Details

analyze6.0ms (0.4%)

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)

sample715.0ms (48.5%)

Results

690.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.4%)

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

prune5.0ms (0.3%)

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

30.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	29.4b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64`
3×	`sqrt-pow1_binary64`
3×	`pow-prod-down_binary64`
1×	`*-un-lft-identity_binary64`
1×	`sqrt-prod_binary64`

Counts

1 → 14

Calls

1 calls:

2.0ms

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

simplify158.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
575×	`cube-prod_binary64`
527×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

26 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	211
1	36	205
2	63	205
3	79	205
4	87	205
5	114	205
6	145	205
7	203	205
8	414	205
9	768	205
10	776	205
11	906	205
12	1060	205
13	1223	205
14	1451	205
15	1752	205
16	2100	205
17	2575	205
18	3193	205
19	3389	205
20	3563	205
21	3677	205
22	3724	205
23	3776	205
24	4654	205
25	4739	205
26	4663	205

prune15.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	18	4	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	5	23

Error

0.2b

Counts

23 → 5

Alt Table

Status	Error	Program
▶	29.8b	(*.f64 (sqrt.f64 2) x)
✓	30.5b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	43.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 290 to 219 computations (24.5% saved)

localize2.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) x)

series3.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

3.0ms

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

rewrite4.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 24

Calls

1 calls:

3.0ms

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

simplify56.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

444×	`cube-div_binary64`
431×	`log-div_binary64`
332×	`associate-l_binary64`
303×	`log-prod_binary64`
288×	`unswap-sqr_binary64`

Counts

24 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	226
1	67	214
2	159	214
3	214	214
4	293	214
5	479	214
6	964	214
7	2475	214
8	3811	214
9	4892	214

prune16.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	24	6	30

Error

0.1b

Counts

30 → 6

Alt Table

Status	Error	Program
✓	29.8b	(*.f64 (sqrt.f64 2) x)
	30.3b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
▶	29.8b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	30.5b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 314 to 252 computations (19.7% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

series8.0ms (0.5%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

rewrite15.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
15×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
6.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)

simplify71.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

455×	`log-div_binary64`
454×	`cube-div_binary64`
378×	`log-prod_binary64`
365×	`associate-l_binary64`
364×	`cube-prod_binary64`

Counts

66 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	697
1	126	642
2	352	642
3	548	642
4	651	642
5	907	642
6	2188	642
7	3602	642
8	4934	642

prune41.0ms (2.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	75	6	81

Error

0.1b

Counts

81 → 6

Alt Table

Status	Error	Program
✓	29.8b	(*.f64 (sqrt.f64 2) x)
✓	29.8b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	30.5b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	29.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x)
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1135 to 1014 computations (10.7% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x)
✓	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))

series3.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x)
0.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))

rewrite25.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`sqrt-prod_binary64`
62×	`add-sqr-sqrt_binary64`
32×	`sqrt-pow1_binary64`
30×	`pow1_binary64`
16×	`rem-sqrt-square_binary64`

Counts

2 → 106

Calls

2 calls:

11.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x)
8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))

simplify86.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

693×	`associate-/l/_binary64`
581×	`associate-/r/_binary64`
417×	`associate-r_binary64`
371×	`*-commutative_binary64`
296×	`sqr-pow_binary64`

Counts

118 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	812
1	144	770
2	427	762
3	917	734
4	1623	734
5	2488	734
6	4534	734
7	4962	734

prune53.0ms (3.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	109	6	115

Error

0.1b

Counts

115 → 6

Alt Table

Status	Error	Program
✓	29.8b	(*.f64 (sqrt.f64 2) x)
✓	29.8b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	30.5b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	29.9b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x)
	33.2b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1442 to 1292 computations (10.4% saved)

regimes77.0ms (5.2%)

Accuracy

Total 0.3b remaining (68.4%)

Threshold costs 0.3b (68.4%)

Counts

16 → 2

Compiler

Compiled 693 to 539 computations (22.2% saved)

bsearch14.0ms (1%)

Steps

Iters	Range		Point
8	-2.118530392705049e-306	1.2361269733177494e-308	1.27146975292896e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	36
1	20	36
2	28	36
3	33	36
4	38	36
5	40	36
6	40	36

end73.0ms (5%)

Compiler: Compiled 92 to 78 computations (15.2% saved)

Details

analyze6.0ms (0.4%)

sample715.0ms (48.5%)

simplify6.0ms (0.4%)

prune5.0ms (0.3%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite3.0ms (0.2%)

simplify158.0ms (10.7%)

prune15.0ms (1%)

localize2.0ms (0.2%)

series3.0ms (0.2%)

rewrite4.0ms (0.3%)

simplify56.0ms (3.8%)

prune16.0ms (1.1%)

localize6.0ms (0.4%)

series8.0ms (0.5%)

rewrite15.0ms (1%)

simplify71.0ms (4.8%)

prune41.0ms (2.8%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite25.0ms (1.7%)

simplify86.0ms (5.8%)

prune53.0ms (3.6%)

regimes77.0ms (5.2%)

bsearch14.0ms (1%)

simplify3.0ms (0.2%)

end73.0ms (5%)

Profiling