Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	253×	pre	80	false

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 13.1b

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))))
12.7b	(/ (- (* 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))

series23.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(- (* a a) (* b b))
10.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify164.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (159.0ms)

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

prune85.0ms

Filtered

61 candidates to 45 candidates (26.2%)

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

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:

5.0ms	(/ (+ a b) a)
1.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
5.0ms	(/ (- a b) a)
16.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series26.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (+ a b) a)
9.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
4.0ms	(/ (- a b) a)
9.0ms	(* (/ (+ 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	951
1	2505	870
2	5002	867

prune165.0ms

Filtered

155 candidates to 106 candidates (31.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Merged error: 0b

Counts

157 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

308×	`sqrt-prod`
290×	`add-sqr-sqrt`
250×	`times-frac`
208×	`*-un-lft-identity`
144×	`add-cube-cbrt`
104×	`associate-r`
38×	`associate-l`
30×	`unswap-sqr`
26×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
12×	`associate-/r*`
8×	`pow1` `sqrt-div`
6×	`div-inv` `distribute-lft-out`
4×	`cbrt-undiv` `sqrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
2×	`frac-times` `flip3--` `frac-2neg` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 360

Calls

4 calls:

29.0ms	(* (sqrt (/ (+ a b) a)) (/ (sqrt (- a b)) (sqrt a)))
31.0ms	(* (sqrt (/ (+ a b) a)) (/ (sqrt (- a b)) (sqrt a)))
7.0ms	(/ (sqrt (- a b)) (sqrt a))
7.0ms	(/ (sqrt (- a b)) (sqrt a))

series50.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (sqrt (/ (+ a b) a)) (/ (sqrt (- a b)) (sqrt a)))
14.0ms	(* (sqrt (/ (+ a b) a)) (/ (sqrt (- a b)) (sqrt a)))
11.0ms	(/ (sqrt (- a b)) (sqrt a))
11.0ms	(/ (sqrt (- a b)) (sqrt a))

simplify90.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	482	3752
1	2115	3636
2	5001	3510

prune281.0ms

Filtered

372 candidates to 194 candidates (47.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	372	3	375

Merged error: 0b

Counts

375 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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:

4.0ms	(cbrt (/ (- a b) a))
4.0ms	(cbrt (/ (- a b) a))
4.0ms	(cbrt (/ (- a b) a))
19.0ms	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (/ (- a b) a))
30.0ms	(cbrt (/ (- a b) a))
30.0ms	(cbrt (/ (- a b) a))
38.0ms	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	1818
1	1047	1763
2	5002	1712

prune224.0ms

Filtered

198 candidates to 144 candidates (27.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	198	3	201

Merged error: 0b

Counts

201 → 3

regimes73.0ms

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

sample943.0ms

Algorithm

intervals

Results

269.0ms	8000×	body	80	valid
138.0ms	8000×	pre	80	true
137.0ms	8006×	pre	80	false

Details

sample33.0ms

simplify49.0ms

prune3.0ms

localize7.0ms

rewrite13.0ms

series23.0ms

simplify164.0ms

prune85.0ms

localize9.0ms

rewrite34.0ms

series26.0ms

simplify64.0ms

prune165.0ms

localize13.0ms

rewrite97.0ms

series50.0ms

simplify90.0ms

prune281.0ms

localize15.0ms

rewrite41.0ms

series130.0ms

simplify50.0ms

prune224.0ms

regimes73.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample943.0ms

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