Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
99.6%	0%	0.4%	1

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.2s (31.4%)

Infinites

40.7% of outputs are infinite.

Symmetry

(sort x y)

(sort z t)

(sort a b)

(sort c i)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

58×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
17×	`+-commutative_binary64`
4×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	28	16
2	61	16
3	105	16
4	121	16
5	123	16
6	123	16

prune3.0ms (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

1.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 75 to 42 computations (44% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	0.3b	(fma.f64 x y (*.f64 z t))
✓	0.8b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))

series67.0ms (1.8%)

Counts

3 → 216

Calls

3 calls:

38.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
20.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
9.0ms	(fma.f64 x y (*.f64 z t))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`add-exp-log_binary64`

Counts

3 → 30

Calls

3 calls:

0.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
0.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
0.0ms	(fma.f64 x y (*.f64 z t))

simplify152.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

864×	`unswap-sqr_binary64`
587×	`fma-def_binary64`
579×	`associate-+r+_binary64`
555×	`associate-+l+_binary64`
395×	`associate-l_binary64`

Counts

246 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	2908
1	95	2833
2	224	2833
3	925	2833
4	3316	2833
5	3461	2833
6	4972	2833

prune110.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	4	76

Error

Counts

76 → 4

Alt Table

Status	Error	Program
	31.1b	(fma.f64 c i (fma.f64 a b (.f64 (sqrt.f64 (fma.f64 x y (.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))))
✓	1.3b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
	15.3b	(fma.f64 c i (fma.f64 t z (*.f64 a b)))
▶	14.0b	(fma.f64 a b (fma.f64 y x (*.f64 c i)))

Compiler

Compiled 1359 to 304 computations (77.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 a b (fma.f64 y x (*.f64 c i)))
✓	0.5b	(fma.f64 y x (*.f64 c i))

series29.0ms (0.8%)

Counts

2 → 120

Calls

2 calls:

19.0ms	(fma.f64 a b (fma.f64 y x (*.f64 c i)))
10.0ms	(fma.f64 y x (*.f64 c i))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 y x (*.f64 c i))
0.0ms	(fma.f64 a b (fma.f64 y x (*.f64 c i)))

simplify140.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

914×	`distribute-lft-in_binary64`
914×	`distribute-rgt-in_binary64`
738×	`unswap-sqr_binary64`
682×	`distribute-rgt-out_binary64`
377×	`fma-def_binary64`

Counts

140 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	1376
1	49	1334
2	136	1334
3	545	1334
4	3027	1334
5	3117	1334
6	3454	1334
7	3827	1334
8	4305	1334
9	4421	1334
10	5641	1334

prune41.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
	31.1b	(fma.f64 c i (fma.f64 a b (.f64 (sqrt.f64 (fma.f64 x y (.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))))
✓	1.3b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
▶	15.3b	(fma.f64 c i (fma.f64 t z (*.f64 a b)))
✓	14.0b	(fma.f64 a b (fma.f64 y x (*.f64 c i)))

Compiler

Compiled 730 to 187 computations (74.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 t z (*.f64 a b))
✓	0.2b	(fma.f64 c i (fma.f64 t z (*.f64 a b)))

series39.0ms (1.1%)

Counts

2 → 120

Calls

2 calls:

28.0ms	(fma.f64 c i (fma.f64 t z (*.f64 a b)))
11.0ms	(fma.f64 t z (*.f64 a b))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 c i (fma.f64 t z (*.f64 a b)))
0.0ms	(fma.f64 t z (*.f64 a b))

simplify134.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
751×	`associate-l_binary64`
519×	`associate-r_binary64`
510×	`associate-/l/_binary64`
342×	`distribute-lft-in_binary64`

Counts

140 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	1376
1	51	1334
2	98	1334
3	313	1334
4	1304	1334
5	2592	1334
6	3195	1334
7	4162	1334
8	4399	1334
9	4534	1334
10	5255	1334

prune30.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	46	4	50

Error

Counts

50 → 4

Alt Table

Status	Error	Program
▶	31.1b	(fma.f64 c i (fma.f64 a b (.f64 (sqrt.f64 (fma.f64 x y (.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))))
✓	1.3b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	15.3b	(fma.f64 c i (fma.f64 t z (*.f64 a b)))
✓	14.0b	(fma.f64 a b (fma.f64 y x (*.f64 c i)))

Compiler

Compiled 711 to 176 computations (75.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 x y (.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))
✓	0.2b	(fma.f64 a b (.f64 (sqrt.f64 (fma.f64 x y (.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))
	0.3b	(fma.f64 x y (*.f64 z t))
✓	6.9b	(sqrt.f64 (fma.f64 x y (*.f64 z t)))

series114.0ms (3.1%)

Counts

3 → 136

Calls

3 calls:

83.0ms

(sqrt.f64 (fma.f64 x y (*.f64 z t)))

18.0ms

(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))

12.0ms

(*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms

(*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))

1.0ms

(sqrt.f64 (fma.f64 x y (*.f64 z t)))

0.0ms

(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))

simplify121.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

405×	`associate-/r*_binary64`
395×	`associate-+l+_binary64`
346×	`fma-neg_binary64`
338×	`unswap-sqr_binary64`
288×	`*-commutative_binary64`

Counts

214 → 129

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	2945
1	291	2767
2	904	2705
3	2251	2677
4	4913	2677
5	5075	2677

prune155.0ms (4.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	202	4	206

Error

Counts

206 → 4

Alt Table

Status	Error	Program
✓	31.1b	(fma.f64 c i (fma.f64 a b (.f64 (sqrt.f64 (fma.f64 x y (.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))))
✓	1.3b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
✓	15.3b	(fma.f64 c i (fma.f64 t z (*.f64 a b)))
✓	14.0b	(fma.f64 a b (fma.f64 y x (*.f64 c i)))

Compiler

Compiled 5742 to 1419 computations (75.3% saved)

regimes1.1s (31.1%)

Accuracy

Total 1.3b remaining (99.8%)

Threshold costs 0b (0%)

Counts

54 → 1

Compiler

Compiled 16996 to 11370 computations (33.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	16
1	20	16
2	18	16

end169.0ms (4.6%)

Remove

(sort c i)

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 283 to 168 computations (40.6% saved)

Details

analyze5.0ms (0.1%)

sample1.2s (31.4%)

simplify11.0ms (0.3%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series67.0ms (1.8%)

rewrite2.0ms (0.1%)

simplify152.0ms (4.1%)

prune110.0ms (3%)

localize8.0ms (0.2%)

series29.0ms (0.8%)

rewrite1.0ms (0%)

simplify140.0ms (3.8%)

prune41.0ms (1.1%)

localize8.0ms (0.2%)

series39.0ms (1.1%)

rewrite1.0ms (0%)

simplify134.0ms (3.7%)

prune30.0ms (0.8%)

localize12.0ms (0.3%)

series114.0ms (3.1%)

rewrite11.0ms (0.3%)

simplify121.0ms (3.3%)

prune155.0ms (4.2%)

regimes1.1s (31.1%)

simplify3.0ms (0.1%)

end169.0ms (4.6%)

Profiling