Details

analyze89.0ms (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)

sample163.0ms (0.7%)

Algorithm

1×

intervals

Results

58.0ms	256×	body	128	valid
30.0ms	256×	pre	128	true

Compiler

Compiled 98 to 72 computations (26.5% saved)

simplify63.0ms (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 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))))))
	0.4b	(/.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))

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))))))

0.4b

(/.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))

Compiler

Compiled 154 to 104 computations (32.5% saved)

localize123.0ms (0.5%)

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 (*.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))

series1.1s (4.6%)

Counts

4 → 96

Calls

4 calls:

928.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
153.0ms	(.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))

rewrite76.0ms (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))))
6.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms	(sinh.f32 (/.f32 1 v))

simplify268.0ms (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

prune797.0ms (3.2%)

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

Compiler

Compiled 9088 to 4921 computations (45.9% saved)

localize127.0ms (0.5%)

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 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓	0.4b	(.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)))))
	0.8b	(sinh.f32 (/.f32 1 v))

series1.4s (5.7%)

Counts

2 → 84

Calls

2 calls:

946.0ms

(*.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)))))

444.0ms

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

rewrite114.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-exp-log_binary32`
88×	`add-cbrt-cube_binary32`
67×	`div-exp_binary32`
63×	`times-frac_binary32`
62×	`prod-exp_binary32`

Counts

2 → 146

Calls

2 calls:

36.0ms

(*.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)))))

24.0ms

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

simplify354.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

922×	`times-frac_binary32`
651×	`associate-/r*_binary32`
579×	`associate-/l*_binary32`
161×	`fma-def_binary32`
146×	`*-commutative_binary32`

Counts

230 → 253

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	438	13215
1	1477	11510
2	5054	11510

prune1.4s (5.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	298	5	303
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	303	12	315

Error

0.1b

Counts

315 → 12

Alt Table

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

Compiler

Compiled 13472 to 7713 computations (42.7% saved)

localize136.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f32 (/.f32 1 v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓	0.4b	(.f32 (/.f32 cosTheta_i v) (exp.f32 (log.f32 (/.f32 (/.f32 1 v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))))
✓	0.6b	(exp.f32 (log.f32 (/.f32 (/.f32 1 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))

series1.4s (5.5%)

Counts

2 → 84

Calls

2 calls:

922.0ms

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

437.0ms

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

rewrite82.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`times-frac_binary32`
38×	`exp-sum_binary32`
38×	`log-prod_binary32`
37×	`add-sqr-sqrt_binary32`
27×	`*-un-lft-identity_binary32`

Counts

2 → 89

Calls

2 calls:

37.0ms

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

20.0ms

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

simplify312.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

726×	`times-frac_binary32`
474×	`associate-/l*_binary32`
454×	`associate-/r*_binary32`
231×	`associate-*r/_binary32`
223×	`associate-*l/_binary32`

Counts

173 → 185

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	411	10641
1	1294	9825
2	5030	9825

prune1.5s (6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	305	6	311
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	311	12	323

Error

0.0b

Counts

323 → 12

Alt Table

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

Compiler

Compiled 15587 to 9587 computations (38.5% saved)

localize160.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series1.1s (4.6%)

Counts

4 → 100

Calls

4 calls:

721.0ms	(.f32 (/.f32 cosTheta_i v) (.f32 (/.f32 (/.f32 1 v) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))) 2))
390.0ms	(/.f32 (/.f32 1 v) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))))
4.0ms	(exp.f32 (/.f32 -1 v))
4.0ms	(exp.f32 (/.f32 1 v))

rewrite149.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

169×	`add-exp-log_binary32`
109×	`add-cbrt-cube_binary32`
90×	`prod-exp_binary32`
68×	`div-exp_binary32`
58×	`times-frac_binary32`

Counts

4 → 179

Calls

4 calls:

45.0ms	(.f32 (/.f32 cosTheta_i v) (.f32 (/.f32 (/.f32 1 v) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))) 2))
28.0ms	(/.f32 (/.f32 1 v) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))))
5.0ms	(exp.f32 (/.f32 -1 v))
5.0ms	(exp.f32 (/.f32 1 v))

simplify407.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

884×	`times-frac_binary32`
609×	`associate-/r*_binary32`
589×	`associate-/l*_binary32`
215×	`fma-def_binary32`
179×	`*-commutative_binary32`

Counts

279 → 288

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	557	15257
1	1730	13301
2	5388	13301

prune1.4s (5.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	287	1	288
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	288	12	300

Error

0.0b

Counts

300 → 12

Alt Table

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

Compiler

Compiled 15486 to 9681 computations (37.5% saved)

regimes6.7s (27.3%)

Accuracy

Total 0.3b remaining (74.7%)

Threshold costs 0.3b (74.7%)

Counts

353 → 1

Compiler

Compiled 89730 to 63448 computations (29.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	27	38
2	26	38

end80.0ms (0.3%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 210 to 154 computations (26.7% saved)

sample5.1s (20.8%)

Algorithm

1×

intervals

Results

1.9s	8000×	body	128	valid
834.0ms	8000×	pre	128	true

Compiler

Compiled 512 to 371 computations (27.5% saved)

Details

analyze89.0ms (0.4%)

sample163.0ms (0.7%)

simplify63.0ms (0.3%)

prune8.0ms (0%)

localize123.0ms (0.5%)

series1.1s (4.6%)

rewrite76.0ms (0.3%)

simplify268.0ms (1.1%)

prune797.0ms (3.2%)

localize127.0ms (0.5%)

series1.4s (5.7%)

rewrite114.0ms (0.5%)

simplify354.0ms (1.4%)

prune1.4s (5.5%)

localize136.0ms (0.6%)

series1.4s (5.5%)

rewrite82.0ms (0.3%)

simplify312.0ms (1.3%)

prune1.5s (6%)

localize160.0ms (0.7%)

series1.1s (4.6%)

rewrite149.0ms (0.6%)

simplify407.0ms (1.7%)

prune1.4s (5.7%)

regimes6.7s (27.3%)

simplify5.0ms (0%)

end80.0ms (0.3%)

sample5.1s (20.8%)

Profiling