Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	63×	body	1280	valid
6.0ms	175×	body	80	valid
5.0ms	46×	body	640	valid
2.0ms	25×	body	320	valid
1.0ms	12×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.9b	(- (exp x) 1.0)

rewrite16.0ms

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:

10.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

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

prune119.0ms

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))
0.2b	(* 1/6 (pow x 2))

rewrite15.0ms

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:

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

series48.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
28.0ms	(* 1/6 (pow x 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	201	231
1	852	202
2	5001	199

prune82.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (pow x 2))
11.4b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
11.4b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
11.4b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite30.0ms

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:

5.0ms	(* 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)))
8.0ms	(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))
57.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
52.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
58.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify175.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (28.0ms)

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

prune235.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (+ 1/6 (* x 1/36)))
0.3b	(* x 1/36)
11.4b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
11.4b	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

7.0ms	(* x (+ 1/6 (* x 1/36)))
3.0ms	(* x 1/36)
8.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
8.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* x (+ 1/6 (* x 1/36)))
14.0ms	(* x 1/36)
52.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
58.0ms	(cbrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify47.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	314	584
1	1306	538
2	5002	532

prune235.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes25.0ms

Accuracy

98.6% (0.3b remaining)

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

bsearch35.0ms

Steps

Iters	Range		Point
9	-3.9934486818618	-2.7899019707608465e-05	-0.00014555533402309655

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	20
1	40	20
2	40	20

end0.0ms

sample849.0ms

Algorithm

intervals

Results

375.0ms	2199×	body	1280	valid
167.0ms	1610×	body	640	valid
99.0ms	5524×	body	80	valid
58.0ms	851×	body	320	valid
18.0ms	426×	body	160	valid