Details

analyze9.0ms (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 (22.1%)

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)

simplify46.0ms (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 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))))))
	0.4b	(/.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))

Status

Error

Program

▶

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))))))

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 154 to 104 computations (32.5% saved)

localize56.0ms (0.5%)

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

series551.0ms (4.5%)

Counts

4 → 96

Calls

4 calls:

463.0ms	(/.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))))
13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite36.0ms (0.3%)

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:

13.0ms	(/.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 (1.1%)

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

prune436.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	209	9	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	10	220

Error

0.1b

Counts

220 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.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))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 cosTheta_i (cbrt.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 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))))))))
	0.4b	(.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))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.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 (.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))))))
▶	0.3b	(.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))))))
	0.4b	(.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))))))
	0.4b	(.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 8958 to 4833 computations (46% saved)

localize57.0ms (0.5%)

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))))
	0.8b	(sinh.f32 (/.f32 1 v))

series648.0ms (5.3%)

Counts

2 → 84

Calls

2 calls:

449.0ms

(*.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)))))

197.0ms

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

rewrite51.0ms (0.4%)

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:

18.0ms

(*.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)))))

10.0ms

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

simplify175.0ms (1.4%)

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

prune619.0ms (5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	297	5	302
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	301	11	312

Error

0.1b

Counts

312 → 11

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)))))
	0.3b	(.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))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (.f32 (/.f32 cosTheta_i (cbrt.f32 v)) (/.f32 (/.f32 1 v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))
▶	0.3b	(.f32 cosTheta_O (/.f32 (.f32 cosTheta_i (/.f32 1 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 (/.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 cosTheta_i (cbrt.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 v (.f32 (.f32 (expm1.f32 (log1p.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))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.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 (/.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 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 (cbrt.f32 v))))))
	0.4b	(.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 13439 to 7718 computations (42.6% saved)

localize56.0ms (0.5%)

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 1 v))
✓	0.3b	(/.f32 (.f32 cosTheta_i (/.f32 1 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))

series458.0ms (3.7%)

Counts

2 → 72

Calls

2 calls:

452.0ms	(/.f32 (.f32 cosTheta_i (/.f32 1 v)) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
6.0ms	(*.f32 cosTheta_i (/.f32 1 v))

rewrite32.0ms (0.3%)

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 → 88

Calls

2 calls:

13.0ms	(/.f32 (.f32 cosTheta_i (/.f32 1 v)) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))
5.0ms	(*.f32 cosTheta_i (/.f32 1 v))

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

822×	`times-frac_binary32`
463×	`fma-def_binary32`
451×	`associate-/l*_binary32`
438×	`associate-/r*_binary32`
423×	`associate-r_binary32`

Counts

160 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	6884
1	952	5960
2	4854	5886
3	5233	5886

prune396.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	191	11	202

Error

0.1b

Counts

202 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (/.f32 (.f32 (.f32 cosTheta_i (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 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 (/.f32 cosTheta_i v) (/.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 (cbrt.f32 v))))))
▶	0.3b	(.f32 cosTheta_O (/.f32 (log1p.f32 (expm1.f32 (.f32 cosTheta_i (/.f32 1 v)))) (.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 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (.f32 (/.f32 cosTheta_i (cbrt.f32 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 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 cosTheta_i (cbrt.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 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))))))))
	0.4b	(.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))))))
	0.4b	(/.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))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.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 (/.f32 1 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))))))
	0.4b	(.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 8231 to 4866 computations (40.9% saved)

localize65.0ms (0.5%)

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 1 v))
✓	0.3b	(/.f32 (log1p.f32 (expm1.f32 (.f32 cosTheta_i (/.f32 1 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))

series577.0ms (4.7%)

Counts

1 → 48

Calls

1 calls:

577.0ms

(/.f32 (log1p.f32 (expm1.f32 (*.f32 cosTheta_i (/.f32 1 v)))) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-cbrt-cube_binary32`
13×	`add-exp-log_binary32`
6×	`cbrt-unprod_binary32`
6×	`prod-exp_binary32`
4×	`cbrt-undiv_binary32`

Counts

1 → 28

Calls

1 calls:

11.0ms

(/.f32 (log1p.f32 (expm1.f32 (*.f32 cosTheta_i (/.f32 1 v)))) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

524×	`times-frac_binary32`
367×	`associate-r_binary32`
321×	`associate-/r*_binary32`
296×	`associate-l_binary32`
295×	`associate-/l*_binary32`

Counts

76 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	5480
1	798	4920
2	4443	4886
3	5169	4886

prune411.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	169	11	180

Error

0.0b

Counts

180 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (/.f32 (.f32 (.f32 cosTheta_i (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 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 (/.f32 cosTheta_i v) (/.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 1 (cbrt.f32 v))))))
	0.4b	(.f32 cosTheta_O (/.f32 (.f32 cosTheta_i (/.f32 1 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))))))
	0.3b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (log1p.f32 (expm1.f32 (.f32 cosTheta_i (/.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 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 cosTheta_i (cbrt.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 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))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (log1p.f32 (expm1.f32 (.f32 cosTheta_i (/.f32 1 v)))) (.f32 v (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
	0.4b	(/.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))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.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 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (.f32 (/.f32 cosTheta_i (cbrt.f32 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 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 7307 to 4505 computations (38.3% saved)

regimes4.2s (34.2%)

Accuracy

Total 0.3b remaining (70.3%)

Threshold costs 0.3b (70.3%)

Counts

371 → 1

Compiler

Compiled 96114 to 67720 computations (29.5% 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	19	38
1	27	38
2	26	38

end257.0ms (2.1%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 569 to 403 computations (29.2% saved)

Details

analyze9.0ms (0.1%)

sample2.7s (22.1%)

simplify46.0ms (0.4%)

prune4.0ms (0%)

localize56.0ms (0.5%)

series551.0ms (4.5%)

rewrite36.0ms (0.3%)

simplify133.0ms (1.1%)

prune436.0ms (3.5%)

localize57.0ms (0.5%)

series648.0ms (5.3%)

rewrite51.0ms (0.4%)

simplify175.0ms (1.4%)

prune619.0ms (5%)

localize56.0ms (0.5%)

series458.0ms (3.7%)

rewrite32.0ms (0.3%)

simplify141.0ms (1.1%)

prune396.0ms (3.2%)

localize65.0ms (0.5%)

series577.0ms (4.7%)

rewrite15.0ms (0.1%)

simplify156.0ms (1.3%)

prune411.0ms (3.3%)

regimes4.2s (34.2%)

simplify2.0ms (0%)

end257.0ms (2.1%)

Profiling