Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	126×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	8×	body	160	valid

simplify21.0ms

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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.4b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite200.0ms

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:

24.0ms	(/ (+ x 1.0) (- x 1.0))
11.0ms	(/ x (+ x 1.0))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(/ x (+ x 1.0))
119.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify199.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (76.0ms)

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

prune676.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0b	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
15.0b	(/ x (- (* x x) (* 1.0 1.0)))
31.1b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite68.0ms

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:

24.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
27.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
12.0ms	(/ 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))))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
32.0ms	(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
60.0ms	(/ x (- (* x x) (* 1.0 1.0)))
155.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (38.0ms)

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

prune377.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.4b	(/ (- 1.0) (pow x 2))
0.6b	(/ 1 (pow x 3))
5.6b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite152.0ms

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:

0.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
11.0ms	(/ (- 1.0) (pow x 2))
9.0ms	(/ 1 (pow x 3))
95.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series157.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
26.0ms	(/ (- 1.0) (pow x 2))
28.0ms	(/ 1 (pow x 3))
31.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify177.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (78.0ms)

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

prune747.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
0.4b	(/ (- 1.0) (pow x 2))
0.6b	(/ 1 (pow x 3))
5.6b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

rewrite152.0ms

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:

0.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
11.0ms	(/ (- 1.0) (pow x 2))
9.0ms	(/ 1 (pow x 3))
95.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
28.0ms	(/ (- 1.0) (pow x 2))
28.0ms	(/ 1 (pow x 3))
30.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

simplify167.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1162	11394
1	4064	6475
2	5002	6466

prune731.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch87.0ms

Steps

Iters	Range		Point
10	8.950540206577903e-05	66689094922.78456	10297.87902655745
9	-3909246627090.811	-1500.694570789724	-12729.81215104019

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	33
1	55	33
2	55	33

end0.0ms

sample555.0ms

Algorithm

intervals

Results

177.0ms	1736×	body	1280	valid
99.0ms	4107×	body	80	valid
99.0ms	1240×	body	640	valid
46.0ms	620×	body	320	valid
12.0ms	297×	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