Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	68×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	17×	body	1280	valid
2.0ms	19×	body	320	valid
1.0ms	19×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	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: 8.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
1.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

1261×	`associate-/r*`
1123×	`*-un-lft-identity`
1080×	`frac-sub`
1012×	`frac-add`
966×	`associate-/l*`
867×	`add-sqr-sqrt`
663×	`add-cube-cbrt`
322×	`frac-2neg` `clear-num`
121×	`distribute-lft-out`
106×	`distribute-lft-out--`
100×	`difference-of-squares`
47×	`times-frac`
13×	`flip3--` `flip--`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `associate-/r/`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `flip3-+` `diff-log` `div-exp` `sum-log` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 1212

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
23.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms	(/ 1.0 (+ x 1.0))
69.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (- x 1.0))
47.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
26.0ms	(/ 1.0 (+ x 1.0))
227.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify285.0ms

Algorithm

egg-herbie

Counts

1224 → 1224

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5001	28253

prune1.5s

Filtered

1224 candidates to 538 candidates (44.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1220	4	1224
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1221	4	1225

Merged error: 0.2b

Counts

1225 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
1.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 1.0 (/ 1 (- x 1.0))))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

1459×	`associate-/r*`
1360×	`*-un-lft-identity`
1350×	`frac-sub`
1288×	`frac-add`
1229×	`associate-/l*`
1012×	`associate-*r/`
981×	`add-sqr-sqrt`
777×	`add-cube-cbrt`
471×	`clear-num`
379×	`frac-2neg`
276×	`un-div-inv`
144×	`distribute-lft-out`
101×	`distribute-lft-out--`
100×	`difference-of-squares`
35×	`times-frac`
16×	`flip3--` `flip--`
11×	`add-log-exp`
10×	`add-exp-log`
8×	`add-cbrt-cube`
5×	`pow1`
4×	`associate-/r/`
3×	`div-exp`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `flip3-+` `diff-log` `associate-l` `sum-log` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-` `rec-exp` `pow-flip` `1-exp` `inv-pow`

Counts

4 → 1490

Calls

4 calls:

24.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
6.0ms	(/ 1 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
87.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 1.0 (/ 1 (- x 1.0))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
33.0ms	(/ 1 (- x 1.0))
27.0ms	(/ 1.0 (+ x 1.0))
237.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 1.0 (/ 1 (- x 1.0))))

simplify365.0ms

Algorithm

egg-herbie

Counts

1502 → 1502

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5001	34767

prune1.6s

Filtered

1502 candidates to 487 candidates (32.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1500	2	1502
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	1502	4	1506

Merged error: 0.2b

Counts

1506 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
11.0b	(/ (+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0)) (* (cbrt (+ x 1.0)) (* x (- x 1.0))))
20.8b	(+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0))

rewrite930.0ms

Algorithm

rewrite-expression-head

Rules

4028×	`associate-*l/`
2392×	`*-un-lft-identity`
1876×	`cbrt-div`
1835×	`associate-l`
944×	`frac-add`
940×	`flip3-+` `flip-+`
924×	`add-sqr-sqrt`
912×	`frac-sub`
798×	`associate-/r*`
749×	`distribute-lft-out`
736×	`cbrt-prod`
632×	`frac-times`
630×	`times-frac`
593×	`associate-r`
474×	`associate-/l/`
416×	`add-cube-cbrt`
406×	`distribute-lft-out--`
331×	`flip3--` `flip--`
254×	`unswap-sqr`
225×	`swap-sqr`
93×	`associate-/l*`
69×	`*-commutative`
25×	`frac-2neg` `clear-num`
22×	`add-cbrt-cube` `difference-of-squares`
18×	`associate-*r/`
15×	`add-exp-log`
11×	`pow1`
10×	`cbrt-unprod`
8×	`associate-/r/`
7×	`pow1/3`
6×	`add-log-exp`
5×	`cbrt-undiv`
4×	`associate-+l+` `prod-exp`
3×	`div-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `pow-plus` `sum-log` `div-inv`

Counts

4 → 1756

Calls

4 calls:

9.0ms	(cbrt (+ x 1.0))
11.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
318.0ms	(/ (+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0)) (* (cbrt (+ x 1.0)) (* x (- x 1.0))))
246.0ms	(+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ x 1.0))
107.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
728.0ms	(/ (+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0)) (* (cbrt (+ x 1.0)) (* x (- x 1.0))))
346.0ms	(+ (* (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0)) (- x 1.0)) (* (* (cbrt (+ x 1.0)) x) 1.0))

simplify639.0ms

Algorithm

egg-herbie

Counts

1768 → 1768

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5001	67793

prune5.8s

Filtered

1768 candidates to 851 candidates (48.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1767	1	1768
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	1769	3	1772

Merged error: 0.2b

Counts

1772 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
11.0b	(/ (+ (* x (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (+ (* (- 1.0) (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (* (* (cbrt (+ x 1.0)) x) 1.0))) (* (cbrt (+ x 1.0)) (* x (- x 1.0))))
20.8b	(+ (* x (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (+ (* (- 1.0) (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (* (* (cbrt (+ x 1.0)) x) 1.0)))

rewrite14.1s

Algorithm

rewrite-expression-head

Rules

144134×	`associate-*l/`
72094×	`cbrt-div`
48996×	`associate-*r/`
48984×	`frac-add`
47728×	`frac-sub`
40222×	`associate-/r*`
36205×	`flip3-+` `flip-+`
32319×	`*-un-lft-identity`
30336×	`cbrt-prod`
23155×	`add-sqr-sqrt`
12755×	`add-cube-cbrt`
12326×	`associate-/l/`
11322×	`swap-sqr`
10326×	`associate-l`
9262×	`associate-r`
8788×	`distribute-lft-out`
5200×	`unswap-sqr`
3791×	`associate-/l*`
1306×	`*-commutative`
1257×	`frac-2neg` `clear-num`
690×	`times-frac`
631×	`flip3--` `flip--`
192×	`distribute-rgt-neg-in`
26×	`add-cbrt-cube`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`pow1`
17×	`add-exp-log`
14×	`cbrt-unprod`
12×	`frac-times` `pow1/3`
9×	`add-log-exp`
8×	`associate-+l+` `associate-/r/`
6×	`associate-+r+`
5×	`cbrt-undiv` `prod-exp`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `pow-sqr` `pow-prod-up`
3×	`div-exp` `sum-log`
2×	`+-commutative` `pow2` `pow-plus`
1×	`div-inv`

Counts

4 → 25573

Calls

4 calls:

11.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
11.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.6s	(/ (+ (* x (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (+ (* (- 1.0) (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (* (* (cbrt (+ x 1.0)) x) 1.0))) (* (cbrt (+ x 1.0)) (* x (- x 1.0))))
736.0ms	(+ (* x (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (+ (* (- 1.0) (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (* (* (cbrt (+ x 1.0)) x) 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
109.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
695.0ms	(/ (+ (* x (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (+ (* (- 1.0) (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (* (* (cbrt (+ x 1.0)) x) 1.0))) (* (cbrt (+ x 1.0)) (* x (- x 1.0))))
341.0ms	(+ (* x (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (+ (* (- 1.0) (- (* (/ 1.0 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) x) (* (cbrt (+ x 1.0)) 2.0))) (* (* (cbrt (+ x 1.0)) x) 1.0)))

simplify17.6s

Algorithm

egg-herbie

Counts

25585 → 25585

Iterations

Useful iterations: 0 (430.0ms)

Iter	Nodes	Cost
0	24151	2044961

prune2.7m

Filtered

25585 candidates to 13942 candidates (54.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	25585	0	25585
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	25585	3	25588

Merged error: 0.2b

Counts

25588 → 3

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 9.7b

bsearch114.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	103.79212150702143
10	-1556119314.230081	-0.05767290693153419	-113.75799676267467

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	19
1	45	19

end0.0ms

sample587.0ms

Algorithm

intervals

Results

194.0ms	1801×	body	640	valid
126.0ms	4258×	body	80	valid
73.0ms	933×	body	320	valid
72.0ms	546×	body	1280	valid
27.0ms	463×	body	160	valid