Details

sample226.0ms

Algorithm

intervals

Results

207.0ms	74×	body	1280	valid
5.0ms	50×	body	640	valid
3.0ms	169×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify6.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.6b	(- (exp x) 1.0)

rewrite37.0ms

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:

25.0ms	(/ (- (exp x) 1.0) x)
10.0ms	(- (exp x) 1.0)

series51.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- (exp x) 1.0) x)
13.0ms	(- (exp x) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	222	329
1	625	311
2	2739	309
3	5001	309

prune113.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

25.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
12.0ms	(* 1/6 (pow x 2))

series40.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
23.0ms	(* 1/6 (pow x 2))

simplify35.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	201	222
1	825	201
2	5001	198

prune83.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))) (cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))))
11.6b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
11.6b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
11.6b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite209.0ms

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:

150.0ms	(* (cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))) (cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))))
18.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
20.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
18.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))) (cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))))
49.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
47.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
50.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify47.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	290	1545
1	1034	1452
2	5001	1359

prune284.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow x 2))
0.3b	(* 1/12 (pow x 2))
0.4b	(* 1/3 x)
11.6b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`associate-r`
16×	`add-exp-log`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
9×	`associate-l` `unswap-sqr`
8×	`unpow-prod-down`
7×	`prod-exp`
6×	`pow1`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`cbrt-prod` `*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `cbrt-div` `pow-exp`
1×	`flip3-+` `pow1/3` `pow-prod-down` `flip-+`

Counts

4 → 85

Calls

4 calls:

12.0ms	(* 1/6 (pow x 2))
14.0ms	(* 1/12 (pow x 2))
7.0ms	(* 1/3 x)
18.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* 1/6 (pow x 2))
23.0ms	(* 1/12 (pow x 2))
15.0ms	(* 1/3 x)
47.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	353	452
1	1368	416
2	5002	408

prune237.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes22.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.8b

bsearch27.0ms

Steps

Iters	Range		Point
9	-0.2945747773639613	-3.489101517161873e-08	-0.00014542173044640355

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample921.0ms

Algorithm

intervals

Results

384.0ms	2242×	body	1280	valid
173.0ms	1669×	body	640	valid
103.0ms	5590×	body	80	valid
53.0ms	800×	body	320	valid
18.0ms	407×	body	160	valid