Details

analyze8.0ms (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)

sample2.8s (18.5%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.7s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify51.0ms (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

0.4b

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)

localize62.0ms (0.4%)

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

series589.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

495.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
75.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite39.0ms (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:

13.0ms	(/.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))))
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

simplify142.0ms (0.9%)

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

prune414.0ms (2.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	205	13	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	206	14	220

Error

0.1b

Counts

220 → 14

Alt Table

Status	Error	Program
	0.5b	(.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 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 (.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)))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 1 (.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 cosTheta_i (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))))))))
	0.6b	(.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))))))))
	23.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 v)) v) (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (sqrt.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) (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))))))
	23.5b	(.f32 cosTheta_O (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 v (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (cbrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 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 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 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 9204 to 4989 computations (45.8% saved)

localize65.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series838.0ms (5.5%)

Counts

3 → 96

Calls

3 calls:

805.0ms

(/.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))))

23.0ms

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

9.0ms

(*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary32`
59×	`*-un-lft-identity_binary32`
54×	`add-sqr-sqrt_binary32`
54×	`add-cube-cbrt_binary32`
15×	`exp-sum_binary32`

Counts

3 → 128

Calls

3 calls:

15.0ms

(/.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))))

9.0ms

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

5.0ms

(*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))

simplify170.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

498×	`times-frac_binary32`
432×	`associate-/r*_binary32`
361×	`associate-/l*_binary32`
340×	`associate-r_binary32`
282×	`associate-l_binary32`

Counts

224 → 261

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	439	10605
1	1252	10186
2	5048	10186

prune680.0ms (4.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	275	7	282
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	285	11	296

Error

0.1b

Counts

296 → 11

Alt Table

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

Compiler

Compiled 12469 to 6836 computations (45.2% saved)

localize64.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series34.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

34.0ms

(/.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))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary32`
50×	`*-un-lft-identity_binary32`
50×	`add-sqr-sqrt_binary32`
50×	`add-cube-cbrt_binary32`
14×	`exp-sum_binary32`

Counts

1 → 89

Calls

1 calls:

15.0ms

(/.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))

simplify188.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

476×	`fma-def_binary32`
462×	`associate-/r*_binary32`
419×	`associate-/l/_binary32`
391×	`associate-*l/_binary32`
387×	`associate-/r/_binary32`

Counts

125 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	5402
1	459	5154
2	1667	5031
3	4711	5021
4	4993	5021
5	5004	5021

prune685.0ms (4.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	247	3	250
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	249	12	261

Error

0.1b

Counts

261 → 12

Alt Table

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

Compiler

Compiled 10162 to 6160 computations (39.4% saved)

localize73.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (/.f32 1 v))))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))
✓	0.3b	(/.f32 v (exp.f32 (/.f32 1 v)))
✓	0.3b	(/.f32 (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (/.f32 1 v))))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))) (/.f32 1 v))
✓	0.8b	(exp.f32 (/.f32 1 v))

series139.0ms (0.9%)

Counts

4 → 88

Calls

4 calls:

73.0ms	(/.f32 (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (/.f32 1 v))))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))) (/.f32 1 v))
59.0ms	(-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (/.f32 1 v))))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))
4.0ms	(/.f32 v (exp.f32 (/.f32 1 v)))
2.0ms	(exp.f32 (/.f32 1 v))

rewrite82.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`*-un-lft-identity_binary32`
159×	`times-frac_binary32`
122×	`add-sqr-sqrt_binary32`
92×	`add-cube-cbrt_binary32`
30×	`distribute-lft-out--_binary32`

Counts

4 → 213

Calls

4 calls:

20.0ms	(/.f32 (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (/.f32 1 v))))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))) (/.f32 1 v))
15.0ms	(-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (/.f32 1 v))))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))
4.0ms	(/.f32 v (exp.f32 (/.f32 1 v)))
2.0ms	(exp.f32 (/.f32 1 v))

simplify297.0ms (2%)

Algorithm

1×	egg-herbie

Rules

788×	`times-frac_binary32`
557×	`div-sub_binary32`
331×	`fma-neg_binary32`
188×	`exp-prod_binary32`
149×	`cancel-sign-sub-inv_binary32`

Counts

301 → 303

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	312	16104
1	762	11313
2	2570	10468
3	4154	10467
4	5213	10467

prune1.2s (7.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	410	1	411
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	411	12	423

Error

0.0b

Counts

423 → 12

Alt Table

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

Compiler

Compiled 21417 to 13528 computations (36.8% saved)

regimes6.1s (39.9%)

Accuracy

Total 0.3b remaining (77.6%)

Threshold costs 0.3b (77.6%)

Counts

486 → 1

Compiler

Compiled 149236 to 102539 computations (31.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
5×	`+-commutative_binary32`
4×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	35	50
2	43	50
3	49	50
4	53	50
5	54	50
6	53	50

end417.0ms (2.7%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 773 to 520 computations (32.7% saved)

Details

analyze8.0ms (0.1%)

sample2.8s (18.5%)

simplify51.0ms (0.3%)

prune5.0ms (0%)

localize62.0ms (0.4%)

series589.0ms (3.9%)

rewrite39.0ms (0.3%)

simplify142.0ms (0.9%)

prune414.0ms (2.7%)

localize65.0ms (0.4%)

series838.0ms (5.5%)

rewrite45.0ms (0.3%)

simplify170.0ms (1.1%)

prune680.0ms (4.5%)

localize64.0ms (0.4%)

series34.0ms (0.2%)

rewrite28.0ms (0.2%)

simplify188.0ms (1.2%)

prune685.0ms (4.5%)

localize73.0ms (0.5%)

series139.0ms (0.9%)

rewrite82.0ms (0.5%)

simplify297.0ms (2%)

prune1.2s (7.9%)

regimes6.1s (39.9%)

simplify4.0ms (0%)

end417.0ms (2.7%)

Profiling