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)

sample713.0ms (28.8%)

Results

686.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.2%)

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

32.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.7b	(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
✓	31.5b	(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))

simplify157.0ms (6.4%)

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 (0.6%)

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
▶	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.6b	(*.f64 (sqrt.f64 2) x)
✓	32.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	32.9b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	33.7b	(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))

Compiler

Compiled 320 to 241 computations (24.7% 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 (2.4%)

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

prune15.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	25	6	31

Error

0.1b

Counts

31 → 6

Alt Table

Status	Error	Program
✓	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.6b	(*.f64 (sqrt.f64 2) x)
	29.4b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
▶	29.3b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	32.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 346 to 292 computations (15.6% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.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))

series205.0ms (8.3%)

Counts

2 → 24

Calls

2 calls:

202.0ms	(*.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))

rewrite17.0ms (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))
7.0ms	(*.f64 (cbrt.f64 (sqrt.f64 2)) x)

simplify173.0ms (7%)

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	675
2	456	675
3	785	672
4	1500	662
5	2968	662
6	4812	662
7	4839	662

prune84.0ms (3.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Error

0.1b

Counts

79 → 7

Alt Table

Status	Error	Program
✓	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.6b	(*.f64 (sqrt.f64 2) x)
	29.4b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
✓	29.3b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	32.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	29.3b	(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))))

Compiler

Compiled 1501 to 1367 computations (8.9% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) x)
✓	0.3b	(.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)))
✓	0.4b	(.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))

series456.0ms (18.4%)

Counts

3 → 36

Calls

3 calls:

246.0ms

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

207.0ms

(*.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))

3.0ms

(*.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)))

rewrite45.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
58×	`pow1_binary64`
40×	`cbrt-unprod_binary64`
40×	`prod-exp_binary64`
40×	`pow-prod-down_binary64`

Counts

3 → 98

Calls

3 calls:

18.0ms

(*.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)))

13.0ms

(*.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))

5.0ms

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

simplify117.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

619×	`unswap-sqr_binary64`
594×	`fma-def_binary64`
455×	`*-commutative_binary64`
396×	`sqr-pow_binary64`
302×	`log-prod_binary64`

Counts

134 → 126

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	2495
1	244	1401
2	896	1388
3	1801	1378
4	3902	1362
5	4839	1362
6	4872	1362

prune154.0ms (6.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	126	7	133

Error

0.1b

Counts

133 → 7

Alt Table

Status	Error	Program
✓	29.4b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	33.6b	(*.f64 (sqrt.f64 2) x)
	29.4b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
✓	29.3b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	32.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	29.3b	(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))))

Compiler

Compiled 3987 to 3759 computations (5.7% saved)

regimes82.0ms (3.3%)

Accuracy

Total 0.3b remaining (83.2%)

Threshold costs 0.3b (83.2%)

Counts

15 → 2

Compiler

Compiled 723 to 620 computations (14.2% saved)

bsearch15.0ms (0.6%)

Steps

Iters	Range		Point
8	-3.758681916072061e-306	4.478866104257719e-308	2.1786358791023e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	31	41
2	45	41
3	54	41
4	60	41
5	62	41
6	62	41

end110.0ms (4.5%)

Compiler: Compiled 130 to 113 computations (13.1% saved)

Details

analyze4.0ms (0.2%)

sample713.0ms (28.8%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify157.0ms (6.4%)

prune15.0ms (0.6%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify58.0ms (2.4%)

prune15.0ms (0.6%)

localize8.0ms (0.3%)

series205.0ms (8.3%)

rewrite17.0ms (0.7%)

simplify173.0ms (7%)

prune84.0ms (3.4%)

localize10.0ms (0.4%)

series456.0ms (18.4%)

rewrite45.0ms (1.8%)

simplify117.0ms (4.7%)

prune154.0ms (6.2%)

regimes82.0ms (3.3%)

bsearch15.0ms (0.6%)

simplify3.0ms (0.1%)

end110.0ms (4.5%)

Profiling