Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	77×	body	1280	valid
6.0ms	57×	body	640	valid
3.0ms	157×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	9×	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: 41.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.7b	(- (exp x) 1.0)

rewrite19.0ms

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:

13.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series55.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify76.0ms

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

prune120.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

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))

rewrite16.0ms

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:

9.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
6.0ms	(* 1/6 (pow x 2))

series45.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
25.0ms	(* 1/6 (pow x 2))

simplify169.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (29.0ms)

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

prune81.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 (pow x 2))
8.9b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.9b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.9b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

6.0ms	(* 1/6 (pow x 2))
8.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
11.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 1/6 (pow x 2))
55.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
58.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
54.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify180.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	238	734
1	845	687
2	4682	673
3	5002	673

prune223.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.9b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.9b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.9b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

9.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
57.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
52.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
55.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify86.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	158	852
1	507	800
2	2712	792
3	5001	788

prune237.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes24.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch40.0ms

Steps

Iters	Range		Point
10	-64880754058.88788	-5.5985807885592334e-05	-0.00016775901941409424

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	40
1	42	40

end0.0ms

sample866.0ms

Algorithm

intervals

Results

392.0ms	2343×	body	1280	valid
172.0ms	1637×	body	640	valid
96.0ms	5409×	body	80	valid
57.0ms	811×	body	320	valid
17.0ms	401×	body	160	valid