Details

sample42.0ms

Algorithm

intervals

Results

14.0ms	65×	body	1280	valid
9.0ms	62×	body	640	valid
4.0ms	20×	body	320	valid
3.0ms	97×	body	80	valid
3.0ms	80×	body	80	overflowed
1.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.5b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

8.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series40.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2210	354
3	5001	354

prune305.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
0.0b	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

6.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
12.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
14.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)

series141.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* (pow x 2) (+ (* x 1/6) 1/2)) x)
36.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
64.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
13.0ms	(* x 1/6)

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	429	746
1	2022	686
2	5001	684

prune222.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

16.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
6.0ms	(+ (* 1/12 x) (/ 1 x))
3.0ms	(* 1/12 x)

series69.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
39.0ms	(+ (* 1/12 x) (/ 1 x))
16.0ms	(* 1/12 x)

simplify104.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	200	216
1	705	205
2	3820	204
3	5002	204

prune85.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))
0.6b	(cbrt (+ (* 1/12 x) (/ 1 x)))
0.6b	(cbrt (+ (* 1/12 x) (/ 1 x)))
0.6b	(cbrt (+ (* 1/12 x) (/ 1 x)))

rewrite66.0ms

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:

47.0ms	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))
5.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
5.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
6.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))
108.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
108.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
106.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	361	1208
1	1237	1135
2	5001	1081

prune253.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

96.9% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

469.0ms	2207×	body	1280	valid
240.0ms	1658×	body	640	valid
102.0ms	2876×	body	80	valid
90.0ms	2535×	body	80	overflowed
83.0ms	818×	body	320	valid
32.0ms	442×	body	160	valid