Details

sample27.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 75.009155%

Guaranteed chance to sample good point: 99.975577%

Results

12.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	7
1	16	7
2	16	7

prune2.0ms

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: 0.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

2.0ms	(sqrt (- 1.0 (* x x)))
17.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
17.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series38.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(sqrt (- 1.0 (* x x)))
10.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
21.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	421	620
1	1466	576
2	5001	566

prune156.0ms

Filtered

52 candidates to 62 candidates (-19.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	3	63

Merged error: 0b

Counts

63 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (/ 1 x))
0.0b	(sqrt (- 1.0 (* x x)))
0.2b	(+ (log (/ 1 x)) (log (+ 1.0 (sqrt (- 1.0 (* x x))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
18×	`times-frac`
13×	`associate-+l+`
10×	`pow1`
8×	`add-exp-log`
7×	`log-pow`
5×	`distribute-lft-out`
4×	`log-div` `associate-+r+` `rem-log-exp` `sqrt-prod`
3×	`add-cbrt-cube` `add-log-exp`
2×	`associate-+r-` `flip3-+` `sqrt-div` `div-exp` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-` `rem-sqrt-square` `rec-exp` `flip3--` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `log-rec` `sum-log` `flip--` `inv-pow` `difference-of-squares`

Counts

3 → 80

Calls

3 calls:

2.0ms	(log (/ 1 x))
2.0ms	(sqrt (- 1.0 (* x x)))
10.0ms	(+ (log (/ 1 x)) (log (+ 1.0 (sqrt (- 1.0 (* x x))))))

series30.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(log (/ 1 x))
4.0ms	(sqrt (- 1.0 (* x x)))
15.0ms	(+ (log (/ 1 x)) (log (+ 1.0 (sqrt (- 1.0 (* x x))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	466	675
1	1659	623
2	5002	597

prune160.0ms

Filtered

67 candidates to 89 candidates (-32.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	89	3	92

Merged error: 0b

Counts

92 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.3b	(/ 1 (sqrt x))
0.3b	(/ 1.0 (sqrt x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac`
104×	`*-un-lft-identity`
93×	`add-sqr-sqrt` `sqrt-prod`
82×	`add-cube-cbrt`
35×	`log-prod`
22×	`associate-+l+`
18×	`associate-/r*`
13×	`associate-+r+` `distribute-lft-out` `associate-/l*`
12×	`add-exp-log`
10×	`pow1` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`div-inv`
4×	`log-div` `div-exp` `log-pow` `add-log-exp`
3×	`cbrt-undiv` `associate-+r-` `pow-flip` `frac-2neg` `clear-num`
2×	`flip3-+` `sqrt-div` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l-` `rec-exp` `sqrt-undiv` `distribute-rgt-out` `flip3--` `sqrt-pow1` `pow1/2` `1-exp` `frac-add` `sum-log` `flip--` `inv-pow`

Counts

4 → 208

Calls

4 calls:

51.0ms	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
7.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
4.0ms	(/ 1 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))

series45.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
7.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
10.0ms	(/ 1 (sqrt x))
12.0ms	(/ 1.0 (sqrt x))

simplify81.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	796	2055
1	3169	1885
2	5001	1841

prune305.0ms

Filtered

134 candidates to 220 candidates (-64.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	220	3	223

Merged error: 0b

Counts

223 → 3

regimes101.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

end0.0ms

sample535.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 75.009155%

Guaranteed chance to sample good point: 99.975577%

Results

401.0ms	8000×	body	80	valid
0.0ms	2×	body	80	nan

Details

sample27.0ms

simplify4.0ms

prune2.0ms

localize9.0ms

rewrite39.0ms

series38.0ms

simplify51.0ms

prune156.0ms

localize11.0ms

rewrite17.0ms

series30.0ms

simplify43.0ms

prune160.0ms

localize16.0ms

rewrite78.0ms

series45.0ms

simplify81.0ms

prune305.0ms

regimes101.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample535.0ms

Profiling