Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample888.0ms (15%)

Results

833.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify13.0ms (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

prune4.0ms (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

26.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

series7.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

7.0ms

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

rewrite18.0ms (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))

simplify311.0ms (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

prune31.0ms (0.5%)

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
	31.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
	36.9b	(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))))
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.9b	(*.f64 (sqrt.f64 2) x)
▶	27.4b	(.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))))

Compiler

Compiled 362 to 271 computations (25.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))
✓	0.5b	(.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
✓	0.5b	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))
	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

series938.0ms (15.9%)

Counts

3 → 36

Calls

3 calls:

565.0ms

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

369.0ms

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

4.0ms

(*.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))))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`cbrt-prod_binary64`
29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
16×	`pow1/3_binary64`
14×	`associate-r_binary64`

Counts

3 → 98

Calls

3 calls:

11.0ms

(*.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))))

7.0ms

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

3.0ms

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

simplify471.0ms (8%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
572×	`exp-prod_binary64`
423×	`log-prod_binary64`
412×	`*-commutative_binary64`
342×	`associate-l_binary64`

Counts

134 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	2452
1	215	2281
2	494	1919
3	1371	1712
4	2664	1166
5	4156	1166
6	4348	1166
7	4775	1166
8	4962	1166
9	4871	1166

prune414.0ms (7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	254	8	262

Error

0.1b

Counts

262 → 8

Alt Table

Status	Error	Program
	36.9b	(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))))
	31.6b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))
	31.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	30.9b	(*.f64 (sqrt.f64 2) x)
	27.2b	(.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 x) x)) (sqrt.f64 (.f64 (.f64 2 x) x)))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
▶	27.2b	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

Compiler

Compiled 6932 to 5296 computations (23.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
	0.5b	(cbrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))
	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	27.6b	(cbrt.f64 (.f64 x (.f64 2 x)))

series532.0ms (9%)

Counts

2 → 24

Calls

2 calls:

460.0ms	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
71.0ms	(cbrt.f64 (.f64 x (.f64 2 x)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`cbrt-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

13.0ms	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))
5.0ms	(cbrt.f64 (.f64 x (.f64 2 x)))

simplify191.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

691×	`unswap-sqr_binary64`
507×	`associate-/l*_binary64`
312×	`fma-def_binary64`
307×	`log-div_binary64`
237×	`*-commutative_binary64`

Counts

62 → 70

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	66	1167
1	119	1167
2	287	1167
3	545	1167
4	670	1167
5	1007	1149
6	1449	1149
7	2784	881
8	4931	881
9	5104	881

prune144.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	117	8	125

Error

0.1b

Counts

125 → 8

Alt Table

Status	Error	Program
▶	27.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))))
	31.6b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))
	36.9b	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (sqrt.f64 (.f64 (*.f64 2 x) x))))
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.9b	(*.f64 (sqrt.f64 2) x)
✓	27.2b	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

Compiler

Compiled 2374 to 1738 computations (26.8% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x)))))
✓	0.6b	(cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))
	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
	27.6b	(cbrt.f64 (.f64 x (.f64 2 x)))

series853.0ms (14.5%)

Counts

2 → 24

Calls

2 calls:

454.0ms	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x)))))
399.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`cbrt-prod_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`sqrt-prod_binary64`
10×	`associate-r_binary64`
8×	`*-un-lft-identity_binary64`

Counts

2 → 48

Calls

2 calls:

12.0ms	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x)))))
8.0ms	(cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))

simplify208.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-def_binary64`
545×	`times-frac_binary64`
312×	`fma-neg_binary64`
302×	`div-sub_binary64`
273×	`associate-l_binary64`

Counts

72 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1655
1	187	1639
2	365	1575
3	724	1511
4	1464	1511
5	2839	1511
6	4897	1511
7	4866	1511

prune178.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	182	8	190

Error

0.1b

Counts

190 → 8

Alt Table

Status	Error	Program
✓	27.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 x) x)))))
	31.6b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x)) (sqrt.f64 (*.f64 (sqrt.f64 2) x)))
	36.9b	(cbrt.f64 (.f64 (.f64 x (.f64 2 x)) (sqrt.f64 (.f64 (*.f64 2 x) x))))
	32.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	31.4b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	26.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
	30.9b	(*.f64 (sqrt.f64 2) x)
✓	27.2b	(.f64 (cbrt.f64 (.f64 x (.f64 2 x))) (cbrt.f64 (sqrt.f64 (.f64 (*.f64 2 x) x))))

Compiler

Compiled 5627 to 4314 computations (23.3% saved)

regimes331.0ms (5.6%)

Accuracy

Total 0.2b remaining (61.8%)

Threshold costs 0.2b (61.8%)

Counts

35 → 2

Compiler

Compiled 2217 to 1729 computations (22% saved)

bsearch25.0ms (0.4%)

Steps

Iters	Range		Point
10	-2.3119816531597982e-307	2.7659793173174092e-297	-3.7663053235543e-311

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (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

end194.0ms (3.3%)

Compiler: Compiled 126 to 96 computations (23.8% saved)

Details

analyze2.0ms (0%)

sample888.0ms (15%)

simplify13.0ms (0.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series7.0ms (0.1%)

rewrite18.0ms (0.3%)

simplify311.0ms (5.3%)

prune31.0ms (0.5%)

localize19.0ms (0.3%)

series938.0ms (15.9%)

rewrite32.0ms (0.5%)

simplify471.0ms (8%)

prune414.0ms (7%)

localize17.0ms (0.3%)

series532.0ms (9%)

rewrite22.0ms (0.4%)

simplify191.0ms (3.2%)

prune144.0ms (2.4%)

localize22.0ms (0.4%)

series853.0ms (14.5%)

rewrite26.0ms (0.4%)

simplify208.0ms (3.5%)

prune178.0ms (3%)

regimes331.0ms (5.6%)

bsearch25.0ms (0.4%)

simplify7.0ms (0.1%)

end194.0ms (3.3%)

Profiling