Details

analyze7.0ms (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 (30.2%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.4s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify47.0ms (0.6%)

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 (0.1%)

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
▶	0.4b	(.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))))))
	0.5b	(/.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

▶

0.4b

(*.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))))))

0.5b

(/.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)

localize59.0ms (0.7%)

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)))))
✓	0.8b	(sinh.f32 (/.f32 1 v))

series524.0ms (6.5%)

Counts

4 → 96

Calls

4 calls:

435.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
71.0ms	(.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))

rewrite38.0ms (0.5%)

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))))
5.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

simplify130.0ms (1.6%)

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

prune403.0ms (5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	208	10	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	209	11	220

Error

0.1b

Counts

220 → 11

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.f32 v (/.f32 (cbrt.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 v) (exp.f32 (+.f32 (log.f32 v) (+.f32 (+.f32 (log.f32 (sinh.f32 (/.f32 1 v))) (log.f32 2)) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.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) (sqrt.f32 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 (/.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))))))
	24.0b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 v)) v) (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (sqrt.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))
	0.6b	(.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))))))
	0.5b	(.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 9060 to 4879 computations (46.1% saved)

localize57.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	0.8b	(sinh.f32 (/.f32 1 v))

series20.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

12.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
7.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-cbrt-cube_binary32`
12×	`add-exp-log_binary32`
7×	`pow1_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-sqr-sqrt_binary32`

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-def_binary32`
421×	`times-frac_binary32`
389×	`associate-/l*_binary32`
283×	`distribute-rgt-in_binary32`
280×	`distribute-lft-in_binary32`

Counts

56 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	812
1	268	701
2	893	701
3	2978	663
4	4643	663
5	5162	663

prune263.0ms (3.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	115	15	130

Error

0.1b

Counts

130 → 15

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.f32 v (/.f32 (cbrt.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 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.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) (sqrt.f32 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 (/.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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (+.f32 (+.f32 (log.f32 (sinh.f32 (/.f32 1 v))) (log.f32 2)) (log.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 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	24.0b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 v)) v) (/.f32 (/.f32 (sqrt.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) (/.f32 1 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 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))
	0.6b	(.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))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))) (cbrt.f32 (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))

Compiler

Compiled 4304 to 2115 computations (50.9% saved)

localize57.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))
	0.8b	(sinh.f32 (/.f32 1 v))

series13.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

13.0ms

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

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary32`
13×	`associate-r_binary32`
13×	`add-cbrt-cube_binary32`
12×	`prod-exp_binary32`
9×	`times-frac_binary32`

Counts

1 → 40

Calls

1 calls:

6.0ms

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

simplify107.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

712×	`times-frac_binary32`
572×	`fabs-mul_binary32`
379×	`sqr-pow_binary32`
372×	`associate-/r*_binary32`
284×	`associate-/l/_binary32`

Counts

76 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	678
1	157	600
2	509	600
3	1136	600
4	2655	600
5	3014	600
6	3380	600
7	3885	600
8	4595	600
9	4925	600
10	5300	600

prune297.0ms (3.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	139	7	146
Fresh	8	5	13
Picked	1	0	1
Done	1	0	1
Total	149	12	161

Error

0.0b

Counts

161 → 12

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) (/.f32 1 v))) (exp.f32 (+.f32 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (log.f32 v))))
	11.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (sqrt.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))) (sqrt.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.f32 v (/.f32 (cbrt.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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.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) (sqrt.f32 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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))) (.f32 (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 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))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 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) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))) (exp.f32 (log.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))) (cbrt.f32 (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (cbrt.f32 (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 5210 to 2835 computations (45.6% saved)

localize65.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (*.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v)))
	0.8b	(sinh.f32 (/.f32 1 v))

series40.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v)))
16.0ms	(.f32 (.f32 (*.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-r_binary32`
26×	`sqrt-prod_binary32`
18×	`times-frac_binary32`
18×	`*-un-lft-identity_binary32`
18×	`add-sqr-sqrt_binary32`

Counts

2 → 73

Calls

2 calls:

12.0ms	(.f32 (.f32 (*.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))
7.0ms	(.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v)))

simplify100.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

528×	`sqr-pow_binary32`
491×	`associate-/r*_binary32`
468×	`associate-/l/_binary32`
347×	`*-commutative_binary32`
323×	`associate-/r/_binary32`

Counts

121 → 107

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	87	1541
1	203	1364
2	760	1364
3	1706	1364
4	3724	1364
5	4641	1211
6	4469	1211
7	5104	1211

prune644.0ms (8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	156	13	169

Error

0.0b

Counts

169 → 13

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) (/.f32 1 v))) (exp.f32 (+.f32 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2)) (log.f32 v))))
	11.0b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (sqrt.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))) (sqrt.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.f32 v (/.f32 (cbrt.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 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.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) (sqrt.f32 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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))) (.f32 (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 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))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) cosTheta_O)) (cbrt.f32 (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) cosTheta_O))) (cbrt.f32 (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) cosTheta_O))) (sqrt.f32 (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 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) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 1 v))) (exp.f32 (log.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))) (cbrt.f32 (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (cbrt.f32 (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 6126 to 3481 computations (43.2% saved)

regimes2.3s (28.9%)

Accuracy

Total 0.3b remaining (79.9%)

Threshold costs 0.3b (79.9%)

Counts

246 → 1

Compiler

Compiled 63738 to 44960 computations (29.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	48
1	43	48
2	58	48
3	68	48
4	74	48
5	76	48
6	74	48

end298.0ms (3.7%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 706 to 498 computations (29.5% saved)

Details

analyze7.0ms (0.1%)

sample2.4s (30.2%)

simplify47.0ms (0.6%)

prune4.0ms (0.1%)

localize59.0ms (0.7%)

series524.0ms (6.5%)

rewrite38.0ms (0.5%)

simplify130.0ms (1.6%)

prune403.0ms (5%)

localize57.0ms (0.7%)

series20.0ms (0.2%)

rewrite10.0ms (0.1%)

simplify63.0ms (0.8%)

prune263.0ms (3.3%)

localize57.0ms (0.7%)

series13.0ms (0.2%)

rewrite9.0ms (0.1%)

simplify107.0ms (1.3%)

prune297.0ms (3.7%)

localize65.0ms (0.8%)

series40.0ms (0.5%)

rewrite24.0ms (0.3%)

simplify100.0ms (1.2%)

prune644.0ms (8%)

regimes2.3s (28.9%)

simplify4.0ms (0.1%)

end298.0ms (3.7%)

Profiling