Details

analyze3.3s (28.4%)

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)

sample206.0ms (1.8%)

Algorithm

1×

intervals

Results

162.0ms	256×	body	128	valid
13.0ms	256×	pre	128	true

Compiler

Compiled 219 to 155 computations (29.2% saved)

simplify50.0ms (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)

localize100.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))
✓	12.4b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
✓	13.7b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

series177.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

125.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
25.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
24.0ms	(cos.f32 (atan.f32 (.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))

rewrite16.0ms (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:

6.0ms	(.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))))))

simplify113.0ms (1%)

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

prune1.1s (9.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	550	0	550
Fresh	0	0	0
Picked	0	1	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 (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 48109 to 30229 computations (37.2% saved)

regimes455.0ms (3.9%)

Accuracy

Total -0.0b remaining (-0.2%)

Threshold costs -0.0b (-0.2%)

Counts

14 → 1

Compiler

Compiled 14993 to 10331 computations (31.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
5×	`+-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	33	146
1	45	146
2	49	146
3	51	146
4	52	146
5	51	146

end2.0ms (0%)

Compiler: Compiled 92 to 64 computations (30.4% saved)

sample6.1s (52.3%)

Algorithm

1×

intervals

Results

4.8s	8000×	body	128	valid
369.0ms	8000×	pre	128	true

Compiler

Compiled 296 to 208 computations (29.7% saved)

Details

analyze3.3s (28.4%)

sample206.0ms (1.8%)

simplify50.0ms (0.4%)

prune7.0ms (0.1%)

localize100.0ms (0.9%)

series177.0ms (1.5%)

rewrite16.0ms (0.1%)

simplify113.0ms (1%)

prune1.1s (9.6%)

regimes455.0ms (3.9%)

simplify5.0ms (0%)

end2.0ms (0%)

sample6.1s (52.3%)

Profiling