Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	48×	body	640	valid
11.0ms	136×	body	80	valid
9.0ms	27×	body	1280	valid
6.0ms	29×	body	320	valid
2.0ms	16×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite362.0ms

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))
6.0ms	(/ 1.0 (- x 1.0))
54.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
247.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1.0 (+ x 1.0))
31.0ms	(/ 1.0 (- x 1.0))
40.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
217.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify152.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (73.0ms)

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

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (- x 1.0)) (/ 2.0 x))
1.5b	(+ (/ 1.0 (+ x 1.0)) (- (/ 1.0 (- x 1.0)) (/ 2.0 x)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

842×	`times-frac`
796×	`*-un-lft-identity`
750×	`add-sqr-sqrt`
568×	`add-cube-cbrt`
546×	`prod-diff`
275×	`associate-+r+`
96×	`distribute-lft-out--`
89×	`difference-of-squares`
72×	`div-inv`
60×	`associate-/r/`
30×	`flip3--` `flip--`
21×	`fma-neg`
18×	`fma-def`
15×	`distribute-lft-out`
11×	`add-log-exp`
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-+r-`

Counts

4 → 707

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
57.0ms	(- (/ 1.0 (- x 1.0)) (/ 2.0 x))
143.0ms	(+ (/ 1.0 (+ x 1.0)) (- (/ 1.0 (- x 1.0)) (/ 2.0 x)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1.0 (+ x 1.0))
26.0ms	(/ 1.0 (- x 1.0))
48.0ms	(- (/ 1.0 (- x 1.0)) (/ 2.0 x))
219.0ms	(+ (/ 1.0 (+ x 1.0)) (- (/ 1.0 (- x 1.0)) (/ 2.0 x)))

simplify200.0ms

Algorithm

egg-herbie

Counts

719 → 719

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1700	13352
1	4705	10693
2	5001	10693

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) (- (* 1.0 x) (* (- x 1.0) 2.0)))
0.0b	(- (* 1.0 x) (* (- x 1.0) 2.0))
0.0b	(* (+ x 1.0) (* (- x 1.0) x))
17.3b	(fma 1.0 (* (- x 1.0) x) (* (+ x 1.0) (- (* 1.0 x) (* (- x 1.0) 2.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
10×	`associate-*l/`
9×	`add-sqr-sqrt`
8×	`frac-times` `associate-l`
7×	`add-cube-cbrt` `flip3--` `flip--`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff`
2×	`*-commutative` `distribute-lft-out`
1×	`fma-neg` `diff-log` `fma-udef` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

22.0ms	(* (+ x 1.0) (- (* 1.0 x) (* (- x 1.0) 2.0)))
3.0ms	(- (* 1.0 x) (* (- x 1.0) 2.0))
22.0ms	(* (+ x 1.0) (* (- x 1.0) x))
0.0ms	(fma 1.0 (* (- x 1.0) x) (* (+ x 1.0) (- (* 1.0 x) (* (- x 1.0) 2.0))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (+ x 1.0) (- (* 1.0 x) (* (- x 1.0) 2.0)))
35.0ms	(- (* 1.0 x) (* (- x 1.0) 2.0))
95.0ms	(* (+ x 1.0) (* (- x 1.0) x))
155.0ms	(fma 1.0 (* (- x 1.0) x) (* (+ x 1.0) (- (* 1.0 x) (* (- x 1.0) 2.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	462	826
1	2402	737
2	5001	737

prune253.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
104×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`add-cube-cbrt`
51×	`add-exp-log`
47×	`unpow-prod-down`
40×	`associate-r`
26×	`associate-/r*`
24×	`div-exp`
23×	`cube-prod`
17×	`sqr-pow`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
10×	`prod-exp`
9×	`associate-/l*` `unswap-sqr`
7×	`cube-mult` `unpow3`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `frac-2neg` `associate-l` `clear-num` `inv-pow`
2×	`cbrt-unprod`
1×	`associate-r/` `pow-prod-down` `un-div-inv` `-commutative`

Counts

4 → 262

Calls

4 calls:

20.0ms	(* 2.0 (/ 1 (pow x 3)))
4.0ms	(/ 1 (pow x 5))
4.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 3))

series173.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 2.0 (/ 1 (pow x 3)))
48.0ms	(/ 1 (pow x 5))
52.0ms	(/ 1 (pow x 7))
38.0ms	(/ 1 (pow x 3))

simplify266.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	591	1188
1	3164	890
2	5001	890

prune462.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 9.8b

bsearch130.0ms

Steps

Iters	Range		Point
9	15.365363555117188	8982319.97820102	480.38612570457826
9	-152849402421631.16	-48882.64719934817	-674651.7526657664

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	23
1	44	23

end0.0ms

sample1.4s

Algorithm

intervals

Results

486.0ms	1824×	body	640	valid
351.0ms	4157×	body	80	valid
214.0ms	1008×	body	320	valid
181.0ms	541×	body	1280	valid
68.0ms	473×	body	160	valid