Details

analyze3.1s (16.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 123 to 87 computations (29.3% saved)

sample6.3s (33.9%)

Results

6.2s

8256×

body

128

valid

Compiler

Compiled 338 to 238 computations (29.6% saved)

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary32`
676×	`div-sub_binary32`
601×	`times-frac_binary32`
366×	`associate-/l/_binary32`
346×	`distribute-rgt-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	138
1	66	133
2	117	125
3	212	117
4	404	117
5	1310	117
6	4092	117
7	5339	117

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Status

Error

Program

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 319 to 215 computations (32.6% saved)

localize103.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
✓	0.4b	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
✓	11.8b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
✓	12.2b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

series202.0ms (1.1%)

Counts

4 → 96

Calls

4 calls:

144.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
28.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
28.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))
2.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary32`
16×	`associate-l_binary32`
14×	`*-un-lft-identity_binary32`
14×	`add-cube-cbrt_binary32`
11×	`add-cbrt-cube_binary32`

Counts

4 → 84

Calls

4 calls:

9.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
3.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
1.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
1.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

simplify114.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-def_binary32`
585×	`associate-*l/_binary32`
298×	`associate-/r/_binary32`
226×	`associate-r_binary32`
190×	`distribute-lft-in_binary32`

Counts

180 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	4788
1	644	4574
2	2492	4519
3	5474	4519

prune1.5s (7.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	549	1	550
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	550	1	551

Error

0.2b

Counts

551 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Status

Error

Program

▶

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 48204 to 30296 computations (37.2% saved)

localize130.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))
	11.8b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
✓	11.8b	(tan.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))
	12.2b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

series31.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

28.0ms

(tan.f32 (*.f32 (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))

3.0ms

(*.f32 (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`pow1_binary32`
28×	`sqrt-pow1_binary32`
20×	`pow-prod-down_binary32`
10×	`pow-prod-up_binary32`
10×	`pow1/2_binary32`

Counts

2 → 61

Calls

2 calls:

7.0ms

(*.f32 (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))

2.0ms

(tan.f32 (*.f32 (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

745×	`times-frac_binary32`
470×	`associate-/l*_binary32`
304×	`associate-/r*_binary32`
269×	`fma-def_binary32`
260×	`associate-+l+_binary32`

Counts

85 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	1606
1	272	1411
2	1043	1340
3	5192	1340

prune490.0ms (2.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	1	186

Error

0.2b

Counts

186 → 1

Alt Table

Status	Error	Program
✓	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (.f32 alphax alphax)) (/.f32 (.f32 (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Status

Error

Program

✓

0.2b

(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.f32 (cos.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (*.f32 alphax alphax)) (/.f32 (*.f32 (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (sin.f32 (atan.f32 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))) (sqrt.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))))) (*.f32 alphay alphay)))) (-.f32 1 u0)))))

Compiler

Compiled 17952 to 11808 computations (34.2% saved)

regimes6.4s (34.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

214 → 1

Compiler

Compiled 224826 to 156165 computations (30.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	132
1	44	132
2	48	132
3	50	132
4	51	132
5	50	132

end131.0ms (0.7%)

Compiler: Compiled 258 to 180 computations (30.2% saved)

Details

analyze3.1s (16.5%)

sample6.3s (33.9%)

simplify48.0ms (0.3%)

prune7.0ms (0%)

localize103.0ms (0.6%)

series202.0ms (1.1%)

rewrite18.0ms (0.1%)

simplify114.0ms (0.6%)

prune1.5s (7.9%)

localize130.0ms (0.7%)

series31.0ms (0.2%)

rewrite13.0ms (0.1%)

simplify57.0ms (0.3%)

prune490.0ms (2.6%)

regimes6.4s (34.5%)

simplify5.0ms (0%)

end131.0ms (0.7%)

Profiling