Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 75.009155%

Results

43.0ms	78×	body	1280	valid
18.0ms	57×	body	640	valid
8.0ms	21×	body	2560	valid
5.0ms	27×	body	320	valid
3.0ms	65×	body	80	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

prune4.0ms

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: 54.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (sqrt (+ (* x x) 1.0)))
2.3b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.5b	(sqrt (+ (* x x) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
6.0ms	(sqrt (+ (* x x) 1.0))

series22.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify137.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	309	393
1	1027	364
2	4764	348
3	5002	347

prune121.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.0b

Counts

52 → 6

localize11.0ms

Local error

Found 1 expressions with local error:

0.2b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
181×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
117×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`unswap-sqr`
24×	`add-exp-log`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 270

Calls

1 calls:

54.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify95.0ms

Algorithm

egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	725	1757
1	3832	1368
2	5001	1368

prune327.0ms

Filtered

95 candidates to 273 candidates (-187.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	273	6	279

Merged error: 0.0b

Counts

279 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ 0.5 x))
0.0b	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.3b	(/ 0.125 (pow x 3))
11.7b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt`
13×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
11×	`add-log-exp`
10×	`add-exp-log`
6×	`log-prod` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `difference-of-squares` `sqr-pow`
4×	`cube-mult` `unpow3` `distribute-lft-out--`
3×	`flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`log-div` `diff-log` `sum-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `associate--l+` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 117

Calls

4 calls:

6.0ms	(+ x (/ 0.5 x))
21.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
5.0ms	(/ 0.125 (pow x 3))
21.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ x (/ 0.5 x))
4.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
4.0ms	(/ 0.125 (pow x 3))
10.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	478	840
1	2197	799
2	5001	799

prune191.0ms

Filtered

77 candidates to 129 candidates (-67.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	129	6	135

Merged error: 0.0b

Counts

135 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (neg 0.0625) (pow x 5))
0.3b	(/ 0.125 (pow x 3))
14.6b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
20.6b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
110×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
47×	`unpow-prod-down`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
19×	`associate-/r*`
17×	`sqr-pow`
15×	`add-exp-log`
14×	`cube-prod` `distribute-lft-out--`
13×	`associate-/l*`
12×	`log-prod`
10×	`difference-of-squares`
9×	`add-log-exp`
8×	`neg-mul-1` `frac-sub` `add-cbrt-cube`
6×	`div-exp`
5×	`pow1` `log-div`
4×	`cube-mult` `flip3--` `unpow3` `flip--`
3×	`diff-log` `associate--r+`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `pow-exp` `clear-num` `div-inv` `associate--r-`
1×	`distribute-frac-neg` `rem-log-exp` `log-pow`

Counts

4 → 223

Calls

4 calls:

6.0ms	(/ (neg 0.0625) (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
74.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
75.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ (neg 0.0625) (pow x 5))
7.0ms	(/ 0.125 (pow x 3))
10.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
5.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify99.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	837	1963
1	3794	1884
2	5002	1876

prune437.0ms

Filtered

152 candidates to 235 candidates (-54.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	235	6	241

Merged error: 0.0b

Counts

241 → 6

regimes213.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch39.0ms

Steps

Iters	Range		Point
9	0.5242211761776224	53458.31144213736	0.8885932039891381
9	-807.5111341838605	-0.0062853381699669985	-1.0160302187393464

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 75.009155%

Results

1.1s	2262×	body	1280	valid
490.0ms	1659×	body	640	valid
287.0ms	789×	body	2560	valid
144.0ms	782×	body	320	valid
96.0ms	2108×	body	80	valid
43.0ms	400×	body	160	valid

Details

sample1.1s

simplify5.0ms

prune4.0ms

localize10.0ms

rewrite24.0ms

series22.0ms

simplify137.0ms

prune121.0ms

localize11.0ms

rewrite74.0ms

series16.0ms

simplify95.0ms

prune327.0ms

localize10.0ms

rewrite57.0ms

series22.0ms

simplify64.0ms

prune191.0ms

localize13.0ms

rewrite170.0ms

series28.0ms

simplify99.0ms

prune437.0ms

regimes213.0ms

bsearch39.0ms

simplify1.0ms

end0.0ms

sample3.4s

Profiling