Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	57×	body	640	valid
7.0ms	137×	body	80	valid
5.0ms	34×	body	320	valid
3.0ms	14×	body	1280	valid
1.0ms	14×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

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)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite142.0ms

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))
23.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
55.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
30.0ms	(/ 1.0 (+ x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
233.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify155.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (74.0ms)

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

prune1.4s

Filtered

630 candidates to 390 candidates (61.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
5.6b	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

13024×	`times-frac`
9784×	`*-un-lft-identity`
7160×	`add-sqr-sqrt`
7050×	`add-cube-cbrt`
5428×	`sqrt-prod`
5070×	`prod-diff`
2537×	`associate-+l+`
1356×	`distribute-lft-out`
616×	`div-inv`
452×	`sqrt-div` `associate-/r/`
227×	`flip3-+` `flip-+`
195×	`fma-neg`
30×	`associate-/l*`
28×	`difference-of-squares`
19×	`fma-def`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`distribute-lft-out--`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`frac-add`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+l-` `associate-/l/`

Counts

4 → 5628

Calls

4 calls:

205.0ms	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
603.0ms	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x))
76.0ms	(/ 1.0 (sqrt (+ x 1.0)))
25.0ms	(/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
219.0ms	(+ (- (/ (/ 1.0 (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.2s

Algorithm

egg-herbie

Counts

5640 → 5640

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	4220	138593
1	5003	123204

prune12.0s

Filtered

5640 candidates to 2323 candidates (41.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.1b	(pow (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))) 3)
1.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
18.9b	(cbrt (pow (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))) 3))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

828×	`*-un-lft-identity`
724×	`times-frac`
503×	`add-sqr-sqrt`
479×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
123×	`distribute-lft-out`
63×	`div-inv`
54×	`associate-/r/`
41×	`distribute-lft-out--`
30×	`flip3-+` `flip-+`
24×	`cbrt-prod`
18×	`unpow-prod-down` `fma-neg` `cube-prod`
11×	`add-log-exp`
10×	`cube-div` `fma-def`
9×	`frac-add`
8×	`difference-of-squares`
5×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3--` `frac-sub` `flip--` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `diff-log` `unpow3` `sum-log` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l-` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 626

Calls

4 calls:

27.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
33.0ms	(pow (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))) 3)
57.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
34.0ms	(cbrt (pow (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))) 3))

series797.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
316.0ms	(pow (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))) 3)
213.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
220.0ms	(cbrt (pow (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))) 3))

simplify184.0ms

Algorithm

egg-herbie

Counts

638 → 638

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1226	11621
1	4209	8921
2	5001	8327

prune1.7s

Filtered

638 candidates to 372 candidates (58.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 2.0 (pow x 3))
8.0ms	(/ 1 (pow x 7))

series199.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
46.0ms	(/ 1 (pow x 5))
40.0ms	(/ 2.0 (pow x 3))
52.0ms	(/ 1 (pow x 7))

simplify59.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	460	949
1	2326	816
2	5001	816

prune373.0ms

Filtered

199 candidates to 96 candidates (48.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes92.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 25.6b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	35
1	43	35

end0.0ms

sample552.0ms

Algorithm

intervals

Results

192.0ms	1895×	body	640	valid
112.0ms	4175×	body	80	valid
69.0ms	560×	body	1280	valid
66.0ms	880×	body	320	valid
26.0ms	490×	body	160	valid