Details

sample49.0ms

Algorithm

intervals

Results

11.0ms	239×	body	160	nan
11.0ms	511×	body	80	nan
8.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
31.5b	(sqrt (- (* x x) 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cube-cbrt` `log-prod` `sqrt-prod`
3×	`add-exp-log`
2×	`expm1-log1p-u` `log-div` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `log-pow` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

17.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
13.0ms	(sqrt (- (* x x) 1.0))

series229.0ms

Counts

2 → 6

Calls

2 calls:

180.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
49.0ms	(sqrt (- (* x x) 1.0))

simplify124.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	288	316
1	967	295
2	4452	288
3	5001	288

prune110.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (/ 0.25 x) x)
0.2b	(/ 0.09375 (pow x 4))
0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

rewrite534.0ms

Algorithm

rewrite-expression-head

Rules

609×	`add-sqr-sqrt`
603×	`times-frac`
479×	`*-un-lft-identity`
384×	`add-cube-cbrt`
379×	`associate-+r+`
372×	`prod-diff`
180×	`associate--l+`
84×	`unpow-prod-down`
78×	`pow1`
75×	`log-pow` `difference-of-squares`
60×	`distribute-lft-out--`
30×	`div-inv`
28×	`sqr-pow`
16×	`associate-/l*`
13×	`add-exp-log`
10×	`associate-/r*` `add-cbrt-cube`
8×	`distribute-lft-out` `add-log-exp`
6×	`log-prod` `div-exp`
4×	`cbrt-undiv` `fma-def`
3×	`expm1-log1p-u` `associate-+l+` `diff-log` `sum-log` `log1p-expm1-u`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3-+` `pow-exp` `flip-+` `associate-/l/`

Counts

3 → 529

Calls

3 calls:

11.0ms	(/ (/ 0.25 x) x)
7.0ms	(/ 0.09375 (pow x 4))
465.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series151.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ (/ 0.25 x) x)
37.0ms	(/ 0.09375 (pow x 4))
91.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify107.0ms

Algorithm

egg-herbie

Counts

538 → 538

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2453	8348
1	5001	7154

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
0.2b	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
0.6b	(/ 0.125 (pow x 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
9×	`add-exp-log`
5×	`log-prod` `add-cbrt-cube`
4×	`pow1` `cube-mult` `unpow3` `sqr-pow`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`log-div` `distribute-lft-out`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `flip-+` `fma-udef` `div-inv` `distribute-lft-out--`

Counts

3 → 95

Calls

3 calls:

0.0ms	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
13.0ms	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
8.0ms	(/ 0.125 (pow x 3))

series279.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
167.0ms	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
34.0ms	(/ 0.125 (pow x 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	356	622
1	1608	576
2	5001	576

prune234.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

358.0ms	7632×	body	160	nan
348.0ms	16185×	body	80	nan
242.0ms	8000×	body	80	valid