Details

sample77.0ms

Algorithm

intervals

Results

48.0ms	177×	body	1280	valid
8.0ms	289×	body	80	valid
6.0ms	42×	body	640	valid
2.0ms	23×	body	320	valid
0.0ms	7×	body	160	valid

simplify212.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

9.0ms	(- (exp x) 2.0)
46.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series73.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
60.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune88.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
23.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
11.0ms	(* 1/360 (pow x 6))
11.0ms	(* 1/12 (pow x 4))

series284.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
54.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
54.0ms	(* 1/360 (pow x 6))
38.0ms	(* 1/12 (pow x 4))

simplify49.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423

prune194.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (* 1/360 (pow x 6)))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+l+`

Counts

4 → 74

Calls

4 calls:

48.0ms	(+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
14.0ms	(+ (pow x 2) (* 1/360 (pow x 6)))
11.0ms	(* 1/360 (pow x 6))
11.0ms	(* 1/12 (pow x 4))

series276.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
129.0ms	(+ (pow x 2) (* 1/360 (pow x 6)))
52.0ms	(* 1/360 (pow x 6))
39.0ms	(* 1/12 (pow x 4))

simplify48.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	324	443
1	1453	420
2	5001	405

prune192.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))) (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))))
29.2b	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))
29.2b	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))
29.2b	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

61.0ms	(* (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))) (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))))
7.0ms	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))
7.0ms	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))
7.0ms	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))

series2.3s

Counts

4 → 12

Calls

4 calls:

614.0ms	(* (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))) (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))))
582.0ms	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))
563.0ms	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))
566.0ms	(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))

simplify49.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	360	1390
1	1222	1311
2	5001	1240

prune358.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5720×	body	1280	valid
180.0ms	1227×	body	640	valid
172.0ms	8143×	body	80	valid
49.0ms	576×	body	320	valid
16.0ms	289×	body	160	valid