Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample730.0ms (12.5%)

Results

702.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
3	11	9

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	26.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

rewrite45.0ms (0.8%)

Algorithm

1×	egg-rewrite

Rules

57× egg

Counts

1 → 57

Calls

1 calls:

44.0ms

(sqrt.f64 (*.f64 (*.f64 2 x) x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	6
2	1317	6
3	4961	6

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

69 → 58

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune39.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	52	6	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	7	59

Error

0.1b

Counts

59 → 7

Alt Table

Status	Error	Program
▶	11.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	11.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (.f64 (cbrt.f64 x) (+.f64 x x)) 1/2))
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 774 to 510 computations (34.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
✓	0.5b	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (+.f64 x x))
✓	11.0b	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

series1.1s (19.2%)

Counts

4 → 48

Calls

4 calls:

1.0s	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)
47.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
33.0ms	(cbrt.f64 (+.f64 x x))
23.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

rewrite308.0ms (5.3%)

Algorithm

4×	egg-rewrite

Rules

228×	`egg`
188×	`egg`
33×	`egg`
30×	`egg`

Counts

4 → 479

Calls

4 calls:

85.0ms	(pow.f64 (cbrt.f64 (+.f64 x x)) 2)
80.0ms	(cbrt.f64 (+.f64 x x))
77.0ms	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)
60.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	152	9
2	1432	9
3	4784	9
4	5000	9
0	4	4
1	85	4
2	809	4
3	4277	4
4	5198	4
0	6	4
1	127	4
2	969	4
3	4545	4
4	5642	4
0	11	11
1	215	9
2	1624	9
3	4958	9

simplify140.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
790×	`unswap-sqr_binary64`
662×	`sqr-pow_binary64`
468×	`*-commutative_binary64`
344×	`distribute-rgt-in_binary64`

Counts

527 → 291

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	516
1	64	516
2	129	516
3	324	516
4	1021	516
5	1715	516
6	1918	516
7	2288	516
8	2999	516
9	3608	516
10	4272	516
11	4564	516
12	4655	516

prune294.0ms (5.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	479	2	481
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	480	8	488

Error

0.1b

Counts

488 → 8

Alt Table

Status	Error	Program
✓	11.8b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.2b	(*.f64 (sqrt.f64 2) x)
	11.7b	(.f64 (sqrt.f64 (pow.f64 (.f64 (pow.f64 (sqrt.f64 2) 2/3) (cbrt.f64 x)) 2)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
▶	11.7b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 9558 to 5098 computations (46.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (+.f64 x x))
✓	0.6b	(cbrt.f64 x)
✓	1.0b	(cbrt.f64 2)
✓	11.0b	(pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2)

series1.2s (20.7%)

Counts

3 → 24

Calls

3 calls:

1.2s	(pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2)
30.0ms	(cbrt.f64 x)
0.0ms	(cbrt.f64 2)

rewrite192.0ms (3.3%)

Algorithm

3×	egg-rewrite

Rules

33×	`egg`
32×	`egg`
29×	`egg`

Counts

3 → 94

Calls

3 calls:

74.0ms	(cbrt.f64 x)
72.0ms	(cbrt.f64 2)
45.0ms	(pow.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 x)) x) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	184	11
2	1903	11
3	4889	11
0	3	3
1	58	3
2	578	3
3	4445	3
4	5288	3
0	3	3
1	56	3
2	621	3
3	4737	3
4	5240	3

simplify119.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1302×	`fma-def_binary64`
866×	`unswap-sqr_binary64`
710×	`sqr-pow_binary64`
439×	`cube-prod_binary64`
351×	`associate-l_binary64`

Counts

118 → 100

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	248
1	45	248
2	84	248
3	149	248
4	309	248
5	781	248
6	1125	248
7	1950	248
8	2451	248
9	3078	248
10	3648	248
11	4266	248
12	4680	248
13	4782	248

prune185.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	287	3	290
Fresh	0	5	5
Picked	1	0	1
Done	1	1	2
Total	289	9	298

Error

0.0b

Counts

298 → 9

Alt Table

Status	Error	Program
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))))))
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (*.f64 2 x))) (sqrt.f64 x)))
	32.2b	(*.f64 (sqrt.f64 2) x)
▶	11.7b	(.f64 (sqrt.f64 (pow.f64 (.f64 (pow.f64 (sqrt.f64 2) 2/3) (cbrt.f64 x)) 2)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	11.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (cbrt.f64 2)) 3) 1) (+.f64 (.f64 (+.f64 1 (cbrt.f64 2)) (+.f64 1 (cbrt.f64 2))) (+.f64 1 (*.f64 (+.f64 1 (cbrt.f64 2)) 1)))) (cbrt.f64 x)) x) 1/2))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 6343 to 4377 computations (31% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (cbrt.f64 x)) 2)
	0.6b	(cbrt.f64 (+.f64 x x))
	0.6b	(cbrt.f64 x)
	11.0b	(pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2)

series307.0ms (5.3%)

Counts

1 → 12

Calls

1 calls:

307.0ms

(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (cbrt.f64 x)) 2)

rewrite46.0ms (0.8%)

Algorithm

1×	egg-rewrite

Rules

32× egg

Counts

1 → 32

Calls

1 calls:

45.0ms

(pow.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2/3) (cbrt.f64 x)) 2)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	187	9
2	1737	9
3	4932	9

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

769×	`exp-sum_binary64`
541×	`fma-def_binary64`
440×	`associate-+l+_binary64`
301×	`exp-diff_binary64`
252×	`distribute-rgt-in_binary64`

Counts

44 → 36

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	296
1	73	236
2	131	200
3	434	128
4	1712	116
5	4245	116
6	5550	116

prune181.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	293	2	295
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	294	10	304

Error

0.0b

Counts

304 → 10

Alt Table

Status	Error	Program
	30.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	12.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (cbrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (cbrt.f64 (.f64 2 x)))))))
	11.8b	(.f64 (sqrt.f64 (pow.f64 (.f64 (pow.f64 (sqrt.f64 2) 2/3) (cbrt.f64 x)) 2)) (pow.f64 (.f64 (.f64 (pow.f64 (sqrt.f64 2) 2/3) (cbrt.f64 x)) x) 1/2))
	12.0b	(.f64 (sqrt.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 2 x)) 4)))) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x x)) x) 1/2))
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	27.0b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (*.f64 2 x))) (sqrt.f64 x)))
	32.2b	(*.f64 (sqrt.f64 2) x)
	11.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x x)) 2)) (pow.f64 (.f64 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (cbrt.f64 2)) 3) 1) (+.f64 (.f64 (+.f64 1 (cbrt.f64 2)) (+.f64 1 (cbrt.f64 2))) (+.f64 1 (*.f64 (+.f64 1 (cbrt.f64 2)) 1)))) (cbrt.f64 x)) x) 1/2))
	32.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 6869 to 4735 computations (31.1% saved)

regimes589.0ms (10.1%)

Accuracy

Total 0.3b remaining (73.3%)

Threshold costs 0.3b (73.3%)

Counts

80 → 2

Compiler

Compiled 4590 to 3644 computations (20.6% saved)

bsearch20.0ms (0.3%)

Steps

Iters	Range		Point
10	-3.497324545450821e-304	3.1612837875203375e-298	3.57210598636777e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	24	25
2	32	25
3	37	25
4	39	25
5	39	25

end160.0ms (2.8%)

Compiler: Compiled 202 to 161 computations (20.3% saved)

Details

analyze6.0ms (0.1%)

sample730.0ms (12.5%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite45.0ms (0.8%)

simplify11.0ms (0.2%)

prune39.0ms (0.7%)

localize15.0ms (0.3%)

series1.1s (19.2%)

rewrite308.0ms (5.3%)

simplify140.0ms (2.4%)

prune294.0ms (5.1%)

localize14.0ms (0.2%)

series1.2s (20.7%)

rewrite192.0ms (3.3%)

simplify119.0ms (2.1%)

prune185.0ms (3.2%)

localize15.0ms (0.3%)

series307.0ms (5.3%)

rewrite46.0ms (0.8%)

simplify63.0ms (1.1%)

prune181.0ms (3.1%)

regimes589.0ms (10.1%)

bsearch20.0ms (0.3%)

simplify3.0ms (0%)

end160.0ms (2.8%)

Profiling