Details

analyze64.0ms (0.5%)

Algorithm

1×

Search

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

Compiler

Compiled 50 to 36 computations (28% saved)

sample78.0ms (0.6%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify50.0ms (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 → 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

prune4.0ms (0%)

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)

localize56.0ms (0.4%)

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))

rewrite203.0ms (1.6%)

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:

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)
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 3186 to 1444 computations (54.7% saved)

series306.0ms (2.5%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

187.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
59.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
23.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
16.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 3340 to 2368 computations (29.1% saved)

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-/r/_binary32`
260×	`associate-/r*_binary32`
232×	`associate-l_binary32`
218×	`associate-r_binary32`
195×	`times-frac_binary32`

Counts

149 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	4454
1	717	3655
2	2714	3563
3	4674	3555
4	4976	3555
5	4962	3555

prune126.0ms (1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	98	13	111
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	98	15	113

Error

0.1b

Counts

113 → 15

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)))))))))
	0.7b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.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 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 (.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 (/.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 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 1 (sqrt.f32 v)) (/.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 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 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 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))))
	0.6b	(.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)))))))))
	23.8b	(.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)) 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)))))))))
	0.6b	(.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))))))))

Compiler

Compiled 2819 to 1512 computations (46.4% saved)

localize63.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite148.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-cbrt-cube_binary32`
19×	`add-exp-log_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-sqr-sqrt_binary32`
9×	`add-cube-cbrt_binary32`

Counts

4 → 69

Calls

4 calls:

5.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
5.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
2.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 1869 to 828 computations (55.7% saved)

series94.0ms (0.8%)

Error

0.1b

Counts

4 → 36

Calls

4 calls:

23.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
22.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
16.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
14.0ms	(sinh.f32 (/.f32 1 v))

Compiler

Compiled 1987 to 1363 computations (31.4% saved)

simplify105.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

889×	`associate-/l*_binary32`
434×	`associate-*l/_binary32`
343×	`associate-/l/_binary32`
322×	`associate-*r/_binary32`
316×	`associate-/r*_binary32`

Counts

105 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	1340
1	416	1171
2	1433	1171
3	4437	1133
4	4767	1133
5	4999	1133
6	4934	1133

prune94.0ms (0.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	5	8	13
Picked	1	0	1
Done	0	1	1
Total	50	15	65

Error

0.1b

Counts

65 → 15

Alt Table

Status	Error	Program
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 (/.f32 cosTheta_i (.f32 (cbrt.f32 v) (cbrt.f32 v))) cosTheta_O) (cbrt.f32 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.7b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) v) (/.f32 (/.f32 (cbrt.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 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 1 (sqrt.f32 v)) (/.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 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 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.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)))))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (cbrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (cbrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (.f32 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 (.f32 2 (sinh.f32 (/.f32 1 v))) (sqrt.f32 v)) (sqrt.f32 v)))
	0.5b	(/.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 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) cosTheta_O) (sqrt.f32 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 (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)))))))
	0.6b	(.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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (sqrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))

Compiler

Compiled 1916 to 1066 computations (44.4% saved)

localize47.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))
0.4b	(/.f32 (/.f32 cosTheta_i v) (*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
0.7b	(exp.f32 (/.f32 1 v))
0.7b	(exp.f32 (/.f32 -1 v))

rewrite214.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

49×	`times-frac_binary32`
35×	`*-un-lft-identity_binary32`
35×	`add-sqr-sqrt_binary32`
33×	`add-cube-cbrt_binary32`
26×	`exp-prod_binary32`

Counts

4 → 106

Calls

4 calls:

10.0ms	(/.f32 (/.f32 cosTheta_i v) (*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
6.0ms	(-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))
5.0ms	(exp.f32 (/.f32 -1 v))
3.0ms	(exp.f32 (/.f32 1 v))

Compiler

Compiled 2672 to 1643 computations (38.5% saved)

series104.0ms (0.8%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

42.0ms	(/.f32 (/.f32 cosTheta_i v) (*.f32 v (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
10.0ms	(exp.f32 (/.f32 1 v))
10.0ms	(-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))
8.0ms	(exp.f32 (/.f32 -1 v))

Compiler

Compiled 1618 to 1199 computations (25.9% saved)

simplify139.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

602×	`associate-/r*_binary32`
539×	`associate-/l*_binary32`
517×	`associate-/l/_binary32`
300×	`associate-*l/_binary32`
205×	`associate-/r/_binary32`

Counts

145 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	2913
1	554	2625
2	1429	2602
3	4880	2602
4	4987	2602
5	4961	2602

prune133.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	7	6	13
Picked	1	0	1
Done	1	0	1
Total	91	12	103

Error

0.0b

Counts

103 → 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)) (exp.f32 (log.f32 (.f32 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 (/.f32 cosTheta_i (sqrt.f32 v)) cosTheta_O) (sqrt.f32 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 (/.f32 cosTheta_i (.f32 (cbrt.f32 v) (cbrt.f32 v))) cosTheta_O) (cbrt.f32 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (sqrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (-.f32 (pow.f32 E.f32 (/.f32 1 v)) (exp.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 1 v)) (exp.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 (cbrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (cbrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.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 1 v)) (exp.f32 (/.f32 -1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (-.f32 (exp.f32 (/.f32 2 v)) (exp.f32 (neg.f32 (/.f32 2 v)))))) (+.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (*.f32 (+.f32 (sqrt.f32 (exp.f32 (/.f32 -1 v))) (sqrt.f32 (exp.f32 (/.f32 1 v)))) (-.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) (sqrt.f32 (exp.f32 (/.f32 -1 v))))))))

Compiler

Compiled 2138 to 1367 computations (36.1% saved)

localize53.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
0.4b	(*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
0.7b	(exp.f32 (/.f32 1 v))
0.7b	(exp.f32 (/.f32 -1 v))

rewrite947.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

643×	`times-frac_binary32`
489×	`add-sqr-sqrt_binary32`
374×	`*-un-lft-identity_binary32`
276×	`add-cube-cbrt_binary32`
157×	`sqrt-prod_binary32`

Counts

4 → 458

Calls

4 calls:

111.0ms	(*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
12.0ms	(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
3.0ms	(exp.f32 (/.f32 -1 v))
3.0ms	(exp.f32 (/.f32 1 v))

Compiler

Compiled 13901 to 8045 computations (42.1% saved)

series105.0ms (0.8%)

Error

0.0b

Counts

4 → 33

Calls

4 calls:

37.0ms	(*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
28.0ms	(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))
10.0ms	(exp.f32 (/.f32 1 v))
9.0ms	(exp.f32 (/.f32 -1 v))

Compiler

Compiled 1723 to 1261 computations (26.8% saved)

simplify387.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

614×	`associate-*r/_binary32`
606×	`associate-*l/_binary32`
387×	`associate-/l/_binary32`
365×	`associate-/l*_binary32`
213×	`associate-/r*_binary32`

Counts

491 → 376

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	499	18582
1	1412	17062
2	4668	17062
3	4975	17062

prune430.0ms (3.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	371	5	376
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	373	15	388

Error

0.0b

Counts

388 → 15

Alt Table

Status	Error	Program
	23.8b	(.f32 cosTheta_O (.f32 (*.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (sqrt.f32 cosTheta_i) (fabs.f32 (cbrt.f32 v)))) (/.f32 (/.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 (cbrt.f32 v))) (-.f32 (exp.f32 (/.f32 1 v)) (exp.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)))))))
	0.6b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 (sqrt.f32 v)))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 (sqrt.f32 v))) (-.f32 (exp.f32 (/.f32 1 v)) (exp.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 (sqrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (sqrt.f32 (.f32 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)) (exp.f32 (log.f32 (.f32 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 (/.f32 cosTheta_i (sqrt.f32 v)) cosTheta_O) (sqrt.f32 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 (/.f32 cosTheta_i (.f32 (cbrt.f32 v) (cbrt.f32 v))) cosTheta_O) (cbrt.f32 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.6b	(.f32 cosTheta_O (.f32 (.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))))) (/.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (-.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (-.f32 (pow.f32 E.f32 (/.f32 1 v)) (exp.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 1 v)) (exp.f32 (/.f32 -1 v))))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (fabs.f32 (cbrt.f32 v))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 (cbrt.f32 v))) (-.f32 (exp.f32 (/.f32 1 v)) (exp.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 (cbrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))) (cbrt.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.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 1 v)) (exp.f32 (/.f32 -1 v)))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 cosTheta_i v) (*.f32 v (-.f32 (exp.f32 (/.f32 2 v)) (exp.f32 (neg.f32 (/.f32 2 v)))))) (+.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v)))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 v) (sqrt.f32 v)) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (-.f32 (pow.f32 E.f32 (/.f32 1 v)) (exp.f32 (/.f32 -1 v))))))

Compiler

Compiled 8038 to 4655 computations (42.1% saved)

regimes5.4s (43.8%)

Accuracy

Total 0.3b remaining (80.9%)

Threshold costs 0.3b (80.9%)

Compiler

Compiled 115784 to 80975 computations (30.1% 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	35
1	26	35
2	25	35

end38.0ms (0.3%)

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

sample2.8s (22.6%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
393.0ms	8000×	pre	128	true

Compiler

Compiled 607 to 414 computations (31.8% saved)

Details

analyze64.0ms (0.5%)

sample78.0ms (0.6%)

simplify50.0ms (0.4%)

prune4.0ms (0%)

localize56.0ms (0.4%)

rewrite203.0ms (1.6%)

series306.0ms (2.5%)

simplify164.0ms (1.3%)

prune126.0ms (1%)

localize63.0ms (0.5%)

rewrite148.0ms (1.2%)

series94.0ms (0.8%)

simplify105.0ms (0.9%)

prune94.0ms (0.8%)

localize47.0ms (0.4%)

rewrite214.0ms (1.7%)

series104.0ms (0.8%)

simplify139.0ms (1.1%)

prune133.0ms (1.1%)

localize53.0ms (0.4%)

rewrite947.0ms (7.7%)

series105.0ms (0.8%)

simplify387.0ms (3.1%)

prune430.0ms (3.5%)

regimes5.4s (43.8%)

simplify3.0ms (0%)

end38.0ms (0.3%)

sample2.8s (22.6%)

Profiling