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)

sample2.6s (41.8%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.5s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify46.0ms (0.7%)

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
	0.5b	(.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)

localize63.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.3b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	0.9b	(sinh.f32 (/.f32 1 v))

series38.0ms (0.6%)

Counts

4 → 24

Calls

4 calls:

13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
13.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
7.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
5.0ms	(sinh.f32 (/.f32 1 v))

rewrite72.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

292×	`expm1-udef_binary32`
292×	`log1p-udef_binary32`
163×	`add-sqr-sqrt_binary32`
152×	`log1p-expm1-u_binary32`
152×	`expm1-log1p-u_binary32`

Counts

4 → 135

Calls

4 calls:

69.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
69.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
69.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
69.0ms	(sinh.f32 (/.f32 1 v))

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 (1%)

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

159 → 153

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

prune283.0ms (4.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	139	14	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	140	15	155

Error

0.1b

Counts

155 → 15

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

Compiler

Compiled 5038 to 2532 computations (49.7% saved)

localize61.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	0.3b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.3b	(*.f32 cosTheta_i (/.f32 1 v))
	0.9b	(sinh.f32 (/.f32 1 v))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite35.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

495×	`log1p-expm1-u_binary32`
495×	`expm1-log1p-u_binary32`
413×	`unpow-prod-down_binary32`
272×	`log-prod_binary32`
142×	`pow2_binary32`

Counts

1 → 30

Calls

1 calls:

35.0ms

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

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

54 → 30

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	4	96

prune581.0ms (9.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	136	15	151

Error

0.1b

Counts

151 → 15

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) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	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))))))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	11.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 cosTheta_i v))) 2)) (log.f32 (cbrt.f32 (exp.f32 (/.f32 cosTheta_i 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)) (exp.f32 (log.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (pow.f32 (sqrt.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
	0.6b	(/.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))
	0.5b	(/.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 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2) 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 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 v -1/2) (/.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.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 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) 2))) (.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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	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 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 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 (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))

Compiler

Compiled 4774 to 2849 computations (40.3% saved)

localize65.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 cosTheta_O (/.f32 1 v))
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	0.3b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
	0.9b	(sinh.f32 (/.f32 1 v))

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite37.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

495×	`log1p-expm1-u_binary32`
495×	`expm1-log1p-u_binary32`
413×	`unpow-prod-down_binary32`
272×	`log-prod_binary32`
142×	`pow2_binary32`

Counts

1 → 30

Calls

1 calls:

36.0ms

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

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

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

54 → 30

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	4	96

prune382.0ms (6.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	136	15	151

Error

0.1b

Counts

151 → 15

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) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	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))))))
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	11.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 cosTheta_i v))) 2)) (log.f32 (cbrt.f32 (exp.f32 (/.f32 cosTheta_i 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 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (.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)) (exp.f32 (log.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (pow.f32 (sqrt.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
	9.3b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (/.f32 (sqrt.f32 cosTheta_O) (/.f32 v (sqrt.f32 cosTheta_O))))) (.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 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 v -1/2) (/.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.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 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) 2))) (.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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	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 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2) 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 (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))

Compiler

Compiled 4743 to 2822 computations (40.5% saved)

localize69.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v)
	0.3b	(*.f32 cosTheta_i (/.f32 1 v))
✓	0.8b	(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))
	0.9b	(sinh.f32 (/.f32 1 v))

series14.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v)
5.0ms	(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))

rewrite98.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

742×	`expm1-log1p-u_binary32`
741×	`log1p-expm1-u_binary32`
151×	`log1p-udef_binary32`
85×	`add-sqr-sqrt_binary32`
80×	`add-log-exp_binary32`

Counts

2 → 46

Calls

2 calls:

97.0ms	(.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v)
97.0ms	(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	183	18
2	1977	18
3	4993	18
4	4979	18
5	4914	18
0	0	0
1	0	0

simplify62.0ms (1%)

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

70 → 64

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

prune278.0ms (4.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	126	16	142

Error

0.0b

Counts

142 → 16

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) v)) (.f32 (*.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) v))
	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))))))
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	11.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 cosTheta_i v))) 2)) (log.f32 (cbrt.f32 (exp.f32 (/.f32 cosTheta_i 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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2))) 2) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (cbrt.f32 (/.f32 cosTheta_O v)) 3))) (.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)) (exp.f32 (log.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (pow.f32 (sqrt.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
	9.3b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (/.f32 (sqrt.f32 cosTheta_O) (/.f32 v (sqrt.f32 cosTheta_O))))) (.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 cosTheta_O (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 3))) (.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 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (pow.f32 v -1/2) (/.f32 (.f32 cosTheta_i cosTheta_O) (sqrt.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 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) 2))) (.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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	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 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2) 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))

Compiler

Compiled 4298 to 2540 computations (40.9% saved)

regimes1.0s (16.4%)

Accuracy

Total 0.3b remaining (78.3%)

Threshold costs 0.3b (78.3%)

Counts

94 → 1

Compiler

Compiled 23362 to 16920 computations (27.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary32`
13×	`neg-sub0_binary32`
13×	`neg-mul-1_binary32`
12×	`+-commutative_binary32`
12×	`sub-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	39
1	43	39
2	70	37
3	94	37
4	110	37
5	118	37
6	120	37
7	118	37

end314.0ms (5%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 682 to 490 computations (28.2% saved)

Details

analyze8.0ms (0.1%)

sample2.6s (41.8%)

simplify46.0ms (0.7%)

prune4.0ms (0.1%)

localize63.0ms (1%)

series38.0ms (0.6%)

rewrite72.0ms (1.1%)

simplify65.0ms (1%)

prune283.0ms (4.5%)

localize61.0ms (1%)

series7.0ms (0.1%)

rewrite35.0ms (0.6%)

simplify8.0ms (0.1%)

prune581.0ms (9.3%)

localize65.0ms (1%)

series6.0ms (0.1%)

rewrite37.0ms (0.6%)

simplify11.0ms (0.2%)

prune382.0ms (6.1%)

localize69.0ms (1.1%)

series14.0ms (0.2%)

rewrite98.0ms (1.6%)

simplify62.0ms (1%)

prune278.0ms (4.5%)

regimes1.0s (16.4%)

simplify4.0ms (0.1%)

end314.0ms (5%)

Profiling