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)

sample2.4s (15.9%)

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)

simplify47.0ms (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

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

0.4b

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))
▶	0.5b	(.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))))))

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 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)

localize52.0ms (0.3%)

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)))))
✓	0.8b	(sinh.f32 (/.f32 1 v))

series523.0ms (3.5%)

Counts

4 → 96

Calls

4 calls:

436.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
68.0ms	(.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))

rewrite36.0ms (0.2%)

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))

simplify133.0ms (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

prune681.0ms (4.5%)

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 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 (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)))))
	22.7b	(.f32 cosTheta_O (exp.f32 (log.f32 (/.f32 (/.f32 cosTheta_i v) (.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 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 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 1 v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.7b	(.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))))))
▶	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.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 (/.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 (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 v v))) (.f32 (/.f32 sinTheta_i (pow.f32 v 3)) (-.f32 (/.f32 (.f32 cosTheta_i sinTheta_O) (.f32 (exp.f32 (/.f32 1 v)) (pow.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))) (/.f32 (.f32 (exp.f32 (/.f32 1 v)) (.f32 cosTheta_i sinTheta_O)) (pow.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) 2))))))
	0.6b	(.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)))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.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))))))

Compiler

Compiled 9232 to 5019 computations (45.6% saved)

localize55.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series901.0ms (6%)

Counts

3 → 132

Calls

3 calls:

450.0ms

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

355.0ms

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

95.0ms

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

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-exp-log_binary32`
71×	`add-cbrt-cube_binary32`
56×	`prod-exp_binary32`
34×	`cbrt-unprod_binary32`
30×	`div-exp_binary32`

Counts

3 → 120

Calls

3 calls:

16.0ms

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

10.0ms

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

8.0ms

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

simplify196.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

607×	`associate-/l*_binary32`
599×	`associate-/r*_binary32`
457×	`associate-l_binary32`
240×	`associate-*r/_binary32`
237×	`fma-def_binary32`

Counts

252 → 223

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	458	14334
1	1529	13042
2	5261	13042

prune656.0ms (4.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	238	6	244
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	242	16	258

Error

0.1b

Counts

258 → 16

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))) (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.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 (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)))))
	22.7b	(.f32 cosTheta_O (exp.f32 (log.f32 (/.f32 (/.f32 cosTheta_i v) (.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 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 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 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 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (expm1.f32 (log1p.f32 (.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)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.7b	(.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)))))
▶	0.4b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.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 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) v)) (/.f32 (cbrt.f32 cosTheta_i) (.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) (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 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))))
	0.6b	(.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 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Compiler

Compiled 12405 to 7531 computations (39.3% saved)

localize55.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))
✓	0.5b	(.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))
✓	0.5b	(*.f32 (/.f32 1 v) (/.f32 1 v))
	0.8b	(sinh.f32 (/.f32 1 v))

series799.0ms (5.3%)

Counts

3 → 108

Calls

3 calls:

475.0ms

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

321.0ms

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

2.0ms

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

rewrite84.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

350×	`add-exp-log_binary32`
202×	`prod-exp_binary32`
134×	`div-exp_binary32`
126×	`add-cbrt-cube_binary32`
60×	`add-sqr-sqrt_binary32`

Counts

3 → 242

Calls

3 calls:

19.0ms

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

13.0ms

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

7.0ms

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

simplify295.0ms (2%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary32`
845×	`fma-def_binary32`
540×	`associate-/l*_binary32`
501×	`associate-/r*_binary32`
141×	`*-commutative_binary32`

Counts

350 → 341

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	479	15268
1	1407	13186
2	4796	12966
3	5428	12966

prune982.0ms (6.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	354	8	362
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	364	14	378

Error

0.1b

Counts

378 → 14

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 (/.f32 1 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 (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 1 v))) (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 1 v)))) (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 1 v)))) (/.f32 cosTheta_i (.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) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))))
	0.7b	(.f32 cosTheta_O (.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (expm1.f32 (log1p.f32 (.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 (/.f32 1 v) (/.f32 1 v)) (.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.7b	(.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 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 (/.f32 1 v))) (.f32 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 (/.f32 1 v)))) (/.f32 cosTheta_i (.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 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))))
	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 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (cbrt.f32 cosTheta_i) (*.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))))))

Compiler

Compiled 17234 to 10545 computations (38.8% saved)

localize63.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))))
	0.5b	(*.f32 (/.f32 1 v) (/.f32 1 v))
✓	0.8b	(exp.f32 (/.f32 1 v))
✓	0.8b	(exp.f32 (/.f32 -1 v))

series343.0ms (2.3%)

Counts

3 → 64

Calls

3 calls:

338.0ms

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

2.0ms

(exp.f32 (/.f32 -1 v))

2.0ms

(exp.f32 (/.f32 1 v))

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

211×	`add-exp-log_binary32`
116×	`prod-exp_binary32`
82×	`div-exp_binary32`
72×	`add-cbrt-cube_binary32`
32×	`cbrt-unprod_binary32`

Counts

3 → 144

Calls

3 calls:

20.0ms

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

2.0ms

(exp.f32 (/.f32 -1 v))

2.0ms

(exp.f32 (/.f32 1 v))

simplify186.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary32`
500×	`associate-l_binary32`
477×	`associate-r_binary32`
464×	`fma-def_binary32`
334×	`associate-/l*_binary32`

Counts

208 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	388	9654
1	1054	8075
2	4731	7963
3	5069	7963

prune902.0ms (6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	324	3	327
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	327	14	341

Error

0.1b

Counts

341 → 14

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))))))))
	0.4b	(.f32 cosTheta_O (.f32 (exp.f32 (log.f32 (.f32 (/.f32 1 v) (/.f32 1 v)))) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (-.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 (sinh.f32 (/.f32 1 v)) 2) 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))))))
	0.6b	(.f32 cosTheta_O (.f32 (.f32 (.f32 (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 1 v))) (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 1 v)))) (cbrt.f32 (.f32 (/.f32 1 v) (/.f32 1 v)))) (/.f32 cosTheta_i (.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) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))))
	0.7b	(.f32 cosTheta_O (.f32 (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (/.f32 cosTheta_i (.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 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (-.f32 (pow.f32 (E.f32) (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))))
	0.8b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (-.f32 (pow.f32 (exp.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (/.f32 1 (cbrt.f32 v))) (exp.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))))))
	0.7b	(.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 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 (/.f32 1 v))) (.f32 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 (/.f32 1 v)))) (/.f32 cosTheta_i (.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) (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 1 v) (/.f32 1 v)) (/.f32 cosTheta_i (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))))))))

Compiler

Compiled 13962 to 8393 computations (39.9% saved)

regimes5.1s (33.8%)

Accuracy

Total 0.3b remaining (79.8%)

Threshold costs 0.3b (79.8%)

Counts

424 → 1

Compiler

Compiled 113522 to 81472 computations (28.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	46
1	31	46
2	34	46
3	36	46
4	37	46
5	36	46

end436.0ms (2.9%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 786 to 574 computations (27% saved)

Details

analyze8.0ms (0.1%)

sample2.4s (15.9%)

simplify47.0ms (0.3%)

prune4.0ms (0%)

localize52.0ms (0.3%)

series523.0ms (3.5%)

rewrite36.0ms (0.2%)

simplify133.0ms (0.9%)

prune681.0ms (4.5%)

localize55.0ms (0.4%)

series901.0ms (6%)

rewrite51.0ms (0.3%)

simplify196.0ms (1.3%)

prune656.0ms (4.4%)

localize55.0ms (0.4%)

series799.0ms (5.3%)

rewrite84.0ms (0.6%)

simplify295.0ms (2%)

prune982.0ms (6.5%)

localize63.0ms (0.4%)

series343.0ms (2.3%)

rewrite53.0ms (0.4%)

simplify186.0ms (1.2%)

prune902.0ms (6%)

regimes5.1s (33.8%)

simplify3.0ms (0%)

end436.0ms (2.9%)

Profiling