Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 50.015258%

Results

18.0ms	87×	body	2560	nan
12.0ms	76×	body	1280	nan
10.0ms	256×	body	80	valid
7.0ms	56×	body	640	nan
1.0ms	15×	body	320	nan
1.0ms	16×	body	160	nan
0.0ms	11×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
28.2b	(sqrt (- (* x x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

5.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

series20.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (- (* x x) 1.0)))
11.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify132.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	316	408
1	1042	379
2	4663	366
3	5002	365

prune87.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0b

Counts

53 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
0.1b	(/ (/ 0.25 x) x)
0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.3b	(/ 0.09375 (pow x 4))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
92×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
16×	`associate--l+` `associate-/l*`
15×	`distribute-lft-out--`
14×	`add-exp-log`
13×	`unpow-prod-down` `add-log-exp`
11×	`pow1` `add-cbrt-cube`
10×	`associate-/r*`
9×	`log-prod`
8×	`distribute-lft-out`
7×	`associate-+r+` `log-pow`
6×	`diff-log` `div-exp` `div-inv`
5×	`sqr-pow`
4×	`cbrt-undiv` `sub-neg` `difference-of-squares`
3×	`associate-+l+` `sum-log`
2×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--`
1×	`+-commutative` `associate--l-` `pow-to-exp` `associate-+r-` `flip3-+` `pow-exp` `flip-+` `associate-/l/`

Counts

4 → 175

Calls

4 calls:

27.0ms	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
6.0ms	(/ (/ 0.25 x) x)
32.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))

series27.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
5.0ms	(/ (/ 0.25 x) x)
10.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))

simplify67.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	758	1413
1	2796	1305
2	5002	1288

prune262.0ms

Filtered

121 candidates to 187 candidates (-54.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	187	2	189

Merged error: 0b

Counts

189 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`*-un-lft-identity` `sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series34.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
14.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	426	933
1	1611	866
2	5001	852

prune166.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	76	2	78

Merged error: 0b

Counts

78 → 2

regimes24.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9

end0.0ms

sample2.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.996948%

Guaranteed chance to sample good point: 50.015258%

Results

551.0ms	2970×	body	2560	nan
380.0ms	2461×	body	1280	nan
319.0ms	8000×	body	80	valid
161.0ms	1292×	body	640	nan
56.0ms	611×	body	320	nan
20.0ms	313×	body	160	nan
9.0ms	283×	body	80	nan

Details

sample1.1s

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite16.0ms

series20.0ms

simplify132.0ms

prune87.0ms

localize14.0ms

rewrite77.0ms

series27.0ms

simplify67.0ms

prune262.0ms

localize10.0ms

rewrite18.0ms

series34.0ms

simplify46.0ms

prune166.0ms

regimes24.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

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