Details

analyze511.0ms (18.9%)

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)

sample109.0ms (4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	32×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify52.0ms (1.9%)

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

9.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.9b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	9.3b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series27.0ms (1%)

Counts

2 → 72

Calls

2 calls:

19.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
7.0ms	(fma.f64 x (-.f64 y z) x)

rewrite4.0ms (0.2%)

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)

simplify74.0ms (2.7%)

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

prune45.0ms (1.7%)

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
	36.8b	(.f64 (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 z)))
▶	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	9.9b	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
	40.1b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (fma.f64 y x x) z) x) 3))
	36.4b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
	10.1b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	10.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))

Compiler

Compiled 1193 to 317 computations (73.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	3.1b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series33.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

17.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
16.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
0.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify94.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
438×	`associate-l_binary64`
352×	`associate-r_binary64`
336×	`fma-def_binary64`
307×	`distribute-rgt-out_binary64`

Counts

113 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1698
1	160	1621
2	607	1157
3	2730	1152
4	4468	1152
5	4961	1152

prune43.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Error

Counts

81 → 7

Alt Table

Status	Error	Program
	36.8b	(.f64 (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 z)))
✓	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
▶	2.7b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	36.4b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
	10.1b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	10.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
	3.3b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)

Compiler

Compiled 1557 to 357 computations (77.1% saved)

localize13.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	2.6b	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series53.0ms (1.9%)

Counts

3 → 75

Calls

3 calls:

22.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
20.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
10.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite43.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

3 → 89

Calls

3 calls:

12.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
12.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
12.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify86.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

757×	`times-frac_binary64`
585×	`fma-def_binary64`
393×	`fma-neg_binary64`
381×	`distribute-rgt-in_binary64`
362×	`distribute-lft-in_binary64`

Counts

164 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2112
1	301	2041
2	1225	1572
3	3819	1517
4	4989	1517

prune99.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	145	7	152

Error

Counts

152 → 7

Alt Table

Status	Error	Program
	10.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (fma.f64 x (-.f64 y z) x) (cbrt.f64 z)))
▶	3.3b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
✓	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.7b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	10.1b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	3.4b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
	26.2b	(-.f64 (/.f64 (.f64 x (fma.f64 z y z)) (.f64 z z)) x)

Compiler

Compiled 2579 to 1211 computations (53% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
✓	3.2b	(/.f64 (fma.f64 x y x) z)

series26.0ms (1%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(-.f64 (/.f64 (fma.f64 x y x) z) x)
13.0ms	(/.f64 (fma.f64 x y x) z)

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

2 → 100

Calls

2 calls:

6.0ms	(-.f64 (/.f64 (fma.f64 x y x) z) x)
2.0ms	(/.f64 (fma.f64 x y x) z)

simplify136.0ms (5%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-def_binary64`
431×	`fma-neg_binary64`
395×	`times-frac_binary64`
374×	`associate-/l*_binary64`
228×	`associate-*l/_binary64`

Counts

172 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	2897
1	271	2796
2	947	2007
3	3816	1989
4	4876	1989
5	4998	1989
6	4907	1989

prune76.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	122	7	129

Error

Counts

129 → 7

Alt Table

Status	Error	Program
✓	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.7b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	10.1b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
✓	3.3b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
	4.0b	(+.f64 (-.f64 (/.f64 (fma.f64 x y x) (pow.f64 (cbrt.f64 z) 3)) x) 0)
	3.4b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
	26.2b	(-.f64 (/.f64 (.f64 x (fma.f64 z y z)) (.f64 z z)) x)

Compiler

Compiled 2734 to 551 computations (79.8% saved)

regimes358.0ms (13.3%)

Accuracy

Total 0.1b remaining (92%)

Threshold costs 0.1b (92%)

Counts

55 → 3

Compiler

Compiled 3288 to 1778 computations (45.9% saved)

bsearch10.0ms (0.4%)

Steps

Iters	Range		Point
1	6210875.4037806755	1686444901641.8125	3236902952.627435
4	-4.313075276753847e+29	-2.602722893073134e+29	-2.9584660166947206e+29

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	43
1	33	43
2	38	43
3	40	43
4	41	43
5	40	43

end1.0ms (0%)

Compiler: Compiled 32 to 20 computations (37.5% saved)

sample759.0ms (28.1%)

Algorithm

1×

intervals

Results

344.0ms	8000×	body	128	valid
42.0ms	1015×	body	128	invalid

Compiler

Compiled 143 to 88 computations (38.5% saved)

Details

analyze511.0ms (18.9%)

sample109.0ms (4%)

simplify52.0ms (1.9%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series27.0ms (1%)

rewrite4.0ms (0.2%)

simplify74.0ms (2.7%)

prune45.0ms (1.7%)

localize7.0ms (0.2%)

series33.0ms (1.2%)

rewrite7.0ms (0.2%)

simplify94.0ms (3.5%)

prune43.0ms (1.6%)

localize13.0ms (0.5%)

series53.0ms (1.9%)

rewrite43.0ms (1.6%)

simplify86.0ms (3.2%)

prune99.0ms (3.6%)

localize7.0ms (0.3%)

series26.0ms (1%)

rewrite17.0ms (0.6%)

simplify136.0ms (5%)

prune76.0ms (2.8%)

regimes358.0ms (13.3%)

bsearch10.0ms (0.4%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample759.0ms (28.1%)

Profiling