Details

analyze620.0ms (9.1%)

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 (16.8%)

Results

921.0ms	8256×	body	128	valid
120.0ms	1119×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify54.0ms (0.8%)

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%)

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

6.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.9b	(/.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)
✓	6.4b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series28.0ms (0.4%)

Counts

2 → 72

Calls

2 calls:

16.0ms	(/.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)

simplify73.0ms (1.1%)

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

prune53.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Error

0.0b

Counts

74 → 6

Alt Table

Status	Error	Program
	33.8b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))
	7.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	7.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	8.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 (fma.f64 x (-.f64 y z) x))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 z)))
▶	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	38.6b	(/.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 x (-.f64 y z) x) (fma.f64 x (-.f64 y z) x)) (fma.f64 x (-.f64 y z) x))) z)

Compiler

Compiled 1185 to 299 computations (74.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.5b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series33.0ms (0.5%)

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))

rewrite5.0ms (0.1%)

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))

simplify86.0ms (1.3%)

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

prune38.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Error

0.0b

Counts

80 → 4

Alt Table

Status	Error	Program
	7.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	4.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y x x) z)) (cbrt.f64 (/.f64 (fma.f64 y x x) z))) (cbrt.f64 (/.f64 (fma.f64 y x x) z))) x)
▶	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 1455 to 301 computations (79.3% saved)

localize8.0ms (0.1%)

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 (0.6%)

Counts

3 → 75

Calls

3 calls:

18.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
17.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
6.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite43.0ms (0.6%)

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:

13.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))
13.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
12.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

simplify79.0ms (1.2%)

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

prune101.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	144	5	149

Error

0.0b

Counts

149 → 5

Alt Table

Status	Error	Program
	7.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	4.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y x x) z)) (cbrt.f64 (/.f64 (fma.f64 y x x) z))) (cbrt.f64 (/.f64 (fma.f64 y x x) z))) x)
✓	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
▶	2.6b	(-.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z)) x) x)
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 2565 to 1185 computations (53.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))
✓	2.3b	(.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z)) x)
✓	10.9b	(cbrt.f64 (/.f64 y z))

series3.4s (50.2%)

Counts

4 → 108

Calls

4 calls:

1.6s	(.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z)) x)
740.0ms	(fma.f64 (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z))
664.0ms	(*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))
417.0ms	(cbrt.f64 (/.f64 y z))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`cbrt-prod_binary64`
71×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`

Counts

4 → 134

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))
3.0ms	(.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z)) x)
2.0ms	(cbrt.f64 (/.f64 y z))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z))

simplify144.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
760×	`times-frac_binary64`
254×	`*-commutative_binary64`
201×	`unsub-neg_binary64`
190×	`exp-sum_binary64`

Counts

242 → 242

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	5619
1	491	5156
2	1151	4427
3	2543	4017
4	4980	4017

prune247.0ms (3.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	320	5	325

Error

0.0b

Counts

325 → 5

Alt Table

Status	Error	Program
	7.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	4.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 y x x) z)) (cbrt.f64 (/.f64 (fma.f64 y x x) z))) (cbrt.f64 (/.f64 (fma.f64 y x x) z))) x)
✓	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	2.6b	(-.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z))) (cbrt.f64 (/.f64 y z)) (/.f64 1 z)) x) x)
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)

Compiler

Compiled 9017 to 3185 computations (64.7% saved)

regimes422.0ms (6.2%)

Accuracy

Total 0.7b remaining (97.7%)

Threshold costs 0.7b (97.7%)

Counts

83 → 3

Compiler

Compiled 5800 to 3126 computations (46.1% saved)

bsearch22.0ms (0.3%)

Steps

Iters	Range		Point
1	3.8961788027096304e-150	2.2361793904941676e-147	9.311628134350187e-149
6	-9.832280945479793e+58	-3.645918904472437e+39	-2.568575037803819e+51

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	50
1	32	50
2	38	50
3	40	50
4	41	50
5	40	50

end81.0ms (1.2%)

Compiler: Compiled 168 to 83 computations (50.6% saved)

Details

analyze620.0ms (9.1%)

sample1.1s (16.8%)

simplify54.0ms (0.8%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series28.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify73.0ms (1.1%)

prune53.0ms (0.8%)

localize6.0ms (0.1%)

series33.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify86.0ms (1.3%)

prune38.0ms (0.6%)

localize8.0ms (0.1%)

series41.0ms (0.6%)

rewrite43.0ms (0.6%)

simplify79.0ms (1.2%)

prune101.0ms (1.5%)

localize16.0ms (0.2%)

series3.4s (50.2%)

rewrite28.0ms (0.4%)

simplify144.0ms (2.1%)

prune247.0ms (3.6%)

regimes422.0ms (6.2%)

bsearch22.0ms (0.3%)

simplify3.0ms (0%)

end81.0ms (1.2%)

Profiling