Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	259×	pre	80	false
4.0ms	256×	pre	80	true

simplify52.0ms

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: 14.3b

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))))
13.9b	(/ (- (* 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))

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

prune117.0ms

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)
0.0b	(* (/ (+ a b) a) (/ (- a b) a))
0.0b	(/ (- 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))))
6.0ms	(/ (+ a b) a)
18.0ms	(* (/ (+ a b) a) (/ (- a b) a))
6.0ms	(/ (- 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)
62.0ms	(* (/ (+ a b) a) (/ (- a b) a))
29.0ms	(/ (- a b) a)

simplify67.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (56.0ms)

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

prune264.0ms

Filtered

155 candidates to 106 candidates (68.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0b

Counts

157 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (- a b))
0.0b	(/ (+ a b) a)
0.0b	(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
0.1b	(/ 1 (/ a (- a b)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

287×	`times-frac`
221×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
138×	`add-cube-cbrt`
68×	`associate-r`
64×	`add-exp-log`
34×	`add-cbrt-cube`
30×	`div-exp`
29×	`associate-/r*`
25×	`distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
16×	`associate-l`
14×	`cbrt-undiv` `prod-exp`
12×	`div-inv`
10×	`associate-/l*` `unswap-sqr`
8×	`flip3--` `flip--`
7×	`pow1` `distribute-lft-out`
6×	`rec-exp` `1-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`frac-times` `pow-flip` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 305

Calls

4 calls:

5.0ms	(/ a (- a b))
6.0ms	(/ (+ a b) a)
38.0ms	(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
9.0ms	(/ 1 (/ a (- a b)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ a (- a b))
22.0ms	(/ (+ a b) a)
64.0ms	(* (/ (+ a b) a) (/ 1 (/ a (- a b))))
30.0ms	(/ 1 (/ a (- a b)))

simplify50.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1036	2352
1	5002	2074

prune523.0ms

Filtered

317 candidates to 200 candidates (63.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	317	0	317
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	317	2	319

Merged error: 0b

Counts

319 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
46×	`times-frac`
41×	`add-cube-cbrt`
19×	`add-exp-log` `associate-r` `add-cbrt-cube`
18×	`cbrt-prod`
16×	`associate-l`
12×	`unpow-prod-down` `cube-prod` `sqrt-prod`
8×	`pow1`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `associate-/r*` `div-inv` `distribute-lft-out`
2×	`cube-mult` `unpow3` `associate-/l/` `sqr-pow`
1×	`frac-times` `pow-to-exp` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `*-commutative` `sqrt-pow2` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 156

Calls

4 calls:

3.0ms	(pow (sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a)))) 3)
3.0ms	(cbrt (pow (sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a)))) 3))
16.0ms	(* (/ (+ a b) a) (/ (- a b) a))
6.0ms	(/ (- a b) a)

series148.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a)))) 3)
16.0ms	(cbrt (pow (sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a)))) 3))
62.0ms	(* (/ (+ a b) a) (/ (- a b) a))
30.0ms	(/ (- a b) a)

simplify76.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	561	1330
1	2817	1233
2	5001	1221

prune288.0ms

Filtered

168 candidates to 98 candidates (58.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	168	2	170

Merged error: 0b

Counts

170 → 2

regimes28.0ms

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	8
1	15	8

end0.0ms

sample768.0ms

Algorithm

intervals

Results

252.0ms	8000×	body	80	valid
142.0ms	8096×	pre	80	false
138.0ms	8000×	pre	80	true

Details

sample29.0ms

simplify52.0ms

prune2.0ms

localize7.0ms

rewrite13.0ms

series100.0ms

simplify168.0ms

prune117.0ms

localize8.0ms

rewrite37.0ms

series128.0ms

simplify67.0ms

prune264.0ms

localize9.0ms

rewrite76.0ms

series160.0ms

simplify50.0ms

prune523.0ms

localize15.0ms

rewrite34.0ms

series148.0ms

simplify76.0ms

prune288.0ms

regimes28.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample768.0ms

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