Details

analyze2.2s (25.9%)

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
0.6%	0.9%	98.5%	11
0.6%	0.9%	98.5%	12
0.6%	0.9%	98.5%	13
0.6%	0.9%	98.5%	14

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.5s (29.3%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.4s	8256×	body	128	valid
31.0ms	116×	body	128	invalid

Compiler

Compiled 168 to 124 computations (26.2% saved)

simplify49.0ms (0.6%)

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 (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(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)))))
▶	0.0b	(*.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)))))

Status

Error

Program

0.0b

(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)))))

▶

0.0b

(*.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)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize53.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.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)))))
✓	0.0b	(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	(-.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)

series200.0ms (2.3%)

Counts

4 → 180

Calls

4 calls:

108.0ms	(*.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)))))
42.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
39.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
11.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary32`
39×	`*-un-lft-identity_binary32`
35×	`add-cube-cbrt_binary32`
28×	`exp-sum_binary32`
27×	`prod-diff_binary32`

Counts

4 → 123

Calls

4 calls:

14.0ms	(*.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)))))
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))))
3.0ms	(-.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)

simplify182.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

392×	`times-frac_binary32`
288×	`associate-/l*_binary32`
278×	`associate-r_binary32`
275×	`associate-+r+_binary32`
243×	`fma-def_binary32`

Counts

303 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	441	10899
1	1203	10395
2	5156	10395

prune316.0ms (3.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	234	2	236
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	236	2	238

Error

0.0b

Counts

238 → 2

Alt Table

Status	Error	Program
	13.2b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
▶	0.0b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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)))))))

Status

Error

Program

13.2b

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

▶

0.0b

(*.f32 (sqrt.f32 (*.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)))))) (sqrt.f32 (*.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)))))))

Compiler

Compiled 11058 to 6361 computations (42.5% saved)

localize56.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series203.0ms (2.4%)

Counts

1 → 48

Calls

1 calls:

203.0ms

(sqrt.f32 (*.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))))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary32`
3×	`sqrt-div_binary32`
2×	`exp-diff_binary32`
2×	`sqrt-pow1_binary32`
1×	`*-un-lft-identity_binary32`

Counts

1 → 16

Calls

1 calls:

8.0ms

(sqrt.f32 (*.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))))))

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-def_binary32`
423×	`*-commutative_binary32`
371×	`associate-/l*_binary32`
274×	`times-frac_binary32`
234×	`associate-/l/_binary32`

Counts

64 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	3039
1	388	2923
2	1013	2899
3	2348	2883
4	4959	2883
5	4984	2883

prune578.0ms (6.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	338	0	338
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	338	2	340

Error

0.0b

Counts

340 → 2

Alt Table

Status	Error	Program
▶	13.2b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
✓	0.0b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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)))))))

Status

Error

Program

▶

13.2b

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

✓

0.0b

(*.f32 (sqrt.f32 (*.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)))))) (sqrt.f32 (*.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)))))))

Compiler

Compiled 23209 to 13291 computations (42.7% saved)

localize74.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.2b	(sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.5b	(*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
✓	30.4b	(fma.f32 (neg.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

series412.0ms (4.8%)

Counts

3 → 59

Calls

3 calls:

343.0ms

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

55.0ms

(sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))

14.0ms

(*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary32`
21×	`sqrt-prod_binary32`
19×	`pow1_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-cube-cbrt_binary32`

Counts

3 → 78

Calls

3 calls:

6.0ms

(*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

1.0ms

(sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))

0.0ms

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

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

549×	`distribute-rgt-in_binary32`
542×	`fma-neg_binary32`
448×	`associate-l_binary32`
432×	`associate-r_binary32`
378×	`cancel-sign-sub-inv_binary32`

Counts

137 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	2520
1	180	2226
2	529	1912
3	2289	1595
4	4893	1593
5	4806	1593

prune296.0ms (3.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	192	2	194

Error

0.0b

Counts

194 → 2

Alt Table

Status	Error	Program
✓	13.2b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
✓	0.0b	(.f32 (sqrt.f32 (.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)))))) (sqrt.f32 (*.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)))))))

Status

Error

Program

✓

13.2b

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

✓

0.0b

(*.f32 (sqrt.f32 (*.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)))))) (sqrt.f32 (*.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)))))))

Compiler

Compiled 12811 to 6822 computations (46.7% saved)

regimes1.0s (11.9%)

Accuracy

Total 0.0b remaining (13.1%)

Threshold costs 0.0b (13.1%)

Counts

91 → 1

Compiler

Compiled 31525 to 21335 computations (32.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	35	59
2	44	59
3	48	59
4	50	59
5	48	59

end120.0ms (1.4%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 378 to 248 computations (34.4% saved)

Details

analyze2.2s (25.9%)

sample2.5s (29.3%)

simplify49.0ms (0.6%)

prune5.0ms (0.1%)

localize53.0ms (0.6%)

series200.0ms (2.3%)

rewrite35.0ms (0.4%)

simplify182.0ms (2.1%)

prune316.0ms (3.7%)

localize56.0ms (0.7%)

series203.0ms (2.4%)

rewrite9.0ms (0.1%)

simplify102.0ms (1.2%)

prune578.0ms (6.8%)

localize74.0ms (0.9%)

series412.0ms (4.8%)

rewrite13.0ms (0.2%)

simplify102.0ms (1.2%)

prune296.0ms (3.5%)

regimes1.0s (11.9%)

simplify4.0ms (0%)

end120.0ms (1.4%)

Profiling