Details

analyze11.0ms (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)

sample127.0ms (1.1%)

Algorithm

1×

intervals

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

31.0ms	256×	body	128	valid
14.0ms	256×	pre	128	true

Compiler

Compiled 98 to 72 computations (26.5% saved)

simplify46.0ms (0.4%)

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%)

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)

localize55.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)))))
✓	0.7b	(sinh.f32 (/.f32 1 v))

series559.0ms (4.6%)

Counts

4 → 96

Calls

4 calls:

467.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
73.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	(sinh.f32 (/.f32 1 v))

rewrite37.0ms (0.3%)

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)))))
10.0ms	(.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))

simplify139.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

584×	`times-frac_binary32`
466×	`associate-/r*_binary32`
456×	`associate-/l*_binary32`
371×	`associate-l_binary32`
150×	`fma-def_binary32`

Counts

210 → 218

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	419	9291
1	1297	8518
2	5043	8518

prune371.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	209	9	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	10	220

Error

0.1b

Counts

220 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.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 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))))))
	0.5b	(.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 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
▶	0.3b	(.f32 cosTheta_O (/.f32 cosTheta_i (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 cosTheta_i (cbrt.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 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) v) (/.f32 (cbrt.f32 cosTheta_i) (.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 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 8980 to 4841 computations (46.1% saved)

localize59.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.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)
✓	0.3b	(/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))
	0.7b	(sinh.f32 (/.f32 1 v))

series77.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

77.0ms

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

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-exp-log_binary32`
33×	`add-cbrt-cube_binary32`
31×	`times-frac_binary32`
24×	`prod-exp_binary32`
24×	`div-exp_binary32`

Counts

1 → 65

Calls

1 calls:

15.0ms

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

simplify135.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary32`
519×	`fma-def_binary32`
263×	`associate-+l+_binary32`
219×	`associate-/l*_binary32`
198×	`associate-r_binary32`

Counts

101 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	3942
1	545	3338
2	2316	3194
3	4340	3182
4	4962	3182
5	4956	3182

prune446.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	211	4	215
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	214	11	225

Error

0.0b

Counts

225 → 11

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 cosTheta_i (cbrt.f32 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
▶	0.3b	(.f32 cosTheta_O (/.f32 cosTheta_i (/.f32 (.f32 v (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 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 (sinh.f32 (/.f32 1 v)) 2) v))
	0.4b	(.f32 cosTheta_O (/.f32 cosTheta_i (exp.f32 (-.f32 (log.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))) (log.f32 (/.f32 1 v))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.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 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))))))
	0.5b	(.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 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) v) (/.f32 (cbrt.f32 cosTheta_i) (.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 cosTheta_i (/.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))))
	0.5b	(.f32 cosTheta_O (/.f32 cosTheta_i (/.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (cbrt.f32 (/.f32 1 v)))))

Compiler

Compiled 7871 to 4514 computations (42.7% saved)

localize65.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))
✓	0.3b	(/.f32 (.f32 v (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))
✓	0.6b	(exp.f32 (/.f32 -1 v))
✓	0.6b	(exp.f32 (/.f32 1 v))

series57.0ms (0.5%)

Counts

4 → 60

Calls

4 calls:

49.0ms	(/.f32 (.f32 v (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))
4.0ms	(-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))
2.0ms	(exp.f32 (/.f32 1 v))
2.0ms	(exp.f32 (/.f32 -1 v))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`times-frac_binary32`
42×	`*-un-lft-identity_binary32`
42×	`add-sqr-sqrt_binary32`
40×	`add-cube-cbrt_binary32`
39×	`add-exp-log_binary32`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/.f32 (.f32 v (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (/.f32 1 v))
6.0ms	(-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))
2.0ms	(exp.f32 (/.f32 1 v))
2.0ms	(exp.f32 (/.f32 -1 v))

simplify150.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

387×	`fma-neg_binary32`
344×	`cancel-sign-sub-inv_binary32`
298×	`distribute-rgt-in_binary32`
234×	`associate-r_binary32`
214×	`associate-l_binary32`

Counts

196 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	5666
1	755	4772
2	2836	4548
3	4848	4548
4	4980	4548

prune458.0ms (3.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	216	10	226

Error

0.0b

Counts

226 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))) (cbrt.f32 (/.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 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))))))
	0.5b	(.f32 cosTheta_O (/.f32 cosTheta_i (/.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.f32 (/.f32 1 v)))) (cbrt.f32 (/.f32 1 v)))))
	0.5b	(.f32 cosTheta_O (/.f32 cosTheta_i (/.f32 (.f32 v (.f32 (-.f32 (pow.f32 (E.f32) (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.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 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 cosTheta_i (cbrt.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 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) v) (/.f32 (cbrt.f32 cosTheta_i) (.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 cosTheta_i (/.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))))

Compiler

Compiled 8491 to 5062 computations (40.4% saved)

localize64.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (/.f32 1 v)))
✓	0.4b	(/.f32 (/.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (/.f32 1 v))) (sqrt.f32 (/.f32 1 v)))
	0.7b	(sinh.f32 (/.f32 1 v))

series203.0ms (1.7%)

Counts

2 → 56

Calls

2 calls:

112.0ms

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

90.0ms

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

rewrite150.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

993×	`times-frac_binary32`
533×	`sqrt-prod_binary32`
347×	`*-un-lft-identity_binary32`
347×	`add-sqr-sqrt_binary32`
347×	`add-cube-cbrt_binary32`

Counts

2 → 452

Calls

2 calls:

24.0ms

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

13.0ms

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

simplify672.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-def_binary32`
360×	`associate-/l*_binary32`
295×	`times-frac_binary32`
274×	`associate-/l/_binary32`
229×	`fma-neg_binary32`

Counts

508 → 521

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	26704
1	1007	24859
2	3687	24496
3	4855	24496
4	4989	24496
5	4994	24496

prune1.3s (10.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	570	1	571
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	572	9	581

Error

0.0b

Counts

581 → 9

Alt Table

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

Compiler

Compiled 25473 to 15948 computations (37.4% saved)

regimes4.1s (34.5%)

Accuracy

Total 0.3b remaining (71.9%)

Threshold costs 0.3b (71.9%)

Counts

396 → 1

Compiler

Compiled 101170 to 72152 computations (28.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	26	35
2	25	35

end32.0ms (0.3%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 196 to 140 computations (28.6% saved)

sample2.6s (21.7%)

Algorithm

1×

intervals

Results

975.0ms	8000×	body	128	valid
491.0ms	8000×	pre	128	true

Compiler

Compiled 435 to 295 computations (32.2% saved)

Details

analyze11.0ms (0.1%)

sample127.0ms (1.1%)

simplify46.0ms (0.4%)

prune4.0ms (0%)

localize55.0ms (0.5%)

series559.0ms (4.6%)

rewrite37.0ms (0.3%)

simplify139.0ms (1.2%)

prune371.0ms (3.1%)

localize59.0ms (0.5%)

series77.0ms (0.6%)

rewrite23.0ms (0.2%)

simplify135.0ms (1.1%)

prune446.0ms (3.7%)

localize65.0ms (0.5%)

series57.0ms (0.5%)

rewrite39.0ms (0.3%)

simplify150.0ms (1.2%)

prune458.0ms (3.8%)

localize64.0ms (0.5%)

series203.0ms (1.7%)

rewrite150.0ms (1.2%)

simplify672.0ms (5.6%)

prune1.3s (10.8%)

regimes4.1s (34.5%)

simplify2.0ms (0%)

end32.0ms (0.3%)

sample2.6s (21.7%)

Profiling