Details

analyze58.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 50 to 36 computations (28% saved)

sample80.0ms (0.4%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify54.0ms (0.3%)

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

prune8.0ms (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
	0.5b	(/.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))
▶	0.4b	(.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

0.5b

(/.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))

▶

0.4b

(*.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)

localize56.0ms (0.3%)

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))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-cbrt-cube_binary32`
44×	`add-exp-log_binary32`
34×	`times-frac_binary32`
21×	`*-un-lft-identity_binary32`
21×	`add-sqr-sqrt_binary32`

Counts

4 → 114

Calls

4 calls:

12.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
8.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

series754.0ms (3.8%)

Counts

4 → 96

Calls

4 calls:

583.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
121.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
43.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
7.0ms	(sinh.f32 (/.f32 1 v))

simplify146.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

686×	`times-frac_binary32`
536×	`associate-/l*_binary32`
516×	`associate-/r*_binary32`
259×	`fma-def_binary32`
166×	`associate-*l/_binary32`

Counts

210 → 387

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	490	9428
1	1523	8560
2	5108	8560

prune673.0ms (3.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	376	11	387
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	377	12	389

Error

0.0b

Counts

389 → 12

Alt Table

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

Compiler

Compiled 10835 to 6270 computations (42.1% saved)

localize63.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite116.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

381×	`times-frac_binary32`
211×	`add-sqr-sqrt_binary32`
191×	`*-un-lft-identity_binary32`
189×	`add-cube-cbrt_binary32`
189×	`add-exp-log_binary32`

Counts

3 → 377

Calls

3 calls:

66.0ms

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

12.0ms

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

6.0ms

(/.f32 (/.f32 1 v) (sqrt.f32 v))

series1.2s (6.1%)

Counts

3 → 80

Calls

3 calls:

630.0ms

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

564.0ms

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

12.0ms

(/.f32 (/.f32 1 v) (sqrt.f32 v))

simplify367.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

907×	`times-frac_binary32`
686×	`associate-/l*_binary32`
289×	`fma-def_binary32`
227×	`associate-/l/_binary32`
200×	`*-commutative_binary32`

Counts

457 → 819

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	653	22443
1	2047	19673
2	5290	19673

prune1.2s (6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	849	4	853
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	854	11	865

Error

0.0b

Counts

865 → 11

Alt Table

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

Compiler

Compiled 25064 to 13313 computations (46.9% saved)

localize61.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

273×	`add-exp-log_binary32`
163×	`prod-exp_binary32`
112×	`div-exp_binary32`
91×	`add-cbrt-cube_binary32`
39×	`cbrt-unprod_binary32`

Counts

2 → 143

Calls

2 calls:

18.0ms

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

8.0ms

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

series888.0ms (4.5%)

Counts

2 → 84

Calls

2 calls:

622.0ms

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

265.0ms

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

simplify197.0ms (1%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-/l*_binary32`
675×	`associate-/r*_binary32`
348×	`associate-*l/_binary32`
333×	`fma-def_binary32`
176×	`*-commutative_binary32`

Counts

227 → 444

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	526	13342
1	1723	11425
2	4978	11425

prune622.0ms (3.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	543	1	544
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	544	11	555

Error

0.0b

Counts

555 → 11

Alt Table

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

Compiler

Compiled 16175 to 10534 computations (34.9% saved)

localize82.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.f32 (/.f32 (.f32 (/.f32 1 v) cosTheta_i) v) (/.f32 1 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))
✓	0.7b	(expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))
	0.8b	(sinh.f32 (/.f32 1 v))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`add-exp-log_binary32`
154×	`prod-exp_binary32`
106×	`div-exp_binary32`
82×	`add-cbrt-cube_binary32`
36×	`cbrt-unprod_binary32`

Counts

2 → 117

Calls

2 calls:

17.0ms

(*.f32 (/.f32 (*.f32 (/.f32 1 v) cosTheta_i) v) (/.f32 1 (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))

0.0ms

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

series2.8s (14.3%)

Counts

2 → 60

Calls

2 calls:

2.6s

(*.f32 (/.f32 (*.f32 (/.f32 1 v) cosTheta_i) v) (/.f32 1 (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))

220.0ms

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

simplify212.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-def_binary32`
568×	`times-frac_binary32`
395×	`associate-/r*_binary32`
343×	`associate-l_binary32`
335×	`associate-/l*_binary32`

Counts

177 → 342

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	10547
1	1071	8534
2	4430	8022
3	4975	8022

prune490.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	542	0	542
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	542	11	553

Error

0.0b

Counts

553 → 11

Alt Table

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

Compiler

Compiled 11972 to 7921 computations (33.8% saved)

regimes4.5s (22.8%)

Accuracy

Total 0.3b remaining (70.3%)

Threshold costs 0.3b (70.3%)

Compiler

Compiled 108466 to 77184 computations (28.8% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	28	39
2	27	39

end90.0ms (0.5%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 210 to 154 computations (26.7% saved)

sample4.8s (24.6%)

Algorithm

1×

intervals

Results

1.9s	8000×	body	128	valid
761.0ms	8000×	pre	128	true

Compiler

Compiled 458 to 317 computations (30.8% saved)

Details

analyze58.0ms (0.3%)

sample80.0ms (0.4%)

simplify54.0ms (0.3%)

prune8.0ms (0%)

localize56.0ms (0.3%)

rewrite32.0ms (0.2%)

series754.0ms (3.8%)

simplify146.0ms (0.7%)

prune673.0ms (3.4%)

localize63.0ms (0.3%)

rewrite116.0ms (0.6%)

series1.2s (6.1%)

simplify367.0ms (1.9%)

prune1.2s (6%)

localize61.0ms (0.3%)

rewrite40.0ms (0.2%)

series888.0ms (4.5%)

simplify197.0ms (1%)

prune622.0ms (3.2%)

localize82.0ms (0.4%)

rewrite28.0ms (0.1%)

series2.8s (14.3%)

simplify212.0ms (1.1%)

prune490.0ms (2.5%)

regimes4.5s (22.8%)

simplify6.0ms (0%)

end90.0ms (0.5%)

sample4.8s (24.6%)

Profiling