Details

analyze480.0ms (18.8%)

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)

sample113.0ms (4.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	38×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify53.0ms (2.1%)

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

prune11.0ms (0.4%)

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

11.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	10.4b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series20.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(/.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)

simplify88.0ms (3.5%)

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

prune40.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Error

0.0b

Counts

74 → 7

Alt Table

Status	Error	Program
✓	11.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
	35.1b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
▶	2.6b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	38.4b	(*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)))
	12.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 (fma.f64 x (-.f64 y z) x))) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) z))
	38.0b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (fma.f64 y x x) z) x) 3))

Compiler

Compiled 1176 to 303 computations (74.2% saved)

localize5.0ms (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)
✓	3.5b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series34.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))
16.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

rewrite6.0ms (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:

3.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
0.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify89.0ms (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

prune41.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	74	7	81

Error

0.0b

Counts

81 → 7

Alt Table

Status	Error	Program
✓	11.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
	35.1b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
✓	2.6b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	38.4b	(*.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)))
	38.0b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (fma.f64 y x x) z) x) 3))
▶	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)

Compiler

Compiled 1512 to 343 computations (77.3% saved)

localize9.0ms (0.3%)

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))
✓	2.3b	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series41.0ms (1.6%)

Counts

3 → 75

Calls

3 calls:

19.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
16.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
6.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite41.0ms (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:

14.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
13.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
9.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify85.0ms (3.3%)

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

prune107.0ms (4.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	145	7	152

Error

0.0b

Counts

152 → 7

Alt Table

Status	Error	Program
	38.0b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (fma.f64 y x x) z) x) 3))
▶	2.6b	(-.f64 (.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x)) x)
✓	11.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
	35.1b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
✓	2.6b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)

Compiler

Compiled 2568 to 1205 computations (53.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x)) x)
✓	0.2b	(*.f64 (/.f64 1 z) x)
✓	3.5b	(.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x))

series34.0ms (1.3%)

Counts

3 → 96

Calls

3 calls:

16.0ms	(-.f64 (.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x)) x)
12.0ms	(.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x))
6.0ms	(*.f64 (/.f64 1 z) x)

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 87

Calls

3 calls:

9.0ms	(-.f64 (.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x)) x)
7.0ms	(.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x))
5.0ms	(*.f64 (/.f64 1 z) x)

simplify101.0ms (4%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
375×	`associate-*l/_binary64`
363×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`
281×	`associate-*r/_binary64`

Counts

183 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	2112
1	359	1965
2	1367	1597
3	4414	1597
4	4875	1597
5	4911	1597

prune93.0ms (3.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

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

Error

0.0b

Counts

152 → 7

Alt Table

Status	Error	Program
	38.0b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (fma.f64 y x x) z) x) 3))
✓	2.6b	(-.f64 (.f64 (+.f64 y 1) (.f64 (/.f64 1 z) x)) x)
✓	11.2b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
	35.1b	(/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 z (sqrt.f64 (fma.f64 x (-.f64 y z) x))))
	11.3b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
✓	2.6b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)

Compiler

Compiled 2506 to 1416 computations (43.5% saved)

regimes300.0ms (11.8%)

Accuracy

Total 0.3b remaining (96.8%)

Threshold costs 0.3b (96.8%)

Counts

56 → 3

Compiler

Compiled 3016 to 1722 computations (42.9% saved)

bsearch7.0ms (0.3%)

Steps

Iters	Range		Point
2	3.061495323554843e+21	7.197147841774278e+28	2.1558912601142047e+23
1	-6.808419456783476e-148	-3.508160951740505e-150	-4.934159841637241e-149

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	29	41
2	34	41
3	36	41
4	37	41
5	36	41

end1.0ms (0%)

Compiler: Compiled 31 to 18 computations (41.9% saved)

sample709.0ms (27.8%)

Algorithm

1×

intervals

Results

296.0ms	8000×	body	128	valid
35.0ms	1041×	body	128	invalid

Compiler

Compiled 146 to 86 computations (41.1% saved)

Details

analyze480.0ms (18.8%)

sample113.0ms (4.4%)

simplify53.0ms (2.1%)

prune11.0ms (0.4%)

localize5.0ms (0.2%)

series20.0ms (0.8%)

rewrite4.0ms (0.2%)

simplify88.0ms (3.5%)

prune40.0ms (1.6%)

localize5.0ms (0.2%)

series34.0ms (1.3%)

rewrite6.0ms (0.2%)

simplify89.0ms (3.5%)

prune41.0ms (1.6%)

localize9.0ms (0.3%)

series41.0ms (1.6%)

rewrite41.0ms (1.6%)

simplify85.0ms (3.3%)

prune107.0ms (4.2%)

localize6.0ms (0.2%)

series34.0ms (1.3%)

rewrite25.0ms (1%)

simplify101.0ms (4%)

prune93.0ms (3.7%)

regimes300.0ms (11.8%)

bsearch7.0ms (0.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample709.0ms (27.8%)

Profiling