Details

analyze71.0ms (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)

sample70.0ms (0.4%)

Algorithm

1×

intervals

Results

22.0ms	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

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	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))))))
	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))

Status

Error

Program

▶

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))))))

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))

Compiler

Compiled 132 to 92 computations (30.3% saved)

localize52.0ms (0.3%)

Local error

Found 4 expressions with local error:

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)))))
0.9b	(sinh.f32 (/.f32 1 v))

rewrite366.0ms (2%)

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:

16.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
15.0ms	(.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)
4.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 3186 to 1444 computations (54.7% saved)

series389.0ms (2.2%)

Error

0.2b

Counts

4 → 41

Calls

4 calls:

181.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
87.0ms	(.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)
35.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 2774 to 1918 computations (30.9% saved)

simplify183.0ms (1%)

Algorithm

1×	egg-herbie

Rules

752×	`associate-*l/_binary32`
551×	`associate-/r/_binary32`
237×	`associate-/r*_binary32`
219×	`associate-l_binary32`
200×	`associate-r_binary32`

Counts

147 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	4259
1	681	3425
2	2419	3387
3	4706	3375
4	4980	3375
5	4977	3375

prune221.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	11	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Error

0.1b

Counts

111 → 12

Alt Table

Status	Error	Program
	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)))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 (pow.f32 v 3/2) (/.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 cosTheta_i v) (.f32 (sqrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.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 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	24.2b	(.f32 cosTheta_O (.f32 (sqrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (sqrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
▶	0.3b	(.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 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) 1) (/.f32 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)))))))))
	24.4b	(.f32 cosTheta_O (exp.f32 (-.f32 (log.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (/.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 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.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))))))))
	0.5b	(.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)))))))

Compiler

Compiled 2630 to 1401 computations (46.7% saved)

localize53.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))
0.3b	(.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)))))))
0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
0.9b	(sinh.f32 (/.f32 1 v))

rewrite444.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

98×	`add-exp-log_binary32`
68×	`add-cbrt-cube_binary32`
51×	`prod-exp_binary32`
32×	`div-exp_binary32`
29×	`cbrt-unprod_binary32`

Counts

4 → 121

Calls

4 calls:

20.0ms	(.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)))))))
13.0ms	(/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 4073 to 2174 computations (46.6% saved)

series479.0ms (2.7%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

183.0ms	(.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)))))))
173.0ms	(/.f32 cosTheta_i (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))
44.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
31.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 3079 to 2173 computations (29.4% saved)

simplify206.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

473×	`associate-/r/_binary32`
327×	`times-frac_binary32`
290×	`associate-r_binary32`
255×	`associate-l_binary32`
231×	`associate-/r*_binary32`

Counts

163 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	5055
1	684	3923
2	2744	3911
3	4410	3911
4	4975	3911
5	4962	3911

prune227.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	115	13	128

Error

0.1b

Counts

128 → 13

Alt Table

Status	Error	Program
	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)))))))))
	0.4b	(.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 cosTheta_i v) (.f32 (sqrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.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 (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 (/.f32 cosTheta_i v) (.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 (cbrt.f32 (/.f32 1 v)) (cbrt.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)))))) (cbrt.f32 (/.f32 1 v)))))
	24.2b	(.f32 cosTheta_O (.f32 (sqrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))) (sqrt.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
✓	0.3b	(.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 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)))))))))
	24.4b	(.f32 cosTheta_O (exp.f32 (-.f32 (log.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (/.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 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.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))))))))
	0.5b	(.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)))))))

Compiler

Compiled 2496 to 1447 computations (42% saved)

localize58.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
0.4b	(/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
0.5b	(exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
0.9b	(sinh.f32 (/.f32 1 v))

rewrite577.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

100×	`times-frac_binary32`
61×	`*-un-lft-identity_binary32`
56×	`add-sqr-sqrt_binary32`
56×	`add-cube-cbrt_binary32`
15×	`exp-sum_binary32`

Counts

4 → 132

Calls

4 calls:

27.0ms	(/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
14.0ms	(exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
4.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 4662 to 2423 computations (48% saved)

series325.0ms (1.8%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

153.0ms	(/.f32 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
49.0ms	(exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
43.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
32.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 2355 to 1669 computations (29.1% saved)

simplify236.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-/r/_binary32`
421×	`associate-r_binary32`
419×	`associate-*l/_binary32`
297×	`associate-*r/_binary32`
228×	`associate-/r*_binary32`

Counts

171 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	5759
1	623	5469
2	1930	5461
3	4644	5461
4	4953	5461
5	4988	5461

prune426.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	129	6	135
Fresh	6	5	11
Picked	0	1	1
Done	1	0	1
Total	136	12	148

Error

0.0b

Counts

148 → 12

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O)) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v)))))))
▶	0.3b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 v (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2)) (exp.f32 (log.f32 2))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (sqrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.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 (cbrt.f32 (/.f32 1 v)) (cbrt.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)))))) (cbrt.f32 (/.f32 1 v)))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) (.f32 (cbrt.f32 (.f32 v (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (cbrt.f32 (.f32 v (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (cbrt.f32 (.f32 v (.f32 (.f32 2 (sinh.f32 (/.f32 1 v))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 E.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (.f32 2 (.f32 v (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 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (exp.f32 (.f32 (cbrt.f32 (+.f32 (log.f32 (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (cbrt.f32 (+.f32 (log.f32 (.f32 2 (.f32 v (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 v (*.f32 2 (sinh.f32 (/.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 (/.f32 cosTheta_i v) (exp.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.5b	(.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))))))))
	0.5b	(.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)))))))

Compiler

Compiled 4419 to 2224 computations (49.7% saved)

localize84.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite567.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`times-frac_binary32`
41×	`add-cbrt-cube_binary32`
39×	`add-exp-log_binary32`
34×	`*-un-lft-identity_binary32`
34×	`add-sqr-sqrt_binary32`

Counts

4 → 119

Calls

4 calls:

21.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 v (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2))
5.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
4.0ms	(exp.f32 (/.f32 1 v))
3.0ms	(exp.f32 (/.f32 -1 v))

Compiler

Compiled 4707 to 2587 computations (45% saved)

series326.0ms (1.8%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

172.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 v (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2))
51.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
28.0ms	(exp.f32 (/.f32 -1 v))
27.0ms	(exp.f32 (/.f32 1 v))

Compiler

Compiled 2774 to 2037 computations (26.6% saved)

simplify125.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

658×	`associate-*l/_binary32`
451×	`associate-/r/_binary32`
243×	`associate-/r*_binary32`
220×	`associate-/l*_binary32`
218×	`associate-l_binary32`

Counts

158 → 93

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	276	4270
1	710	3501
2	2499	3501
3	5442	3501

prune246.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	9	10
Picked	1	0	1
Done	1	0	1
Total	93	12	105

Error

0.0b

Counts

105 → 12

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O)) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v)))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (sqrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))) (sqrt.f32 (.f32 v (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.8b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (-.f32 (pow.f32 (exp.f32 (/.f32 1 (.f32 (cbrt.f32 v) (cbrt.f32 v)))) (/.f32 (cbrt.f32 1) (cbrt.f32 v))) (exp.f32 (/.f32 -1 v))) (.f32 v (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) 2)) (exp.f32 (log.f32 2))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (-.f32 (pow.f32 E.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 v (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2)) (exp.f32 (log.f32 2))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 1 v)) (cbrt.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)))))) (cbrt.f32 (/.f32 1 v)))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 (/.f32 2 (/.f32 cosTheta_i (.f32 (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))) (.f32 (.f32 v v) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))) (exp.f32 (log.f32 2))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 E.f32 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (.f32 2 (.f32 v (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 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (pow.f32 (exp.f32 (.f32 (cbrt.f32 (+.f32 (log.f32 (.f32 2 (.f32 v (sinh.f32 (/.f32 1 v))))) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (cbrt.f32 (+.f32 (log.f32 (.f32 2 (.f32 v (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 v (*.f32 2 (sinh.f32 (/.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))
	0.5b	(.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))))))))
	0.5b	(.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)))))))

Compiler

Compiled 2414 to 1403 computations (41.9% saved)

regimes9.2s (51.3%)

Accuracy

Total 0.3b remaining (71.9%)

Threshold costs 0.3b (71.9%)

Compiler

Compiled 117506 to 80744 computations (31.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	26	38
2	25	38

end47.0ms (0.3%)

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

sample2.9s (16.1%)

Algorithm

1×

intervals

Results

740.0ms	8000×	body	128	valid
386.0ms	8000×	pre	128	true

Compiler

Compiled 551 to 381 computations (30.9% saved)

Details

analyze71.0ms (0.4%)

sample70.0ms (0.4%)

simplify53.0ms (0.3%)

prune15.0ms (0.1%)

localize52.0ms (0.3%)

rewrite366.0ms (2%)

series389.0ms (2.2%)

simplify183.0ms (1%)

prune221.0ms (1.2%)

localize53.0ms (0.3%)

rewrite444.0ms (2.5%)

series479.0ms (2.7%)

simplify206.0ms (1.2%)

prune227.0ms (1.3%)

localize58.0ms (0.3%)

rewrite577.0ms (3.2%)

series325.0ms (1.8%)

simplify236.0ms (1.3%)

prune426.0ms (2.4%)

localize84.0ms (0.5%)

rewrite567.0ms (3.2%)

series326.0ms (1.8%)

simplify125.0ms (0.7%)

prune246.0ms (1.4%)

regimes9.2s (51.3%)

simplify3.0ms (0%)

end47.0ms (0.3%)

sample2.9s (16.1%)

Profiling