Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	256×	pre	80	true
7.0ms	248×	pre	80	false
5.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	12	3
2	12	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 8.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
7.4b	(- (/ x0 (- 1.0 x1)) x0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`times-frac`
12×	`add-cube-cbrt`
6×	`difference-of-squares`
5×	`associate-/r*` `distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/ x0 (- 1.0 x1))
12.0ms	(- (/ x0 (- 1.0 x1)) x0)

series79.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ x0 (- 1.0 x1))
42.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify94.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	244	328
1	801	315
2	3123	310
3	5001	310

prune80.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	2	59

Merged error: 7.2b

Counts

59 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
6.9b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
34×	`times-frac`
26×	`add-cube-cbrt`
20×	`sqrt-prod` `difference-of-squares`
12×	`distribute-lft-out--`
11×	`associate-r`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
6×	`pow1` `flip3--` `flip--` `associate-/l*` `add-log-exp`
5×	`associate-l`
4×	`frac-times` `associate-/r/`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r/` `div-exp` `associate-l/` `clear-num` `div-inv` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

38.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
6.0ms	(/ x0 (- 1.0 x1))
6.0ms	(/ x0 (- 1.0 x1))
16.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series308.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
36.0ms	(/ x0 (- 1.0 x1))
34.0ms	(/ x0 (- 1.0 x1))
68.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify60.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	459	1265
1	2078	1135
2	5001	1115

prune271.0ms

Filtered

146 candidates to 104 candidates (71.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	146	2	148

Merged error: 5.8b

Counts

148 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
5.8b	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
6.9b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
7.4b	(+ (/ x0 (- 1.0 x1)) (- x0))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt`
66×	`sqrt-prod`
60×	`difference-of-squares`
42×	`unpow-prod-down` `cube-prod`
36×	`*-un-lft-identity`
16×	`times-frac`
14×	`sqr-pow`
13×	`distribute-lft-out--`
12×	`add-log-exp`
11×	`associate-r`
10×	`associate-*l/`
8×	`frac-times`
7×	`flip3--` `flip3-+` `flip--` `flip-+`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `sqrt-div` `frac-add` `add-cbrt-cube`
4×	`sub-neg`
3×	`associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-*r/` `sum-log` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `neg-sub0` `associate-+r-` `distribute-rgt-neg-in` `unsub-neg` `pow-prod-down` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

33.0ms	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
57.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
16.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
19.0ms	(+ (/ x0 (- 1.0 x1)) (- x0))

series489.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
109.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
65.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
46.0ms	(+ (/ x0 (- 1.0 x1)) (- x0))

simplify112.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	781	2534
1	3656	2391
2	5002	2389

prune372.0ms

Filtered

163 candidates to 89 candidates (54.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	163	2	165

Merged error: 4.7b

Counts

165 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
5.8b	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
6.6b	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
6.9b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt`
59×	`difference-of-squares`
57×	`sqrt-prod`
44×	`*-un-lft-identity`
42×	`unpow-prod-down` `cube-prod`
29×	`times-frac`
15×	`distribute-lft-out--`
14×	`add-cube-cbrt` `sqr-pow`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `flip3--` `flip--`
3×	`sub-neg` `diff-log` `associate-/l*`
2×	`associate-/r/`
1×	`difference-cubes` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 140

Calls

4 calls:

6.0ms	(/ x0 (- 1.0 x1))
58.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
13.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
19.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series285.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ x0 (- 1.0 x1))
113.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
70.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
68.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify72.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	569	1717
1	2124	1637
2	5003	1636

prune401.0ms

Filtered

152 candidates to 86 candidates (56.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	152	2	154

Merged error: 4.7b

Counts

154 → 2

regimes40.0ms

Accuracy

0% (0.8b remaining)

Error of 5.5b against oracle of 4.7b and baseline of 5.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	43
1	33	43
2	33	43

end0.0ms

sample921.0ms

Algorithm

intervals

Results

230.0ms	8151×	pre	80	false
229.0ms	8000×	pre	80	true
179.0ms	8000×	body	80	valid

Details

sample33.0ms

simplify5.0ms

prune2.0ms

localize8.0ms

rewrite19.0ms

series79.0ms

simplify94.0ms

prune80.0ms

localize9.0ms

rewrite71.0ms

series308.0ms

simplify60.0ms

prune271.0ms

localize21.0ms

rewrite133.0ms

series489.0ms

simplify112.0ms

prune372.0ms

localize24.0ms

rewrite102.0ms

series285.0ms

simplify72.0ms

prune401.0ms

regimes40.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample921.0ms

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