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)

sample119.0ms (1.1%)

Algorithm

1×

intervals

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

28.0ms	256×	body	128	valid
13.0ms	256×	pre	128	true

Compiler

Compiled 98 to 72 computations (26.5% saved)

simplify49.0ms (0.5%)

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)

localize55.0ms (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 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)))))
✓	0.8b	(sinh.f32 (/.f32 1 v))

series751.0ms (7.1%)

Counts

4 → 96

Calls

4 calls:

668.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
66.0ms	(.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)
5.0ms	(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:

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))))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

simplify131.0ms (1.2%)

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

prune409.0ms (3.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	210	8	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	211	9	220

Error

0.1b

Counts

220 → 9

Alt Table

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

Compiler

Compiled 8888 to 4785 computations (46.2% saved)

localize55.0ms (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 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)))))))
	0.8b	(sinh.f32 (/.f32 1 v))

series496.0ms (4.7%)

Counts

2 → 84

Calls

2 calls:

427.0ms

(*.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)))))))

68.0ms

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

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-exp-log_binary32`
56×	`add-cbrt-cube_binary32`
50×	`prod-exp_binary32`
28×	`cbrt-unprod_binary32`
26×	`div-exp_binary32`

Counts

2 → 92

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)))))))

8.0ms

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

simplify172.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

670×	`times-frac_binary32`
546×	`fma-def_binary32`
409×	`associate-l_binary32`
399×	`associate-/r*_binary32`
394×	`associate-/l*_binary32`

Counts

176 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	354	9257
1	1137	8255
2	4820	8191
3	5223	8191

prune444.0ms (4.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	213	4	217
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	216	10	226

Error

0.1b

Counts

226 → 10

Alt Table

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

Compiler

Compiled 9580 to 5664 computations (40.9% saved)

localize59.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series19.0ms (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 (0.6%)

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

prune244.0ms (2.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Error

0.0b

Counts

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

Compiler

Compiled 4189 to 2040 computations (51.3% saved)

localize62.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.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 (exp.f32 (log.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
✓	0.6b	(exp.f32 (log.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.8b	(sinh.f32 (/.f32 1 v))

series500.0ms (4.7%)

Counts

2 → 84

Calls

2 calls:

434.0ms

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

65.0ms

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

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary32`
28×	`times-frac_binary32`
20×	`add-exp-log_binary32`
20×	`*-un-lft-identity_binary32`
18×	`add-cube-cbrt_binary32`

Counts

2 → 81

Calls

2 calls:

19.0ms

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

9.0ms

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

simplify171.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

538×	`times-frac_binary32`
407×	`associate-r_binary32`
384×	`associate-/l*_binary32`
311×	`associate-/r*_binary32`
294×	`associate-l_binary32`

Counts

165 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	339	8462
1	1070	7932
2	4890	7924
3	5017	7924

prune563.0ms (5.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	231	13	244

Error

0.0b

Counts

244 → 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 (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 cosTheta_O (cbrt.f32 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
✓	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (exp.f32 (log.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))))
	0.4b	(.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)))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v)))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (sqrt.f32 (exp.f32 (log.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (sqrt.f32 (exp.f32 (log.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.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 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 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 (.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(.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) (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))))))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 10685 to 6446 computations (39.7% saved)

regimes3.6s (34%)

Accuracy

Total 0.3b remaining (75.4%)

Threshold costs 0.3b (75.4%)

Counts

340 → 1

Compiler

Compiled 91668 to 64001 computations (30.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	27	35
2	26	35

end22.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 140 to 100 computations (28.6% saved)

sample2.4s (23.1%)

Algorithm

1×

intervals

Results

910.0ms	8000×	body	128	valid
458.0ms	8000×	pre	128	true

Compiler

Compiled 607 to 414 computations (31.8% saved)

Details

analyze9.0ms (0.1%)

sample119.0ms (1.1%)

simplify49.0ms (0.5%)

prune4.0ms (0%)

localize55.0ms (0.5%)

series751.0ms (7.1%)

rewrite36.0ms (0.3%)

simplify131.0ms (1.2%)

prune409.0ms (3.9%)

localize55.0ms (0.5%)

series496.0ms (4.7%)

rewrite38.0ms (0.4%)

simplify172.0ms (1.6%)

prune444.0ms (4.2%)

localize59.0ms (0.6%)

series19.0ms (0.2%)

rewrite10.0ms (0.1%)

simplify63.0ms (0.6%)

prune244.0ms (2.3%)

localize62.0ms (0.6%)

series500.0ms (4.7%)

rewrite36.0ms (0.3%)

simplify171.0ms (1.6%)

prune563.0ms (5.3%)

regimes3.6s (34%)

simplify3.0ms (0%)

end22.0ms (0.2%)

sample2.4s (23.1%)

Profiling