Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	249×	body	80	valid
0.0ms	3×	body	1280	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	640	valid
0.0ms	2×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:

5.0ms

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

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify108.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	83	100
1	207	91
2	481	91
3	1288	91
4	3899	91
5	5001	91

prune32.0ms

Filtered

15 candidates to 11 candidates (26.7%)

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

localize11.0ms

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))))

rewrite34.0ms

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:

5.0ms	(+ x (/ (fabs (- y x)) 2.0))
5.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
5.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
15.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ x (/ (fabs (- y x)) 2.0))
78.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
78.0ms	(sqrt (+ x (/ (fabs (- y x)) 2.0)))
19.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	290	1059
1	1130	983
2	5002	957

prune237.0ms

Filtered

118 candidates to 66 candidates (44.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
0.4b	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-div`
112×	`sqrt-prod`
91×	`sqrt-pow1`
69×	`pow1`
60×	`add-sqr-sqrt`
47×	`pow1/2`
42×	`*-un-lft-identity`
39×	`pow-prod-up`
35×	`flip3-+` `flip-+`
32×	`frac-times`
22×	`add-cube-cbrt`
20×	`swap-sqr`
17×	`associate-l`
16×	`associate-*r/`
12×	`pow-prod-down`
11×	`add-exp-log` `associate-r` `pow-sqr` `add-cbrt-cube` `unswap-sqr`
10×	`associate-*l/`
9×	`distribute-lft-out`
4×	`rem-sqrt-square` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`pow2` `pow-plus` `rem-square-sqrt`

Counts

4 → 205

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
6.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
28.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
19.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
56.0ms	(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
19.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
80.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	660	2756
1	2499	2410
2	5001	2374

prune693.0ms

Filtered

217 candidates to 104 candidates (52.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	217	4	221

Merged error: 0b

Counts

221 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))))
0.4b	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)))
0.5b	(cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
0.6b	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod`
122×	`sqrt-div`
82×	`add-sqr-sqrt`
76×	`cbrt-prod`
47×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
35×	`flip3-+` `flip-+`
32×	`frac-times`
31×	`add-cube-cbrt`
30×	`associate-r`
28×	`cube-div`
27×	`unswap-sqr`
26×	`cbrt-div`
17×	`associate-l`
16×	`associate-*r/`
14×	`pow1`
12×	`add-exp-log`
10×	`associate-*l/` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`sqr-pow`
5×	`pow-pow`
4×	`sqrt-pow1` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`pow1/2` `*-commutative`
1×	`pow-to-exp` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 214

Calls

4 calls:

25.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))))
27.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)))
9.0ms	(cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
8.0ms	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

series260.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))))
79.0ms	(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)))
54.0ms	(cbrt (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3))
107.0ms	(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

simplify120.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	890	4090
1	3571	3264
2	5001	3042

prune1.1s

Filtered

226 candidates to 109 candidates (51.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	226	4	230

Merged error: 0b

Counts

230 → 4

regimes141.0ms

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

sample379.0ms

Algorithm

intervals

Results

164.0ms	7696×	body	80	valid
12.0ms	120×	body	1280	valid
6.0ms	74×	body	640	valid
6.0ms	48×	body	2560	valid
2.0ms	34×	body	320	valid
1.0ms	31×	body	160	valid

Details

sample17.0ms

simplify4.0ms

prune3.0ms

localize10.0ms

rewrite6.0ms

series19.0ms

simplify108.0ms

prune32.0ms

localize11.0ms

rewrite34.0ms

series197.0ms

simplify44.0ms

prune237.0ms

localize13.0ms

rewrite72.0ms

series209.0ms

simplify88.0ms

prune693.0ms

localize14.0ms

rewrite81.0ms

series260.0ms

simplify120.0ms

prune1.1s

regimes141.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample379.0ms

Profiling