Details

analyze9.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample133.0ms (0.7%)

Algorithm

1×

intervals

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

32.0ms	256×	body	128	valid
14.0ms	256×	pre	128	true

Compiler

Compiled 98 to 72 computations (26.5% saved)

simplify52.0ms (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

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

0.3b

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))
▶	0.4b	(.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

0.5b

(/.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))

▶

0.4b

(*.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)

localize58.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.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)))))
✓	0.9b	(sinh.f32 (/.f32 1 v))

series568.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

462.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
85.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
15.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite40.0ms (0.2%)

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:

12.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
10.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

simplify140.0ms (0.7%)

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

prune420.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	207	11	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	208	12	220

Error

0.1b

Counts

220 → 12

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))
	0.6b	(.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 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 cosTheta_i (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i v) (/.f32 (/.f32 1 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 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) v) (/.f32 (/.f32 (cbrt.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) (.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 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) (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))) 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 (/.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 (/.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)))))))

Compiler

Compiled 9034 to 4891 computations (45.9% saved)

localize60.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
✓	0.3b	(/.f32 cosTheta_i (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v)))
✓	0.4b	(/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))
	0.9b	(sinh.f32 (/.f32 1 v))

series812.0ms (4.1%)

Counts

2 → 84

Calls

2 calls:

726.0ms

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

86.0ms

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

rewrite55.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

173×	`times-frac_binary32`
124×	`add-exp-log_binary32`
76×	`add-cbrt-cube_binary32`
67×	`*-un-lft-identity_binary32`
67×	`add-sqr-sqrt_binary32`

Counts

2 → 179

Calls

2 calls:

13.0ms

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

13.0ms

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

simplify255.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

637×	`times-frac_binary32`
510×	`fma-def_binary32`
506×	`associate-/l*_binary32`
404×	`associate-/r*_binary32`
248×	`associate-/r/_binary32`

Counts

263 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	427	12881
1	1275	11485
2	4884	11433
3	5229	11433

prune824.0ms (4.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	365	11	376
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	375	13	388

Error

0.0b

Counts

388 → 13

Alt Table

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

Compiler

Compiled 15298 to 8754 computations (42.8% saved)

localize68.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 cosTheta_i (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v)))
✓	0.3b	(/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v))
✓	0.4b	(.f32 (/.f32 1 (/.f32 v 1)) (/.f32 cosTheta_i (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v))))
	0.9b	(sinh.f32 (/.f32 1 v))

series900.0ms (4.6%)

Counts

3 → 132

Calls

3 calls:

477.0ms

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

352.0ms

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

70.0ms

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

rewrite187.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

763×	`add-exp-log_binary32`
527×	`div-exp_binary32`
386×	`times-frac_binary32`
284×	`prod-exp_binary32`
191×	`add-sqr-sqrt_binary32`

Counts

3 → 462

Calls

3 calls:

50.0ms

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

13.0ms

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

11.0ms

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

simplify438.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-/l*_binary32`
669×	`associate-/r*_binary32`
466×	`associate-/r/_binary32`
245×	`associate-/l/_binary32`
238×	`fma-def_binary32`

Counts

594 → 715

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	665	27848
1	1902	24037
2	5494	24037

prune2.6s (13.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	732	4	736
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	738	11	749

Error

0.0b

Counts

749 → 11

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))
	0.4b	(.f32 cosTheta_O (/.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 (/.f32 v 1)) (.f32 (.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v))) (/.f32 cosTheta_i (/.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (sqrt.f32 (/.f32 1 v)))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 1 (/.f32 v (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))))) (/.f32 cosTheta_i (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 (cbrt.f32 v))))))
▶	0.3b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 1 (/.f32 v 1)) cosTheta_i) (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v))))
	0.4b	(.f32 cosTheta_O (/.f32 cosTheta_i (/.f32 (.f32 v (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))
	0.4b	(.f32 cosTheta_O (/.f32 cosTheta_i (/.f32 (.f32 v (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 (/.f32 v 1)) (/.f32 cosTheta_i (/.f32 (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 (.f32 (cbrt.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))) (cbrt.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))) (/.f32 cosTheta_i (cbrt.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))))
	0.4b	(.f32 cosTheta_O (/.f32 cosTheta_i (expm1.f32 (log1p.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) 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)) (cbrt.f32 (/.f32 1 v))))))

Compiler

Compiled 31438 to 18810 computations (40.2% saved)

localize68.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (.f32 (/.f32 1 (/.f32 v 1)) cosTheta_i) (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v)))
✓	0.3b	(*.f32 (/.f32 1 (/.f32 v 1)) cosTheta_i)
	0.3b	(/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v))
	0.9b	(sinh.f32 (/.f32 1 v))

series472.0ms (2.4%)

Counts

2 → 72

Calls

2 calls:

465.0ms	(/.f32 (.f32 (/.f32 1 (/.f32 v 1)) cosTheta_i) (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v)))
7.0ms	(*.f32 (/.f32 1 (/.f32 v 1)) cosTheta_i)

rewrite121.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

731×	`add-exp-log_binary32`
509×	`div-exp_binary32`
272×	`prod-exp_binary32`
169×	`add-cbrt-cube_binary32`
138×	`times-frac_binary32`

Counts

2 → 301

Calls

2 calls:

20.0ms	(/.f32 (.f32 (/.f32 1 (/.f32 v 1)) cosTheta_i) (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 v)))
13.0ms	(*.f32 (/.f32 1 (/.f32 v 1)) cosTheta_i)

simplify269.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary32`
568×	`associate-/l*_binary32`
433×	`fma-def_binary32`
400×	`associate-/r*_binary32`
265×	`associate-/r/_binary32`

Counts

373 → 416

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	14389
1	1103	11801
2	4664	11769
3	5000	11769

prune1.3s (6.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	541	4	545
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	547	9	556

Error

0.0b

Counts

556 → 9

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

Compiler

Compiled 21634 to 13130 computations (39.3% saved)

regimes7.3s (37.2%)

Accuracy

Total 0.2b remaining (69.5%)

Threshold costs 0.2b (69.5%)

Counts

624 → 1

Compiler

Compiled 169882 to 123456 computations (27.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
1×	`/-rgt-identity_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	28	38
2	27	38

end20.0ms (0.1%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 150 to 110 computations (26.7% saved)

sample2.6s (13%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
477.0ms	8000×	pre	128	true

Compiler

Compiled 451 to 327 computations (27.5% saved)

Details

analyze9.0ms (0%)

sample133.0ms (0.7%)

simplify52.0ms (0.3%)

prune5.0ms (0%)

localize58.0ms (0.3%)

series568.0ms (2.9%)

rewrite40.0ms (0.2%)

simplify140.0ms (0.7%)

prune420.0ms (2.1%)

localize60.0ms (0.3%)

series812.0ms (4.1%)

rewrite55.0ms (0.3%)

simplify255.0ms (1.3%)

prune824.0ms (4.2%)

localize68.0ms (0.3%)

series900.0ms (4.6%)

rewrite187.0ms (0.9%)

simplify438.0ms (2.2%)

prune2.6s (13.1%)

localize68.0ms (0.3%)

series472.0ms (2.4%)

rewrite121.0ms (0.6%)

simplify269.0ms (1.4%)

prune1.3s (6.4%)

regimes7.3s (37.2%)

simplify2.0ms (0%)

end20.0ms (0.1%)

sample2.6s (13%)

Profiling