Details

analyze3.2s (26.6%)

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)

sample6.6s (54.8%)

Results

6.5s

8256×

body

128

valid

Compiler

Compiled 338 to 238 computations (29.6% saved)

simplify44.0ms (0.4%)

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 (0.1%)

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)

localize107.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
✓	0.4b	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
✓	12.8b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))
✓	13.2b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))

series203.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

143.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
31.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))
26.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
3.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))

rewrite17.0ms (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:

7.0ms	(.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 (0.9%)

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 → 145

Iterations

Useful iterations: 2 (0.0ms)

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

prune1.2s (10.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	542	0	542
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	542	1	543

Error

0.2b

Counts

543 → 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 47625 to 29927 computations (37.2% saved)

regimes391.0ms (3.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

10 → 1

Compiler

Compiled 11145 to 7679 computations (31.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	29	117
1	36	117
2	40	117
3	42	117
4	43	117
5	42	117

end119.0ms (1%)

Compiler: Compiled 231 to 159 computations (31.2% saved)

Details

analyze3.2s (26.6%)

sample6.6s (54.8%)

simplify44.0ms (0.4%)

prune7.0ms (0.1%)

localize107.0ms (0.9%)

series203.0ms (1.7%)

rewrite17.0ms (0.1%)

simplify114.0ms (0.9%)

prune1.2s (10.2%)

regimes391.0ms (3.2%)

simplify5.0ms (0%)

end119.0ms (1%)

Profiling