Details

analyze8.0ms (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)

sample2.9s (34.7%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.8s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify49.0ms (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

prune5.0ms (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

0.3b

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)

localize64.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series39.0ms (0.5%)

Counts

4 → 24

Calls

4 calls:

13.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
8.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite73.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

131× egg-rr

Counts

4 → 131

Calls

2 calls:

71.0ms	((sinh.f32 (/.f32 1 v)) (/.f32 (.f32 sinTheta_i sinTheta_O) v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v) (/.f32 (.f32 cosTheta_i cosTheta_O) v))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	332	32
2	4166	32
3	5199	32
0	0	0
1	0	0

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

595×	`associate-/r/_binary32`
510×	`unswap-sqr_binary32`
482×	`times-frac_binary32`
374×	`fma-def_binary32`
331×	`associate-*l/_binary32`

Counts

155 → 149

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	408
1	124	392
2	269	392
3	589	392
4	1389	392
5	3918	392
6	4974	392
7	4886	392

prune285.0ms (3.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	137	12	149
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	138	13	151

Error

0.1b

Counts

151 → 13

Alt Table

Status	Error	Program
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.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 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.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 (expm1.f32 (log1p.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) 1) (/.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 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 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_O (cbrt.f32 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)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))
	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 (.f32 cosTheta_i cosTheta_O) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)))) (.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (sqrt.f32 v)) (/.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	2.1b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (log.f32 (pow.f32 (exp.f32 v) (.f32 (sinh.f32 (/.f32 1 v)) 2))))
	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 4842 to 2426 computations (49.9% saved)

localize69.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite40.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

30× egg-rr

Counts

1 → 30

Calls

2 calls:

39.0ms	((*.f32 cosTheta_i (/.f32 1 v)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	120	4
2	1322	4
3	4993	4
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

54 → 30

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	4	96

prune290.0ms (3.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	128	5	133
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	133	13	146

Error

0.0b

Counts

146 → 13

Alt Table

Status	Error	Program
	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))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.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 (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_O (cbrt.f32 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)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	11.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (-.f32 (exp.f32 (log1p.f32 (/.f32 cosTheta_i v))) 1))) (.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 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))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)))) (.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (sqrt.f32 v)) (/.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	2.1b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (log.f32 (pow.f32 (exp.f32 v) (.f32 (sinh.f32 (/.f32 1 v)) 2))))

Compiler

Compiled 4588 to 2729 computations (40.5% saved)

localize73.0ms (0.9%)

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))
✓	0.7b	(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))
	0.8b	(sinh.f32 (/.f32 1 v))

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))

rewrite73.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

42× egg-rr

Counts

1 → 42

Calls

2 calls:

72.0ms	((expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	121	6
2	1324	6
3	4921	6
4	5480	6
0	0	0
1	0	0

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary32`
516×	`associate-l_binary32`
354×	`associate-/l*_binary32`
347×	`associate-r_binary32`
314×	`associate-*l/_binary32`

Counts

54 → 51

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	216
1	74	208
2	155	208
3	287	208
4	494	208
5	1218	208
6	3682	208
7	3898	208
8	4880	208

prune413.0ms (5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	157	15	172

Error

0.0b

Counts

172 → 15

Alt Table

Status	Error	Program
	0.7b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) 3) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (.f32 (pow.f32 (.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 1/3) (cbrt.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))))) 2) v))
	2.1b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (log.f32 (pow.f32 (exp.f32 v) (.f32 (sinh.f32 (/.f32 1 v)) 2))))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (+.f32 (fma.f32 (sinh.f32 (exp.f32 (log1p.f32 (/.f32 1 v)))) (cosh.f32 1) (neg.f32 (.f32 (sinh.f32 1) (cosh.f32 (exp.f32 (log1p.f32 (/.f32 1 v))))))) (fma.f32 (neg.f32 (sinh.f32 1)) (cosh.f32 (exp.f32 (log1p.f32 (/.f32 1 v)))) (.f32 (sinh.f32 1) (cosh.f32 (exp.f32 (log1p.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 (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.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 (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_O (cbrt.f32 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)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	11.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (-.f32 (exp.f32 (log1p.f32 (/.f32 cosTheta_i v))) 1))) (.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 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))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)))) (.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (sqrt.f32 v)) (/.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 5970 to 3733 computations (37.5% saved)

localize62.0ms (0.7%)

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)
✓	0.4b	(/.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))

series521.0ms (6.3%)

Counts

2 → 84

Calls

2 calls:

449.0ms

(/.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))))

rewrite87.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

67× egg-rr

Counts

2 → 67

Calls

2 calls:

85.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	359	52
2	4813	52
3	4981	52
0	0	0
1	0	0

simplify118.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

445×	`times-frac_binary32`
293×	`associate-/l*_binary32`
287×	`cancel-sign-sub-inv_binary32`
274×	`associate-r_binary32`
265×	`unswap-sqr_binary32`

Counts

151 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	5796
1	768	5460
2	4112	5422
3	5297	5422

prune414.0ms (5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	183	15	198

Error

0.0b

Counts

198 → 15

Alt Table

Status	Error	Program
	0.7b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) 3) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (.f32 (pow.f32 (.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 2) (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2)) 1/3) (cbrt.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))))) 2) v))
	2.1b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (log.f32 (pow.f32 (exp.f32 v) (.f32 (sinh.f32 (/.f32 1 v)) 2))))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (+.f32 (fma.f32 (sinh.f32 (exp.f32 (log1p.f32 (/.f32 1 v)))) (cosh.f32 1) (neg.f32 (.f32 (sinh.f32 1) (cosh.f32 (exp.f32 (log1p.f32 (/.f32 1 v))))))) (fma.f32 (neg.f32 (sinh.f32 1)) (cosh.f32 (exp.f32 (log1p.f32 (/.f32 1 v)))) (.f32 (sinh.f32 1) (cosh.f32 (exp.f32 (log1p.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 (sqrt.f32 v)) (/.f32 cosTheta_O (sqrt.f32 v)))) (.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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	11.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (-.f32 (exp.f32 (log1p.f32 (/.f32 cosTheta_i v))) 1))) (.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 v -2)))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)))) (.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (sqrt.f32 v)) (/.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	2.1b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (log.f32 (pow.f32 (exp.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)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))

Compiler

Compiled 7313 to 4304 computations (41.1% saved)

regimes2.2s (27%)

Accuracy

Total 0.3b remaining (80.1%)

Threshold costs 0.3b (80.1%)

Counts

227 → 1

Compiler

Compiled 54826 to 39344 computations (28.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
4×	`+-commutative_binary32`
4×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	37
1	33	37
2	43	37
3	50	37
4	55	37
5	57	37
6	56	37

end366.0ms (4.4%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 705 to 519 computations (26.4% saved)

Details

analyze8.0ms (0.1%)

sample2.9s (34.7%)

simplify49.0ms (0.6%)

prune5.0ms (0.1%)

localize64.0ms (0.8%)

series39.0ms (0.5%)

rewrite73.0ms (0.9%)

simplify65.0ms (0.8%)

prune285.0ms (3.4%)

localize69.0ms (0.8%)

series6.0ms (0.1%)

rewrite40.0ms (0.5%)

simplify7.0ms (0.1%)

prune290.0ms (3.5%)

localize73.0ms (0.9%)

series6.0ms (0.1%)

rewrite73.0ms (0.9%)

simplify55.0ms (0.7%)

prune413.0ms (5%)

localize62.0ms (0.7%)

series521.0ms (6.3%)

rewrite87.0ms (1%)

simplify118.0ms (1.4%)

prune414.0ms (5%)

regimes2.2s (27%)

simplify3.0ms (0%)

end366.0ms (4.4%)

Profiling