Details

sample951.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 6.054688%

Guaranteed chance to sample good point: 76.195426%

Results

15.0ms	238×	body	80	valid
3.0ms	77×	body	80	overflowed
2.0ms	5×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	7×	body	320	valid
1.0ms	10×	body	80	invalid
0.0ms	4×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	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: 1.0b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.7b	(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `log-div` `associate--l+`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

5.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(+ 1.0 (exp x))
3.0ms	(log (+ 1.0 (exp x)))

series21.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (log (+ 1.0 (exp x))) (* x y))
2.0ms	(+ 1.0 (exp x))
10.0ms	(log (+ 1.0 (exp x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune81.0ms

Filtered

40 candidates to 54 candidates (-35.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.7b

Counts

55 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ 1.0 (exp x)))
0.2b	(sqrt (+ 1.0 (exp x)))
1.1b	(log (sqrt (+ 1.0 (exp x))))
1.1b	(log (sqrt (+ 1.0 (exp x))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (exp x)))
3.0ms	(sqrt (+ 1.0 (exp x)))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 (exp x)))
4.0ms	(sqrt (+ 1.0 (exp x)))
13.0ms	(log (sqrt (+ 1.0 (exp x))))
13.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	162	564
1	453	526
2	1549	508
3	5001	496

prune148.0ms

Filtered

60 candidates to 84 candidates (-40.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	83	5	88

Merged error: 0.7b

Counts

88 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
6.8b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

5.0ms	(* 1/2 (pow x 2))
10.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
6.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 1/2 (pow x 2))
9.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
2.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
4.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	371	575
1	1439	529
2	5001	520

prune143.0ms

Filtered

61 candidates to 83 candidates (-36.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	82	6	88

Merged error: 0.7b

Counts

88 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))
1.1b	(log (sqrt (+ 1.0 (exp x))))
7.5b	(log (+ (* 1/2 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
56×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
43×	`sqrt-prod`
21×	`unpow-prod-down`
13×	`add-exp-log`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`log-prod`
8×	`add-cbrt-cube`
7×	`pow1` `unpow2` `sqr-pow`
6×	`log-div`
4×	`div-exp` `log-pow` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `associate-*r/` `rem-log-exp` `frac-add` `clear-num` `div-inv`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `distribute-lft-out`

Counts

4 → 151

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
4.0ms	(/ x (sqrt 2.0))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
8.0ms	(log (+ (* 1/2 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0))))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
8.0ms	(/ x (sqrt 2.0))
13.0ms	(log (sqrt (+ 1.0 (exp x))))
9.0ms	(log (+ (* 1/2 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	623	1438
1	2400	1267
2	5003	1254

prune408.0ms

Filtered

100 candidates to 163 candidates (-63.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	163	6	169

Merged error: 0.7b

Counts

169 → 6

regimes169.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

end0.0ms

sample1.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 6.054688%

Guaranteed chance to sample good point: 76.195426%

Results

359.0ms	7321×	body	80	valid
105.0ms	2499×	body	80	overflowed
80.0ms	258×	body	640	valid
65.0ms	116×	body	1280	valid
38.0ms	196×	body	320	valid
20.0ms	364×	body	80	invalid
13.0ms	109×	body	160	valid

Details

sample951.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite13.0ms

series21.0ms

simplify45.0ms

prune81.0ms

localize10.0ms

rewrite16.0ms

series33.0ms

simplify52.0ms

prune148.0ms

localize10.0ms

rewrite29.0ms

series18.0ms

simplify44.0ms

prune143.0ms

localize24.0ms

rewrite27.0ms

series35.0ms

simplify66.0ms

prune408.0ms

regimes169.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.9s

Profiling