Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	249×	pre	80	false
5.0ms	256×	pre	80	true

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

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: 15.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
14.8b	(/ (- (* a a) (* b b)) (* a a))

rewrite13.0ms

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:

4.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
7.0ms	(/ (- (* a a) (* b b)) (* a a))

series104.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(- (* a a) (* b b))
19.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
54.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify178.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (165.0ms)

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

prune121.0ms

Filtered

61 candidates to 45 candidates (73.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 0.0b

Counts

62 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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)
16.0ms	(* (/ (+ a b) a) (/ (- a b) a))
6.0ms	(/ (- a b) a)

series139.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms	(/ (+ a b) a)
64.0ms	(* (/ (+ a b) a) (/ (- a b) a))
31.0ms	(/ (- a b) a)

simplify72.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (60.0ms)

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

prune286.0ms

Filtered

155 candidates to 106 candidates (68.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	154	3	157

Merged error: 0b

Counts

157 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-sqr-sqrt`
140×	`*-un-lft-identity`
121×	`times-frac`
102×	`sqrt-prod`
76×	`add-cube-cbrt`
38×	`associate-l`
30×	`swap-sqr`
26×	`distribute-lft-out--`
24×	`pow1`
23×	`associate-r`
22×	`add-exp-log` `add-cbrt-cube`
20×	`difference-of-squares`
12×	`sqrt-div`
11×	`unswap-sqr`
10×	`associate-/l*`
8×	`sqrt-pow1` `pow1/2`
7×	`prod-exp` `cbrt-unprod` `div-inv`
6×	`frac-times` `associate-r/` `pow-prod-down` `associate-/r`
5×	`pow-prod-up`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `associate-/l/` `add-log-exp`
3×	`pow-sqr` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `div-sub` `clear-num` `*-commutative` `flip--`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 231

Calls

4 calls:

21.0ms	(* (/ (+ a b) a) (* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a))))
6.0ms	(/ (- a b) a)
6.0ms	(/ (- a b) a)
26.0ms	(* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ (+ a b) a) (* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a))))
30.0ms	(/ (- a b) a)
29.0ms	(/ (- a b) a)
45.0ms	(* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a)))

simplify111.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	535	1560
1	3057	1394
2	5001	1385

prune451.0ms

Filtered

243 candidates to 150 candidates (61.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	243	3	246

Merged error: 0b

Counts

246 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))
0.1b	(cbrt (/ (- a b) a))
0.1b	(cbrt (/ (- a b) a))
0.1b	(cbrt (/ (- a b) a))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

157×	`cbrt-prod`
141×	`add-sqr-sqrt`
135×	`*-un-lft-identity`
123×	`times-frac`
75×	`add-cube-cbrt`
28×	`swap-sqr`
27×	`distribute-lft-out--`
22×	`associate-r` `associate-l`
21×	`difference-of-squares`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 186

Calls

4 calls:

20.0ms	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))
4.0ms	(cbrt (/ (- a b) a))
4.0ms	(cbrt (/ (- a b) a))
4.0ms	(cbrt (/ (- a b) a))

series848.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))
217.0ms	(cbrt (/ (- a b) a))
224.0ms	(cbrt (/ (- a b) a))
228.0ms	(cbrt (/ (- a b) a))

simplify57.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	284	1846
1	948	1790
2	5001	1710

prune498.0ms

Filtered

198 candidates to 144 candidates (72.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	198	3	201

Merged error: 0b

Counts

201 → 3

regimes37.0ms

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	13	12
1	13	12

end0.0ms

sample830.0ms

Algorithm

intervals

Results

274.0ms	8000×	body	80	valid
150.0ms	8000×	pre	80	true
148.0ms	7995×	pre	80	false