Details

analyze8.0ms (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)

sample2.1s (32.8%)

Infinites

100% of outputs are infinite.

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify50.0ms (0.8%)

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 (0.1%)

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	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 (.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

0.5b

(*.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 (*.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 154 to 104 computations (32.5% saved)

localize58.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series40.0ms (0.6%)

Counts

4 → 24

Calls

4 calls:

13.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
8.0ms	(sinh.f32 (/.f32 1 v))
8.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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 → 77

Calls

4 calls:

5.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

simplify111.0ms (1.7%)

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

101 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	1396
1	428	1227
2	1461	1227
3	4514	1159
4	4805	1159
5	5000	1159
6	4999	1159
7	4940	1159

prune183.0ms (2.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	14	118
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	105	15	120

Error

0.1b

Counts

120 → 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 (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 cosTheta_i cosTheta_O) v)) (exp.f32 (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
	10.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (sqrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (sqrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.6b	(/.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 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))) (cbrt.f32 (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) 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) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	11.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (exp.f32 (log.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (+.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2)) (log.f32 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 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (sqrt.f32 v)) (sqrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (expm1.f32 (log1p.f32 (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))))

Compiler

Compiled 4230 to 2095 computations (50.5% saved)

localize72.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.5b	(exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))
	0.8b	(sinh.f32 (/.f32 1 v))

series22.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))
8.0ms	(.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary32`
7×	`add-cbrt-cube_binary32`
7×	`add-exp-log_binary32`
6×	`exp-prod_binary32`
6×	`pow-prod-down_binary32`

Counts

2 → 39

Calls

2 calls:

7.0ms	(.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))
5.0ms	(exp.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

498×	`associate-+l+_binary32`
430×	`associate-l_binary32`
311×	`distribute-rgt-in_binary32`
303×	`distribute-lft-in_binary32`
287×	`associate-r_binary32`

Counts

63 → 49

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	996
1	178	908
2	513	908
3	1793	837
4	4721	813
5	5000	813
6	4966	813

prune231.0ms (3.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	99	14	113

Error

0.1b

Counts

113 → 14

Alt Table

Status	Error	Program
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (+.f32 (log.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2)) (log.f32 v))))
	3.1b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (log.f32 (pow.f32 (exp.f32 v) (.f32 2 (sinh.f32 (/.f32 1 v))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.6b	(/.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 (.f32 (sqrt.f32 (sinh.f32 (/.f32 1 v))) (sqrt.f32 (sinh.f32 (/.f32 1 v)))))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (expm1.f32 (log1p.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 (sqrt.f32 v)) cosTheta_O) (sqrt.f32 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))))))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (exp.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.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 cosTheta_i cosTheta_O) v)) (pow.f32 (E.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 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (sqrt.f32 v)) (sqrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.6b	(/.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 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))) (cbrt.f32 (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))))

Compiler

Compiled 3883 to 2088 computations (46.2% saved)

localize69.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.7b	(pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))
	0.8b	(sinh.f32 (/.f32 1 v))

series201.0ms (3.1%)

Counts

1 → 12

Calls

1 calls:

201.0ms

(pow.f32 (E.f32) (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary32`
6×	`pow-unpow_binary32`
3×	`log-pow_binary32`
3×	`pow-prod-down_binary32`
3×	`*-un-lft-identity_binary32`

Counts

1 → 25

Calls

1 calls:

7.0ms

(pow.f32 (E.f32) (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

592×	`fma-def_binary32`
455×	`distribute-rgt-in_binary32`
369×	`associate-l_binary32`
314×	`times-frac_binary32`
273×	`associate-r_binary32`

Counts

37 → 40

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	76	752
1	171	702
2	369	702
3	893	666
4	2426	594
5	5010	594

prune206.0ms (3.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	106	14	120

Error

0.0b

Counts

120 → 14

Alt Table

Status	Error	Program
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (+.f32 (log.f32 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))) (log.f32 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 cosTheta_i cosTheta_O) v)) (exp.f32 (.f32 1 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.7b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (E.f32) (sqrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (sqrt.f32 (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (expm1.f32 (log1p.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))))))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (exp.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.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 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (sqrt.f32 v)) (sqrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (sqrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (.f32 (log.f32 (E.f32)) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))))

Compiler

Compiled 4299 to 2277 computations (47% saved)

localize70.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.5b	(exp.f32 (.f32 1 (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.8b	(sinh.f32 (/.f32 1 v))

series8.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(exp.f32 (*.f32 1 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary32`
2×	`exp-sum_binary32`
2×	`log-prod_binary32`
1×	`*-un-lft-identity_binary32`
1×	`add-sqr-sqrt_binary32`

Counts

1 → 14

Calls

1 calls:

2.0ms

(exp.f32 (*.f32 1 (log.f32 (*.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary32`
813×	`associate-l_binary32`
749×	`associate-r_binary32`
402×	`unswap-sqr_binary32`
268×	`associate-/r*_binary32`

Counts

26 → 30

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	436
1	111	349
2	248	349
3	824	329
4	4783	329
5	5394	329

prune471.0ms (7.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	96	14	110

Error

0.0b

Counts

110 → 14

Alt Table

Status	Error	Program
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (+.f32 (log.f32 (-.f32 (exp.f32 (/.f32 1 v)) (/.f32 1 (exp.f32 (/.f32 1 v))))) (log.f32 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 cosTheta_i cosTheta_O) v)) (exp.f32 (.f32 1 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (sqrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.7b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (pow.f32 (E.f32) (sqrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (sqrt.f32 (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (expm1.f32 (log1p.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))))))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (pow.f32 (exp.f32 (.f32 (cbrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))) (cbrt.f32 (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.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 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (sqrt.f32 v)) (sqrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (*.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v)))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (sqrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (sqrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.6b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (cbrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))) (cbrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v)))))))) (cbrt.f32 (pow.f32 (E.f32) (log.f32 (.f32 v (*.f32 2 (sinh.f32 (/.f32 1 v)))))))))
	0.8b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (exp.f32 (.f32 (log.f32 (E.f32)) (log.f32 (.f32 v (.f32 2 (sinh.f32 (/.f32 1 v))))))))

Compiler

Compiled 3506 to 1889 computations (46.1% saved)

regimes2.0s (30.1%)

Accuracy

Total 0.3b remaining (74.2%)

Threshold costs 0.3b (74.2%)

Counts

175 → 1

Compiler

Compiled 45850 to 33272 computations (27.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
4×	`+-commutative_binary32`
4×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	37
1	33	37
2	43	37
3	50	37
4	55	37
5	57	37
6	56	37

end355.0ms (5.5%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 685 to 499 computations (27.2% saved)

Details

analyze8.0ms (0.1%)

sample2.1s (32.8%)

simplify50.0ms (0.8%)

prune4.0ms (0.1%)

localize58.0ms (0.9%)

series40.0ms (0.6%)

rewrite15.0ms (0.2%)

simplify111.0ms (1.7%)

prune183.0ms (2.8%)

localize72.0ms (1.1%)

series22.0ms (0.3%)

rewrite14.0ms (0.2%)

simplify86.0ms (1.3%)

prune231.0ms (3.6%)

localize69.0ms (1.1%)

series201.0ms (3.1%)

rewrite8.0ms (0.1%)

simplify55.0ms (0.8%)

prune206.0ms (3.2%)

localize70.0ms (1.1%)

series8.0ms (0.1%)

rewrite2.0ms (0%)

simplify63.0ms (1%)

prune471.0ms (7.3%)

regimes2.0s (30.1%)

simplify3.0ms (0.1%)

end355.0ms (5.5%)

Profiling