Details

analyze7.0ms (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)

sample2.4s (25.3%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.3s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify50.0ms (0.5%)

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

0.3b

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)

localize54.0ms (0.6%)

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))

series522.0ms (5.5%)

Counts

4 → 96

Calls

4 calls:

437.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
67.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite36.0ms (0.4%)

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)))))
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))

simplify134.0ms (1.4%)

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

prune388.0ms (4.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	209	9	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	10	220

Error

0.1b

Counts

220 → 10

Alt Table

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

Compiler

Compiled 9034 to 4869 computations (46.1% saved)

localize57.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series20.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

12.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
8.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-cbrt-cube_binary32`
12×	`add-exp-log_binary32`
7×	`pow1_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-sqr-sqrt_binary32`

Counts

2 → 44

Calls

2 calls:

6.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-def_binary32`
421×	`times-frac_binary32`
389×	`associate-/l*_binary32`
283×	`distribute-rgt-in_binary32`
280×	`distribute-lft-in_binary32`

Counts

56 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	812
1	268	701
2	893	701
3	2978	663
4	4643	663
5	5162	663

prune250.0ms (2.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Error

0.1b

Counts

129 → 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))))))))
	0.5b	(.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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.4b	(.f32 cosTheta_O (.f32 1/2 (/.f32 cosTheta_i (-.f32 (.f32 1/2 (.f32 (pow.f32 v 2) (.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (.f32 1/2 (/.f32 (.f32 (pow.f32 v 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (exp.f32 (/.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 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 v)) (sqrt.f32 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)) (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))))))
	0.6b	(.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 cosTheta_i v) (exp.f32 (+.f32 (log.f32 v) (+.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (*.f32 sinTheta_i sinTheta_O) 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 (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))))))))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 4229 to 2042 computations (51.7% saved)

localize62.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	0.3b	(-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.7b	(exp.f32 (/.f32 1 v))

series8.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

6.0ms	(-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))
2.0ms	(exp.f32 (/.f32 1 v))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary32`
55×	`*-un-lft-identity_binary32`
51×	`add-cube-cbrt_binary32`
47×	`times-frac_binary32`
39×	`prod-diff_binary32`

Counts

2 → 97

Calls

2 calls:

9.0ms	(-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))
2.0ms	(exp.f32 (/.f32 1 v))

simplify166.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-neg_binary32`
362×	`associate-/l/_binary32`
358×	`distribute-rgt-in_binary32`
309×	`distribute-lft-in_binary32`
264×	`times-frac_binary32`

Counts

113 → 128

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	143	3286
1	307	1839
2	697	1525
3	2171	1521
4	4530	1521
5	4240	1514
6	4861	1514
7	4982	1514
8	4844	1514

prune844.0ms (8.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	222	13	235

Error

0.0b

Counts

235 → 13

Alt Table

Status	Error	Program
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 v)) (sqrt.f32 v))) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 v) (+.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.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 v (-.f32 (pow.f32 (E.f32) (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))))
	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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.4b	(.f32 cosTheta_O (.f32 1/2 (/.f32 cosTheta_i (-.f32 (.f32 1/2 (.f32 (pow.f32 v 2) (.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (.f32 1/2 (/.f32 (.f32 (pow.f32 v 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (exp.f32 (/.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 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
▶	0.3b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))) (*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.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))))))
	0.6b	(.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))))))
	0.4b	(.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)))))))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 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 10074 to 5828 computations (42.1% saved)

localize63.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))
	0.7b	(exp.f32 (/.f32 1 v))

series12.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(*.f32 (*.f32 cosTheta_i cosTheta_O) (/.f32 1 v))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary32`
13×	`associate-r_binary32`
13×	`add-cbrt-cube_binary32`
12×	`prod-exp_binary32`
9×	`times-frac_binary32`

Counts

1 → 40

Calls

1 calls:

7.0ms

(*.f32 (*.f32 cosTheta_i cosTheta_O) (/.f32 1 v))

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

712×	`times-frac_binary32`
572×	`fabs-mul_binary32`
379×	`sqr-pow_binary32`
372×	`associate-/r*_binary32`
284×	`associate-/l/_binary32`

Counts

76 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	678
1	157	600
2	509	600
3	1136	600
4	2655	600
5	3014	600
6	3380	600
7	3885	600
8	4595	600
9	4925	600
10	5300	600

prune675.0ms (7.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	249	13	262

Error

0.0b

Counts

262 → 13

Alt Table

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

Compiler

Compiled 11021 to 6846 computations (37.9% saved)

regimes3.3s (34.3%)

Accuracy

Total 0.3b remaining (80.5%)

Threshold costs 0.3b (80.5%)

Counts

312 → 1

Compiler

Compiled 80386 to 56536 computations (29.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
6×	`+-commutative_binary32`
5×	`sub-neg_binary32`
5×	`neg-sub0_binary32`
5×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	42
1	38	42
2	50	42
3	58	42
4	63	42
5	65	42
6	64	42

end267.0ms (2.8%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 639 to 443 computations (30.7% saved)

Details

analyze7.0ms (0.1%)

sample2.4s (25.3%)

simplify50.0ms (0.5%)

prune4.0ms (0%)

localize54.0ms (0.6%)

series522.0ms (5.5%)

rewrite36.0ms (0.4%)

simplify134.0ms (1.4%)

prune388.0ms (4.1%)

localize57.0ms (0.6%)

series20.0ms (0.2%)

rewrite11.0ms (0.1%)

simplify63.0ms (0.7%)

prune250.0ms (2.6%)

localize62.0ms (0.7%)

series8.0ms (0.1%)

rewrite20.0ms (0.2%)

simplify166.0ms (1.7%)

prune844.0ms (8.9%)

localize63.0ms (0.7%)

series12.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify107.0ms (1.1%)

prune675.0ms (7.1%)

regimes3.3s (34.3%)

simplify3.0ms (0%)

end267.0ms (2.8%)

Profiling