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)

sample2.3s (32%)

Results

2.3s

8256×

body

128

valid

Compiler

Compiled 132 to 96 computations (27.3% saved)

preprocess73.0ms (1%)

Algorithm

2×	egg-herbie

Rules

696×	`associate-/l*_binary32`
691×	`associate-/l/_binary32`
677×	`times-frac_binary32`
373×	`associate-/r/_binary32`
359×	`associate-/r*_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	374
1	361	374
2	1272	352
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

914×	`times-frac_binary32`
551×	`associate-/l*_binary32`
460×	`associate-/l/_binary32`
360×	`associate-*l/_binary32`
311×	`associate-/r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	54	34
2	173	32
3	800	32

Stop Event

1×	node limit

Counts

1 → 2

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
▶	0.5b	(/.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))
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))

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 (sinh.f32 (/.f32 1 v)) 2) v))

0.5b

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

Compiler

Compiled 154 to 106 computations (31.2% saved)

localize70.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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)
✓	0.8b	(sinh.f32 (/.f32 1 v))

series39.0ms (0.5%)

Counts

4 → 24

Calls

24 calls:

5.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)	v	0
4.0ms	(sinh.f32 (/.f32 1 v))	v	0
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)	cosTheta_O	-inf
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)	sinTheta_O	-inf
2.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)	sinTheta_i	-inf

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`log1p-udef_binary32`
163×	`add-sqr-sqrt_binary32`
152×	`log1p-expm1-u_binary32`
152×	`expm1-log1p-u_binary32`
150×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	332	32
2	4356	32

Stop Event

1×	node limit

Counts

4 → 131

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

509×	`unswap-sqr_binary32`
478×	`times-frac_binary32`
374×	`fma-def_binary32`
322×	`associate-*l/_binary32`
302×	`associate-/r*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	408
1	125	392
2	279	392
3	636	392
4	1902	392

Stop Event

1×	node limit

Counts

155 → 149

prune329.0ms (4.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	135	14	149
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	15	151

Error

0.1b

Counts

151 → 15

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)) (pow.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)) 3) 1/3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (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)) (exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 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))
	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 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (cbrt.f32 (.f32 v v))) (/.f32 cosTheta_O (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_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 (pow.f32 v -1/2) (/.f32 (.f32 cosTheta_i 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 (.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 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	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 (sinh.f32 (/.f32 1 v)) (*.f32 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 (exp.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))) 1))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (pow.f32 (cbrt.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 (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))

Compiler

Compiled 4940 to 2497 computations (49.5% saved)

localize64.0ms (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_O (/.f32 1 v))
	0.3b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
	0.8b	(sinh.f32 (/.f32 1 v))

series7.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(*.f32 cosTheta_O (/.f32 1 v))	v	-inf
1.0ms	(*.f32 cosTheta_O (/.f32 1 v))	cosTheta_O	-inf
1.0ms	(*.f32 cosTheta_O (/.f32 1 v))	cosTheta_O	inf
1.0ms	(*.f32 cosTheta_O (/.f32 1 v))	cosTheta_O	0
1.0ms	(*.f32 cosTheta_O (/.f32 1 v))	v	0

rewrite39.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	120	4
2	1434	4

Stop Event

1×	node limit

Counts

1 → 30

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96

Stop Event

1×

saturated

Counts

54 → 30

prune292.0ms (4.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	126	7	133
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	133	15	148

Error

0.0b

Counts

148 → 15

Alt Table

Status	Error	Program
	9.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 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 cosTheta_O) v)) (expm1.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (cbrt.f32 (.f32 v v))) (/.f32 cosTheta_O (cbrt.f32 v)))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	7.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (/.f32 (pow.f32 cosTheta_O 3) (pow.f32 v 3)) 1/3))) (.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 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 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.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 (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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2)))))
	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 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (pow.f32 (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))) 3))
	4.1b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (log.f32 (pow.f32 (pow.f32 (exp.f32 2) (sinh.f32 (/.f32 1 v))) 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)))) (cbrt.f32 (.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 3) (pow.f32 v 3))))

Compiler

Compiled 4684 to 2806 computations (40.1% saved)

localize69.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f32 cosTheta_O (/.f32 1 v))
✓	0.3b	(.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 3) (pow.f32 v 3))
✓	0.7b	(pow.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 3)
	0.8b	(sinh.f32 (/.f32 1 v))

series23.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

10.0ms	(.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 3) (pow.f32 v 3))	v	0
8.0ms	(pow.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 3)	v	0
1.0ms	(.f32 (pow.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) 3) (pow.f32 v 3))	v	inf
1.0ms	(pow.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 3)	v	inf
1.0ms	(pow.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) 3)	v	-inf

rewrite43.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`log1p-expm1-u_binary32`
877×	`expm1-log1p-u_binary32`
101×	`add-sqr-sqrt_binary32`
98×	`add-cbrt-cube_binary32`
95×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	232	27
2	2582	27

Stop Event

1×	node limit

Counts

2 → 43

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

953×	`fma-def_binary32`
579×	`associate-l_binary32`
451×	`associate-r_binary32`
324×	`associate-/r*_binary32`
178×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	456
1	128	440
2	319	440
3	978	440
4	4318	440

Stop Event

1×	node limit

Counts

67 → 61

prune329.0ms (4.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	124	14	138

Error

0.0b

Counts

138 → 14

Alt Table

Status	Error	Program
	9.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 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 cosTheta_O) v)) (expm1.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (/.f32 cosTheta_i (cbrt.f32 (.f32 v v))) (/.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 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2)))) (pow.f32 v 3))))
	7.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (/.f32 (pow.f32 cosTheta_O 3) (pow.f32 v 3)) 1/3))) (.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 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 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.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 (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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (pow.f32 (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))) 3))
	4.1b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (log.f32 (pow.f32 (pow.f32 (exp.f32 2) (sinh.f32 (/.f32 1 v))) v)))

Compiler

Compiled 4972 to 3163 computations (36.4% saved)

localize65.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series15.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

5.0ms	(exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))))	v	0
5.0ms	(.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))	v	0
1.0ms	(exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))))	v	inf
1.0ms	(.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))	v	inf
1.0ms	(exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))))	v	-inf

rewrite43.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

761×	`log1p-expm1-u_binary32`
761×	`expm1-log1p-u_binary32`
152×	`log1p-udef_binary32`
87×	`add-sqr-sqrt_binary32`
80×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	186	24
2	2126	24

Stop Event

1×	node limit

Counts

2 → 56

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary32`
519×	`associate-l_binary32`
351×	`associate-r_binary32`
333×	`associate-/l/_binary32`
289×	`unswap-sqr_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	384
1	67	368
2	142	368
3	330	368
4	967	368
5	4068	368

Stop Event

1×	node limit

Counts

80 → 47

prune258.0ms (3.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Error

0.0b

Counts

123 → 15

Alt Table

Status	Error	Program
	9.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (exp.f32 (log.f32 (/.f32 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 cosTheta_O) v)) (expm1.f32 (log1p.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
	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))) (exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (cbrt.f32 (.f32 (exp.f32 (.f32 3 (log.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2)))) (pow.f32 v 3))))
	7.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (pow.f32 (/.f32 (pow.f32 cosTheta_O 3) (pow.f32 v 3)) 1/3))) (.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 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 (.f32 cosTheta_i cosTheta_O) v)) (.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
	0.5b	(.f32 (/.f32 (/.f32 1/2 (sinh.f32 (/.f32 1 v))) (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))) (.f32 (/.f32 cosTheta_i (*.f32 v v)) cosTheta_O))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (pow.f32 (cbrt.f32 (.f32 (sinh.f32 (/.f32 1 v)) (.f32 v 2))) 3))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (expm1.f32 (log1p.f32 (/.f32 cosTheta_O v))))) (exp.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) (*.f32 v 2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 cosTheta_i (.f32 cosTheta_O (/.f32 1 v)))) (.f32 (pow.f32 (cbrt.f32 (.f32 v 2)) 2) (.f32 (cbrt.f32 (.f32 v 2)) (sinh.f32 (/.f32 1 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))

Compiler

Compiled 3690 to 2175 computations (41.1% saved)

regimes2.5s (34.4%)

Accuracy

Total 0.3b remaining (81%)

Threshold costs 0.3b (81%)

Counts

225 → 1

Compiler

Compiled 58493 to 43145 computations (26.2% 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	24	45
1	37	45
2	47	45
3	54	45
4	59	45
5	61	45

Stop Event

1×

saturated

end465.0ms (6.5%)

Stop Event

1×

fuel

Remove

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 747 to 557 computations (25.4% saved)

Details

analyze7.0ms (0.1%)

sample2.3s (32%)

preprocess73.0ms (1%)

simplify14.0ms (0.2%)

prune5.0ms (0.1%)

localize70.0ms (1%)

series39.0ms (0.5%)

rewrite62.0ms (0.9%)

simplify28.0ms (0.4%)

prune329.0ms (4.6%)

localize64.0ms (0.9%)

series7.0ms (0.1%)

rewrite39.0ms (0.5%)

simplify7.0ms (0.1%)

prune292.0ms (4.1%)

localize69.0ms (1%)

series23.0ms (0.3%)

rewrite43.0ms (0.6%)

simplify34.0ms (0.5%)

prune329.0ms (4.6%)

localize65.0ms (0.9%)

series15.0ms (0.2%)

rewrite43.0ms (0.6%)

simplify34.0ms (0.5%)

prune258.0ms (3.6%)

regimes2.5s (34.4%)

simplify3.0ms (0%)

end465.0ms (6.5%)

Profiling