Details

analyze258.0ms (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
50%	50%	0.1%	6
68.7%	31.2%	0.1%	7
81.2%	18.7%	0.1%	8
89%	10.9%	0.1%	9
92.1%	7.8%	0.1%	10
95.6%	4.3%	0.1%	11
96.4%	3.5%	0.1%	12
98%	1.9%	0.1%	13
98.2%	1.7%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample18.0ms (0.9%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify130.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

890×	`div-sub_binary64`
546×	`times-frac_binary64`
503×	`sub-neg_binary64`
395×	`neg-sub0_binary64`
385×	`neg-mul-1_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	16	13
2	40	13
3	80	13
4	151	13
5	244	13
6	386	13
7	990	13
8	2799	13
9	3328	13
10	3729	13
11	3928	13
12	4147	13
13	4322	13
14	4853	13

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

16.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 22 to 14 computations (36.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

15.6b

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

rewrite23.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

6.0ms

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 468 to 221 computations (52.8% saved)

series25.0ms (1.2%)

Error

0.4b

Counts

1 → 18

Calls

1 calls:

21.0ms

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 434 to 339 computations (21.9% saved)

simplify61.0ms (3%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-l_binary64`
461×	`associate-r_binary64`
448×	`associate-*l/_binary64`
421×	`associate-/l/_binary64`
394×	`associate-/r*_binary64`

Counts

47 → 34

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	891
1	274	757
2	1158	727
3	4502	727
4	5231	727

prune15.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	6	35

Error

Counts

35 → 6

Alt Table

Status	Error	Program
	39.9b	(/.f64 (.f64 (/.f64 (.f64 x 2) (sqrt.f64 (-.f64 x y))) y) (sqrt.f64 (-.f64 x y)))
	9.0b	(/.f64 (.f64 (/.f64 (.f64 x 2) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) y) (cbrt.f64 (-.f64 x y)))
	37.8b	(.f64 (/.f64 (.f64 x (.f64 2 y)) (-.f64 (.f64 x x) (*.f64 y y))) (+.f64 x y))
▶	0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
	6.8b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
	34.4b	(.f64 2 (+.f64 y (/.f64 (.f64 y y) x)))

Compiler

Compiled 458 to 247 computations (46.1% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))
0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

rewrite89.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

96×	`add-sqr-sqrt_binary64`
95×	`times-frac_binary64`
76×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
25×	`distribute-lft-out--_binary64`

Counts

2 → 104

Calls

2 calls:

13.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
10.0ms	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))

Compiler

Compiled 1910 to 1537 computations (19.5% saved)

series42.0ms (2.1%)

Error

Counts

2 → 30

Calls

2 calls:

21.0ms	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
16.0ms	(-.f64 (/.f64 1/2 y) (/.f64 1/2 x))

Compiler

Compiled 679 to 550 computations (19% saved)

simplify136.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

322×	`associate-l_binary64`
303×	`cancel-sign-sub-inv_binary64`
293×	`associate-/l*_binary64`
288×	`associate-r_binary64`
287×	`associate-*l/_binary64`

Counts

134 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2367
1	406	2247
2	1117	2212
3	3607	2212
4	4835	2212
5	4877	2212

prune37.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	95	6	101

Error

Counts

101 → 6

Alt Table

Status	Error	Program
	39.9b	(/.f64 (.f64 (/.f64 (.f64 x 2) (sqrt.f64 (-.f64 x y))) y) (sqrt.f64 (-.f64 x y)))
	9.0b	(/.f64 (.f64 (/.f64 (.f64 x 2) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) y) (cbrt.f64 (-.f64 x y)))
✓	0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
▶	6.8b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
	34.4b	(.f64 2 (+.f64 y (/.f64 (.f64 y y) x)))
	16.3b	(.f64 (/.f64 2 (-.f64 x y)) (.f64 y x))

Compiler

Compiled 755 to 533 computations (29.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 y (-.f64 x y))
6.8b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))

rewrite43.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
21×	`associate-r_binary64`
21×	`add-cube-cbrt_binary64`

Counts

2 → 78

Calls

2 calls:

8.0ms	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
4.0ms	(/.f64 y (-.f64 x y))

Compiler

Compiled 1223 to 429 computations (64.9% saved)

series49.0ms (2.4%)

Error

Counts

2 → 39

Calls

2 calls:

22.0ms	(/.f64 y (-.f64 x y))
21.0ms	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))

Compiler

Compiled 996 to 744 computations (25.3% saved)

simplify85.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/l*_binary64`
451×	`associate-*r/_binary64`
439×	`times-frac_binary64`
375×	`associate-*l/_binary64`
218×	`associate-/r*_binary64`

Counts

117 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	1963
1	403	1777
2	1513	1702
3	4423	1693
4	5104	1693

prune19.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	62	5	67

Error

Counts

67 → 5

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
✓	6.8b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
	34.4b	(.f64 2 (+.f64 y (/.f64 (.f64 y y) x)))
	16.3b	(.f64 (/.f64 2 (-.f64 x y)) (.f64 y x))
▶	7.4b	(.f64 (.f64 x 2) (/.f64 1 (+.f64 (/.f64 x y) -1)))

Compiler

Compiled 439 to 228 computations (48.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 x y) -1)
0.5b	(/.f64 1 (+.f64 (/.f64 x y) -1))
6.8b	(.f64 (.f64 x 2) (/.f64 1 (+.f64 (/.f64 x y) -1)))

rewrite83.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

48×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64`
29×	`add-exp-log_binary64`
24×	`associate-r_binary64`

Counts

3 → 108

Calls

3 calls:

11.0ms	(.f64 (.f64 x 2) (/.f64 1 (+.f64 (/.f64 x y) -1)))
7.0ms	(+.f64 (/.f64 x y) -1)
6.0ms	(/.f64 1 (+.f64 (/.f64 x y) -1))

Compiler

Compiled 1969 to 1283 computations (34.8% saved)

series61.0ms (3%)

Error

Counts

3 → 51

Calls

3 calls:

20.0ms	(/.f64 1 (+.f64 (/.f64 x y) -1))
19.0ms	(.f64 (.f64 x 2) (/.f64 1 (+.f64 (/.f64 x y) -1)))
14.0ms	(+.f64 (/.f64 x y) -1)

Compiler

Compiled 1239 to 930 computations (24.9% saved)

simplify144.0ms (7%)

Algorithm

1×	egg-herbie

Rules

426×	`div-sub_binary64`
299×	`associate-/l*_binary64`
289×	`times-frac_binary64`
218×	`*-commutative_binary64`
197×	`associate-*r/_binary64`

Counts

159 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2477
1	365	2246
2	1138	2160
3	2790	2151
4	4833	2151
5	4997	2151
6	4934	2151

prune43.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	131	5	136

Error

Counts

136 → 5

Alt Table

Status	Error	Program
	0.2b	(/.f64 1 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
	6.8b	(.f64 (.f64 x 2) (/.f64 y (-.f64 x y)))
	34.4b	(.f64 2 (+.f64 y (/.f64 (.f64 y y) x)))
	16.3b	(.f64 (/.f64 2 (-.f64 x y)) (.f64 y x))
	7.4b	(.f64 (.f64 x 2) (/.f64 1 (+.f64 (/.f64 x y) -1)))

Compiler

Compiled 1286 to 772 computations (40% saved)

regimes126.0ms (6.2%)

Accuracy

Total 0.2b remaining (95.9%)

Threshold costs 0.2b (95.9%)

Compiler

Compiled 1972 to 1352 computations (31.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	16	13
2	23	13
3	25	13
4	26	13
5	23	13

end0.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample533.0ms (26%)

Algorithm

1×

intervals

Results

291.0ms

8000×

body

128

valid

Compiler

Compiled 82 to 59 computations (28% saved)

Details

analyze258.0ms (12.6%)

sample18.0ms (0.9%)

simplify130.0ms (6.4%)

prune1.0ms (0.1%)

localize5.0ms (0.3%)

rewrite23.0ms (1.1%)

series25.0ms (1.2%)

simplify61.0ms (3%)

prune15.0ms (0.7%)

localize6.0ms (0.3%)

rewrite89.0ms (4.4%)

series42.0ms (2.1%)

simplify136.0ms (6.7%)

prune37.0ms (1.8%)

localize6.0ms (0.3%)

rewrite43.0ms (2.1%)

series49.0ms (2.4%)

simplify85.0ms (4.2%)

prune19.0ms (0.9%)

localize7.0ms (0.3%)

rewrite83.0ms (4.1%)

series61.0ms (3%)

simplify144.0ms (7%)

prune43.0ms (2.1%)

regimes126.0ms (6.2%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample533.0ms (26%)

Profiling