Details

analyze4.0ms (0.3%)

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)

sample718.0ms (50.7%)

Results

688.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.4%)

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

29.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 27 to 19 computations (29.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.1b	(sqrt.f64 (.f64 (.f64 2 x) x))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(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))

simplify165.0ms (11.6%)

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

prune13.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	4	23

Error

0.2b

Counts

23 → 4

Alt Table

Status	Error	Program
▶	28.7b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
	29.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	34.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 270 to 203 computations (24.8% saved)

localize2.0ms (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)

rewrite5.0ms (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:

4.0ms

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

simplify60.0ms (4.3%)

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

prune15.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	24	5	29

Error

0.1b

Counts

29 → 5

Alt Table

Status	Error	Program
✓	28.7b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	28.7b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
	29.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	34.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 290 to 238 computations (17.9% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
✓	0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

series11.0ms (0.8%)

Counts

2 → 12

Calls

2 calls:

8.0ms	(*.f64 (sqrt.f64 (sqrt.f64 2)) x)
3.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))

rewrite14.0ms (1%)

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)

simplify79.0ms (5.6%)

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 (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	75	5	80

Error

0.1b

Counts

80 → 5

Alt Table

Status	Error	Program
✓	28.7b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	28.7b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
▶	29.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	34.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 1115 to 996 computations (10.7% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.4%)

Counts

1 → 8

Calls

1 calls:

6.0ms

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

rewrite7.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64`
5×	`sqrt-prod_binary64`
5×	`pow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

5.0ms

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

simplify76.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-neg_binary64`
251×	`*-commutative_binary64`
218×	`associate-*l/_binary64`
212×	`log-div_binary64`
211×	`cube-div_binary64`

Counts

37 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	428
1	79	416
2	211	416
3	349	416
4	395	416
5	478	416
6	597	416
7	1666	416
8	2312	416
9	4654	416
10	5166	416

prune15.0ms (1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	33	5	38

Error

0.1b

Counts

38 → 5

Alt Table

Status	Error	Program
✓	28.7b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	28.7b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (sqrt.f64 2)) x))
✓	29.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	34.5b	(neg.f64 (*.f64 (sqrt.f64 2) x))

Compiler

Compiled 433 to 287 computations (33.7% saved)

regimes57.0ms (4.1%)

Accuracy

Total 0.3b remaining (67%)

Threshold costs 0.3b (67%)

Counts

10 → 2

Compiler

Compiled 333 to 272 computations (18.3% saved)

bsearch27.0ms (1.9%)

Steps

Iters	Range		Point
11	-2.2999089514730885e-287	2.8479958288668977e-301	-3.2220197881532e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.2%)

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	36
1	25	36
2	33	36
3	38	36
4	40	36
5	40	36

end71.0ms (5%)

Compiler: Compiled 82 to 69 computations (15.9% saved)

Details

analyze4.0ms (0.3%)

sample718.0ms (50.7%)

simplify6.0ms (0.4%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite3.0ms (0.2%)

simplify165.0ms (11.6%)

prune13.0ms (0.9%)

localize2.0ms (0.2%)

series3.0ms (0.2%)

rewrite5.0ms (0.3%)

simplify60.0ms (4.3%)

prune15.0ms (1.1%)

localize4.0ms (0.3%)

series11.0ms (0.8%)

rewrite14.0ms (1%)

simplify79.0ms (5.6%)

prune40.0ms (2.8%)

localize4.0ms (0.3%)

series6.0ms (0.4%)

rewrite7.0ms (0.5%)

simplify76.0ms (5.3%)

prune15.0ms (1%)

regimes57.0ms (4.1%)

bsearch27.0ms (1.9%)

simplify3.0ms (0.2%)

end71.0ms (5%)

Profiling