Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	248×	body	80	valid
1.0ms	4×	body	640	valid
0.0ms	2×	body	1280	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	320	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 12

Calls

1 calls:

11.0ms

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

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify122.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	83	100
1	207	91
2	481	91
3	1288	91
4	3899	91
5	5002	91

prune42.0ms

Filtered

15 candidates to 11 candidates (73.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Merged error: 0.0b

Counts

16 → 4

localize9.0ms

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))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity` `sqrt-prod`
28×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
14×	`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×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 106

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))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ x (/ (fabs (- y x)) 2.0))
60.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
53.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
24.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	273	1063
1	1071	971
2	5001	937

prune224.0ms

Filtered

118 candidates to 64 candidates (54.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	117	5	122

Merged error: 0.0b

Counts

122 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.7b	(pow (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 4)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
22×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`cbrt-div` `sqrt-div`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

6.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
6.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
9.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
9.0ms	(pow (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 4)

series310.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
75.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
77.0ms	(cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
95.0ms	(pow (cbrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 4)

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	416	1169
1	1389	1103
2	5002	1078

prune306.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Merged error: 0.0b

Counts

93 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
0.0b	(- x (/ (fabs (- y x)) 2.0))
11.9b	(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
27.8b	(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
70×	`times-frac`
56×	`*-un-lft-identity`
44×	`add-cube-cbrt`
20×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
8×	`add-log-exp`
6×	`associate-/r*` `distribute-lft-out--`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`flip3--` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 146

Calls

4 calls:

15.0ms	(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
7.0ms	(- x (/ (fabs (- y x)) 2.0))
4.0ms	(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
13.0ms	(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
22.0ms	(- x (/ (fabs (- y x)) 2.0))
39.0ms	(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
58.0ms	(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

simplify113.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	646	2135
1	3374	1888
2	5002	1853

prune436.0ms

Filtered

158 candidates to 115 candidates (72.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	158	5	163

Merged error: 0b

Counts

163 → 5

regimes117.0ms

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

sample334.0ms

Algorithm

intervals

Results

166.0ms	7672×	body	80	valid
12.0ms	126×	body	1280	valid
6.0ms	50×	body	2560	valid
5.0ms	72×	body	640	valid
4.0ms	61×	body	320	valid
1.0ms	20×	body	160	valid