Details

sample74.0ms

Algorithm

intervals

Results

51.0ms	185×	body	1280	valid
6.0ms	41×	body	640	valid
5.0ms	251×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	8×	body	160	valid

simplify221.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 29.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.0b	(+ (- (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:

4.0ms	(- (exp x) 2.0)
9.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- (exp x) 2.0)
54.0ms	(+ (- (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

prune167.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0.0b

Counts

72 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(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 x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))

series219.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
126.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))

simplify97.0ms

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

prune152.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Merged error: 0.0b

Counts

59 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))
2.9b	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
30.0b	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))
2.0ms	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
1.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))
58.0ms	(exp (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
98.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	237	495
1	823	442
2	3640	429
3	5001	428

prune227.0ms

Filtered

80 candidates to 55 candidates (68.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	80	4	84

Merged error: 0.0b

Counts

84 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))
3.2b	(pow E (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
30.0b	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))
3.0ms	(pow E (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
1.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))
174.0ms	(pow E (log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))))
96.0ms	(log (fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	334	632
1	1199	568
2	5001	554

prune255.0ms

Filtered

87 candidates to 62 candidates (71.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Merged error: 0.0b

Counts

91 → 4

regimes18.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.7s	5678×	body	1280	valid
195.0ms	1238×	body	640	valid
192.0ms	8156×	body	80	valid
56.0ms	602×	body	320	valid
20.0ms	336×	body	160	valid