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)

sample2.7s (28.8%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.6s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify15.0ms (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

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 (/.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

▶

0.4b

(/.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 (/.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)

localize57.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series38.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

12.0ms	(/.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))

rewrite61.0ms (0.7%)

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

Calls

4 calls:

59.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
59.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
59.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
59.0ms	(sinh.f32 (/.f32 1 v))

simplify27.0ms (0.3%)

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

prune287.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	136	13	149
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	137	14	151

Error

0.1b

Counts

151 → 14

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)) (pow.f32 (sqrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
	0.4b	(.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))
	13.2b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (cbrt.f32 (pow.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) 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)) (exp.f32 (log.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	2.5b	(/.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))))
	0.5b	(/.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))
▶	0.4b	(/.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)) (.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))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	11.3b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 2 (/.f32 1/3 (.f32 v 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))
	0.5b	(/.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) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (.f32 (/.f32 cosTheta_i v) 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_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 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2)) 3) 1/3))

Compiler

Compiled 4870 to 2474 computations (49.2% saved)

localize58.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series5.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

5.0ms

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

rewrite31.0ms (0.3%)

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

Calls

1 calls:

30.0ms

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

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

prune300.0ms (3.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	127	6	133
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	134	13	147

Error

0.1b

Counts

147 → 13

Alt Table

Status	Error	Program
	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 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 3) 2) v))
	0.6b	(/.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_i (.f32 cosTheta_O (/.f32 1 v)))) (pow.f32 (pow.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)) 3) 1/3))
	0.5b	(/.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)) (pow.f32 (sqrt.f32 (.f32 v (*.f32 (sinh.f32 (/.f32 1 v)) 2))) 2))
▶	0.4b	(.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))
	0.4b	(/.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 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 (-.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))) (/.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 (pow.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) 2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (.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 (pow.f32 (cbrt.f32 cosTheta_O) 2) (/.f32 v (cbrt.f32 cosTheta_O))))) (.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)))) (expm1.f32 (log1p.f32 (.f32 v (.f32 (sinh.f32 (/.f32 1 v)) 2)))))
	11.3b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 2 (/.f32 1/3 (.f32 v v))))

Compiler

Compiled 4566 to 2731 computations (40.2% saved)

localize57.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series1.1s (11.7%)

Counts

3 → 96

Calls

3 calls:

1.0s

(*.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))

24.0ms

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

16.0ms

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

rewrite33.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

206×	`add-sqr-sqrt_binary32`
192×	`log1p-expm1-u_binary32`
192×	`expm1-log1p-u_binary32`
191×	`add-cbrt-cube_binary32`
191×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	413	48

Stop Event

1×	node limit

Counts

3 → 78

Calls

3 calls:

32.0ms

(*.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))

32.0ms

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

32.0ms

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

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Rules

455×	`times-frac_binary32`
275×	`associate-r_binary32`
262×	`associate-/l*_binary32`
243×	`cancel-sign-sub-inv_binary32`
237×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	5654
1	665	5316
2	3843	5264

Stop Event

1×	node limit

Counts

174 → 110

prune296.0ms (3.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	143	12	155

Error

0.0b

Counts

155 → 12

Alt Table

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

Compiler

Compiled 6020 to 3497 computations (41.9% saved)

localize60.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 cosTheta_i cosTheta_O)
✓	0.2b	(/.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (.f32 (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v)) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (*.f32 v v)))
✓	0.4b	(.f32 (.f32 (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v)) (.f32 (sinh.f32 (/.f32 1 v)) 2)) (.f32 v v))
	0.8b	(sinh.f32 (/.f32 1 v))

series1.2s (13.2%)

Counts

3 → 96

Calls

3 calls:

1.0s

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

188.0ms

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

5.0ms

(*.f32 cosTheta_i cosTheta_O)

rewrite37.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

197×	`add-sqr-sqrt_binary32`
185×	`log1p-expm1-u_binary32`
185×	`expm1-log1p-u_binary32`
183×	`add-log-exp_binary32`
182×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	62
1	402	62

Stop Event

1×	node limit

Counts

3 → 88

Calls

3 calls:

35.0ms

(*.f32 cosTheta_i cosTheta_O)

35.0ms

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

35.0ms

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

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

476×	`times-frac_binary32`
325×	`associate-r_binary32`
307×	`associate-/l*_binary32`
249×	`associate-/r*_binary32`
246×	`unswap-sqr_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	6840
1	808	6462
2	4502	6414

Stop Event

1×	node limit

Counts

184 → 125

prune314.0ms (3.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	157	12	169

Error

0.0b

Counts

169 → 12

Alt Table

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

Compiler

Compiled 6502 to 3665 computations (43.6% saved)

regimes2.1s (23.2%)

Accuracy

Total 0.3b remaining (79.7%)

Threshold costs 0.3b (79.7%)

Counts

212 → 1

Compiler

Compiled 50676 to 36660 computations (27.7% 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

Stop Event

1×

saturated

end235.0ms (2.5%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 534 to 388 computations (27.3% saved)

Details

analyze8.0ms (0.1%)

sample2.7s (28.8%)

simplify15.0ms (0.2%)

prune4.0ms (0%)

localize57.0ms (0.6%)

series38.0ms (0.4%)

rewrite61.0ms (0.7%)

simplify27.0ms (0.3%)

prune287.0ms (3.1%)

localize58.0ms (0.6%)

series5.0ms (0.1%)

rewrite31.0ms (0.3%)

simplify7.0ms (0.1%)

prune300.0ms (3.3%)

localize57.0ms (0.6%)

series1.1s (11.7%)

rewrite33.0ms (0.4%)

simplify91.0ms (1%)

prune296.0ms (3.2%)

localize60.0ms (0.6%)

series1.2s (13.2%)

rewrite37.0ms (0.4%)

simplify103.0ms (1.1%)

prune314.0ms (3.4%)

regimes2.1s (23.2%)

simplify3.0ms (0%)

end235.0ms (2.5%)

Profiling