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)

sample2.7s (19.9%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.6s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify48.0ms (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

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)

localize58.0ms (0.4%)

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)))))
✓	0.7b	(sinh.f32 (/.f32 1 v))

series543.0ms (4.1%)

Counts

4 → 96

Calls

4 calls:

452.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
70.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
14.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
7.0ms	(sinh.f32 (/.f32 1 v))

rewrite93.0ms (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:

90.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
90.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
90.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
90.0ms	(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

simplify122.0ms (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

prune324.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	177	9	186
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	178	10	188

Error

0.1b

Counts

188 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2) (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (/.f32 1 (.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 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.3b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) (/.f32 (/.f32 1 v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
▶	0.3b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.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 sinTheta_i (.f32 (exp.f32 (/.f32 1 v)) sinTheta_O)) (.f32 v (exp.f32 (/.f32 1 v)))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (pow.f32 (cbrt.f32 cosTheta_i) 2) (.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)))
	0.5b	(.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))))))
	0.4b	(.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))))))))
	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 (.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 7569 to 4425 computations (41.5% saved)

localize56.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.f32 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 1 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.7b	(sinh.f32 (/.f32 1 v))

series841.0ms (6.3%)

Counts

2 → 84

Calls

2 calls:

611.0ms

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

230.0ms

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

rewrite87.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

184×	`add-sqr-sqrt_binary32`
183×	`associate-r_binary32`
171×	`add-log-exp_binary32`
171×	`log1p-expm1-u_binary32`
171×	`expm1-log1p-u_binary32`

Counts

2 → 72

Calls

2 calls:

85.0ms

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

85.0ms

(*.f32 (/.f32 1 v) (/.f32 1 (*.f32 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	18	61
1	378	55
2	4829	55
3	4969	55
0	0	0
1	0	0

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

693×	`times-frac_binary32`
428×	`associate-/l*_binary32`
408×	`associate-/r*_binary32`
313×	`associate-r_binary32`
206×	`associate-l_binary32`

Counts

156 → 109

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	243	7844
1	956	7336
2	5089	7336

prune427.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	184	6	190
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	190	10	200

Error

0.1b

Counts

200 → 10

Alt Table

Status	Error	Program
	0.4b	(.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))))))))
▶	0.3b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))))))))
	0.4b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.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))))))))
	0.3b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 cosTheta_i v) (/.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) (-.f32 (+.f32 (.f32 sinTheta_i (.f32 (exp.f32 (/.f32 1 v)) sinTheta_O)) (.f32 v (exp.f32 (/.f32 1 v)))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))
	0.4b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.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 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2) (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (/.f32 1 (.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 cosTheta_i (log.f32 (exp.f32 (/.f32 (pow.f32 v -2) (.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 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.f32 v (.f32 (.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))

Compiler

Compiled 9525 to 6333 computations (33.5% saved)

localize56.0ms (0.4%)

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 v) sinTheta_O))))
✓	0.3b	(.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))))
✓	0.4b	(.f32 (/.f32 1 v) (/.f32 1 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))))))
	0.7b	(sinh.f32 (/.f32 1 v))

series827.0ms (6.2%)

Counts

3 → 120

Calls

3 calls:

477.0ms

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

229.0ms

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

120.0ms

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

rewrite99.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

326×	`log1p-udef_binary32`
187×	`associate-r_binary32`
184×	`add-sqr-sqrt_binary32`
171×	`add-log-exp_binary32`
171×	`log1p-expm1-u_binary32`

Counts

3 → 95

Calls

3 calls:

97.0ms

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

96.0ms

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

96.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	84
1	379	78
2	4788	78
3	5479	78
0	0	0
1	0	0

simplify256.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

748×	`times-frac_binary32`
487×	`associate-/l*_binary32`
443×	`associate-/r*_binary32`
324×	`associate-r_binary32`
245×	`fma-def_binary32`

Counts

215 → 152

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	290	9322
1	1127	8776
2	5215	8776

prune530.0ms (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	184	10	194

Error

0.1b

Counts

194 → 10

Alt Table

Status	Error	Program
	0.4b	(.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))))))))
✓	0.3b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))))))))
	0.4b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.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))))))))
▶	0.3b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 cosTheta_i v) (/.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) (-.f32 (+.f32 (.f32 sinTheta_i (.f32 (exp.f32 (/.f32 1 v)) sinTheta_O)) (.f32 v (exp.f32 (/.f32 1 v)))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))
	0.4b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.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 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2) (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (/.f32 1 (.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 cosTheta_i (log.f32 (exp.f32 (/.f32 (pow.f32 v -2) (.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 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.f32 v (.f32 (.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))

Compiler

Compiled 10038 to 6702 computations (33.2% saved)

localize54.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series466.0ms (3.5%)

Counts

2 → 72

Calls

2 calls:

440.0ms	(/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
26.0ms	(*.f32 (/.f32 cosTheta_i v) (/.f32 1 v))

rewrite88.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

225×	`prod-diff_binary32`
196×	`times-frac_binary32`
180×	`add-sqr-sqrt_binary32`
168×	`add-log-exp_binary32`
168×	`log1p-expm1-u_binary32`

Counts

2 → 102

Calls

2 calls:

85.0ms	(/.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 1 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
85.0ms	(*.f32 (/.f32 cosTheta_i v) (/.f32 1 v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	36
1	365	36
2	4880	36
3	5397	36
0	0	0
1	0	0

simplify122.0ms (0.9%)

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 (3.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	202	11	213

Error

0.1b

Counts

213 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (/.f32 (/.f32 cosTheta_i v) 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 cosTheta_i v) (-.f32 (+.f32 (.f32 sinTheta_i (.f32 (exp.f32 (/.f32 1 v)) sinTheta_O)) (.f32 v (exp.f32 (/.f32 1 v)))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))
	0.4b	(.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))))))))
✓	0.3b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))))))))
	0.4b	(.f32 cosTheta_O (.f32 cosTheta_i (.f32 (/.f32 1 v) (/.f32 1 (.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 cosTheta_O (.f32 (/.f32 (pow.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) v)) (.f32 (sinh.f32 (/.f32 1 v)) 2))))
	0.4b	(.f32 cosTheta_O (.f32 (/.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 (/.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 (/.f32 cosTheta_i v) (/.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 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2) (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (/.f32 1 (.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 cosTheta_i (log.f32 (exp.f32 (/.f32 (pow.f32 v -2) (.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 7461 to 4254 computations (43% saved)

regimes4.5s (33.9%)

Accuracy

Total 0.3b remaining (68.5%)

Threshold costs 0.3b (68.5%)

Counts

388 → 1

Compiler

Compiled 103327 to 74075 computations (28.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	41
1	28	41
2	27	41

end415.0ms (3.1%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 654 to 466 computations (28.7% saved)

Details

analyze8.0ms (0.1%)

sample2.7s (19.9%)

simplify48.0ms (0.4%)

prune4.0ms (0%)

localize58.0ms (0.4%)

series543.0ms (4.1%)

rewrite93.0ms (0.7%)

simplify122.0ms (0.9%)

prune324.0ms (2.4%)

localize56.0ms (0.4%)

series841.0ms (6.3%)

rewrite87.0ms (0.7%)

simplify104.0ms (0.8%)

prune427.0ms (3.2%)

localize56.0ms (0.4%)

series827.0ms (6.2%)

rewrite99.0ms (0.7%)

simplify256.0ms (1.9%)

prune530.0ms (4%)

localize54.0ms (0.4%)

series466.0ms (3.5%)

rewrite88.0ms (0.7%)

simplify122.0ms (0.9%)

prune524.0ms (3.9%)

regimes4.5s (33.9%)

simplify2.0ms (0%)

end415.0ms (3.1%)

Profiling