Details

analyze4.0ms (0.2%)

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)

sample716.0ms (35%)

Results

686.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (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

32.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.3b	(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
✓	31.2b	(sqrt.f64 (.f64 (.f64 2 x) x))

series6.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(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:

3.0ms

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

simplify162.0ms (7.9%)

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

prune24.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	17	5	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	6	23

Error

0.2b

Counts

23 → 6

Alt Table

Status	Error	Program
	32.7b	(*.f64 (sqrt.f64 2) x)
✓	32.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	42.8b	(cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 x) x)) (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (.f64 (.f64 2 x) x))))
▶	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 346 to 259 computations (25.1% saved)

localize4.0ms (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)

rewrite6.0ms (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:

5.0ms

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

simplify57.0ms (2.8%)

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

prune18.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	24	7	31

Error

0.1b

Counts

31 → 7

Alt Table

Status	Error	Program
	32.7b	(*.f64 (sqrt.f64 2) x)
	30.2b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
▶	30.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	32.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
✓	30.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 378 to 316 computations (16.4% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series243.0ms (11.9%)

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))

rewrite15.0ms (0.7%)

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:

8.0ms	(.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)

simplify85.0ms (4.2%)

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

prune53.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	4	4
Picked	0	1	1
Done	1	1	2
Total	72	8	80

Error

0.1b

Counts

80 → 8

Alt Table

Status	Error	Program
✓	32.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.3b	(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3))))
	32.7b	(*.f64 (sqrt.f64 2) x)
▶	30.2b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
✓	30.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	30.3b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

Compiler

Compiled 1550 to 1407 computations (9.2% saved)

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

rewrite18.0ms (0.9%)

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:

8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

simplify75.0ms (3.7%)

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

prune50.0ms (2.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	75	8	83

Error

0.1b

Counts

83 → 8

Alt Table

Status	Error	Program
✓	32.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.3b	(neg.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (pow.f64 (sqrt.f64 2) 2/3))))
	32.7b	(*.f64 (sqrt.f64 2) x)
✓	30.2b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
✓	30.2b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
	30.3b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x))))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

Compiler

Compiled 1240 to 1118 computations (9.8% saved)

regimes157.0ms (7.7%)

Accuracy

Total 0.3b remaining (85.3%)

Threshold costs 0.3b (85.3%)

Counts

36 → 2

Compiler

Compiled 1712 to 1511 computations (11.7% saved)

bsearch19.0ms (0.9%)

Steps

Iters	Range		Point
11	-6.545684543728382e-289	3.457178502137674e-296	1.12248846736665e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify127.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	50
1	36	50
2	50	50
3	65	50
4	75	50
5	81	50
6	83	50
7	83	50

end165.0ms (8.1%)

Compiler: Compiled 162 to 141 computations (13% saved)

Details

analyze4.0ms (0.2%)

sample716.0ms (35%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite3.0ms (0.2%)

simplify162.0ms (7.9%)

prune24.0ms (1.2%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite6.0ms (0.3%)

simplify57.0ms (2.8%)

prune18.0ms (0.9%)

localize7.0ms (0.3%)

series243.0ms (11.9%)

rewrite15.0ms (0.7%)

simplify85.0ms (4.2%)

prune53.0ms (2.6%)

localize10.0ms (0.5%)

series9.0ms (0.4%)

rewrite18.0ms (0.9%)

simplify75.0ms (3.7%)

prune50.0ms (2.5%)

regimes157.0ms (7.7%)

bsearch19.0ms (0.9%)

simplify127.0ms (6.2%)

end165.0ms (8.1%)

Profiling