Details

analyze2.7s (43.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample89.0ms (1.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
10.0ms	177×	body	128	invalid

Compiler

Compiled 55 to 39 computations (29.1% saved)

simplify8.0ms (0.1%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 75 to 42 computations (44% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z t))
✓	0.0b	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

series65.0ms (1%)

Counts

3 → 216

Calls

3 calls:

32.0ms	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))
23.0ms	(fma.f64 a b (fma.f64 x y (*.f64 z t)))
9.0ms	(fma.f64 x y (*.f64 z t))

rewrite2.0ms (0%)

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

simplify115.0ms (1.9%)

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	3318	2833
5	3463	2833
6	4972	2833

prune60.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	3	76

Error

Counts

76 → 3

Alt Table

Status	Error	Program
	37.2b	(fma.f64 c i (cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)))
▶	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 1304 to 281 computations (78.5% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a b (fma.f64 t z (*.f64 c i)))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))

series55.0ms (0.9%)

Counts

2 → 168

Calls

2 calls:

34.0ms	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
20.0ms	(fma.f64 a b (fma.f64 t z (*.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 (fma.f64 a b (fma.f64 t z (*.f64 c i))))
0.0ms	(fma.f64 a b (fma.f64 t z (*.f64 c i)))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-+r+_binary64`
693×	`associate-+l+_binary64`
597×	`fma-def_binary64`
389×	`associate-l_binary64`
318×	`associate-r_binary64`

Counts

188 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	2448
1	77	2390
2	203	2390
3	964	2390
4	5083	2390

prune28.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	46	3	49

Error

Counts

49 → 3

Alt Table

Status	Error	Program
▶	37.2b	(fma.f64 c i (cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 752 to 151 computations (79.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a b (fma.f64 y x (*.f64 t z)))
✓	0.0b	(fma.f64 c i (cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)))
✓	0.2b	(pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)
✓	39.5b	(cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3))

series249.0ms (4%)

Counts

4 → 312

Calls

4 calls:

173.0ms	(pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)
34.0ms	(fma.f64 c i (cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)))
23.0ms	(fma.f64 a b (fma.f64 y x (*.f64 t z)))
20.0ms	(cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3))
1.0ms	(pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)
0.0ms	(fma.f64 c i (cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)))
0.0ms	(fma.f64 a b (fma.f64 y x (*.f64 t z)))

simplify217.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

797×	`+-commutative_binary64`
550×	`distribute-rgt-out_binary64`
409×	`distribute-rgt-in_binary64`
334×	`unswap-sqr_binary64`
307×	`associate-r_binary64`

Counts

380 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	454	11961
1	1602	11672
2	2543	10159
3	5210	10159

prune151.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
✓	37.2b	(fma.f64 c i (cbrt.f64 (pow.f64 (fma.f64 a b (fma.f64 y x (*.f64 t z))) 3)))
✓	0.0b	(fma.f64 y x (fma.f64 a b (fma.f64 t z (*.f64 c i))))
✓	0.0b	(fma.f64 c i (fma.f64 a b (fma.f64 x y (*.f64 z t))))

Compiler

Compiled 9199 to 4334 computations (52.9% saved)

regimes725.0ms (11.8%)

Accuracy

Total 0.0b remaining (56.5%)

Threshold costs 0.0b (56.5%)

Counts

42 → 1

Compiler

Compiled 13538 to 8860 computations (34.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	14	16
2	14	16

end83.0ms (1.3%)

Remove

(sort c i)

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 180 to 108 computations (40% saved)

sample1.5s (25%)

Algorithm

1×

intervals

Results

468.0ms	8000×	body	128	valid
325.0ms	5668×	body	128	invalid

Compiler

Compiled 115 to 75 computations (34.8% saved)

Details

analyze2.7s (43.2%)

sample89.0ms (1.4%)

simplify8.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series65.0ms (1%)

rewrite2.0ms (0%)

simplify115.0ms (1.9%)

prune60.0ms (1%)

localize9.0ms (0.2%)

series55.0ms (0.9%)

rewrite1.0ms (0%)

simplify67.0ms (1.1%)

prune28.0ms (0.4%)

localize12.0ms (0.2%)

series249.0ms (4%)

rewrite7.0ms (0.1%)

simplify217.0ms (3.5%)

prune151.0ms (2.4%)

regimes725.0ms (11.8%)

simplify3.0ms (0.1%)

end83.0ms (1.3%)

sample1.5s (25%)

Profiling