Details

sample21.0ms

Algorithm

intervals

Results

8.0ms	246×	body	80	valid
0.0ms	3×	body	1280	valid
0.0ms	2×	body	2560	valid
0.0ms	2×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	4
1	11	4
2	11	4

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

9.0ms

(+ x (/ (fabs (- y x)) 2.0))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

(+ x (/ (fabs (- y x)) 2.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	83	110
1	206	97
2	480	97
3	1339	97
4	4294	97
5	5001	97

prune40.0ms

Filtered

20 candidates to 16 candidates (80.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	16	4	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	5	21

Merged error: 0.0b

Counts

21 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
8×	`add-cbrt-cube`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 106

Calls

4 calls:

14.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
53.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
59.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
56.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	385	1612
1	1318	1502
2	5002	1359

prune251.0ms

Filtered

118 candidates to 83 candidates (70.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	118	5	123

Merged error: 0.0b

Counts

123 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

6.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
52.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
54.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))
55.0ms	(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	208	892
1	593	840
2	2098	828
3	5001	824

prune255.0ms

Filtered

76 candidates to 68 candidates (89.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	76	5	81

Merged error: 0.0b

Counts

81 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `hypot-def` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `times-frac` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 121

Calls

4 calls:

6.0ms	(+ x (/ (fabs (- y x)) 2.0))
6.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
6.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ x (/ (fabs (- y x)) 2.0))
46.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
50.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	281	1107
1	1089	1001
2	5001	967

prune199.0ms

Filtered

133 candidates to 80 candidates (60.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	132	6	138

Merged error: 0b

Counts

138 → 6

regimes71.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample283.0ms

Algorithm

intervals

Results

142.0ms	7684×	body	80	valid
11.0ms	134×	body	1280	valid
5.0ms	70×	body	640	valid
5.0ms	44×	body	2560	valid
2.0ms	42×	body	320	valid
1.0ms	27×	body	160	valid