Details

analyze69.0ms (0.4%)

Algorithm

1×

Search

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

Compiler

Compiled 50 to 36 computations (28% saved)

sample71.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify53.0ms (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 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	54	34
2	171	32
3	710	32
4	3624	32
5	4571	32
6	5009	32

prune15.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.4b

Counts

2 → 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 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))

▶

0.5b

(*.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 132 to 92 computations (30.3% saved)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
0.2b	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.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))

rewrite350.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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 → 106

Calls

4 calls:

15.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
14.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 3186 to 1444 computations (54.7% saved)

series471.0ms (2.4%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

258.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
86.0ms	(.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)
28.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 3440 to 2436 computations (29.2% saved)

simplify171.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-/r/_binary32`
273×	`associate-/r*_binary32`
238×	`associate-l_binary32`
221×	`associate-r_binary32`
219×	`times-frac_binary32`

Counts

149 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	271	4473
1	748	3621
2	2814	3545
3	4660	3537
4	4966	3537
5	4951	3537

prune214.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Error

0.1b

Counts

113 → 12

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 1 v) (/.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 1 (pow.f32 v 3/2)) (/.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 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 (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) 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)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	24.6b	(.f32 cosTheta_O (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 v)) (.f32 (/.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 cosTheta_i)) (pow.f32 v 3/2))))
	24.6b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 cosTheta_i) v) (/.f32 (sqrt.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 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 v v)))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.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 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 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))))

Compiler

Compiled 2569 to 1372 computations (46.6% saved)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))
0.3b	(/.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 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.8b	(sinh.f32 (/.f32 1 v))

rewrite441.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

100×	`add-exp-log_binary32`
72×	`add-cbrt-cube_binary32`
56×	`prod-exp_binary32`
34×	`cbrt-unprod_binary32`
30×	`div-exp_binary32`

Counts

4 → 122

Calls

4 calls:

21.0ms	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
12.0ms	(/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))
11.0ms	(.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 4115 to 2166 computations (47.4% saved)

series711.0ms (3.7%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

259.0ms	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
242.0ms	(/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))
91.0ms	(.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))
31.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 4686 to 3398 computations (27.5% saved)

simplify211.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

473×	`associate-/r/_binary32`
398×	`times-frac_binary32`
323×	`associate-r_binary32`
268×	`associate-/r*_binary32`
265×	`associate-l_binary32`

Counts

170 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	6171
1	727	4847
2	3052	4771
3	4756	4771
4	4982	4771
5	4991	4771

prune213.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	132	11	143

Error

0.1b

Counts

143 → 11

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))
	24.6b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (sqrt.f32 cosTheta_i) (/.f32 v (/.f32 (sqrt.f32 cosTheta_i) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) 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 (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) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (.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 1 v) (/.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (/.f32 v (/.f32 (cbrt.f32 cosTheta_i) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	24.6b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 cosTheta_i) v) (/.f32 (sqrt.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 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.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 (sqrt.f32 (/.f32 1 v)) (.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (/.f32 1 v)))))
▶	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v))))))

Compiler

Compiled 2435 to 1408 computations (42.2% saved)

localize58.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))
0.3b	(.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v))
0.4b	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))))
0.8b	(sinh.f32 (/.f32 1 v))

rewrite493.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

129×	`add-exp-log_binary32`
87×	`add-cbrt-cube_binary32`
80×	`prod-exp_binary32`
48×	`cbrt-unprod_binary32`
32×	`div-exp_binary32`

Counts

4 → 133

Calls

4 calls:

24.0ms	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))))
20.0ms	(.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))
13.0ms	(.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v))
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 5043 to 2439 computations (51.6% saved)

series575.0ms (3%)

Error

0.1b

Counts

4 → 45

Calls

4 calls:

260.0ms	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))))
113.0ms	(.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v))
94.0ms	(.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 v)))
30.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 4216 to 3003 computations (28.8% saved)

simplify192.0ms (1%)

Algorithm

1×	egg-herbie

Rules

622×	`associate-/l/_binary32`
408×	`associate-l_binary32`
406×	`associate-r_binary32`
307×	`times-frac_binary32`
236×	`*-commutative_binary32`

Counts

178 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	294	7288
1	793	4969
2	3092	4897
3	4765	4885
4	4951	4885

prune243.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	150	12	162

Error

0.1b

Counts

162 → 12

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 cosTheta_i (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (pow.f32 v 3/2)))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	24.6b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (sqrt.f32 cosTheta_i) (/.f32 v (/.f32 (sqrt.f32 cosTheta_i) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
▶	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) 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 (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) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (.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 1 v) (/.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (sqrt.f32 v) (.f32 (sqrt.f32 (.f32 (sqrt.f32 v) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (.f32 (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 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.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 (sqrt.f32 (/.f32 1 v)) (.f32 (/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (/.f32 1 v)))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (sqrt.f32 (sqrt.f32 v)) (.f32 (sqrt.f32 v) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (sqrt.f32 (sqrt.f32 v))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))) (.f32 (.f32 (sqrt.f32 v) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))) (cbrt.f32 (sqrt.f32 v)))))))

Compiler

Compiled 3064 to 1738 computations (43.3% saved)

localize55.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) v)))))
0.4b	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) v))))))
0.6b	(exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) v))))
0.8b	(sinh.f32 (/.f32 1 v))

rewrite518.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

46×	`add-sqr-sqrt_binary32`
40×	`times-frac_binary32`
36×	`*-un-lft-identity_binary32`
29×	`add-cube-cbrt_binary32`
23×	`add-exp-log_binary32`

Counts

4 → 118

Calls

4 calls:

24.0ms	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) v))))))
20.0ms	(/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) v)))))
13.0ms	(exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) v))))
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 4229 to 2523 computations (40.3% saved)

series502.0ms (2.6%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

170.0ms	(.f32 (/.f32 1 v) (/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) v))))))
159.0ms	(/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) v)))))
68.0ms	(exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) v))))
34.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 3312 to 2419 computations (27% saved)

simplify236.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

485×	`associate-/l/_binary32`
293×	`*-commutative_binary32`
278×	`associate-/r/_binary32`
218×	`prod-exp_binary32`
217×	`exp-prod_binary32`

Counts

166 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	222	5404
1	489	4875
2	1706	4813
3	3766	4813
4	4782	4648
5	4881	4648
6	5220	4648

prune582.0ms (3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	143	5	148
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	148	12	160

Error

0.1b

Counts

160 → 12

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))
	24.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (sqrt.f32 cosTheta_i) (.f32 (/.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (sqrt.f32 cosTheta_i)) (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) 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 (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) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (.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 1 v) (/.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (.f32 (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (pow.f32 E.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (*.f32 2 (sinh.f32 (/.f32 1 v))) v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (pow.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) v))))))))
	0.7b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (pow.f32 (exp.f32 (.f32 (cbrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (cbrt.f32 (+.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (cbrt.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) v))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 cosTheta_i v) (-.f32 (/.f32 1 (.f32 2 (sinh.f32 (/.f32 1 v)))) (/.f32 (.f32 sinTheta_i sinTheta_O) (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))) (.f32 (.f32 (sqrt.f32 v) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))) (cbrt.f32 (sqrt.f32 v)))))))

Compiler

Compiled 3558 to 1917 computations (46.1% saved)

regimes9.4s (48.5%)

Accuracy

Total 0.3b remaining (70.5%)

Threshold costs 0.3b (70.5%)

Compiler

Compiled 118290 to 82520 computations (30.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	27	38
2	26	38

end44.0ms (0.2%)

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

sample3.4s (17.6%)

Algorithm

1×

intervals

Results

852.0ms	8000×	body	128	valid
407.0ms	8000×	pre	128	true

Compiler

Compiled 561 to 377 computations (32.8% saved)

Details

analyze69.0ms (0.4%)

sample71.0ms (0.4%)

simplify53.0ms (0.3%)

prune15.0ms (0.1%)

localize48.0ms (0.2%)

rewrite350.0ms (1.8%)

series471.0ms (2.4%)

simplify171.0ms (0.9%)

prune214.0ms (1.1%)

localize48.0ms (0.2%)

rewrite441.0ms (2.3%)

series711.0ms (3.7%)

simplify211.0ms (1.1%)

prune213.0ms (1.1%)

localize58.0ms (0.3%)

rewrite493.0ms (2.5%)

series575.0ms (3%)

simplify192.0ms (1%)

prune243.0ms (1.3%)

localize55.0ms (0.3%)

rewrite518.0ms (2.7%)

series502.0ms (2.6%)

simplify236.0ms (1.2%)

prune582.0ms (3%)

regimes9.4s (48.5%)

simplify3.0ms (0%)

end44.0ms (0.2%)

sample3.4s (17.6%)

Profiling