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)

sample2.3s (18.2%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify47.0ms (0.4%)

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 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

▶

0.5b

(*.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)

localize52.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series523.0ms (4.2%)

Counts

4 → 96

Calls

4 calls:

438.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
65.0ms	(.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)
7.0ms	(sinh.f32 (/.f32 1 v))

rewrite91.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary32`
165×	`add-log-exp_binary32`
165×	`log1p-expm1-u_binary32`
165×	`expm1-log1p-u_binary32`
163×	`add-cbrt-cube_binary32`

Counts

4 → 139

Calls

4 calls:

88.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
88.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
88.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
88.0ms	(sinh.f32 (/.f32 1 v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	65
1	359	65
2	4813	65
3	4981	65
0	0	0
1	0	0

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

445×	`times-frac_binary32`
293×	`associate-/l*_binary32`
274×	`associate-r_binary32`
265×	`unswap-sqr_binary32`
262×	`associate-/r*_binary32`

Counts

235 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	6012
1	811	5668
2	4214	5630
3	5028	5630

prune375.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	174	12	186
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	175	13	188

Error

0.1b

Counts

188 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (pow.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) 3) 1/3)))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 1 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 1 v) (/.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 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (.f32 v (.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 (exp.f32 (log.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 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) 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))))))))
	0.6b	(.f32 cosTheta_O (pow.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)))))) 3))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 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))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (exp.f32 (log1p.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) 1)))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (sqrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (/.f32 (/.f32 1 v) (sqrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))))

Compiler

Compiled 7729 to 4545 computations (41.2% saved)

localize50.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.4b	(/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓	0.4b	(.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i 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))

series975.0ms (7.8%)

Counts

2 → 96

Calls

2 calls:

552.0ms

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

423.0ms

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

rewrite50.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

178×	`add-sqr-sqrt_binary32`
166×	`add-log-exp_binary32`
166×	`log1p-expm1-u_binary32`
166×	`expm1-log1p-u_binary32`
164×	`add-cbrt-cube_binary32`

Counts

2 → 123

Calls

2 calls:

47.0ms

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

47.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	55
1	362	55
2	4996	55
0	0	0
1	0	0

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

689×	`times-frac_binary32`
416×	`associate-/l*_binary32`
390×	`associate-/r*_binary32`
287×	`associate-r_binary32`
202×	`associate-l_binary32`

Counts

219 → 164

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	254	8498
1	949	7932
2	5016	7932

prune635.0ms (5.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	237	8	245
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	243	15	258

Error

0.1b

Counts

258 → 15

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 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 cosTheta_i v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v)))
	24.0b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (pow.f32 (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2)) (/.f32 (sqrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (.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 (pow.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 1 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 1 v) (.f32 (/.f32 cosTheta_i (sinh.f32 (/.f32 1 v))) (/.f32 (/.f32 1 v) (.f32 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 (.f32 v (.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 (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 1 v) (.f32 (/.f32 cosTheta_i (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (/.f32 1 v) (sqrt.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 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (.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 v) (.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2)) (/.f32 (/.f32 1 v) (cbrt.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 1 v) (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.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) (pow.f32 (pow.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) 3) 1/3)))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (exp.f32 (log1p.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) 1)))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Compiler

Compiled 10968 to 6661 computations (39.3% saved)

localize51.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 cosTheta_i (sinh.f32 (/.f32 1 v)))
✓	0.4b	(.f32 (/.f32 1 v) (.f32 (/.f32 cosTheta_i (sinh.f32 (/.f32 1 v))) (/.f32 (/.f32 1 v) (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
✓	0.4b	(.f32 (/.f32 cosTheta_i (sinh.f32 (/.f32 1 v))) (/.f32 (/.f32 1 v) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
	0.8b	(sinh.f32 (/.f32 1 v))

series879.0ms (7%)

Counts

3 → 120

Calls

3 calls:

496.0ms

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

329.0ms

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

54.0ms

(/.f32 cosTheta_i (sinh.f32 (/.f32 1 v)))

rewrite102.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

183×	`add-sqr-sqrt_binary32`
170×	`add-log-exp_binary32`
169×	`log1p-expm1-u_binary32`
169×	`expm1-log1p-u_binary32`
168×	`add-cbrt-cube_binary32`

Counts

3 → 151

Calls

3 calls:

98.0ms

(/.f32 cosTheta_i (sinh.f32 (/.f32 1 v)))

98.0ms

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

98.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	366	64
2	4880	64
3	5029	64
0	0	0
1	0	0

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

693×	`times-frac_binary32`
420×	`associate-/l*_binary32`
396×	`associate-/r*_binary32`
287×	`associate-r_binary32`
226×	`fma-neg_binary32`

Counts

271 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	8996
1	1010	8390
2	4948	8382
3	5116	8382

prune634.0ms (5.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	229	6	235
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	238	12	250

Error

0.1b

Counts

250 → 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))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 cosTheta_i (.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2) (cbrt.f32 (sinh.f32 (/.f32 1 v))))) (/.f32 (/.f32 1 v) (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (exp.f32 (log1p.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) 1)))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i (sinh.f32 (/.f32 1 v)))) 3) (/.f32 (/.f32 1 v) (.f32 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 (.f32 v (.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 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (pow.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 (.f32 (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) v) (sinh.f32 (/.f32 1 v))))) 3)))
▶	0.4b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (sinh.f32 (/.f32 1 v)) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 cosTheta_i (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)) (/.f32 (/.f32 1 v) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 1 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 v) (/.f32 (/.f32 (/.f32 cosTheta_i (.f32 (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v)) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) (cbrt.f32 (sinh.f32 (/.f32 1 v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Compiler

Compiled 10407 to 6622 computations (36.4% saved)

localize51.0ms (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 (/.f32 cosTheta_i v) (/.f32 1 v))
✓	0.3b	(/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (sinh.f32 (/.f32 1 v)) (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.8b	(sinh.f32 (/.f32 1 v))

series491.0ms (3.9%)

Counts

2 → 72

Calls

2 calls:

462.0ms	(/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (sinh.f32 (/.f32 1 v)) (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
29.0ms	(*.f32 (/.f32 cosTheta_i v) (/.f32 1 v))

rewrite91.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

184×	`times-frac_binary32`
182×	`add-sqr-sqrt_binary32`
169×	`add-log-exp_binary32`
168×	`log1p-expm1-u_binary32`
168×	`expm1-log1p-u_binary32`

Counts

2 → 102

Calls

2 calls:

88.0ms	(*.f32 (/.f32 cosTheta_i v) (/.f32 1 v))
88.0ms	(/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (sinh.f32 (/.f32 1 v)) (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	36
1	365	36
2	4892	36
3	5145	36
0	0	0
1	0	0

simplify130.0ms (1%)

Algorithm

1×	egg-herbie

Rules

384×	`times-frac_binary32`
233×	`unswap-sqr_binary32`
232×	`associate-/l*_binary32`
231×	`associate-r_binary32`
230×	`cancel-sign-sub-inv_binary32`

Counts

174 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	4486
1	575	4190
2	3259	3928
3	4858	3928
4	5110	3928

prune524.0ms (4.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	202	13	215

Error

0.1b

Counts

215 → 13

Alt Table

Status	Error	Program
✓	0.4b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (sinh.f32 (/.f32 1 v)) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (pow.f32 (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 cosTheta_i v) (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (exp.f32 (log1p.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))) 1)))
	0.4b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (pow.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i (sinh.f32 (/.f32 1 v)))) 3) (/.f32 (/.f32 1 v) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 1 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 v) (pow.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 (.f32 (.f32 2 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) v) (sinh.f32 (/.f32 1 v))))) 3)))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 cosTheta_i (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)) (/.f32 (/.f32 1 v) (.f32 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))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (/.f32 (/.f32 cosTheta_i (.f32 (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v)) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) (cbrt.f32 (sinh.f32 (/.f32 1 v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (log.f32 (.f32 v (.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 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Compiler

Compiled 7497 to 4294 computations (42.7% saved)

regimes3.8s (30.3%)

Accuracy

Total 0.3b remaining (76%)

Threshold costs 0.3b (76%)

Counts

373 → 1

Compiler

Compiled 91330 to 64904 computations (28.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	26	38
2	25	38

end273.0ms (2.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 612 to 444 computations (27.5% saved)

Details

analyze7.0ms (0.1%)

sample2.3s (18.2%)

simplify47.0ms (0.4%)

prune5.0ms (0%)

localize52.0ms (0.4%)

series523.0ms (4.2%)

rewrite91.0ms (0.7%)

simplify117.0ms (0.9%)

prune375.0ms (3%)

localize50.0ms (0.4%)

series975.0ms (7.8%)

rewrite50.0ms (0.4%)

simplify110.0ms (0.9%)

prune635.0ms (5.1%)

localize51.0ms (0.4%)

series879.0ms (7%)

rewrite102.0ms (0.8%)

simplify164.0ms (1.3%)

prune634.0ms (5.1%)

localize51.0ms (0.4%)

series491.0ms (3.9%)

rewrite91.0ms (0.7%)

simplify130.0ms (1%)

prune524.0ms (4.2%)

regimes3.8s (30.3%)

simplify2.0ms (0%)

end273.0ms (2.2%)

Profiling