Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	57×	body	640	valid
5.0ms	248×	body	80	nan
4.0ms	149×	body	80	valid
4.0ms	29×	body	1280	valid
1.0ms	18×	body	320	valid
0.0ms	3×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

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: 17.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
1.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
875×	`*-un-lft-identity`
742×	`add-sqr-sqrt`
712×	`add-cube-cbrt`
594×	`prod-diff`
562×	`sqrt-prod`
73×	`distribute-lft-out`
54×	`div-inv`
46×	`sqrt-div` `associate-/r/`
23×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 739

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
50.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series259.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ 1.0 (sqrt (+ x 1.0)))
38.0ms	(/ 1.0 (sqrt x))
143.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify263.0ms

Algorithm

egg-herbie

Counts

748 → 748

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	1517	24924
1	4197	18301
2	5001	18266

prune1.1s

Filtered

748 candidates to 285 candidates (38.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	734	14	748
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	734	15	749

Merged error: 17.4b

Counts

749 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.3b	(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
1.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

2210×	`times-frac`
1853×	`*-un-lft-identity`
1727×	`add-sqr-sqrt`
1415×	`add-cube-cbrt`
1350×	`sqrt-prod`
1188×	`prod-diff`
156×	`distribute-lft-out`
113×	`div-inv`
112×	`sqrt-div`
88×	`associate-/r/`
86×	`difference-of-squares`
80×	`distribute-lft-out--`
52×	`swap-sqr`
44×	`flip3-+` `fma-neg` `flip-+`
26×	`associate-r` `associate-l`
19×	`pow1`
10×	`flip3--` `frac-sub` `flip--`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `associate-/l*`
2×	`sub-neg` `diff-log`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 1493

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt x))
78.0ms	(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
47.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
45.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt x))
141.0ms	(* (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))) (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
134.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
147.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify399.0ms

Algorithm

egg-herbie

Counts

1505 → 1505

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1658	50237
1	5001	38792

prune2.1s

Filtered

1505 candidates to 422 candidates (28.0%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	1501	4	1505
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	1503	17	1520

Merged error: 17.3b

Counts

1520 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.4b	(pow (sqrt (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))) 3)
1.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
1.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

2070×	`times-frac`
1750×	`*-un-lft-identity`
1514×	`add-sqr-sqrt`
1394×	`add-cube-cbrt`
1214×	`sqrt-prod`
1188×	`prod-diff`
144×	`distribute-lft-out`
109×	`div-inv`
94×	`sqrt-div`
88×	`associate-/r/`
44×	`flip3-+` `fma-neg` `flip-+` `distribute-lft-out--`
36×	`difference-of-squares`
29×	`unpow-prod-down` `cube-prod`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u`
3×	`cube-div` `pow-unpow` `flip3--` `frac-sub` `flip--` `associate-/l*`
2×	`sub-neg` `pow1/2` `diff-log`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `frac-2neg` `unpow3` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 1428

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
41.0ms	(pow (sqrt (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))) 3)
48.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
45.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series2.2s

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1.0 (sqrt x))
1.8s	(pow (sqrt (sqrt (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))) 3)
141.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
149.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify421.0ms

Algorithm

egg-herbie

Counts

1440 → 1440

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2185	50576
1	5001	39756

prune3.2s

Filtered

1440 candidates to 519 candidates (36.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	1437	3	1440
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	1439	18	1457

Merged error: 17.3b

Counts

1457 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt x))
0.8b	(pow (sqrt (sqrt (* (sqrt x) (sqrt (+ x 1.0))))) 3)
1.2b	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
1.2b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

1014×	`times-frac`
857×	`*-un-lft-identity`
732×	`add-sqr-sqrt`
702×	`add-cube-cbrt`
595×	`prod-diff`
556×	`sqrt-prod`
69×	`distribute-lft-out`
53×	`div-inv`
50×	`sqrt-div`
44×	`associate-/r/`
23×	`flip3-+` `fma-neg` `flip-+`
12×	`sqrt-pow1`
11×	`pow1` `distribute-lft-out--`
9×	`difference-of-squares`
8×	`pow-pow` `add-log-exp`
7×	`add-exp-log` `unpow-prod-down` `cube-prod` `add-cbrt-cube`
6×	`associate-/r*`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u`
3×	`pow-unpow` `pow-prod-down` `associate-/l*`
2×	`cube-div` `sub-neg` `flip3--` `diff-log` `associate-*r/` `flip--`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `frac-2neg` `unpow3` `div-exp` `pow-exp` `clear-num` `frac-sub` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 751

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
10.0ms	(pow (sqrt (sqrt (* (sqrt x) (sqrt (+ x 1.0))))) 3)
7.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
47.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (sqrt x))
173.0ms	(pow (sqrt (sqrt (* (sqrt x) (sqrt (+ x 1.0))))) 3)
102.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
134.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify212.0ms

Algorithm

egg-herbie

Counts

763 → 763

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1900	25206
1	5001	19094

prune1.7s

Filtered

763 candidates to 238 candidates (31.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	762	1	763
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	764	17	781

Merged error: 17.3b

Counts

781 → 17

regimes167.0ms

Accuracy

0% (0.6b remaining)

Error of 19.6b against oracle of 19.0b and baseline of 19.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	6
1	9	6

end0.0ms

sample820.0ms

Algorithm

intervals

Results

179.0ms	1839×	body	640	valid
169.0ms	7900×	body	80	nan
130.0ms	1106×	body	1280	valid
105.0ms	4112×	body	80	valid
43.0ms	630×	body	320	valid
15.0ms	313×	body	160	valid