Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	255×	body	80	valid
1.0ms	84×	body	80	nan
0.0ms	1×	body	1280	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune4.0ms

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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series225.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ 1.0 (sqrt (+ x 1.0)))
31.0ms	(sqrt (+ x 1.0))
147.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	314	484
1	1135	435
2	5001	427

prune100.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

242×	`*-un-lft-identity`
210×	`associate-/r*`
196×	`add-sqr-sqrt`
183×	`sqrt-prod`
169×	`frac-times`
149×	`add-cube-cbrt`
106×	`times-frac`
91×	`associate-/l*`
43×	`distribute-lft-out`
32×	`add-exp-log`
31×	`clear-num`
30×	`frac-2neg`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
13×	`associate-r/` `associate-l/`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv`
5×	`flip3-+` `flip-+`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`sqrt-pow1` `pow1/2` `un-div-inv`
1×	`rem-sqrt-square` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 399

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
40.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
9.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series919.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
430.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
147.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
212.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

411 → 411

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1300	5163
1	5001	4445

prune394.0ms

Filtered

411 candidates to 166 candidates (40.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	410	1	411
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	412	3	415

Merged error: 0b

Counts

415 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.6b	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-prod`
106×	`*-un-lft-identity`
92×	`times-frac`
84×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
34×	`sqrt-div`
28×	`associate-/r*`
16×	`distribute-lft-out`
14×	`pow1` `sqrt-pow1`
12×	`add-exp-log` `pow-flip` `associate-/l*`
10×	`rem-sqrt-square`
8×	`associate-/r/` `add-cbrt-cube`
6×	`pow1/2`
4×	`frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `inv-pow` `add-log-exp`
2×	`cbrt-undiv` `rec-exp` `1-exp`

Counts

4 → 218

Calls

4 calls:

10.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
10.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
8.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
9.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

364.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
353.0ms	(sqrt (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
208.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
208.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	446	2380
1	1685	2138
2	5001	1940

prune324.0ms

Filtered

230 candidates to 100 candidates (43.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	230	3	233

Merged error: 0b

Counts

233 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.0b	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
42×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
16×	`distribute-lft-out`
13×	`associate-r/` `associate-/l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`pow1`
6×	`associate-l` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`clear-num`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `prod-exp` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 146

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
21.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series531.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ 1.0 (sqrt (+ x 1.0)))
31.0ms	(sqrt (+ x 1.0))
305.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
145.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	542	1323
1	2297	1172
2	5001	1140

prune214.0ms

Filtered

158 candidates to 98 candidates (62.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	158	3	161

Merged error: 0b

Counts

161 → 3

regimes32.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample304.0ms

Algorithm

intervals

Results

148.0ms	7997×	body	80	valid
45.0ms	2601×	body	80	nan
0.0ms	3×	body	1280	valid