Details

sample42.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

20.0ms	95×	body	1280	valid
5.0ms	9×	body	320	valid
5.0ms	131×	body	80	valid
3.0ms	16×	body	640	valid
0.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.9b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2309	463
3	5002	463

prune149.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 13.4b

Counts

79 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
10×	`associate-*r/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/l*` `add-log-exp`
4×	`flip3--` `associate--l+` `frac-sub` `flip--` `associate-/l/` `distribute-lft-out`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`pow1/2` `diff-log` `div-sub` `pow-prod-down` `sqrt-prod`

Counts

4 → 96

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
8.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
32.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	450	1238
1	1712	1158
2	5001	1154

prune291.0ms

Filtered

78 candidates to 108 candidates (-38.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	110	3	113

Merged error: 13.4b

Counts

113 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.1b	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`cbrt-undiv` `sqrt-pow1` `times-frac` `sqrt-div` `div-exp` `associate-/r*`
3×	`distribute-rgt-out--` `div-inv`
2×	`pow1/2` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `distribute-lft-out`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `frac-sub` `flip--` `associate-/l/` `associate-/l*` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 73

Calls

4 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
17.0ms	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
33.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
64.0ms	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	400	1251
1	1634	1129
2	5001	1102

prune289.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 13.2b

Counts

88 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.1b	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.1b	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b	(- (sqrt (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
22×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
19×	`add-sqr-sqrt`
12×	`times-frac`
10×	`add-cube-cbrt` `associate-/r/`
8×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `sqrt-div` `flip-+` `div-inv` `distribute-lft-out`
4×	`prod-exp` `cbrt-unprod` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `associate-r/` `clear-num` `associate-/l/` `associate-/l` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 100

Calls

4 calls:

7.0ms	(sqrt (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
8.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
10.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
20.0ms	(- (sqrt (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
34.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
31.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
78.0ms	(- (sqrt (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	374	2043
1	1485	1812
2	5001	1811

prune708.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Merged error: 13.2b

Counts

116 → 4

regimes149.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	47
1	28	47

end0.0ms

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

622.0ms	2827×	body	1280	valid
159.0ms	4061×	body	80	valid
111.0ms	646×	body	640	valid
38.0ms	310×	body	320	valid
12.0ms	156×	body	160	valid

Details

sample42.0ms

simplify9.0ms

prune3.0ms

localize8.0ms

rewrite20.0ms

series41.0ms

simplify65.0ms

prune149.0ms

localize13.0ms

rewrite32.0ms

series58.0ms

simplify52.0ms

prune291.0ms

localize15.0ms

rewrite40.0ms

series123.0ms

simplify48.0ms

prune289.0ms

localize22.0ms

rewrite49.0ms

series184.0ms

simplify51.0ms

prune708.0ms

regimes149.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

Profiling