Details

analyze5.8s (29.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample2.7s (14.2%)

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))
▶	0.5b	(.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)

localize59.0ms (0.3%)

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)))))
✓	0.9b	(sinh.f32 (/.f32 1 v))

series614.0ms (3.2%)

Counts

4 → 96

Calls

4 calls:

504.0ms	(/.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	(.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))

rewrite42.0ms (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:

16.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
11.0ms	(.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)
2.0ms	(sinh.f32 (/.f32 1 v))

simplify138.0ms (0.7%)

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

prune501.0ms (2.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	206	12	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	207	13	220

Error

0.1b

Counts

220 → 13

Alt Table

Status	Error	Program
	0.6b	(.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 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))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.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) v))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) 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 (.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 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.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 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 (.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))))))
	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))))))))
	0.5b	(.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 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 (/.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)))))))

Compiler

Compiled 9180 to 4981 computations (45.7% saved)

localize58.0ms (0.3%)

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 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)))))))
	0.9b	(sinh.f32 (/.f32 1 v))

series901.0ms (4.7%)

Counts

2 → 96

Calls

2 calls:

536.0ms

(*.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)))))))

365.0ms

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

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-exp-log_binary32`
61×	`add-cbrt-cube_binary32`
50×	`prod-exp_binary32`
30×	`div-exp_binary32`
28×	`cbrt-unprod_binary32`

Counts

2 → 96

Calls

2 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)))))))

11.0ms

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

simplify219.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

954×	`times-frac_binary32`
767×	`fma-def_binary32`
562×	`associate-/r*_binary32`
546×	`associate-/l*_binary32`
136×	`*-commutative_binary32`

Counts

192 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	12145
1	1332	10950
2	4927	10864
3	5515	10864

prune485.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	230	11	241

Error

0.1b

Counts

241 → 11

Alt Table

Status	Error	Program
	0.5b	(.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))))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) 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 (.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 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (/.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))) (cbrt.f32 cosTheta_i)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (.f32 (cbrt.f32 (/.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 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.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 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 (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))))))
	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))))))))
	0.5b	(.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))))))))

Compiler

Compiled 11251 to 6829 computations (39.3% saved)

localize65.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series386.0ms (2%)

Counts

4 → 100

Calls

4 calls:

358.0ms	(/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))
21.0ms	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
4.0ms	(/.f32 v (exp.f32 (/.f32 1 v)))
2.0ms	(exp.f32 (/.f32 1 v))

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`times-frac_binary32`
153×	`*-un-lft-identity_binary32`
111×	`add-sqr-sqrt_binary32`
83×	`add-cube-cbrt_binary32`
28×	`distribute-lft-out--_binary32`

Counts

4 → 188

Calls

4 calls:

19.0ms	(/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))
8.0ms	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
5.0ms	(/.f32 v (exp.f32 (/.f32 1 v)))
2.0ms	(exp.f32 (/.f32 1 v))

simplify255.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

806×	`times-frac_binary32`
564×	`associate-/l*_binary32`
317×	`associate-/l/_binary32`
218×	`fma-def_binary32`
176×	`associate-/r/_binary32`

Counts

288 → 333

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	672	18622
1	2020	17034
2	5543	17034

prune1.3s (6.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	434	7	441
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	439	13	452

Error

0.0b

Counts

452 → 13

Alt Table

Status	Error	Program
	0.7b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (pow.f32 (exp.f32 (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v))) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (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))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (expm1.f32 (log1p.f32 (exp.f32 (/.f32 1 v)))) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.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))))))))
	6.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (+.f32 1 (+.f32 (/.f32 1 v) (+.f32 (/.f32 1/2 (.f32 v v)) (/.f32 1/6 (pow.f32 v 3)))))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.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))))))))))
	0.5b	(.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) (expm1.f32 (log1p.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 cosTheta_i 1) (/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (pow.f32 (E.f32) (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.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 1 (sqrt.f32 v)) (/.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (+.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))) (/.f32 cosTheta_i (sqrt.f32 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 cosTheta_O (.f32 (/.f32 (/.f32 1 (sqrt.f32 v)) (sqrt.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (+.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (sqrt.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (+.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))

Compiler

Compiled 28184 to 16719 computations (40.7% saved)

localize79.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 v (exp.f32 (/.f32 1 v)))
✓	0.4b	(/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))
	0.8b	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
	0.8b	(exp.f32 (/.f32 1 v))

series157.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

157.0ms

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

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary32`
134×	`*-un-lft-identity_binary32`
92×	`add-sqr-sqrt_binary32`
64×	`add-cube-cbrt_binary32`
28×	`distribute-lft-out--_binary32`

Counts

1 → 118

Calls

1 calls:

25.0ms

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

simplify206.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-/r*_binary32`
403×	`times-frac_binary32`
283×	`associate-r_binary32`
280×	`associate-/l*_binary32`
245×	`associate-l_binary32`

Counts

154 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	440	15804
1	1376	14272
2	5005	14272

prune1.3s (6.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	403	1	404
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	405	12	417

Error

0.0b

Counts

417 → 12

Alt Table

Status	Error	Program
	0.7b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (pow.f32 (exp.f32 (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v))) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (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))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (expm1.f32 (log1p.f32 (exp.f32 (/.f32 1 v)))) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.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))))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (pow.f32 (E.f32) (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.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 1 (sqrt.f32 v)) (/.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (+.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))) (/.f32 cosTheta_i (sqrt.f32 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))))))))))
	0.5b	(.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) (expm1.f32 (log1p.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 cosTheta_i 1) (/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.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 (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 cosTheta_O (.f32 (/.f32 (/.f32 1 (sqrt.f32 v)) (sqrt.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (+.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (sqrt.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (+.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))

Compiler

Compiled 26441 to 17228 computations (34.8% saved)

regimes3.4s (17.6%)

Accuracy

Total 0.3b remaining (74.7%)

Threshold costs 0.3b (74.7%)

Counts

328 → 1

Compiler

Compiled 94802 to 64856 computations (31.6% 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

end427.0ms (2.2%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 723 to 498 computations (31.1% saved)

Details

analyze5.8s (29.9%)

sample2.7s (14.2%)

simplify51.0ms (0.3%)

prune5.0ms (0%)

localize59.0ms (0.3%)

series614.0ms (3.2%)

rewrite42.0ms (0.2%)

simplify138.0ms (0.7%)

prune501.0ms (2.6%)

localize58.0ms (0.3%)

series901.0ms (4.7%)

rewrite43.0ms (0.2%)

simplify219.0ms (1.1%)

prune485.0ms (2.5%)

localize65.0ms (0.3%)

series386.0ms (2%)

rewrite67.0ms (0.3%)

simplify255.0ms (1.3%)

prune1.3s (6.5%)

localize79.0ms (0.4%)

series157.0ms (0.8%)

rewrite57.0ms (0.3%)

simplify206.0ms (1.1%)

prune1.3s (6.9%)

regimes3.4s (17.6%)

simplify2.0ms (0%)

end427.0ms (2.2%)

Profiling