Details

sample31.0ms

Algorithm

intervals

Results

14.0ms	87×	body	1280	valid
5.0ms	50×	body	640	valid
3.0ms	172×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	10×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 41.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.5b	(- (exp x) 1.0)

rewrite12.0ms

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:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series56.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (19.0ms)

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

prune116.0ms

Filtered

58 candidates to 43 candidates (74.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Merged error: 0.0b

Counts

59 → 4

localize7.0ms

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))

rewrite13.0ms

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:

7.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
5.0ms	(* 1/6 (pow x 2))

series48.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
25.0ms	(* 1/6 (pow x 2))

simplify34.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (30.0ms)

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

prune81.0ms

Filtered

46 candidates to 29 candidates (63.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Merged error: 0.0b

Counts

50 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
0.0b	(pow (exp x) 3)
2.4b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-sqr-sqrt`
48×	`difference-of-squares`
42×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log`
8×	`add-log-exp`
5×	`pow1`
4×	`pow-pow`
3×	`difference-cubes` `pow-unpow` `exp-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 142

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
25.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
3.0ms	(pow (exp x) 3)
14.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series215.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ 1.0 (exp x))
138.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
24.0ms	(pow (exp x) 3)
41.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify82.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	543	1574
1	2534	1469
2	5001	1425

prune389.0ms

Filtered

154 candidates to 88 candidates (57.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	154	4	158

Merged error: 0.0b

Counts

158 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(exp (* x 3))
0.0b	(/ (- (exp (* x 3)) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
2.4b	(- (exp (* x 3)) (pow 1.0 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`add-log-exp`
12×	`difference-of-squares`
11×	`times-frac` `associate-/l*`
9×	`difference-cubes` `add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`pow1` `exp-lft-cube` `exp-prod` `exp-to-pow`
3×	`unpow-prod-down` `cube-prod` `distribute-lft-out--` `sqr-pow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `rem-exp-log` `distribute-lft-out`

Counts

4 → 85

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
2.0ms	(exp (* x 3))
21.0ms	(/ (- (exp (* x 3)) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
6.0ms	(- (exp (* x 3)) (pow 1.0 3))

series139.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
6.0ms	(exp (* x 3))
107.0ms	(/ (- (exp (* x 3)) (pow 1.0 3)) (* (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x))) x))
18.0ms	(- (exp (* x 3)) (pow 1.0 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	443	991
1	1915	841
2	5002	841

prune233.0ms

Filtered

97 candidates to 66 candidates (68.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	97	4	101

Merged error: 0.0b

Counts

101 → 4

regimes25.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch43.0ms

Steps

Iters	Range		Point
9	-6.308761783247451	-1.485944467815708e-07	-0.00010502760427764326

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	43	26

end0.0ms

sample862.0ms

Algorithm

intervals

Results

381.0ms	2323×	body	1280	valid
169.0ms	1629×	body	640	valid
102.0ms	5547×	body	80	valid
52.0ms	788×	body	320	valid
21.0ms	434×	body	160	valid