Details

sample21.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 100%

Space saved by search: 100%

Guaranteed chance to sample good point: 100%

Results

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

simplify4.0ms

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

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))
7.5b	(- (/ x0 (- 1.0 x1)) x0)

rewrite21.0ms

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))
14.0ms	(- (/ x0 (- 1.0 x1)) x0)

series12.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ x0 (- 1.0 x1))
7.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify92.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	244	328
1	801	315
2	3109	310
3	5001	310

prune65.0ms

Filtered

44 candidates to 58 candidates (-31.8%)

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: 7.3b

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))

rewrite61.0ms

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:

30.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
7.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
14.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series60.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (+ (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))
12.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify65.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	479	1254
1	2218	1139
2	5002	1119

prune216.0ms

Filtered

106 candidates to 146 candidates (-37.7%)

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: 5.9b

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))
7.5b	(+ (/ x0 (- 1.0 x1)) (neg x0))

rewrite118.0ms

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:

30.0ms	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
49.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
15.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
17.0ms	(+ (/ x0 (- 1.0 x1)) (neg x0))

series79.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
27.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
12.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
7.0ms	(+ (/ x0 (- 1.0 x1)) (neg x0))

simplify109.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	764	2500
1	3710	2382
2	5001	2380

prune342.0ms

Filtered

91 candidates to 163 candidates (-79.1%)

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

rewrite87.0ms

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))
49.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
11.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
15.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series52.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ x0 (- 1.0 x1))
24.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
11.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
11.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify75.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	594	1716
1	2282	1652
2	5001	1652

prune365.0ms

Filtered

87 candidates to 152 candidates (-74.7%)

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

regimes86.0ms

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

sample534.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 100%

Space saved by search: 100%

Guaranteed chance to sample good point: 100%

Results

213.0ms	8000×	pre	80	true
163.0ms	8000×	body	80	valid

Details

sample21.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite21.0ms

series12.0ms

simplify92.0ms

prune65.0ms

localize9.0ms

rewrite61.0ms

series60.0ms

simplify65.0ms

prune216.0ms

localize21.0ms

rewrite118.0ms

series79.0ms

simplify109.0ms

prune342.0ms

localize24.0ms

rewrite87.0ms

series52.0ms

simplify75.0ms

prune365.0ms

regimes86.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample534.0ms

Profiling