Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true
4.0ms	255×	pre	80	false

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	47	7
2	106	7
3	265	7
4	1495	7
5	5001	7

prune2.0ms

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: 14.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
0.0b	(- (* a a) (* b b))
13.9b	(/ (- (* a a) (* b b)) (* a a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
4.0ms	(- (* a a) (* b b))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

series103.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
32.0ms	(- (* a a) (* b b))
55.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify168.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (162.0ms)

Iter	Nodes	Cost
0	228	417
1	970	368
2	4781	367
3	5001	366

prune123.0ms

Filtered

61 candidates to 45 candidates (73.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	3	62

Merged error: 0.0b

Counts

62 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b	(/ (+ a b) a)
0.0b	(/ (- a b) a)
0.0b	(* (/ (+ a b) a) (/ (- a b) a))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 143

Calls

4 calls:

1.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
6.0ms	(/ (+ a b) a)
10.0ms	(/ (- a b) a)
18.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series135.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
22.0ms	(/ (+ a b) a)
37.0ms	(/ (- a b) a)
60.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify68.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	493	951
1	2505	870
2	5001	867

prune281.0ms

Filtered

155 candidates to 106 candidates (68.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	155	3	158

Merged error: 0b

Counts

158 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
0.0b	(/ (* (+ a b) (/ (- a b) a)) a)
0.0b	(* (+ a b) (/ (- a b) a))
0.0b	(/ (- a b) a)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
34×	`times-frac`
27×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
7×	`pow1` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
4×	`frac-times` `flip3-+` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out`

Counts

4 → 122

Calls

4 calls:

1.0ms	(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
12.0ms	(/ (* (+ a b) (/ (- a b) a)) a)
14.0ms	(* (+ a b) (/ (- a b) a))
7.0ms	(/ (- a b) a)

series169.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
63.0ms	(/ (* (+ a b) (/ (- a b) a)) a)
56.0ms	(* (+ a b) (/ (- a b) a))
34.0ms	(/ (- a b) a)

simplify67.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	440	816
1	2436	731
2	5001	729

prune227.0ms

Filtered

134 candidates to 94 candidates (70.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	134	3	137

Merged error: 0b

Counts

137 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- a b))
0.0b	(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
0.1b	(/ (sqrt (- a b)) (sqrt a))
0.1b	(/ (sqrt (- a b)) (sqrt a))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

183×	`sqrt-prod`
144×	`times-frac`
141×	`add-sqr-sqrt`
140×	`*-un-lft-identity`
98×	`add-cube-cbrt`
52×	`associate-r`
49×	`add-exp-log` `add-cbrt-cube`
21×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`cbrt-undiv` `div-exp`
12×	`associate-/r*`
10×	`pow1`
6×	`sqrt-div`
5×	`frac-times` `associate-*l/`
4×	`associate-/l/` `add-log-exp`
3×	`flip3--` `associate-*r/` `pow-prod-down` `flip--` `div-inv`
2×	`sqrt-undiv` `frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 261

Calls

4 calls:

4.0ms	(sqrt (- a b))
34.0ms	(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
8.0ms	(/ (sqrt (- a b)) (sqrt a))
9.0ms	(/ (sqrt (- a b)) (sqrt a))

series311.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (- a b))
87.0ms	(* (* (/ (+ a b) a) (/ (sqrt (- a b)) (sqrt a))) (/ (sqrt (- a b)) (sqrt a)))
78.0ms	(/ (sqrt (- a b)) (sqrt a))
83.0ms	(/ (sqrt (- a b)) (sqrt a))

simplify131.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	726	2914
1	4373	2557
2	5001	2391

prune466.0ms

Filtered

273 candidates to 139 candidates (50.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	273	3	276

Merged error: 0b

Counts

276 → 3

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

end0.0ms

sample776.0ms

Algorithm

intervals

Results

263.0ms	8000×	body	80	valid
138.0ms	8000×	pre	80	true
136.0ms	7943×	pre	80	false

Details

sample35.0ms

simplify52.0ms

prune2.0ms

localize7.0ms

rewrite14.0ms

series103.0ms

simplify168.0ms

prune123.0ms

localize9.0ms

rewrite41.0ms

series135.0ms

simplify68.0ms

prune281.0ms

localize9.0ms

rewrite38.0ms

series169.0ms

simplify67.0ms

prune227.0ms

localize12.0ms

rewrite69.0ms

series311.0ms

simplify131.0ms

prune466.0ms

regimes33.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample776.0ms

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