Details

analyze97.0ms (0.4%)

Algorithm

1×

Search

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

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample165.0ms (0.7%)

Algorithm

1×

intervals

Results

62.0ms	256×	body	128	valid
28.0ms	256×	pre	128	true

Compiler

Compiled 98 to 72 computations (26.5% saved)

simplify72.0ms (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

prune8.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(/.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))
▶	0.4b	(.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

0.4b

(/.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))

▶

0.4b

(*.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)

localize126.0ms (0.5%)

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))))
✓	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(/.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))

series1.2s (4.8%)

Counts

4 → 96

Calls

4 calls:

975.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
161.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
28.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
14.0ms	(sinh.f32 (/.f32 1 v))

rewrite78.0ms (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:

25.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
19.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
7.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms	(sinh.f32 (/.f32 1 v))

simplify272.0ms (1.1%)

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

prune940.0ms (3.8%)

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 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
	0.4b	(/.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))
	12.3b	(.f32 cosTheta_O (log.f32 (exp.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
	0.5b	(.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)))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.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) (cbrt.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))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.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) 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)))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 (/.f32 cosTheta_i v) 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 (/.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))))))
	0.5b	(.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 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))))))
▶	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))

Compiler

Compiled 9296 to 5045 computations (45.7% saved)

localize128.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series1.7s (6.9%)

Counts

2 → 96

Calls

2 calls:

940.0ms

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

756.0ms

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

rewrite87.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-exp-log_binary32`
61×	`add-cbrt-cube_binary32`
50×	`prod-exp_binary32`
30×	`div-exp_binary32`
28×	`cbrt-unprod_binary32`

Counts

2 → 96

Calls

2 calls:

33.0ms

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

20.0ms

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

simplify419.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

954×	`times-frac_binary32`
767×	`fma-def_binary32`
562×	`associate-/r*_binary32`
546×	`associate-/l*_binary32`
136×	`*-commutative_binary32`

Counts

192 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	12145
1	1332	10950
2	4927	10864
3	5515	10864

prune1.2s (5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	221	7	228
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	230	13	243

Error

0.1b

Counts

243 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
	0.4b	(/.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))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 v (exp.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O (/.f32 1 v)))) (/.f32 v (exp.f32 (-.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (/.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))) (cbrt.f32 cosTheta_i)))))
	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 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (.f32 (cbrt.f32 (/.f32 1 v)) (/.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 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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.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) v))))
	0.3b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.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) (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 (/.f32 1 v) (.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.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 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))))
▶	0.3b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))

Compiler

Compiled 11373 to 6929 computations (39.1% saved)

localize143.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.5b	(.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
✓	0.5b	(*.f32 (/.f32 1 v) (/.f32 1 v))
	0.8b	(sinh.f32 (/.f32 1 v))

series854.0ms (3.5%)

Counts

2 → 60

Calls

2 calls:

839.0ms	(.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
14.0ms	(*.f32 (/.f32 1 v) (/.f32 1 v))

rewrite129.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

342×	`add-exp-log_binary32`
199×	`prod-exp_binary32`
131×	`div-exp_binary32`
116×	`add-cbrt-cube_binary32`
57×	`add-sqr-sqrt_binary32`

Counts

2 → 216

Calls

2 calls:

35.0ms	(.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
16.0ms	(*.f32 (/.f32 1 v) (/.f32 1 v))

simplify367.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

576×	`times-frac_binary32`
492×	`associate-l_binary32`
487×	`fma-def_binary32`
456×	`associate-r_binary32`
345×	`associate-/l*_binary32`

Counts

276 → 282

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	10727
1	1014	8705
2	4722	8535
3	5121	8535

prune1.6s (6.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	327	5	332
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	330	15	345

Error

0.1b

Counts

345 → 15

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 v (exp.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O (/.f32 1 v)))) (/.f32 v (exp.f32 (-.f32 (/.f32 1 v) (/.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 cosTheta_O (.f32 (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (.f32 (cbrt.f32 (/.f32 1 v)) (/.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 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))))))
	0.7b	(.f32 cosTheta_O (.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.4b	(/.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)) 1) (/.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) v))))
▶	0.3b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.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) (exp.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.4b	(.f32 cosTheta_O (.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 v)) (log.f32 (/.f32 1 v)))) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.4b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.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 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 v)) (/.f32 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 v))) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))

Compiler

Compiled 13684 to 8153 computations (40.4% saved)

localize105.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series1.6s (6.4%)

Counts

2 → 96

Calls

2 calls:

850.0ms

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

730.0ms

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

rewrite154.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

351×	`add-exp-log_binary32`
208×	`prod-exp_binary32`
134×	`div-exp_binary32`
127×	`add-cbrt-cube_binary32`
60×	`cbrt-unprod_binary32`

Counts

2 → 181

Calls

2 calls:

34.0ms

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

31.0ms

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

simplify527.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

926×	`times-frac_binary32`
774×	`fma-def_binary32`
553×	`associate-/l*_binary32`
535×	`associate-/r*_binary32`
157×	`*-commutative_binary32`

Counts

277 → 280

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	452	15964
1	1412	13501
2	4870	13253
3	5454	13253

prune1.5s (6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	327	3	330
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	331	14	345

Error

0.0b

Counts

345 → 14

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (.f32 (/.f32 1 v) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.4b	(/.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 1 v) (.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))))
	0.3b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 1 v) (.f32 (/.f32 1 v) cosTheta_i)) (.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 1 v) (/.f32 1 v)) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (cbrt.f32 cosTheta_i) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (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))))))
	0.7b	(.f32 cosTheta_O (.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (/.f32 cosTheta_i (.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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.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) 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)))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (sqrt.f32 (/.f32 1 v)) (.f32 (sqrt.f32 (/.f32 1 v)) (/.f32 cosTheta_i (.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) (expm1.f32 (log1p.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))
	0.4b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 v)) (/.f32 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 v))) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))

Compiler

Compiled 14780 to 8918 computations (39.7% saved)

regimes6.1s (24.9%)

Accuracy

Total 0.3b remaining (76.5%)

Threshold costs 0.3b (76.5%)

Counts

325 → 1

Compiler

Compiled 82130 to 58360 computations (28.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	41
1	28	41
2	27	41

end72.0ms (0.3%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 224 to 168 computations (25% saved)

sample4.9s (19.8%)

Algorithm

1×

intervals

Results

1.8s	8000×	body	128	valid
802.0ms	8000×	pre	128	true

Compiler

Compiled 607 to 431 computations (29% saved)

Details

analyze97.0ms (0.4%)

sample165.0ms (0.7%)

simplify72.0ms (0.3%)

prune8.0ms (0%)

localize126.0ms (0.5%)

series1.2s (4.8%)

rewrite78.0ms (0.3%)

simplify272.0ms (1.1%)

prune940.0ms (3.8%)

localize128.0ms (0.5%)

series1.7s (6.9%)

rewrite87.0ms (0.4%)

simplify419.0ms (1.7%)

prune1.2s (5%)

localize143.0ms (0.6%)

series854.0ms (3.5%)

rewrite129.0ms (0.5%)

simplify367.0ms (1.5%)

prune1.6s (6.7%)

localize105.0ms (0.4%)

series1.6s (6.4%)

rewrite154.0ms (0.6%)

simplify527.0ms (2.1%)

prune1.5s (6%)

regimes6.1s (24.9%)

simplify4.0ms (0%)

end72.0ms (0.3%)

sample4.9s (19.8%)

Profiling