Details

sample86.0ms

Algorithm

intervals

Results

58.0ms	178×	body	1280	valid
7.0ms	262×	body	80	valid
6.0ms	36×	body	640	valid
3.0ms	27×	body	320	valid
1.0ms	10×	body	160	valid

simplify216.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1454	5
9	5001	5

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: 32.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
5.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

5.0ms	(- (exp x) 2.0)
9.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series67.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
55.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367

prune135.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	2	72

Merged error: 0.0b

Counts

72 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.1b	(* 1/12 (pow x 4))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
1.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
5.0ms	(* 1/12 (pow x 4))

series209.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
52.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
38.0ms	(* 1/12 (pow x 4))

simplify100.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	143	265
1	544	240
2	2626	237
3	5001	237

prune108.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	56	2	58

Merged error: 0.0b

Counts

58 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
5.5b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`add-exp-log` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `associate-r` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+ (exp x) 2.0)
8.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
8.0ms	(* (+ (exp x) 2.0) (exp x))
1.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 2.0)
220.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
21.0ms	(* (+ (exp x) 2.0) (exp x))
89.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	312	834
1	1220	713
2	5001	710

prune205.0ms

Filtered

87 candidates to 70 candidates (80.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (+ (exp x) 2.0))
0.0b	(cbrt (+ (exp x) 2.0))
0.0b	(cbrt (+ (exp x) 2.0))
5.5b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt (+ (exp x) 2.0))
4.0ms	(cbrt (+ (exp x) 2.0))
4.0ms	(cbrt (+ (exp x) 2.0))
1.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series446.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (+ (exp x) 2.0))
121.0ms	(cbrt (+ (exp x) 2.0))
116.0ms	(cbrt (+ (exp x) 2.0))
92.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	188	497
1	575	454
2	2093	445
3	5001	440

prune205.0ms

Filtered

70 candidates to 57 candidates (81.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	70	3	73

Merged error: 0b

Counts

73 → 3

regimes18.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.8s	5599×	body	1280	valid
226.0ms	8292×	body	80	valid
219.0ms	1257×	body	640	valid
66.0ms	615×	body	320	valid
24.0ms	347×	body	160	valid