Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
4.0ms	309×	pre	80	false
3.0ms	256×	pre	80	true

simplify49.0ms

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: 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))

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:

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

series98.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
51.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify162.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (156.0ms)

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

prune113.0ms

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))

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)
6.0ms	(/ (- a b) a)
17.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series128.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms	(/ (+ a b) a)
31.0ms	(/ (- a b) a)
60.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify66.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (54.0ms)

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

prune278.0ms

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

localize13.0ms

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)))

rewrite36.0ms

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)))
10.0ms	(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)))
163.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))
163.0ms	(cbrt (* (/ (+ a b) a) (/ (- a b) a)))

simplify78.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (71.0ms)

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

prune228.0ms

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

localize10.0ms

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))

rewrite41.0ms

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)
16.0ms	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

series170.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (fabs (* (* (+ a b) (/ (- a b) a)) (/ 1 a))))
62.0ms	(* (+ a b) (/ (- a b) a))
29.0ms	(/ (- a b) a)
62.0ms	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

simplify99.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (86.0ms)

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

prune270.0ms

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

regimes115.0ms

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

sample626.0ms

Algorithm

intervals

Results

193.0ms	8000×	body	80	valid
101.0ms	8128×	pre	80	false
96.0ms	8000×	pre	80	true

Details

sample28.0ms

simplify49.0ms

prune2.0ms

localize7.0ms

rewrite14.0ms

series98.0ms

simplify162.0ms

prune113.0ms

localize8.0ms

rewrite35.0ms

series128.0ms

simplify66.0ms

prune278.0ms

localize13.0ms

rewrite36.0ms

series520.0ms

simplify78.0ms

prune228.0ms

localize10.0ms

rewrite41.0ms

series170.0ms

simplify99.0ms

prune270.0ms

regimes115.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample626.0ms

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