Details

analyze16.0ms (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)

sample4.9s (18.8%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

4.7s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify70.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	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))))))
	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))

Status

Error

Program

▶

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))))))

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))

Compiler

Compiled 154 to 104 computations (32.5% saved)

localize127.0ms (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 (4.6%)

Counts

4 → 96

Calls

4 calls:

978.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
160.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
29.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
12.0ms	(sinh.f32 (/.f32 1 v))

rewrite89.0ms (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:

35.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
21.0ms	(.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))

simplify276.0ms (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

prune819.0ms (3.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	206	12	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	207	13	220

Error

0.1b

Counts

220 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) v) (/.f32 (/.f32 (cbrt.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) (exp.f32 (+.f32 (log.f32 v) (+.f32 (+.f32 (log.f32 (sinh.f32 (/.f32 1 v))) (log.f32 2)) (/.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))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.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 cosTheta_i v) (.f32 v (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (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))))
	0.5b	(.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 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (cbrt.f32 (/.f32 cosTheta_i v)))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 cosTheta_i (sqrt.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 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 (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 cosTheta_i v) (cbrt.f32 (.f32 (pow.f32 v 3) (pow.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))) 3)))))
	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))

Compiler

Compiled 9142 to 4957 computations (45.8% saved)

localize121.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series1.1s (4.1%)

Counts

2 → 84

Calls

2 calls:

892.0ms

(/.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)))

159.0ms

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

rewrite116.0ms (0.4%)

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:

28.0ms

(/.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)))

27.0ms

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

simplify464.0ms (1.8%)

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

prune1.5s (5.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	342	8	350
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	352	11	363

Error

0.1b

Counts

363 → 11

Alt Table

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

Compiler

Compiled 14176 to 8092 computations (42.9% saved)

localize147.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series1.2s (4.8%)

Counts

1 → 48

Calls

1 calls:

1.2s

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

rewrite286.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

280×	`times-frac_binary32`
145×	`add-sqr-sqrt_binary32`
119×	`sqrt-prod_binary32`
105×	`*-un-lft-identity_binary32`
99×	`add-cube-cbrt_binary32`

Counts

1 → 177

Calls

1 calls:

173.0ms

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

simplify458.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

604×	`times-frac_binary32`
514×	`associate-/l*_binary32`
410×	`associate-l_binary32`
351×	`associate-/r*_binary32`
259×	`associate-*l/_binary32`

Counts

225 → 305

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	384	17314
1	1170	14653
2	5056	14653

prune4.0s (15.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	628	3	631
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	629	13	642

Error

0.0b

Counts

642 → 13

Alt Table

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

Compiler

Compiled 39339 to 23283 computations (40.8% saved)

localize102.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))
✓	0.4b	(/.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))
✓	0.6b	(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))
	0.8b	(sinh.f32 (/.f32 1 v))

series86.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

80.0ms	(/.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))
6.0ms	(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary32`
34×	`add-cbrt-cube_binary32`
31×	`times-frac_binary32`
24×	`prod-exp_binary32`
24×	`div-exp_binary32`

Counts

2 → 83

Calls

2 calls:

14.0ms	(/.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))
2.0ms	(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))

simplify127.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

569×	`fma-def_binary32`
539×	`fma-neg_binary32`
286×	`associate-+l+_binary32`
226×	`associate-/l*_binary32`
204×	`associate-r_binary32`

Counts

131 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	4350
1	624	3727
2	2508	3583
3	4728	3583
4	5128	3583

prune1.2s (4.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	301	13	314

Error

0.0b

Counts

314 → 13

Alt Table

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

Compiler

Compiled 18168 to 10965 computations (39.6% saved)

regimes7.0s (27.1%)

Accuracy

Total 0.3b remaining (74.3%)

Threshold costs 0.3b (74.3%)

Counts

519 → 1

Compiler

Compiled 171922 to 118696 computations (31% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`distribute-neg-frac_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	49
1	33	49
2	39	49
3	41	49
4	42	49
5	40	49

end421.0ms (1.6%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 891 to 612 computations (31.3% saved)

Details

analyze16.0ms (0.1%)

sample4.9s (18.8%)

simplify70.0ms (0.3%)

prune8.0ms (0%)

localize127.0ms (0.5%)

series1.2s (4.6%)

rewrite89.0ms (0.3%)

simplify276.0ms (1.1%)

prune819.0ms (3.2%)

localize121.0ms (0.5%)

series1.1s (4.1%)

rewrite116.0ms (0.4%)

simplify464.0ms (1.8%)

prune1.5s (5.8%)

localize147.0ms (0.6%)

series1.2s (4.8%)

rewrite286.0ms (1.1%)

simplify458.0ms (1.8%)

prune4.0s (15.6%)

localize102.0ms (0.4%)

series86.0ms (0.3%)

rewrite27.0ms (0.1%)

simplify127.0ms (0.5%)

prune1.2s (4.8%)

regimes7.0s (27.1%)

simplify5.0ms (0%)

end421.0ms (1.6%)

Profiling