Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	62×	body	640	valid
4.0ms	137×	body	80	valid
2.0ms	29×	body	320	valid
2.0ms	15×	body	1280	valid
1.0ms	13×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

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: 7.4b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (+ x 1.0))
1.8b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
27.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
7.0ms	(/ 1.0 (+ x 1.0))
79.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (- x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
31.0ms	(/ 1.0 (+ x 1.0))
219.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify168.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670

prune1.2s

Filtered

630 candidates to 390 candidates (61.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	626	4	630
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	627	4	631

Merged error: 0.5b

Counts

631 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
1.8b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
1.8b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
1.8b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

1097×	`*-un-lft-identity`
1026×	`times-frac`
734×	`add-sqr-sqrt`
708×	`associate-+l+`
702×	`prod-diff`
698×	`add-cube-cbrt`
152×	`distribute-lft-out`
93×	`div-inv`
78×	`associate-/r/`
43×	`flip3-+` `flip-+`
37×	`distribute-lft-out--`
30×	`fma-def`
19×	`add-log-exp`
12×	`frac-add` `difference-of-squares`
9×	`cbrt-prod`
6×	`sum-log`
5×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`+-commutative` `associate-+l-` `sub-neg` `diff-log`
1×	`pow1/3`

Counts

4 → 834

Calls

4 calls:

29.0ms	(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
54.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
55.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
56.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

543.0ms	(cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
227.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
227.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
222.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify157.0ms

Algorithm

egg-herbie

Counts

846 → 846

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	627	12772
1	2312	9865
2	5001	7203

prune3.2s

Filtered

846 candidates to 688 candidates (81.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	846	0	846
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	846	4	850

Merged error: 0.5b

Counts

850 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
29.8b	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt` `prod-diff`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*l/`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`frac-times` `associate-/r/`
7×	`flip3--` `flip--`
6×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`cbrt-undiv` `sub-neg` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
1×	`frac-2neg` `fma-neg` `diff-log` `associate-l` `clear-num` `associate-/r` `-commutative` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

10.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
10.0ms	(* (* (+ x 1.0) x) (- x 1.0))
1.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series797.0ms

Counts

4 → 12

Calls

4 calls:

476.0ms	(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
43.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
96.0ms	(* (* (+ x 1.0) x) (- x 1.0))
182.0ms	(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	637	1498
1	3082	1198
2	5001	1198

prune221.0ms

Filtered

123 candidates to 81 candidates (65.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	123	4	127

Merged error: 0.5b

Counts

127 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
0.1b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 7))
0.5b	(/ 2.0 (pow x 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
27×	`add-exp-log`
26×	`associate-/r*`
15×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`pow-to-exp` `pow-exp`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-flip` `inv-pow`
1×	`fma-udef`

Counts

4 → 187

Calls

4 calls:

1.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 7))
8.0ms	(/ 2.0 (pow x 3))

series199.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
42.0ms	(/ 1 (pow x 5))
57.0ms	(/ 1 (pow x 7))
36.0ms	(/ 2.0 (pow x 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	460	949
1	2326	816
2	5001	816

prune328.0ms

Filtered

199 candidates to 96 candidates (48.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	197	6	203

Merged error: 0.0b

Counts

203 → 6

regimes71.0ms

Accuracy

95.4% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 10.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	37
1	47	37

end0.0ms

sample579.0ms

Algorithm

intervals

Results

201.0ms	1891×	body	640	valid
115.0ms	4147×	body	80	valid
74.0ms	947×	body	320	valid
72.0ms	564×	body	1280	valid
24.0ms	452×	body	160	valid