Details

analyze3.2s (22.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	3%	97%	0
0%	3%	97%	1
0%	3%	97%	2
0%	3%	97%	3
0%	3%	97%	4
0%	3%	97%	5
0%	1.5%	98.5%	6
0%	1.5%	98.5%	7
0%	1.5%	98.5%	8
0%	1.5%	98.5%	9
0%	1.5%	98.5%	10
0%	1.5%	98.5%	11
0%	1.5%	98.5%	12
0%	1.5%	98.5%	13
0%	1.5%	98.5%	14

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.8s (19.8%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.7s	8256×	body	128	valid
43.0ms	128×	body	128	invalid

Compiler

Compiled 99 to 73 computations (26.3% saved)

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-neg_binary32`
718×	`fma-def_binary32`
560×	`exp-diff_binary32`
512×	`exp-sum_binary32`
448×	`sub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	145	31
3	532	29
4	2119	29
5	4431	29
6	4975	29

prune5.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.1b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))

Status

Error

Program

▶

0.1b

(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

0.1b

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize50.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
✓	0.0b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
✓	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

series120.0ms (0.9%)

Counts

4 → 156

Calls

4 calls:

52.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
42.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
15.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))
11.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary32`
24×	`add-sqr-sqrt_binary32`
20×	`add-cube-cbrt_binary32`
18×	`prod-diff_binary32`
14×	`exp-sum_binary32`

Counts

4 → 83

Calls

4 calls:

4.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
4.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
0.0ms	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))

simplify158.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

373×	`distribute-rgt-in_binary32`
252×	`times-frac_binary32`
214×	`fma-neg_binary32`
180×	`associate-r_binary32`
152×	`associate-+r+_binary32`

Counts

239 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	6496
1	704	5860
2	3071	5155
3	4888	5155
4	4936	5155

prune313.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Error

0.0b

Counts

162 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	2.7b	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (exp.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	3.0b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
▶	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))

Compiler

Compiled 6862 to 3939 computations (42.6% saved)

localize58.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
✓	0.0b	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))
✓	0.1b	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
✓	0.3b	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))

series2.1s (14.7%)

Counts

4 → 240

Calls

4 calls:

1.9s	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
72.0ms	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
54.0ms	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
35.0ms	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))

rewrite65.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary32`
15×	`associate-+r-_binary32`
15×	`div-sub_binary32`
14×	`exp-diff_binary32`
13×	`*-un-lft-identity_binary32`

Counts

4 → 96

Calls

4 calls:

31.0ms	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))))
11.0ms	(exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))
7.0ms	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
7.0ms	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))

simplify252.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

520×	`times-frac_binary32`
384×	`associate-r_binary32`
317×	`associate-/l*_binary32`
275×	`associate-l_binary32`
271×	`associate-/r*_binary32`

Counts

336 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	444	13204
1	1276	12954
2	4985	12740
3	5049	12740

prune1.1s (8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	397	4	401
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	400	5	405

Error

0.0b

Counts

405 → 5

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))))
▶	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (exp.f32 (.f32 1/3 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))
	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	2.7b	(.f32 (/.f32 1/2 v) (/.f32 (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v))))) (.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v))) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v)))) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v))))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (pow.f32 (exp.f32 1/3) (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))))

Compiler

Compiled 32993 to 20936 computations (36.5% saved)

localize105.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (.f32 1/3 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.3b	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
✓	0.4b	(.f32 1/3 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
✓	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series73.0ms (0.5%)

Counts

3 → 52

Calls

3 calls:

31.0ms

(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

23.0ms

(exp.f32 (*.f32 1/3 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

19.0ms

(*.f32 1/3 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

rewrite69.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`*-un-lft-identity_binary32`
108×	`prod-diff_binary32`
98×	`div-inv_binary32`
74×	`exp-sum_binary32`
74×	`distribute-lft-in_binary32`

Counts

3 → 209

Calls

3 calls:

18.0ms

(*.f32 1/3 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

16.0ms

(exp.f32 (*.f32 1/3 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

3.0ms

(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

simplify246.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary32`
335×	`distribute-rgt-in_binary32`
289×	`exp-prod_binary32`
206×	`cancel-sign-sub-inv_binary32`
176×	`fma-neg_binary32`

Counts

261 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	9207
1	666	6395
2	2395	4068
3	4547	4068
4	4992	4068
5	4942	4068

prune861.0ms (6.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	298	2	300
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	301	4	305

Error

0.0b

Counts

305 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (exp.f32 (-.f32 6931/30000 (/.f32 1/3 v)))))
	2.7b	(.f32 (/.f32 1/2 v) (/.f32 (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v))))) (.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v))) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v)))) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v))))))
▶	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (exp.f32 (+.f32 (.f32 6931/10000 1/3) (.f32 (.f32 (neg.f32 (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 1/3)))))

Compiler

Compiled 23640 to 14991 computations (36.6% saved)

localize116.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (.f32 (neg.f32 (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 1/3)
✓	0.5b	(.f32 (neg.f32 (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓	1.0b	(*.f32 6931/10000 1/3)
	6.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

series140.0ms (1%)

Counts

3 → 64

Calls

3 calls:

75.0ms

(*.f32 (*.f32 (neg.f32 (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) 1/3)

65.0ms

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

0.0ms

(*.f32 6931/10000 1/3)

rewrite72.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`sqrt-div_binary32`
32×	`associate-l_binary32`
31×	`*-un-lft-identity_binary32`
28×	`sqrt-prod_binary32`
24×	`distribute-neg-frac_binary32`

Counts

3 → 127

Calls

3 calls:

25.0ms

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

24.0ms

(*.f32 (*.f32 (neg.f32 (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))) 1/3)

4.0ms

(*.f32 6931/10000 1/3)

simplify159.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

413×	`distribute-rgt-in_binary32`
394×	`distribute-lft-in_binary32`
234×	`distribute-lft-neg-out_binary32`
208×	`distribute-rgt-neg-out_binary32`
196×	`associate-l_binary32`

Counts

191 → 200

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	4267
1	496	3805
2	1483	3505
3	4480	3500
4	4988	3500
5	4965	3500

prune631.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	256	4	260

Error

0.0b

Counts

260 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (exp.f32 (-.f32 6931/30000 (/.f32 1/3 v)))))
	2.7b	(.f32 (/.f32 1/2 v) (/.f32 (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v))))) (.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v))) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v)))) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O 1) v))))))
✓	0.1b	(.f32 (/.f32 1/2 v) (.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))) (exp.f32 (+.f32 (.f32 6931/10000 1/3) (.f32 (.f32 (neg.f32 (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (sqrt.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 1/3)))))

Compiler

Compiled 18598 to 11160 computations (40% saved)

regimes1.2s (8.3%)

Accuracy

Total 0.0b remaining (35.6%)

Threshold costs 0.0b (35.6%)

Counts

99 → 1

Compiler

Compiled 35289 to 24646 computations (30.2% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary32`
10×	`+-commutative_binary32`
9×	`neg-sub0_binary32`
9×	`neg-mul-1_binary32`
8×	`sub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	92
1	52	92
2	66	92
3	82	90
4	96	90
5	102	90
6	104	90
7	101	90

end184.0ms (1.3%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 588 to 414 computations (29.6% saved)

Details

analyze3.2s (22.5%)

sample2.8s (19.8%)

simplify53.0ms (0.4%)

prune5.0ms (0%)

localize50.0ms (0.4%)

series120.0ms (0.9%)

rewrite16.0ms (0.1%)

simplify158.0ms (1.1%)

prune313.0ms (2.2%)

localize58.0ms (0.4%)

series2.1s (14.7%)

rewrite65.0ms (0.5%)

simplify252.0ms (1.8%)

prune1.1s (8%)

localize105.0ms (0.7%)

series73.0ms (0.5%)

rewrite69.0ms (0.5%)

simplify246.0ms (1.7%)

prune861.0ms (6.1%)

localize116.0ms (0.8%)

series140.0ms (1%)

rewrite72.0ms (0.5%)

simplify159.0ms (1.1%)

prune631.0ms (4.5%)

regimes1.2s (8.3%)

simplify6.0ms (0%)

end184.0ms (1.3%)

Profiling