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)

sample2.8s (40.9%)

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)

simplify48.0ms (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

0.3b

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)

localize57.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	0.2b	(/.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))

series39.0ms (0.6%)

Counts

4 → 24

Calls

4 calls:

13.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
7.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite73.0ms (1.1%)

Algorithm

1×	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:

70.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
70.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
70.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
70.0ms	(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

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

prune290.0ms (4.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	140	13	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	141	14	155

Error

0.1b

Counts

155 → 14

Alt Table

Status	Error	Program
▶	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))
	2.7b	(/.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 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 (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 cosTheta_O) v)) (-.f32 (exp.f32 (log1p.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))) 1))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (sqrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
	0.4b	(/.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 (.f32 cosTheta_i cosTheta_O) 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 cosTheta_O) v)) (.f32 (*.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (pow.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i 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)) (pow.f32 (pow.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) 3) 1/3))
	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_O (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_i (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))

Compiler

Compiled 4958 to 2488 computations (49.8% saved)

localize100.0ms (1.5%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.5%)

Algorithm

1×	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

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

prune313.0ms (4.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	136	14	150

Error

0.1b

Counts

150 → 14

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 (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 cosTheta_O) v)) (.f32 (*.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) v))
	2.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (log.f32 (pow.f32 (exp.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 cosTheta_i cosTheta_O) v)) (-.f32 (exp.f32 (log1p.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))) 1))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (sqrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
	0.4b	(/.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)))))
	11.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 cosTheta_i v)))) (log.f32 (sqrt.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)) (.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))) (pow.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i 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 cosTheta_O (pow.f32 (cbrt.f32 (/.f32 cosTheta_i 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_O (pow.f32 (cbrt.f32 v) 2)) (/.f32 cosTheta_i (cbrt.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)))) (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 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))

Compiler

Compiled 4686 to 2789 computations (40.5% saved)

localize65.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 cosTheta_i (/.f32 1 v))
✓	0.3b	(.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))
✓	0.5b	(exp.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))
	0.8b	(sinh.f32 (/.f32 1 v))

series15.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(exp.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))
7.0ms	(.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))

rewrite76.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`log1p-expm1-u_binary32`
748×	`expm1-log1p-u_binary32`
150×	`log1p-udef_binary32`
85×	`add-sqr-sqrt_binary32`
80×	`add-log-exp_binary32`

Counts

2 → 53

Calls

2 calls:

75.0ms	(.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))
75.0ms	(exp.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	181	24
2	1986	24
3	4995	24
4	4921	24

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary32`
529×	`associate-l_binary32`
394×	`associate-/r/_binary32`
369×	`associate-r_binary32`
354×	`associate-/l/_binary32`

Counts

77 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	384
1	67	368
2	138	368
3	309	368
4	758	368
5	2815	368
6	4376	368
7	4882	368
8	4945	368

prune847.0ms (12.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	106	16	122

Error

0.0b

Counts

122 → 16

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 (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 cosTheta_O) v)) (.f32 (*.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) v))
	2.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (log.f32 (pow.f32 (exp.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 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	11.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 cosTheta_i v)))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 cosTheta_i 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 (.f32 cosTheta_i cosTheta_O) v)) (-.f32 (exp.f32 (log1p.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))) 1))
	25.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (pow.f32 (sqrt.f32 (/.f32 cosTheta_i v)) 2))) (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 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (sqrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 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 (E.f32) (log.f32 (.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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (exp.f32 (log.f32 (.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 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 (.f32 cosTheta_i cosTheta_O) 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))) (pow.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i 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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (pow.f32 (exp.f32 (sqrt.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))) (sqrt.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 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))

Compiler

Compiled 4166 to 2516 computations (39.6% saved)

localize66.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
	0.3b	(.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))
	0.5b	(exp.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))
	0.8b	(sinh.f32 (/.f32 1 v))

prune345.0ms (5.1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	124	17	141

Error

0.0b

Counts

141 → 17

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)) (exp.f32 (log.f32 (.f32 v (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2)))))
	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 (sqrt.f32 (sinh.f32 (/.f32 1 v))) 2) 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 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 cosTheta_O) v)) (.f32 (*.f32 (-.f32 (exp.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 1) 2) v))
	2.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (log.f32 (pow.f32 (exp.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 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 3))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	11.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 cosTheta_i v)))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 cosTheta_i 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 (.f32 cosTheta_i cosTheta_O) v)) (-.f32 (exp.f32 (log1p.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))) 1))
	25.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_O (pow.f32 (sqrt.f32 (/.f32 cosTheta_i v)) 2))) (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 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (sqrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 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 (E.f32) (log.f32 (.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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (exp.f32 (log.f32 (.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 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))) (pow.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i 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 cosTheta_O (.f32 cosTheta_i (/.f32 1 v)))) (pow.f32 (exp.f32 (sqrt.f32 (log.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2))))) (sqrt.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 cosTheta_i cosTheta_O) v)) (pow.f32 (cbrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 3))

Compiler

Compiled 4086 to 2113 computations (48.3% saved)

regimes1.0s (15.1%)

Accuracy

Total 0.4b remaining (81.4%)

Threshold costs 0.4b (81.4%)

Counts

106 → 1

Compiler

Compiled 28265 to 20461 computations (27.6% saved)

simplify5.0ms (0.1%)

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	22	41
1	35	41
2	45	41
3	52	41
4	57	41
5	59	41
6	58	41

end444.0ms (6.5%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 785 to 577 computations (26.5% saved)

Details

analyze8.0ms (0.1%)

sample2.8s (40.9%)

simplify48.0ms (0.7%)

prune4.0ms (0.1%)

localize57.0ms (0.8%)

series39.0ms (0.6%)

rewrite73.0ms (1.1%)

simplify65.0ms (1%)

prune290.0ms (4.3%)

localize100.0ms (1.5%)

series6.0ms (0.1%)

rewrite36.0ms (0.5%)

simplify7.0ms (0.1%)

prune313.0ms (4.6%)

localize65.0ms (1%)

series15.0ms (0.2%)

rewrite76.0ms (1.1%)

simplify77.0ms (1.1%)

prune847.0ms (12.5%)

localize66.0ms (1%)

prune345.0ms (5.1%)

regimes1.0s (15.1%)

simplify5.0ms (0.1%)

end444.0ms (6.5%)

Profiling