Details

analyze19.0ms (0.9%)

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)

sample14.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% 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

29.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.7b	(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
✓	28.5b	(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))

rewrite6.0ms (0.3%)

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:

5.0ms

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

simplify162.0ms (7.1%)

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 (0.7%)

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
	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
✓	29.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	29.9b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

Compiler

Compiled 302 to 227 computations (24.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))
✓	0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	28.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

series13.0ms (0.6%)

Counts

2 → 12

Calls

2 calls:

10.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

rewrite29.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`sqrt-pow1_binary64`
144×	`pow1_binary64`
76×	`pow-prod-down_binary64`
31×	`sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`

Counts

2 → 112

Calls

2 calls:

12.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
3.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))

simplify91.0ms (4%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-*l/_binary64`
417×	`associate-*r/_binary64`
315×	`*-commutative_binary64`
310×	`associate-l_binary64`
252×	`cube-div_binary64`

Counts

124 → 108

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	69	1254
1	106	1164
2	303	1134
3	863	1044
4	1341	1014
5	1815	1014
6	3771	1000
7	4901	1000

prune294.0ms (12.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	175	3	178
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	176	7	183

Error

0.1b

Counts

183 → 7

Alt Table

Status	Error	Program
	33.8b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 x))) (sqrt.f64 (sqrt.f64 (.f64 2 x)))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (sqrt.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x)))) (cbrt.f64 (sqrt.f64 (.f64 x (.f64 2 x))))) (cbrt.f64 (sqrt.f64 (.f64 x (*.f64 2 x)))))))
✓	29.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))))

Compiler

Compiled 3524 to 2684 computations (23.8% 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)

rewrite4.0ms (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)

simplify53.0ms (2.3%)

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

prune53.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	23	9	32

Error

0.0b

Counts

32 → 9

Alt Table

Status	Error	Program
▶	30.0b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	29.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.8b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 x))) (sqrt.f64 (sqrt.f64 (.f64 2 x)))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.0b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
	30.5b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x))))
	30.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))))

Compiler

Compiled 496 to 408 computations (17.7% 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)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))

series253.0ms (11.1%)

Counts

2 → 24

Calls

2 calls:

249.0ms	(*.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:

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)

simplify81.0ms (3.6%)

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

prune50.0ms (2.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	73	9	82

Error

0.0b

Counts

82 → 9

Alt Table

Status	Error	Program
✓	30.0b	(neg.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) x)))
✓	29.7b	(sqrt.f64 (.f64 (.f64 2 x) x))
	33.8b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 2 x))) (sqrt.f64 (sqrt.f64 (.f64 2 x)))) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))
	33.5b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	30.0b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.8b	(*.f64 (sqrt.f64 2) x)
	30.0b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x)))
	30.5b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x)) (cbrt.f64 (.f64 (sqrt.f64 2) x))) (cbrt.f64 (*.f64 (sqrt.f64 2) x))))
	30.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))))

Compiler

Compiled 1499 to 1354 computations (9.7% saved)

regimes512.0ms (22.5%)

Accuracy

Total 0.3b remaining (87.8%)

Threshold costs 0.3b (87.8%)

Counts

99 → 2

Compiler

Compiled 7523 to 5838 computations (22.4% saved)

bsearch12.0ms (0.5%)

Steps

Iters	Range		Point
7	-1.6339340312877537e-307	1.7277814182359533e-308	3.9577417547074e-311

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	14	25
1	25	25
2	33	25
3	38	25
4	40	25
5	40	25

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample558.0ms (24.6%)

Algorithm

1×

intervals

Results

272.0ms

8000×

body

128

valid

Compiler

Compiled 153 to 122 computations (20.3% saved)

Details

analyze19.0ms (0.9%)

sample14.0ms (0.6%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite6.0ms (0.3%)

simplify162.0ms (7.1%)

prune15.0ms (0.7%)

localize6.0ms (0.2%)

series13.0ms (0.6%)

rewrite29.0ms (1.3%)

simplify91.0ms (4%)

prune294.0ms (12.9%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite4.0ms (0.2%)

simplify53.0ms (2.3%)

prune53.0ms (2.3%)

localize7.0ms (0.3%)

series253.0ms (11.1%)

rewrite17.0ms (0.7%)

simplify81.0ms (3.6%)

prune50.0ms (2.2%)

regimes512.0ms (22.5%)

bsearch12.0ms (0.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample558.0ms (24.6%)

Profiling