Details

analyze7.0ms (0%)

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 (1.6%)

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%)

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 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%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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))

series433.0ms (0.3%)

Counts

4 → 96

Calls

4 calls:

353.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
63.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
11.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite35.0ms (0%)

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:

11.0ms	(/.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))

simplify127.0ms (0.1%)

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

prune415.0ms (0.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	204	14	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	205	15	220

Error

0.1b

Counts

220 → 15

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)))))
	0.5b	(.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 v 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 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 (.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 (.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))))))))
	0.4b	(.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 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 cosTheta_i v) (exp.f32 (+.f32 (log.f32 v) (+.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (.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)))))) (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))))))) (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))))))))
	0.5b	(.f32 cosTheta_O (/.f32 cosTheta_i (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 (.f32 v v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) 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 (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)))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 v (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 2 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))) 2)))
▶	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))))))

Compiler

Compiled 9324 to 5065 computations (45.7% saved)

localize51.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.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)))))
✓	0.4b	(/.f32 (/.f32 1 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))

series492.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

333.0ms

(*.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)))))

158.0ms

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

rewrite159.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-exp-log_binary32`
88×	`add-cbrt-cube_binary32`
67×	`div-exp_binary32`
63×	`times-frac_binary32`
62×	`prod-exp_binary32`

Counts

2 → 146

Calls

2 calls:

19.0ms

(*.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)))))

9.0ms

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

simplify302.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

922×	`times-frac_binary32`
651×	`associate-/r*_binary32`
583×	`associate-/l*_binary32`
161×	`fma-def_binary32`
146×	`*-commutative_binary32`

Counts

230 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	438	13239
1	1477	11510
2	5054	11510

prune714.0ms (0.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	296	6	302
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	303	14	317

Error

0.1b

Counts

317 → 14

Alt Table

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

Compiler

Compiled 13697 to 7882 computations (42.5% saved)

localize60.0ms (0%)

Local error

Found 4 expressions with local error:

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

series524.0ms (0.3%)

Counts

3 → 76

Calls

3 calls:

350.0ms

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

163.0ms

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

10.0ms

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

rewrite1.3s (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

8047×	`times-frac_binary32`
3106×	`sqrt-prod_binary32`
2813×	`add-sqr-sqrt_binary32`
2744×	`*-un-lft-identity_binary32`
2740×	`add-cube-cbrt_binary32`

Counts

3 → 2403

Calls

3 calls:

261.0ms

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

35.0ms

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

7.0ms

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

simplify2.5s (1.7%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-/r/_binary32`
357×	`*-commutative_binary32`
289×	`associate-*r/_binary32`
251×	`associate-*l/_binary32`
180×	`associate-+r+_binary32`

Counts

2479 → 2853

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1208	132374
1	3722	131151
2	5003	131151

prune10.4s (6.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	2867	7	2874
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	2875	13	2888

Error

0.1b

Counts

2888 → 13

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i v) (/.f32 (/.f32 (sqrt.f32 (/.f32 1 v)) (sqrt.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (sqrt.f32 (/.f32 1 v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (sqrt.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (sqrt.f32 (/.f32 1 v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i v) (exp.f32 (log.f32 (/.f32 (sqrt.f32 (/.f32 1 v)) (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (sqrt.f32 (/.f32 1 v)) (.f32 2 (sinh.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 (.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 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 cosTheta_i v) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 1 (/.f32 (sqrt.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) 2)))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 (sqrt.f32 (cbrt.f32 (/.f32 1 v))) (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i v) (/.f32 (sqrt.f32 (/.f32 1 v)) (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (exp.f32 (log.f32 (/.f32 (sqrt.f32 (/.f32 1 v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))))
	0.5b	(.f32 cosTheta_O (/.f32 cosTheta_i (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 (.f32 v v) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 1 (/.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 v))) 2)))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (sqrt.f32 (sqrt.f32 (/.f32 1 v))) (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v))) (.f32 (sinh.f32 (/.f32 1 v)) 2))) (/.f32 (cbrt.f32 (/.f32 1 v)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.4b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 cosTheta_i v) (.f32 (fabs.f32 (cbrt.f32 (/.f32 1 v))) (/.f32 (sqrt.f32 (/.f32 1 v)) (.f32 2 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))))) (/.f32 (sqrt.f32 (cbrt.f32 (/.f32 1 v))) (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 2))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i v) (exp.f32 (-.f32 (log.f32 (/.f32 1 v)) (+.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2)) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
▶	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i v) (/.f32 (/.f32 (sqrt.f32 (/.f32 1 v)) (/.f32 1 (/.f32 (sqrt.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) 2))) (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (sqrt.f32 (cbrt.f32 (/.f32 1 v))) (sinh.f32 (/.f32 1 v)))))))

Compiler

Compiled 155953 to 86064 computations (44.8% saved)

localize83.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (sqrt.f32 (cbrt.f32 (/.f32 1 v))) (sinh.f32 (/.f32 1 v)))
✓	0.3b	(/.f32 (/.f32 (sqrt.f32 (/.f32 1 v)) (/.f32 1 (/.f32 (sqrt.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) 2))) (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (sqrt.f32 (cbrt.f32 (/.f32 1 v))) (sinh.f32 (/.f32 1 v)))))
✓	0.5b	(*.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))
	0.9b	(sinh.f32 (/.f32 1 v))

series248.0ms (0.2%)

Counts

3 → 56

Calls

3 calls:

174.0ms

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

39.0ms

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

34.0ms

(/.f32 (sqrt.f32 (cbrt.f32 (/.f32 1 v))) (sinh.f32 (/.f32 1 v)))

rewrite2.2min (86.4%)

Algorithm

1×	rewrite-expression-head

Rules

1049568×	`times-frac_binary32`
381899×	`add-sqr-sqrt_binary32`
381869×	`*-un-lft-identity_binary32`
381859×	`add-cube-cbrt_binary32`
282976×	`sqrt-prod_binary32`

Calls

3 calls:

3.8s

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

11.0ms

(/.f32 (sqrt.f32 (cbrt.f32 (/.f32 1 v))) (sinh.f32 (/.f32 1 v)))

10.0ms

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

Details

analyze7.0ms (0%)

sample2.4s (1.6%)

simplify47.0ms (0%)

prune4.0ms (0%)

localize52.0ms (0%)

series433.0ms (0.3%)

rewrite35.0ms (0%)

simplify127.0ms (0.1%)

prune415.0ms (0.3%)

localize51.0ms (0%)

series492.0ms (0.3%)

rewrite159.0ms (0.1%)

simplify302.0ms (0.2%)

prune714.0ms (0.5%)

localize60.0ms (0%)

series524.0ms (0.3%)

rewrite1.3s (0.9%)

simplify2.5s (1.7%)

prune10.4s (6.9%)

localize83.0ms (0.1%)

series248.0ms (0.2%)

rewrite2.2min (86.4%)

Profiling