Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	76×	body	1280	valid
6.0ms	56×	body	640	valid
3.0ms	174×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	17×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

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: 39.2b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.6b	(- (exp x) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series60.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	220	330
1	621	311
2	2713	309
3	5001	309

prune91.0ms

Filtered

58 candidates to 43 candidates (74.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Merged error: 0.1b

Counts

59 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.4b	(* 1/6 (pow x 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`distribute-lft-out`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`prod-exp` `sum-log`
2×	`+-commutative` `associate-+r+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3-+` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 48

Calls

2 calls:

19.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
6.0ms	(* 1/6 (pow x 2))

series48.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
28.0ms	(* 1/6 (pow x 2))

simplify213.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	199	257
1	800	236
2	4922	235
3	5001	235

prune70.0ms

Filtered

54 candidates to 30 candidates (55.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Merged error: 0.1b

Counts

58 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 (pow x 2))
0.4b	(* 1/6 (pow x 2))
12.4b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
15.6b	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

623×	`*-un-lft-identity`
323×	`distribute-lft-out`
251×	`associate-l`
164×	`unpow-prod-down`
154×	`times-frac`
52×	`pow-unpow` `sum-cubes`
49×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
16×	`add-exp-log` `associate-r`
14×	`associate-/l*`
11×	`associate-/r*`
10×	`add-cbrt-cube`
8×	`pow1` `unswap-sqr`
6×	`prod-exp` `add-log-exp`
4×	`unpow2` `sqr-pow`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `pow-prod-down` `pow-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 273

Calls

4 calls:

6.0ms	(* 1/6 (pow x 2))
6.0ms	(* 1/6 (pow x 2))
29.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
154.0ms	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/6 (pow x 2))
25.0ms	(* 1/6 (pow x 2))
54.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
81.0ms	(/ (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

simplify157.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	489	6017
1	2262	5725
2	5001	5710

prune337.0ms

Filtered

285 candidates to 85 candidates (29.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	285	5	290

Merged error: 0.1b

Counts

290 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

12.4b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
12.4b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
12.4b	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
15.6b	(/ (* (* (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

rewrite651.0ms

Algorithm

rewrite-expression-head

Rules

6319×	`*-un-lft-identity`
3819×	`associate-l`
3513×	`distribute-lft-out`
2196×	`unpow-prod-down`
1908×	`cbrt-prod`
1452×	`times-frac`
905×	`add-sqr-sqrt`
636×	`swap-sqr`
408×	`associate-r`
360×	`unswap-sqr`
281×	`add-cube-cbrt`
252×	`pow-unpow` `sum-cubes`
132×	`associate-/l*`
54×	`cbrt-div`
48×	`*-commutative`
31×	`flip3-+` `add-cbrt-cube` `flip-+`
28×	`frac-times`
26×	`associate-/l/`
18×	`cbrt-unprod`
14×	`associate-*l/`
13×	`add-exp-log`
11×	`cbrt-undiv` `associate-/r*`
10×	`add-log-exp`
8×	`associate-*r/`
4×	`pow1`
3×	`+-commutative` `div-exp` `prod-exp` `sum-log`
2×	`associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 1713

Calls

4 calls:

27.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
30.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
27.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
277.0ms	(/ (* (* (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
50.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
53.0ms	(+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))
84.0ms	(/ (* (* (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (cbrt (+ (pow (* 1/6 (pow x 2)) 3) (pow (+ (* 1/2 x) 1) 3)))) (+ (* (+ (* 1/2 x) 1) (- (+ (* 1/2 x) 1) (* 1/6 (pow x 2)))) (* 1/36 (* (pow x 2) (pow x 2)))))

simplify825.0ms

Algorithm

egg-herbie

Counts

1725 → 1725

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	1588	84594
1	5001	71374

prune1.2s

Filtered

1725 candidates to 240 candidates (13.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1724	1	1725
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	1725	5	1730

Merged error: 0.1b

Counts

1730 → 5

regimes31.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 20.8b

bsearch32.0ms

Steps

Iters	Range		Point
8	-0.00024695944164034034	-6.132196241634436e-08	-0.00020269643688096618

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	17
1	36	17

end0.0ms

sample873.0ms

Algorithm

intervals

Results

367.0ms	2195×	body	1280	valid
182.0ms	1709×	body	640	valid
100.0ms	5364×	body	80	valid
63.0ms	875×	body	320	valid
20.0ms	460×	body	160	valid