Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
6.0ms	309×	pre	80	false
5.0ms	256×	pre	80	true

simplify49.0ms

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: 15.1b

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))))
14.6b	(/ (- (* 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:

3.0ms	(- (* 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:

31.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
52.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify162.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (157.0ms)

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

prune110.0ms

Filtered

61 candidates to 45 candidates (73.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	0	0
Picked	0	1	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))

rewrite36.0ms

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

series126.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
22.0ms	(/ (+ a b) a)
32.0ms	(/ (- a b) a)
57.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify64.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	493	952
1	2505	870
2	5001	867

prune264.0ms

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	0	0	0
Picked	1	0	1
Done	0	1	1
Total	154	3	157

Merged error: 0b

Counts

157 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
14×	`add-cube-cbrt`
9×	`cbrt-div`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/l*`
4×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 74

Calls

4 calls:

6.0ms	(/ (- a b) a)
9.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))
9.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))
9.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (- a b) a)
164.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))
162.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))
164.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))

simplify74.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	202	514
1	607	459
2	2607	449
3	5001	443

prune221.0ms

Filtered

86 candidates to 69 candidates (80.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (* (* (+ a b) (/ (- a b) a)) (/ 1 a))))
0.0b	(* (+ a b) (/ (- a b) a))
0.1b	(/ (- a b) a)
0.2b	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
50×	`add-exp-log`
48×	`*-un-lft-identity`
40×	`times-frac`
32×	`add-cube-cbrt` `associate-r` `add-cbrt-cube`
22×	`prod-exp`
12×	`pow1` `div-exp` `cbrt-unprod`
11×	`frac-times` `associate-*l/`
7×	`cbrt-undiv` `distribute-lft-out--` `difference-of-squares`
6×	`flip3-+` `flip-+`
5×	`associate-l` `associate-/l*`
4×	`associate-*r/` `pow-prod-down` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-/r*` `sqrt-prod` `div-inv`
2×	`*-commutative` `associate-/l/` `unswap-sqr`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num` `un-div-inv` `flip--` `distribute-lft-out`

Counts

4 → 148

Calls

4 calls:

1.0ms	(sqrt (fabs (* (* (+ a b) (/ (- a b) a)) (/ 1 a))))
12.0ms	(* (+ a b) (/ (- a b) a))
6.0ms	(/ (- a b) a)
15.0ms	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

series167.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (fabs (* (* (+ a b) (/ (- a b) a)) (/ 1 a))))
56.0ms	(* (+ a b) (/ (- a b) a))
33.0ms	(/ (- a b) a)
63.0ms	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

simplify101.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	611	1081
1	3832	943
2	5002	928

prune262.0ms

Filtered

160 candidates to 104 candidates (65.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	160	3	163

Merged error: 0b

Counts

163 → 3

regimes108.0ms

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	15	22
1	15	22

end0.0ms

sample813.0ms

Algorithm

intervals

Results

268.0ms	8000×	body	80	valid
148.0ms	8128×	pre	80	false
147.0ms	8000×	pre	80	true