Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
4.0ms	287×	pre	80	false
4.0ms	256×	pre	80	true

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

prune1.0ms

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: 8.3b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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:

5.0ms	(/ x0 (- 1.0 x1))
10.0ms	(- (/ x0 (- 1.0 x1)) x0)

series78.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ x0 (- 1.0 x1))
45.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify91.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (20.0ms)

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

prune89.0ms

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))
7.0b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite66.0ms

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:

35.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
5.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
15.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series315.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
35.0ms	(/ x0 (- 1.0 x1))
40.0ms	(/ x0 (- 1.0 x1))
63.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify61.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (48.0ms)

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

prune288.0ms

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))
7.0b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
7.4b	(+ (/ x0 (- 1.0 x1)) (- x0))

rewrite123.0ms

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:

35.0ms	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
50.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
15.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
15.0ms	(+ (/ x0 (- 1.0 x1)) (- x0))

series503.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
110.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
70.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
43.0ms	(+ (/ x0 (- 1.0 x1)) (- x0))

simplify107.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (85.0ms)

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

prune393.0ms

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

localize23.0ms

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))
6.7b	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
7.0b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite88.0ms

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:

5.0ms	(/ x0 (- 1.0 x1))
50.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
12.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
14.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series285.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ x0 (- 1.0 x1))
109.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
73.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
66.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify71.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (53.0ms)

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

prune398.0ms

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

regimes43.0ms

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

sample575.0ms

Algorithm

intervals

Results

130.0ms	8000×	body	80	valid
114.0ms	8000×	pre	80	true
110.0ms	7873×	pre	80	false