Details

analyze611.0ms (11.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (20.3%)

Results

867.0ms	8256×	body	128	valid
126.0ms	1130×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

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

8.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.4b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	7.9b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series24.0ms (0.4%)

Counts

2 → 72

Calls

2 calls:

16.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
7.0ms	(fma.f64 x (-.f64 y z) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
0.0ms	(fma.f64 x (-.f64 y z) x)

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
629×	`fma-def_binary64`
448×	`associate-/l/_binary64`
308×	`associate-/r*_binary64`
291×	`associate-/r/_binary64`

Counts

111 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1522
1	160	1371
2	374	1332
3	1227	1332
4	4358	1332
5	5042	1332

prune44.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	7	74

Error

0.0b

Counts

74 → 7

Alt Table

Status	Error	Program
	36.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 (fma.f64 x (-.f64 y z) x))) (sqrt.f64 z)) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (sqrt.f64 z)))
	3.9b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	40.1b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 y z) x) 3)) z)
	9.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z))) (cbrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
	36.0b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
	8.5b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
▶	2.8b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 1225 to 311 computations (74.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.6b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series18.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

18.0ms

(fma.f64 (/.f64 x z) y (/.f64 x z))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

662×	`associate-*l/_binary64`
661×	`times-frac_binary64`
661×	`fma-def_binary64`
537×	`associate-*r/_binary64`
435×	`distribute-rgt-in_binary64`

Counts

46 → 25

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	610
1	40	577
2	78	557
3	204	392
4	784	392
5	3618	392
6	4565	392
7	4941	392
8	4972	392

prune18.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	26	6	32

Error

Counts

32 → 6

Alt Table

Status	Error	Program
	36.0b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
▶	2.9b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	8.5b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
✓	2.8b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	3.9b	(-.f64 (/.f64 (fma.f64 y x x) z) x)
	3.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x z) y (/.f64 x z))) (cbrt.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)))) (cbrt.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)))) x)

Compiler

Compiled 526 to 168 computations (68.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	2.8b	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series25.0ms (0.5%)

Counts

2 → 39

Calls

2 calls:

18.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
6.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 68

Calls

2 calls:

13.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
10.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

976×	`fma-def_binary64`
819×	`distribute-rgt-in_binary64`
779×	`distribute-lft-in_binary64`
400×	`times-frac_binary64`
246×	`associate-l_binary64`

Counts

107 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1217
1	198	1132
2	556	932
3	1586	921
4	5383	921

prune82.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	107	5	112

Error

Counts

112 → 5

Alt Table

Status	Error	Program
✓	2.9b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	8.5b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
✓	2.8b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
▶	3.2b	(-.f64 (.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (/.f64 (cbrt.f64 y) z) (/.f64 1 z)) x) x)
	3.9b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)

Compiler

Compiled 1890 to 919 computations (51.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (cbrt.f64 y) z)
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	2.8b	(.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (/.f64 (cbrt.f64 y) z) (/.f64 1 z)) x)

series2.5s (46.3%)

Counts

4 → 84

Calls

4 calls:

2.2s	(.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (/.f64 (cbrt.f64 y) z) (/.f64 1 z)) x)
259.0ms	(/.f64 (cbrt.f64 y) z)
45.0ms	(cbrt.f64 y)
36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`

Counts

4 → 116

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
3.0ms	(.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (/.f64 (cbrt.f64 y) z) (/.f64 1 z)) x)
3.0ms	(/.f64 (cbrt.f64 y) z)
1.0ms	(cbrt.f64 y)

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

663×	`distribute-rgt-in_binary64`
420×	`unswap-sqr_binary64`
373×	`associate-/l*_binary64`
263×	`times-frac_binary64`
249×	`fma-def_binary64`

Counts

200 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2431
1	274	2009
2	860	1876
3	2469	1861
4	4969	1861

prune143.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	204	5	209

Error

Counts

209 → 5

Alt Table

Status	Error	Program
✓	2.9b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	8.5b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
✓	2.8b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	3.2b	(-.f64 (.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 1) (/.f64 (cbrt.f64 y) z) (/.f64 1 z)) x) x)
	3.9b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)

Compiler

Compiled 4996 to 2079 computations (58.4% saved)

regimes316.0ms (5.8%)

Accuracy

Total 0.3b remaining (95.3%)

Threshold costs 0.3b (95.3%)

Counts

55 → 3

Compiler

Compiled 3716 to 1914 computations (48.5% saved)

bsearch13.0ms (0.2%)

Steps

Iters	Range		Point
2	1.8201816752214106e-83	3.041437393688164e-82	1.5045753576773437e-82
2	-1.0473091800064239e-116	-3.461739339589475e-117	-4.6985478038612766e-117

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	52
1	31	52
2	37	52
3	39	52
4	40	52
5	39	52

end77.0ms (1.4%)

Compiler: Compiled 153 to 88 computations (42.5% saved)

Details

analyze611.0ms (11.2%)

sample1.1s (20.3%)

simplify54.0ms (1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series24.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify77.0ms (1.4%)

prune44.0ms (0.8%)

localize5.0ms (0.1%)

series18.0ms (0.3%)

rewrite1.0ms (0%)

simplify79.0ms (1.5%)

prune18.0ms (0.3%)

localize7.0ms (0.1%)

series25.0ms (0.5%)

rewrite27.0ms (0.5%)

simplify60.0ms (1.1%)

prune82.0ms (1.5%)

localize11.0ms (0.2%)

series2.5s (46.3%)

rewrite15.0ms (0.3%)

simplify93.0ms (1.7%)

prune143.0ms (2.6%)

regimes316.0ms (5.8%)

bsearch13.0ms (0.2%)

simplify4.0ms (0.1%)

end77.0ms (1.4%)

Profiling