Details

sample30.0ms

Algorithm

intervals

Results

12.0ms	64×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	118×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

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: 32.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
42.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
36.0ms	(/ x (+ x 1.0))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify218.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune658.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	601	4	605
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	602	4	606

Merged error: 0.2b

Counts

606 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (pow x 3))
0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.2b	(/ (- 1.0) (pow x 2))
4.4b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 559

Calls

4 calls:

6.0ms	(/ 1 (pow x 3))
1.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
7.0ms	(/ (- 1.0) (pow x 2))
41.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1 (pow x 3))
85.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
26.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify193.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1159	12779
1	4167	7106
2	5001	7094

prune702.0ms

Filtered

571 candidates to 218 candidates (38.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	570	1	571
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	571	4	575

Merged error: 0b

Counts

575 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
0.1b	(/ 1 (pow x 3))
0.2b	(/ (- 1.0) (pow x 2))
4.4b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 559

Calls

4 calls:

1.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
6.0ms	(/ 1 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
42.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
37.0ms	(/ 1 (pow x 3))
26.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

simplify184.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1162	11394
1	4062	6475
2	5001	6466

prune672.0ms

Filtered

571 candidates to 217 candidates (38.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	571	0	571
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	571	4	575

Merged error: 0b

Counts

575 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
33.1b	(fma (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0))) (/ (- (pow (cbrt (+ x 1.0)) 3)) (- x 1.0)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(fma (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0))) (/ (- (pow (cbrt (+ x 1.0)) 3)) (- x 1.0)))

series666.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
185.0ms	(cbrt x)
178.0ms	(cbrt x)
119.0ms	(fma (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0))) (/ (- (pow (cbrt (+ x 1.0)) 3)) (- x 1.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	126	324
1	366	281
2	1554	267
3	5001	265

prune209.0ms

Filtered

61 candidates to 54 candidates (88.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	61	4	65

Merged error: 0b

Counts

65 → 4

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch102.0ms

Steps

Iters	Range		Point
10	14.716166499582775	2.5158614700293387e+20	12597.77927646208
11	-2193661101726697.2	-1.4639597033977343e-08	-11900.943894212798

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	18
1	38	18

end0.0ms

sample671.0ms

Algorithm

intervals

Results

244.0ms	1782×	body	1280	valid
137.0ms	1206×	body	640	valid
119.0ms	4076×	body	80	valid
53.0ms	630×	body	320	valid
17.0ms	306×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6