Details

analyze565.0ms (18.5%)

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)

sample1.2s (39.9%)

Results

994.0ms	8256×	body	128	valid
110.0ms	1078×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify55.0ms (1.8%)

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

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

9.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.9b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
▶	9.9b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

Compiler

Compiled 66 to 38 computations (42.4% 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)
✓	9.3b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series26.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

14.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
12.0ms	(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)

simplify79.0ms (2.6%)

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

prune43.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	70	5	75

Error

0.0b

Counts

75 → 5

Alt Table

Status	Error	Program
	10.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
▶	2.2b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	37.9b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
	10.9b	(.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)))
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

Compiler

Compiled 1141 to 275 computations (75.9% 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)
✓	4.4b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series40.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

21.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))
19.0ms	(-.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))

simplify87.0ms (2.8%)

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

prune49.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Error

Counts

79 → 4

Alt Table

Status	Error	Program
	37.9b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
▶	2.8b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
	2.9b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

Compiler

Compiled 1454 to 307 computations (78.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y x) x)
✓	0.0b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
✓	2.7b	(/.f64 (+.f64 (*.f64 y x) x) z)

series34.0ms (1.1%)

Counts

3 → 75

Calls

3 calls:

18.0ms	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
12.0ms	(/.f64 (+.f64 (*.f64 y x) x) z)
4.0ms	(+.f64 (*.f64 y x) x)

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
74×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
57×	`prod-diff_binary64`

Counts

3 → 150

Calls

3 calls:

10.0ms	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
5.0ms	(/.f64 (+.f64 (*.f64 y x) x) z)
3.0ms	(+.f64 (*.f64 y x) x)

simplify133.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
530×	`times-frac_binary64`
439×	`fma-neg_binary64`
245×	`distribute-rgt-in_binary64`
228×	`distribute-lft-in_binary64`

Counts

225 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	4142
1	369	3265
2	1388	2876
3	4348	2874
4	4936	2874

prune122.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	223	4	227

Error

Counts

227 → 4

Alt Table

Status	Error	Program
	37.9b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
✓	2.8b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
▶	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

Compiler

Compiled 4700 to 1025 computations (78.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
✓	2.7b	(fma.f64 (/.f64 y z) x (/.f64 x z))

series39.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

20.0ms	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
18.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))

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

simplify85.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

532×	`fma-neg_binary64`
432×	`fma-def_binary64`
410×	`associate-r_binary64`
323×	`distribute-rgt-out_binary64`
297×	`exp-prod_binary64`

Counts

113 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1550
1	160	1503
2	620	1466
3	2489	1152
4	4207	1152
5	4908	1152

prune33.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	74	4	78

Error

Counts

78 → 4

Alt Table

Status	Error	Program
	37.9b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
✓	2.8b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
✓	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))

Compiler

Compiled 1392 to 273 computations (80.4% saved)

regimes300.0ms (9.8%)

Accuracy

Total 1.7b remaining (98.3%)

Threshold costs 0b (0%)

Counts

63 → 2

Compiler

Compiled 3656 to 1970 computations (46.1% saved)

bsearch11.0ms (0.4%)

Steps

Iters	Range		Point
4	-1.450677168275814e-50	-1.5588998959235472e-52	-6.09357792742113e-51

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	17	32
1	23	32
2	28	32
3	30	32
4	31	32
5	30	32

end61.0ms (2%)

Compiler: Compiled 110 to 62 computations (43.6% saved)

Details

analyze565.0ms (18.5%)

sample1.2s (39.9%)

simplify55.0ms (1.8%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series26.0ms (0.9%)

rewrite4.0ms (0.1%)

simplify79.0ms (2.6%)

prune43.0ms (1.4%)

localize5.0ms (0.2%)

series40.0ms (1.3%)

rewrite6.0ms (0.2%)

simplify87.0ms (2.8%)

prune49.0ms (1.6%)

localize6.0ms (0.2%)

series34.0ms (1.1%)

rewrite30.0ms (1%)

simplify133.0ms (4.4%)

prune122.0ms (4%)

localize7.0ms (0.2%)

series39.0ms (1.3%)

rewrite6.0ms (0.2%)

simplify85.0ms (2.8%)

prune33.0ms (1.1%)

regimes300.0ms (9.8%)

bsearch11.0ms (0.4%)

simplify3.0ms (0.1%)

end61.0ms (2%)

Profiling