Details

analyze6.2s (21.2%)

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)

sample10.6s (36.4%)

Results

10.5s

8256×

body

128

valid

Compiler

Compiled 338 to 238 computations (29.6% saved)

simplify79.0ms (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

prune12.0ms (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)

localize203.0ms (0.7%)

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)))
✓	12.7b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

series352.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

255.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
47.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))
45.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
5.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))

rewrite32.0ms (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:

12.0ms	(.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))
5.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
3.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
2.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

simplify160.0ms (0.5%)

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

prune2.6s (8.8%)

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 (/.f32 1 (hypot.f32 1 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (.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 (/.f32 1 (hypot.f32 1 (/.f32 (*.f32 alphay (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (*.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 48190 to 30288 computations (37.1% saved)

localize295.0ms (1%)

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)))
	12.7b	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

prune2.0s (6.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	453	1	454
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	454	1	455

Error

0.2b

Counts

455 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (/.f32 1 (hypot.f32 1 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (/.f32 (/.f32 1 (hypot.f32 1 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (.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 (/.f32 1 (hypot.f32 1 (/.f32 (*.f32 alphay (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (/.f32 (/.f32 1 (hypot.f32 1 (/.f32 (*.f32 alphay (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (*.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 40745 to 26453 computations (35.1% saved)

localize182.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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))
	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)))

series204.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

204.0ms

(/.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))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary32`
13×	`add-exp-log_binary32`
4×	`sin-atan_binary32`
4×	`associate-/l/_binary32`
4×	`cbrt-unprod_binary32`

Counts

1 → 28

Calls

1 calls:

14.0ms

(/.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))

simplify245.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-neg_binary32`
534×	`times-frac_binary32`
366×	`unswap-sqr_binary32`
354×	`associate-/l*_binary32`
262×	`fma-def_binary32`

Counts

64 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	2299
1	188	1963
2	559	1938
3	2125	1915
4	3219	1915
5	4466	1915
6	4961	1915

prune1.8s (6.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	404	1	405

Error

0.2b

Counts

405 → 1

Alt Table

Status	Error	Program
✓	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (/.f32 1 (hypot.f32 1 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (/.f32 (/.f32 1 (hypot.f32 1 (/.f32 (.f32 alphay (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (.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 (/.f32 1 (hypot.f32 1 (/.f32 (*.f32 alphay (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (/.f32 (/.f32 1 (hypot.f32 1 (/.f32 (*.f32 alphay (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))) alphax))) (*.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 36946 to 24712 computations (33.1% saved)

regimes4.0s (13.8%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

82 → 1

Compiler

Compiled 82957 to 59133 computations (28.7% saved)

simplify6.0ms (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	31	104
1	38	104
2	42	104
3	44	104
4	45	104
5	44	104

end238.0ms (0.8%)

Compiler: Compiled 223 to 167 computations (25.1% saved)

Details

analyze6.2s (21.2%)

sample10.6s (36.4%)

simplify79.0ms (0.3%)

prune12.0ms (0%)

localize203.0ms (0.7%)

series352.0ms (1.2%)

rewrite32.0ms (0.1%)

simplify160.0ms (0.5%)

prune2.6s (8.8%)

localize295.0ms (1%)

prune2.0s (6.7%)

localize182.0ms (0.6%)

series204.0ms (0.7%)

rewrite21.0ms (0.1%)

simplify245.0ms (0.8%)

prune1.8s (6.1%)

regimes4.0s (13.8%)

simplify6.0ms (0%)

end238.0ms (0.8%)

Profiling