Details

analyze1.2s (40.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample716.0ms (24.3%)

Results

689.0ms	8256×	body	128	valid
1.0ms	3×	body	8192	exit

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify9.0ms (0.3%)

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 (0.1%)

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

29.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.2b	(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
✓	28.1b	(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))

rewrite3.0ms (0.1%)

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:

3.0ms

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

simplify156.0ms (5.3%)

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

prune19.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	16	6	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	7	23

Error

0.1b

Counts

23 → 7

Alt Table

Status	Error	Program
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	29.0b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	29.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	29.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
	38.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 x (.f64 2 x))) 3))
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	28.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 370 to 279 computations (24.6% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

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

rewrite5.0ms (0.2%)

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:

4.0ms

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

simplify58.0ms (2%)

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

prune20.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	24	8	32

Error

0.1b

Counts

32 → 8

Alt Table

Status	Error	Program
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	28.9b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
	28.5b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
▶	28.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	29.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
	29.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	28.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 402 to 324 computations (19.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

series243.0ms (8.2%)

Counts

2 → 24

Calls

2 calls:

239.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)
3.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 52

Calls

2 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
4.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)

simplify83.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

501×	`associate-/l/_binary64`
437×	`associate-/r/_binary64`
384×	`*-commutative_binary64`
354×	`fma-def_binary64`
320×	`distribute-rgt-in_binary64`

Counts

76 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	71	778
1	139	669
2	456	669
3	785	669
4	1500	660
5	2968	660
6	4812	660
7	4839	660

prune48.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	73	8	81

Error

0.1b

Counts

81 → 8

Alt Table

Status	Error	Program
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
	28.9b	(.f64 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
▶	28.5b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	28.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	29.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 x)))
	29.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	28.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 1457 to 1301 computations (10.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

series9.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

6.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

rewrite14.0ms (0.5%)

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))
5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)

simplify73.0ms (2.5%)

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

prune40.0ms (1.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	2	2	4
Picked	0	1	1
Done	0	3	3
Total	76	7	83

Error

0.1b

Counts

83 → 7

Alt Table

Status	Error	Program
	28.5b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2))) x)
✓	29.2b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	28.5b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	28.4b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))
	29.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
	34.8b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	28.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 1141 to 1019 computations (10.7% saved)

regimes97.0ms (3.3%)

Accuracy

Total 0.3b remaining (68.1%)

Threshold costs 0.3b (68.1%)

Counts

20 → 2

Compiler

Compiled 911 to 716 computations (21.4% saved)

bsearch19.0ms (0.6%)

Steps

Iters	Range		Point
11	-3.38818498412467e-299	3.6223197135848765e-293	-4.64906815626e-312

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	15	30
1	26	30
2	34	30
3	39	30
4	41	30
5	41	30

end95.0ms (3.2%)

Compiler: Compiled 116 to 97 computations (16.4% saved)

Details

analyze1.2s (40.5%)

sample716.0ms (24.3%)

simplify9.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify156.0ms (5.3%)

prune19.0ms (0.7%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify58.0ms (2%)

prune20.0ms (0.7%)

localize6.0ms (0.2%)

series243.0ms (8.2%)

rewrite16.0ms (0.5%)

simplify83.0ms (2.8%)

prune48.0ms (1.6%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite14.0ms (0.5%)

simplify73.0ms (2.5%)

prune40.0ms (1.4%)

regimes97.0ms (3.3%)

bsearch19.0ms (0.6%)

simplify3.0ms (0.1%)

end95.0ms (3.2%)

Profiling