(/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓	0.5b	(exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
	0.8b	(sinh.f32 (/.f32 1 v))

series845.0ms (6%)

Counts

2 → 84

Calls

2 calls:

820.0ms

(/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

25.0ms

(exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary32`
57×	`*-un-lft-identity_binary32`
52×	`add-sqr-sqrt_binary32`
52×	`add-cube-cbrt_binary32`
15×	`exp-sum_binary32`

Counts

2 → 107

Calls

2 calls:

18.0ms

(/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

9.0ms

(exp.f32 (+.f32 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))

simplify161.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary32`
404×	`associate-/r*_binary32`
359×	`associate-/l*_binary32`
273×	`associate-r_binary32`
212×	`associate-l_binary32`

Counts

191 → 223

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	400	10156
1	1167	9726
2	4983	9726

prune808.0ms (5.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	265	8	273
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	273	15	288

Error

0.0b

Counts

288 → 15

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.f32 (/.f32 1 v) (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) (exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (/.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
▶	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (cbrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	22.4b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (/.f32 (exp.f32 (log.f32 (.f32 v (.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))))) (exp.f32 (-.f32 (log.f32 2) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (sqrt.f32 v)) v) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	22.4b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 cosTheta_i) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (sqrt.f32 cosTheta_i) (.f32 (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v)))) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (cbrt.f32 v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 (.f32 v v) (exp.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 v (/.f32 (exp.f32 (-.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) v))))))

Compiler

Compiled 12351 to 6774 computations (45.2% saved)

localize59.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(/.f32 cosTheta_i (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v)))))
✓	0.4b	(.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
	0.8b	(sinh.f32 (/.f32 1 v))

series559.0ms (4%)

Counts

2 → 72

Calls

2 calls:

482.0ms	(.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
76.0ms	(/.f32 cosTheta_i (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v)))))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`add-exp-log_binary32`
77×	`times-frac_binary32`
65×	`add-cbrt-cube_binary32`
53×	`add-sqr-sqrt_binary32`
43×	`associate-r_binary32`

Counts

2 → 127

Calls

2 calls:

22.0ms	(.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
7.0ms	(/.f32 cosTheta_i (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v)))))

simplify224.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

568×	`times-frac_binary32`
439×	`fma-def_binary32`
425×	`associate-/r*_binary32`
385×	`associate-/l*_binary32`
331×	`associate-l_binary32`

Counts

199 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	375	9589
1	1179	8446
2	4897	8414
3	5227	8414

prune769.0ms (5.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	261	5	266
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	267	14	281

Error

0.0b

Counts

281 → 14

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.f32 (/.f32 1 v) (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) (exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (/.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (cbrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (/.f32 2 (/.f32 (cbrt.f32 cosTheta_i) (.f32 v (sinh.f32 (/.f32 1 v)))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	22.4b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (/.f32 (exp.f32 (log.f32 (.f32 v (.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))))) (exp.f32 (-.f32 (log.f32 2) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
▶	0.3b	(.f32 cosTheta_O (.f32 (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Compiler

Compiled 11457 to 6483 computations (43.4% saved)

localize74.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 v (exp.f32 (/.f32 1 v)))
✓	0.3b	(/.f32 cosTheta_i (-.f32 (*.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))
✓	0.4b	(.f32 (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
✓	0.8b	(exp.f32 (/.f32 1 v))

series444.0ms (3.2%)

Counts

4 → 76

Calls

4 calls:

371.0ms	(.f32 (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
66.0ms	(/.f32 cosTheta_i (-.f32 (*.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))
4.0ms	(/.f32 v (exp.f32 (/.f32 1 v)))
2.0ms	(exp.f32 (/.f32 1 v))

rewrite71.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary32`
82×	`add-exp-log_binary32`
63×	`*-un-lft-identity_binary32`
63×	`add-sqr-sqrt_binary32`
63×	`add-cube-cbrt_binary32`

Counts

4 → 180

Calls

4 calls:

27.0ms	(.f32 (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
10.0ms	(/.f32 cosTheta_i (-.f32 (*.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))
7.0ms	(/.f32 v (exp.f32 (/.f32 1 v)))
2.0ms	(exp.f32 (/.f32 1 v))

simplify222.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary32`
504×	`times-frac_binary32`
408×	`associate-/l*_binary32`
356×	`associate-r_binary32`
303×	`associate-l_binary32`

Counts

256 → 282

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	418	11264
1	1151	10119
2	4801	10069
3	5244	10069

prune901.0ms (6.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	317	1	318
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	318	14	332

Error

0.0b

Counts

332 → 14

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.f32 (/.f32 1 v) (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) (exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (/.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (/.f32 cosTheta_i (cbrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (/.f32 2 (/.f32 (cbrt.f32 cosTheta_i) (.f32 v (sinh.f32 (/.f32 1 v)))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	22.4b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (sqrt.f32 (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (/.f32 (exp.f32 (log.f32 (.f32 v (.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (neg.f32 (/.f32 1 v)))))))) (exp.f32 (-.f32 (log.f32 2) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
✓	0.3b	(.f32 cosTheta_O (.f32 (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 2 (.f32 v (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.4b	(.f32 cosTheta_O (/.f32 (.f32 (.f32 1 cosTheta_i) (/.f32 1 v)) (.f32 (-.f32 (.f32 v (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))

Compiler

Compiled 14780 to 8482 computations (42.6% saved)

regimes4.4s (31.4%)

Accuracy

Total 0.3b remaining (75.2%)

Threshold costs 0.3b (75.2%)

Counts

416 → 1

Compiler

Compiled 106970 to 74200 computations (30.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	28	43
2	34	43
3	38	43
4	41	43
5	42	43
6	40	43

end436.0ms (3.1%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 773 to 536 computations (30.7% saved)

Details

analyze9.0ms (0.1%)

sample2.6s (18.6%)

simplify46.0ms (0.3%)

prune4.0ms (0%)

localize53.0ms (0.4%)

series532.0ms (3.8%)

rewrite38.0ms (0.3%)

simplify132.0ms (0.9%)

prune462.0ms (3.3%)

localize57.0ms (0.4%)

series845.0ms (6%)

rewrite43.0ms (0.3%)

simplify161.0ms (1.1%)

prune808.0ms (5.8%)

localize59.0ms (0.4%)

series559.0ms (4%)

rewrite51.0ms (0.4%)

simplify224.0ms (1.6%)

prune769.0ms (5.5%)

localize74.0ms (0.5%)

series444.0ms (3.2%)

rewrite71.0ms (0.5%)

simplify222.0ms (1.6%)

prune901.0ms (6.4%)

regimes4.4s (31.4%)

simplify3.0ms (0%)

end436.0ms (3.1%)

Profiling