Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	109×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

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: 0.2b

Counts

2 → 1

localize6.0ms

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))))

rewrite21.0ms

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:

9.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series213.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ 1.0 (sqrt (+ x 1.0)))
33.0ms	(sqrt (+ x 1.0))
138.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5001	427

prune122.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Merged error: 0b

Counts

71 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

5.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
12.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
141.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
99.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	452	821
1	1973	707
2	5001	668

prune146.0ms

Filtered

118 candidates to 71 candidates (60.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Merged error: 0b

Counts

123 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
232×	`sqrt-prod`
192×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 317

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
21.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
9.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series821.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
121.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
143.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
426.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	887	5648
1	3495	5039
2	5001	4956

prune386.0ms

Filtered

329 candidates to 142 candidates (43.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	329	5	334

Merged error: 0b

Counts

334 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
4.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

10.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
21.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(pow (sqrt (+ x 1.0)) 3)
65.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
188.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify130.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	771	1703
1	3877	1474
2	5001	1459

prune538.0ms

Filtered

196 candidates to 98 candidates (50.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	196	5	201

Merged error: 0b

Counts

201 → 5

regimes43.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample414.0ms

Algorithm

intervals

Results

216.0ms	7996×	body	80	valid
67.0ms	2683×	body	80	nan
1.0ms	4×	body	1280	valid

Details

sample17.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite21.0ms

series213.0ms

simplify38.0ms

prune122.0ms

localize7.0ms

rewrite34.0ms

series312.0ms

simplify59.0ms

prune146.0ms

localize8.0ms

rewrite66.0ms

series821.0ms

simplify108.0ms

prune386.0ms

localize15.0ms

rewrite58.0ms

series338.0ms

simplify130.0ms

prune538.0ms

regimes43.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample414.0ms

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