Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	67×	body	1280	valid
6.0ms	35×	body	640	valid
6.0ms	121×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	10×	body	160	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
4.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite153.0ms

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:

11.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
80.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
37.0ms	(/ x (+ x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify206.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (76.0ms)

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

prune723.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0) (pow x 2))
0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.6b	(/ 1 (pow x 3))
7.4b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite128.0ms

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	(/ (- 1.0) (pow x 2))
0.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
5.0ms	(/ 1 (pow x 3))
78.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- 1.0) (pow x 2))
81.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
36.0ms	(/ 1 (pow x 3))
36.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify179.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1159	12779
1	4169	7106
2	5001	7094

prune764.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.2b	(/ (- 1.0) (pow x 2))
0.6b	(/ 1 (pow x 3))
7.4b	(- (/ (- 1.0) (pow x 2)) (+ (/ 3.0 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

564×	`times-frac`
442×	`add-sqr-sqrt`
416×	`*-un-lft-identity`
410×	`add-cube-cbrt`
336×	`prod-diff`
207×	`unpow-prod-down`
147×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
92×	`div-inv`
84×	`fma-neg` `distribute-lft-out`
71×	`sqr-pow`
62×	`unpow2`
49×	`neg-mul-1`
40×	`associate-r`
38×	`add-exp-log`
23×	`cube-prod`
20×	`associate-/r*`
15×	`div-exp`
13×	`add-cbrt-cube` `associate-/l*`
10×	`prod-exp`
9×	`add-log-exp` `unswap-sqr`
7×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
6×	`pow1` `rec-exp` `1-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-l`
2×	`neg-sub0` `frac-2neg` `diff-log` `div-sub` `associate-*r/` `frac-add` `clear-num` `un-div-inv` `cbrt-unprod`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `flip3-+` `distribute-frac-neg` `pow-prod-down` `sum-log` `*-commutative` `flip--` `flip-+` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 715

Calls

4 calls:

18.0ms	(* 3.0 (/ 1 (pow x 3)))
8.0ms	(/ (- 1.0) (pow x 2))
5.0ms	(/ 1 (pow x 3))
102.0ms	(- (/ (- 1.0) (pow x 2)) (+ (/ 3.0 x) (* 3.0 (/ 1 (pow x 3)))))

series132.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 3.0 (/ 1 (pow x 3)))
30.0ms	(/ (- 1.0) (pow x 2))
31.0ms	(/ 1 (pow x 3))
34.0ms	(- (/ (- 1.0) (pow x 2)) (+ (/ 3.0 x) (* 3.0 (/ 1 (pow x 3)))))

simplify152.0ms

Algorithm

egg-herbie

Counts

727 → 727

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1651	14818
1	5001	9063

prune861.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

16.8b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
16.8b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
16.8b	(/ x (- (* x x) (* 1.0 1.0)))
32.7b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
44×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`difference-of-squares`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `flip-+`
1×	`fma-udef`

Counts

4 → 129

Calls

4 calls:

11.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
13.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
6.0ms	(/ x (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
36.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
71.0ms	(/ x (- (* x x) (* 1.0 1.0)))
186.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	393	1262
1	1600	1156
2	5001	1097

prune394.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch140.0ms

Steps

Iters	Range		Point
11	21.02059315853866	1.1431332651762801e+24	11856.138291033363
11	-7.192008941699975e+16	-0.00038629318802677867	-11077.767521343081

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	36
1	60	36
2	60	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

404.0ms	1721×	body	1280	valid
231.0ms	1233×	body	640	valid
204.0ms	4093×	body	80	valid
90.0ms	641×	body	320	valid
29.0ms	312×	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