Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	72×	body	640	valid
4.0ms	120×	body	80	valid
3.0ms	38×	body	320	valid
2.0ms	11×	body	1280	valid
1.0ms	15×	body	160	valid

simplify19.0ms

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: 11.0b

localize10.0ms

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))
3.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite139.0ms

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))
5.0ms	(/ 1.0 (+ x 1.0))
22.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
54.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
25.0ms	(/ 1.0 (+ x 1.0))
47.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
224.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify358.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (81.0ms)

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

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
0.1b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 5))
0.3b	(/ 2.0 (pow x 3))

rewrite21.0ms

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

series276.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
53.0ms	(/ 1 (pow x 7))
45.0ms	(/ 1 (pow x 5))
35.0ms	(/ 2.0 (pow x 3))

simplify55.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	450	904
1	2278	777
2	5001	777

prune397.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 5)) (/ (/ 2.0 x) (* x x)))
0.1b	(/ (/ 2.0 x) (* x x))
0.1b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 5))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

73×	`times-frac`
50×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log`
24×	`unpow-prod-down`
20×	`add-cbrt-cube`
19×	`associate-/l*`
18×	`div-exp`
15×	`associate-/r*`
8×	`cbrt-undiv` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `prod-exp` `cbrt-unprod` `inv-pow`
1×	`fma-udef` `associate-/l/`

Counts

4 → 168

Calls

4 calls:

1.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ (/ 2.0 x) (* x x)))
7.0ms	(/ (/ 2.0 x) (* x x))
5.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 5))

series247.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ (/ 2.0 x) (* x x)))
35.0ms	(/ (/ 2.0 x) (* x x))
55.0ms	(/ 1 (pow x 7))
42.0ms	(/ 1 (pow x 5))

simplify50.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	520	883
1	2161	783
2	5002	721

prune375.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ 2.0 x) x) x)
0.1b	(/ (/ 2.0 x) x)
0.1b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 5))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

510×	`times-frac`
262×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
62×	`associate-/l*`
36×	`add-exp-log`
24×	`unpow-prod-down` `div-inv`
22×	`add-cbrt-cube`
21×	`div-exp`
20×	`associate-/r*`
11×	`cbrt-undiv`
8×	`sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 376

Calls

4 calls:

13.0ms	(/ (/ (/ 2.0 x) x) x)
6.0ms	(/ (/ 2.0 x) x)
4.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 5))

series158.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (/ (/ 2.0 x) x) x)
23.0ms	(/ (/ 2.0 x) x)
54.0ms	(/ 1 (pow x 7))
47.0ms	(/ 1 (pow x 5))

simplify59.0ms

Algorithm

egg-herbie

Counts

388 → 388

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1195	2820
1	5001	2549

prune916.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes72.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.3b

bsearch108.0ms

Steps

Iters	Range		Point
10	9.598072339636849e-08	814.2255113159289	131.81767877325998
11	-402.67606408878214	-1.1015269942960052e-19	-122.45163267022434

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	24
1	36	24

end0.0ms

sample633.0ms

Algorithm

intervals

Results

213.0ms	1880×	body	640	valid
127.0ms	4114×	body	80	valid
87.0ms	607×	body	1280	valid
83.0ms	952×	body	320	valid
25.0ms	447×	body	160	valid