Details

analyze76.0ms (0.3%)

Algorithm

1×

Search

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

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample142.0ms (0.5%)

Algorithm

1×

intervals

Results

55.0ms	256×	body	128	valid
24.0ms	256×	pre	128	true

Compiler

Compiled 98 to 72 computations (26.5% saved)

simplify67.0ms (0.2%)

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

prune8.0ms (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 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 154 to 104 computations (32.5% saved)

localize108.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(.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))

series951.0ms (3.4%)

Counts

4 → 96

Calls

4 calls:

786.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
130.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
24.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
10.0ms	(sinh.f32 (/.f32 1 v))

rewrite64.0ms (0.2%)

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:

21.0ms	(/.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))))
7.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
2.0ms	(sinh.f32 (/.f32 1 v))

simplify237.0ms (0.9%)

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

prune926.0ms (3.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	206	12	218
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	208	12	220

Error

0.1b

Counts

220 → 12

Alt Table

Status	Error	Program
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 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))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (exp.f32 (log.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) (expm1.f32 (log1p.f32 (.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 (/.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 cosTheta_O (/.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))))))
	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))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.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 cosTheta_i v) (exp.f32 (+.f32 (log.f32 v) (+.f32 (+.f32 (log.f32 (sinh.f32 (/.f32 1 v))) (log.f32 2)) (/.f32 (.f32 sinTheta_i sinTheta_O) 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 (.f32 (expm1.f32 (log1p.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 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))
	0.4b	(.f32 cosTheta_O (.f32 1 (/.f32 cosTheta_i (-.f32 (.f32 (.f32 v v) (exp.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 v (/.f32 (exp.f32 (-.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))) v))))))

Compiler

Compiled 9146 to 4941 computations (46% saved)

localize158.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))
✓	0.4b	(/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))
✓	0.6b	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
✓	0.7b	(exp.f32 (/.f32 1 v))

series918.0ms (3.3%)

Counts

4 → 128

Calls

4 calls:

741.0ms	(/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))
129.0ms	(-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))
43.0ms	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
4.0ms	(exp.f32 (/.f32 1 v))

rewrite172.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`*-un-lft-identity_binary32`
150×	`times-frac_binary32`
115×	`add-sqr-sqrt_binary32`
85×	`add-cube-cbrt_binary32`
30×	`distribute-lft-out--_binary32`

Counts

4 → 201

Calls

4 calls:

39.0ms	(/.f32 (/.f32 cosTheta_i v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))
31.0ms	(-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))
14.0ms	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
6.0ms	(exp.f32 (/.f32 1 v))

simplify618.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary32`
278×	`associate-/l/_binary32`
253×	`fma-def_binary32`
159×	`*-commutative_binary32`
128×	`associate-/r/_binary32`

Counts

329 → 363

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	702	22322
1	2104	19293
2	5020	19293

prune1.5s (5.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	465	6	471
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	470	13	483

Error

0.0b

Counts

483 → 13

Alt Table

Status	Error	Program
▶	0.3b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 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))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (+.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)) (-.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.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))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.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 (+.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (-.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.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 (/.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))))))
	0.5b	(.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 (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (+.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (*.f32 sinTheta_i sinTheta_O))) (neg.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O v) (exp.f32 (/.f32 1 v)))))))

Compiler

Compiled 30576 to 18212 computations (40.4% saved)

localize79.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))
✓	0.3b	(/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))
	0.6b	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
	0.7b	(exp.f32 (/.f32 1 v))

series140.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

139.0ms

(/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (*.f32 (exp.f32 (/.f32 1 v)) (*.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary32`
134×	`*-un-lft-identity_binary32`
92×	`add-sqr-sqrt_binary32`
64×	`add-cube-cbrt_binary32`
28×	`distribute-lft-out--_binary32`

Counts

1 → 118

Calls

1 calls:

18.0ms

(/.f32 (/.f32 1 v) (-.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (*.f32 (exp.f32 (/.f32 1 v)) (*.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))

simplify210.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

474×	`associate-/r*_binary32`
403×	`times-frac_binary32`
283×	`associate-r_binary32`
280×	`associate-/l*_binary32`
245×	`associate-l_binary32`

Counts

154 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	440	15804
1	1376	14272
2	5005	14272

prune1.8s (6.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	432	2	434
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	436	11	447

Error

0.0b

Counts

447 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (+.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (-.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (.f32 (sqrt.f32 (/.f32 1 v)) (/.f32 (sqrt.f32 (/.f32 1 v)) (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (+.f32 v (.f32 sinTheta_i sinTheta_O))) (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))) (/.f32 v (exp.f32 (/.f32 1 v)))))))))
▶	0.3b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.f32 (/.f32 1 v) (+.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (.f32 sinTheta_i sinTheta_O)))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 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))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.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 (/.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 (/.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))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (+.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)) (-.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))))

Compiler

Compiled 29501 to 19162 computations (35% saved)

localize163.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (.f32 sinTheta_i sinTheta_O)))
✓	0.3b	(/.f32 (/.f32 1 v) (+.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (.f32 sinTheta_i sinTheta_O)))))
	0.6b	(.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))
	0.7b	(exp.f32 (/.f32 1 v))

series345.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

279.0ms

(/.f32 (/.f32 1 v) (+.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (*.f32 (exp.f32 (/.f32 1 v)) (*.f32 sinTheta_i sinTheta_O))) (*.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (*.f32 sinTheta_i sinTheta_O)))))

65.0ms

(*.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (*.f32 sinTheta_i sinTheta_O)))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`times-frac_binary32`
62×	`add-sqr-sqrt_binary32`
60×	`*-un-lft-identity_binary32`
60×	`add-cube-cbrt_binary32`
30×	`associate-l_binary32`

Counts

2 → 131

Calls

2 calls:

19.0ms

(*.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (*.f32 sinTheta_i sinTheta_O)))

13.0ms

(/.f32 (/.f32 1 v) (+.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (*.f32 (exp.f32 (/.f32 1 v)) (*.f32 sinTheta_i sinTheta_O))) (*.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (*.f32 sinTheta_i sinTheta_O)))))

simplify485.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

903×	`fma-def_binary32`
469×	`associate-/r*_binary32`
460×	`times-frac_binary32`
311×	`associate-/l*_binary32`
137×	`*-commutative_binary32`

Counts

203 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	514	13803
1	1695	11813
2	4940	11739
3	5626	11739

prune2.7s (9.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	418	1	419
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	419	11	430

Error

0.0b

Counts

430 → 11

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (.f32 (sqrt.f32 (/.f32 1 v)) (/.f32 (sqrt.f32 (/.f32 1 v)) (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (/.f32 (fma.f32 sinTheta_i sinTheta_O v) (exp.f32 (/.f32 1 v))))))))
✓	0.3b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i 1) (/.f32 (/.f32 1 v) (+.f32 (fma.f32 v (exp.f32 (/.f32 1 v)) (.f32 (exp.f32 (/.f32 1 v)) (.f32 sinTheta_i sinTheta_O))) (.f32 (neg.f32 (/.f32 1 (exp.f32 (/.f32 1 v)))) (+.f32 v (.f32 sinTheta_i sinTheta_O)))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (expm1.f32 (log1p.f32 (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))
	0.6b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 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))))))))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 v)) v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.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 (+.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 1 v) (-.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.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 (/.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))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (+.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)) (-.f32 (sqrt.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v))) (sqrt.f32 (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))))
	0.5b	(.f32 cosTheta_O (.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v)))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))) (cbrt.f32 (/.f32 cosTheta_i (.f32 v (-.f32 (.f32 (exp.f32 (/.f32 1 v)) (fma.f32 sinTheta_i sinTheta_O v)) (+.f32 (/.f32 v (exp.f32 (/.f32 1 v))) (/.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (/.f32 1 v))))))))))

Compiler

Compiled 25527 to 16371 computations (35.9% saved)

regimes13.2s (47.2%)

Accuracy

Total 0.3b remaining (67.7%)

Threshold costs 0.3b (67.7%)

Counts

468 → 1

Compiler

Compiled 188469 to 126678 computations (32.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
3×	`+-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	31	40
2	39	40
3	44	40
4	46	40
5	45	40

end38.0ms (0.1%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 224 to 140 computations (37.5% saved)

sample2.7s (9.5%)

Algorithm

1×

intervals

Results

963.0ms	8000×	body	128	valid
448.0ms	8000×	pre	128	true

Compiler

Compiled 646 to 424 computations (34.4% saved)

Details

analyze76.0ms (0.3%)

sample142.0ms (0.5%)

simplify67.0ms (0.2%)

prune8.0ms (0%)

localize108.0ms (0.4%)

series951.0ms (3.4%)

rewrite64.0ms (0.2%)

simplify237.0ms (0.9%)

prune926.0ms (3.3%)

localize158.0ms (0.6%)

series918.0ms (3.3%)

rewrite172.0ms (0.6%)

simplify618.0ms (2.2%)

prune1.5s (5.3%)

localize79.0ms (0.3%)

series140.0ms (0.5%)

rewrite48.0ms (0.2%)

simplify210.0ms (0.8%)

prune1.8s (6.6%)

localize163.0ms (0.6%)

series345.0ms (1.2%)

rewrite75.0ms (0.3%)

simplify485.0ms (1.7%)

prune2.7s (9.8%)

regimes13.2s (47.2%)

simplify3.0ms (0%)

end38.0ms (0.1%)

sample2.7s (9.5%)

Profiling