Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	237×	pre	80	false

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 16.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
16.1b	(/ (- (* 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))

series100.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
53.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify161.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (155.0ms)

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

prune114.0ms

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

localize8.0ms

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

rewrite37.0ms

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))))
5.0ms	(/ (+ a b) a)
6.0ms	(/ (- a b) a)
19.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series129.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms	(/ (+ a b) a)
33.0ms	(/ (- a b) a)
58.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify65.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	493	951
1	2505	870
2	5002	867

prune269.0ms

Filtered

155 candidates to 106 candidates (68.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Merged error: 0b

Counts

157 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (/ (+ a b) a) (/ (- a b) a)) 3)
0.0b	(cbrt (pow (* (/ (+ a b) a) (/ (- a b) a)) 3))
0.1b	(/ (- a b) a)
0.1b	(* (/ (+ a b) a) (/ (- a b) a))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
33×	`add-cube-cbrt`
31×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`pow1` `cbrt-undiv` `div-exp`
8×	`cbrt-prod` `prod-exp` `cbrt-unprod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`cube-div`
5×	`pow-exp` `associate-/l*` `rem-cube-cbrt`
4×	`add-log-exp` `unswap-sqr`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-l/` `associate-/r*` `div-inv` `distribute-lft-out`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-sub` `clear-num` `*-commutative` `flip--` `rem-cbrt-cube`

Counts

4 → 148

Calls

4 calls:

12.0ms	(pow (* (/ (+ a b) a) (/ (- a b) a)) 3)
2.0ms	(cbrt (pow (* (/ (+ a b) a) (/ (- a b) a)) 3))
6.0ms	(/ (- a b) a)
16.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series279.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(pow (* (/ (+ a b) a) (/ (- a b) a)) 3)
70.0ms	(cbrt (pow (* (/ (+ a b) a) (/ (- a b) a)) 3))
32.0ms	(/ (- a b) a)
59.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify82.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	574	998
1	3144	954
2	5001	951

prune315.0ms

Filtered

160 candidates to 107 candidates (66.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	160	4	164

Merged error: 0b

Counts

164 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

220×	`add-sqr-sqrt`
178×	`times-frac`
172×	`sqrt-prod`
150×	`*-un-lft-identity`
98×	`add-cube-cbrt`
92×	`associate-l`
44×	`associate-r`
30×	`unswap-sqr`
18×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out--` `difference-of-squares`
12×	`distribute-lft-out`
10×	`associate-/l*`
8×	`pow1`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
2×	`frac-times` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-unprod` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 276

Calls

4 calls:

28.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a)))
31.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a)))
6.0ms	(/ (- a b) a)
6.0ms	(/ (- a b) a)

series389.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a)))
163.0ms	(* (/ (sqrt (+ a b)) (sqrt a)) (sqrt (/ (- a b) a)))
30.0ms	(/ (- a b) a)
34.0ms	(/ (- a b) a)

simplify68.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	457	2682
1	1803	2586
2	5001	2572

prune686.0ms

Filtered

288 candidates to 182 candidates (63.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	288	4	292

Merged error: 0b

Counts

292 → 4

regimes39.0ms

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

sample785.0ms

Algorithm

intervals

Results

269.0ms	8000×	body	80	valid
139.0ms	8000×	pre	80	true
132.0ms	7698×	pre	80	false

Details

sample30.0ms

simplify50.0ms

prune2.0ms

localize7.0ms

rewrite13.0ms

series100.0ms

simplify161.0ms

prune114.0ms

localize8.0ms

rewrite37.0ms

series129.0ms

simplify65.0ms

prune269.0ms

localize11.0ms

rewrite44.0ms

series279.0ms

simplify82.0ms

prune315.0ms

localize13.0ms

rewrite85.0ms

series389.0ms

simplify68.0ms

prune686.0ms

regimes39.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample785.0ms

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