Details

analyze3.3s (20.6%)

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 (41.8%)

Results

6.5s

8256×

body

128

valid

Compiler

Compiled 338 to 238 computations (29.6% saved)

simplify57.0ms (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

prune8.0ms (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)

localize112.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (*.f32 alphax alphax))
✓	0.4b	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
✓	12.1b	(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))))))

series116.0ms (0.7%)

Counts

4 → 96

Calls

4 calls:

69.0ms	(/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (*.f32 alphax alphax))
24.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))
20.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
2.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))

rewrite153.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary32`
307×	`log1p-udef_binary32`
171×	`add-sqr-sqrt_binary32`
159×	`add-log-exp_binary32`
159×	`log1p-expm1-u_binary32`

Counts

4 → 99

Calls

4 calls:

150.0ms	(/.f32 (cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (*.f32 alphax alphax))
150.0ms	(*.f32 (PI.f32) (fma.f32 2 u1 1/2))
150.0ms	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))
150.0ms	(cos.f32 (atan.f32 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	68
1	337	67
2	4176	67
3	5271	67
0	0	0
1	0	0

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

714×	`times-frac_binary32`
580×	`associate-r_binary32`
483×	`associate-l_binary32`
462×	`associate-/l*_binary32`
280×	`associate-/r*_binary32`

Counts

195 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	2477
1	210	2437
2	775	2434
3	5112	2434

prune683.0ms (4.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	297	1	298

Error

0.2b

Counts

298 → 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 (pow.f32 alphax -2) (hypot.f32 1 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.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 (pow.f32 alphax -2) (hypot.f32 1 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.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 24761 to 15892 computations (35.8% saved)

localize117.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (pow.f32 alphax -2) (hypot.f32 1 (.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))
	12.1b	(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))))))

series367.0ms (2.3%)

Counts

1 → 36

Calls

1 calls:

366.0ms

(/.f32 (pow.f32 alphax -2) (hypot.f32 1 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

rewrite59.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

303×	`expm1-udef_binary32`
303×	`log1p-udef_binary32`
172×	`add-sqr-sqrt_binary32`
163×	`log1p-expm1-u_binary32`
163×	`expm1-log1p-u_binary32`

Counts

1 → 34

Calls

1 calls:

58.0ms

(/.f32 (pow.f32 alphax -2) (hypot.f32 1 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	354	26
2	4080	26
3	5058	26
0	0	0
1	0	0

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary32`
398×	`associate-r_binary32`
367×	`associate-l_binary32`
315×	`associate-/l*_binary32`
299×	`associate-/r*_binary32`

Counts

70 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	313	5872
1	1058	4878
2	5276	4878

prune913.0ms (5.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	311	1	312

Error

0.2b

Counts

312 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (pow.f32 (hypot.f32 1 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))) -1) (/.f32 (pow.f32 alphax -2) (hypot.f32 1 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.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 (pow.f32 (hypot.f32 1 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))) -1) (/.f32 (pow.f32 alphax -2) (hypot.f32 1 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.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 30365 to 20693 computations (31.9% saved)

localize186.0ms (1.2%)

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))))
	0.3b	(/.f32 (pow.f32 alphax -2) (hypot.f32 1 (.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))
	12.1b	(tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))

series127.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

127.0ms

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

rewrite56.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

599×	`log-prod_binary32`
227×	`expm1-udef_binary32`
227×	`log1p-udef_binary32`
198×	`log-pow_binary32`
126×	`add-sqr-sqrt_binary32`

Counts

1 → 37

Calls

1 calls:

55.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	249	17
2	2988	17
3	5163	17
0	0	0
1	0	0

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

720×	`associate-l_binary32`
712×	`associate-/r*_binary32`
320×	`unswap-sqr_binary32`
314×	`fma-def_binary32`
307×	`associate-*r/_binary32`

Counts

73 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	1476
1	270	1476
2	1192	1430
3	4895	1430
4	5402	1430

prune1.3s (8.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	479	0	479
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	479	1	480

Error

0.2b

Counts

480 → 1

Alt Table

Status	Error	Program
✓	0.2b	(/.f32 1 (sqrt.f32 (+.f32 1 (/.f32 (/.f32 u0 (fma.f32 (pow.f32 (hypot.f32 1 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2))))) -1) (/.f32 (pow.f32 alphax -2) (hypot.f32 1 (.f32 (/.f32 alphay alphax) (tan.f32 (.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.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 (pow.f32 (hypot.f32 1 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2))))) -1) (/.f32 (pow.f32 alphax -2) (hypot.f32 1 (*.f32 (/.f32 alphay alphax) (tan.f32 (*.f32 (PI.f32) (fma.f32 2 u1 1/2)))))) (/.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 46379 to 31562 computations (31.9% saved)

regimes1.3s (8.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

46 → 1

Compiler

Compiled 46089 to 32301 computations (29.9% saved)

simplify4.0ms (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	32	118
1	39	118
2	42	118
3	44	118
4	45	118
5	44	118

end123.0ms (0.8%)

Compiler: Compiled 237 to 168 computations (29.1% saved)

Details

analyze3.3s (20.6%)

sample6.6s (41.8%)

simplify57.0ms (0.4%)

prune8.0ms (0%)

localize112.0ms (0.7%)

series116.0ms (0.7%)

rewrite153.0ms (1%)

simplify75.0ms (0.5%)

prune683.0ms (4.3%)

localize117.0ms (0.7%)

series367.0ms (2.3%)

rewrite59.0ms (0.4%)

simplify86.0ms (0.5%)

prune913.0ms (5.8%)

localize186.0ms (1.2%)

series127.0ms (0.8%)

rewrite56.0ms (0.4%)

simplify71.0ms (0.4%)

prune1.3s (8.5%)

regimes1.3s (8.2%)

simplify4.0ms (0%)

end123.0ms (0.8%)

Profiling