Details

analyze7.0ms (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)

sample2.3s (21.4%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.3s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify46.0ms (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 → 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%)

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)

localize54.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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)))))
✓	0.9b	(sinh.f32 (/.f32 1 v))

series417.0ms (3.9%)

Counts

4 → 96

Calls

4 calls:

340.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
60.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
12.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
5.0ms	(sinh.f32 (/.f32 1 v))

rewrite93.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary32`
165×	`add-log-exp_binary32`
165×	`log1p-expm1-u_binary32`
165×	`expm1-log1p-u_binary32`
163×	`add-cbrt-cube_binary32`

Counts

4 → 139

Calls

4 calls:

89.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
89.0ms	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
89.0ms	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
89.0ms	(sinh.f32 (/.f32 1 v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	65
1	359	65
2	4813	65
3	4981	65
0	0	0
1	0	0

simplify118.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

445×	`times-frac_binary32`
293×	`associate-/l*_binary32`
274×	`associate-r_binary32`
265×	`unswap-sqr_binary32`
262×	`associate-/r*_binary32`

Counts

235 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	6012
1	811	5668
2	4214	5630
3	5028	5630

prune352.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	176	10	186
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	11	188

Error

0.1b

Counts

188 → 11

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (sqrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (/.f32 (/.f32 1 v) (sqrt.f32 (.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 1 v) (/.f32 1 (.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))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (pow.f32 (cbrt.f32 cosTheta_i) 2) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (cbrt.f32 cosTheta_i) v)))
	0.5b	(.f32 cosTheta_O (.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)))))) (pow.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)))))) 2)))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2) v) (/.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.6b	(.f32 cosTheta_O (.f32 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2) (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (/.f32 1 (.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 (pow.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 1 v) (cbrt.f32 (.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 1 v) (/.f32 (/.f32 cosTheta_i 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 1 (pow.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 cosTheta_i v) (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))))

Compiler

Compiled 7691 to 4495 computations (41.6% saved)

localize51.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.3b	(/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓	0.4b	(.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i 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))

series609.0ms (5.6%)

Counts

2 → 96

Calls

2 calls:

335.0ms

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

273.0ms

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

rewrite51.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

178×	`add-sqr-sqrt_binary32`
166×	`add-log-exp_binary32`
166×	`log1p-expm1-u_binary32`
166×	`expm1-log1p-u_binary32`
164×	`add-cbrt-cube_binary32`

Counts

2 → 123

Calls

2 calls:

47.0ms

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

47.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	55
1	362	55
2	4996	55
0	0	0
1	0	0

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Rules

689×	`times-frac_binary32`
416×	`associate-/l*_binary32`
390×	`associate-/r*_binary32`
287×	`associate-r_binary32`
202×	`associate-l_binary32`

Counts

219 → 164

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	254	8498
1	949	7932
2	5016	7932

prune819.0ms (7.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	241	4	245
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	246	10	256

Error

0.1b

Counts

256 → 10

Alt Table

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

Compiler

Compiled 10614 to 6407 computations (39.6% saved)

localize57.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.4b	(/.f32 (.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
✓	0.5b	(*.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v))
	0.9b	(sinh.f32 (/.f32 1 v))

series517.0ms (4.8%)

Counts

2 → 72

Calls

2 calls:

465.0ms

(/.f32 (*.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

51.0ms

(*.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v))

rewrite73.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

316×	`log1p-udef_binary32`
200×	`add-sqr-sqrt_binary32`
186×	`add-log-exp_binary32`
186×	`log1p-expm1-u_binary32`
186×	`expm1-log1p-u_binary32`

Counts

2 → 84

Calls

2 calls:

71.0ms

(/.f32 (*.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

71.0ms

(*.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	42
1	408	36
2	4283	36
3	4992	36
0	0	0
1	0	0

simplify144.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

385×	`times-frac_binary32`
233×	`associate-/l*_binary32`
233×	`unswap-sqr_binary32`
231×	`associate-r_binary32`
230×	`cancel-sign-sub-inv_binary32`

Counts

156 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	4534
1	581	4238
2	3271	3976
3	4872	3976
4	4998	3976
5	4975	3976

prune357.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	187	9	196

Error

0.0b

Counts

196 → 9

Alt Table

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

Compiler

Compiled 7417 to 4315 computations (41.8% saved)

localize78.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v))
✓	0.7b	(pow.f32 (sinh.f32 (/.f32 1 v)) 3)
✓	0.8b	(pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)
	0.9b	(sinh.f32 (/.f32 1 v))

series170.0ms (1.6%)

Counts

2 → 24

Calls

2 calls:

160.0ms	(pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)
10.0ms	(pow.f32 (sinh.f32 (/.f32 1 v)) 3)

rewrite43.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

664×	`log1p-expm1-u_binary32`
664×	`expm1-log1p-u_binary32`
305×	`log-prod_binary32`
132×	`expm1-udef_binary32`
132×	`log1p-udef_binary32`

Counts

2 → 55

Calls

2 calls:

41.0ms	(pow.f32 (sinh.f32 (/.f32 1 v)) 3)
41.0ms	(pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	175	15
2	1755	15
3	5051	15
0	0	0
1	0	0

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

646×	`associate-/r*_binary32`
522×	`associate-/l*_binary32`
426×	`fma-def_binary32`
381×	`associate-l_binary32`
235×	`associate-*l/_binary32`

Counts

79 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	636
1	189	614
2	444	548
3	1255	501
4	4615	501
5	4893	501

prune395.0ms (3.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	148	11	159

Error

0.0b

Counts

159 → 11

Alt Table

Status	Error	Program
✓	0.4b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (.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 (sqrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))) (/.f32 (/.f32 1 v) (sqrt.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 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (.f32 (.f32 (pow.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3) 1/3) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 cosTheta_i (pow.f32 (cbrt.f32 (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) 2)) (/.f32 (/.f32 1 v) (cbrt.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 1 v) (.f32 (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2) (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (/.f32 1 (.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))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (pow.f32 (cbrt.f32 cosTheta_i) 2) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (cbrt.f32 cosTheta_i) v)))
	0.9b	(.f32 cosTheta_O (/.f32 (.f32 (/.f32 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (.f32 (.f32 (-.f32 (.f32 (sinh.f32 (exp.f32 (log1p.f32 (/.f32 1 v)))) (cosh.f32 1)) (.f32 (cosh.f32 (exp.f32 (log1p.f32 (/.f32 1 v)))) (sinh.f32 1))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
✓	0.4b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i 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 (neg.f32 cosTheta_i) v) (/.f32 1 v)) (neg.f32 (.f32 (.f32 (pow.f32 (-.f32 (exp.f32 (log1p.f32 (pow.f32 (sinh.f32 (/.f32 1 v)) 3))) 1) 1/3) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 1 v) (.f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2)) (/.f32 (/.f32 cosTheta_i v) (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))))

Compiler

Compiled 5499 to 3348 computations (39.1% saved)

regimes3.6s (33.6%)

Accuracy

Total 0.2b remaining (68.9%)

Threshold costs 0.2b (68.9%)

Counts

337 → 1

Compiler

Compiled 86834 to 62432 computations (28.1% saved)

simplify2.0ms (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

end241.0ms (2.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 594 to 428 computations (27.9% saved)

Details

analyze7.0ms (0.1%)

sample2.3s (21.4%)

simplify46.0ms (0.4%)

prune4.0ms (0%)

localize54.0ms (0.5%)

series417.0ms (3.9%)

rewrite93.0ms (0.9%)

simplify118.0ms (1.1%)

prune352.0ms (3.3%)

localize51.0ms (0.5%)

series609.0ms (5.6%)

rewrite51.0ms (0.5%)

simplify111.0ms (1%)

prune819.0ms (7.6%)

localize57.0ms (0.5%)

series517.0ms (4.8%)

rewrite73.0ms (0.7%)

simplify144.0ms (1.3%)

prune357.0ms (3.3%)

localize78.0ms (0.7%)

series170.0ms (1.6%)

rewrite43.0ms (0.4%)

simplify51.0ms (0.5%)

prune395.0ms (3.7%)

regimes3.6s (33.6%)

simplify2.0ms (0%)

end241.0ms (2.2%)

Profiling