Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
8.0ms	256×	pre	80	false
7.0ms	256×	pre	80	true

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: 8.6b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
7.8b	(- (/ 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)

series12.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify90.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (19.0ms)

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

prune67.0ms

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: 7.6b

Counts

59 → 2

localize10.0ms

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))
7.3b	(- (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:

31.0ms	(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
5.0ms	(/ x0 (- 1.0 x1))
6.0ms	(/ x0 (- 1.0 x1))
14.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series61.0ms

Counts

4 → 12

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))

simplify61.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (48.0ms)

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

prune221.0ms

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: 6.1b

Counts

148 → 2

localize23.0ms

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)))
6.1b	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
7.3b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
7.8b	(+ (/ x0 (- 1.0 x1)) (neg x0))

rewrite116.0ms

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:

29.0ms	(* (+ (+ (/ 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))
14.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))
14.0ms	(+ (/ x0 (- 1.0 x1)) (neg x0))

series80.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
24.0ms	(- (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))

simplify107.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (86.0ms)

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

prune383.0ms

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: 4.9b

Counts

165 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
6.1b	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
6.9b	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
7.3b	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite86.0ms

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ x0 (- 1.0 x1))
25.0ms	(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))
15.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))
12.0ms	(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify70.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 1 (14.0ms)

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

prune373.0ms

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: 4.8b

Counts

154 → 2

regimes91.0ms

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

sample1.2s

Algorithm

intervals

Results

230.0ms	8237×	pre	80	false
218.0ms	8000×	pre	80	true
174.0ms	8000×	body	80	valid

Details

sample42.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite17.0ms

series12.0ms

simplify90.0ms

prune67.0ms

localize10.0ms

rewrite61.0ms

series61.0ms

simplify61.0ms

prune221.0ms

localize23.0ms

rewrite116.0ms

series80.0ms

simplify107.0ms

prune383.0ms

localize24.0ms

rewrite86.0ms

series57.0ms

simplify70.0ms

prune373.0ms

regimes91.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling