Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	58×	body	640	valid
7.0ms	216×	body	80	nan
7.0ms	37×	body	1280	valid
5.0ms	130×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 19.4b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.8b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
48.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ x 1.0))
74.0ms	(/ 1.0 (sqrt (+ x 1.0)))
38.0ms	(/ 1.0 (sqrt x))
136.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify264.0ms

Algorithm

egg-herbie

Counts

770 → 770

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1538	25021
1	4278	18390
2	5001	18355

prune1.1s

Filtered

770 candidates to 303 candidates (39.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	755	15	770
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	756	15	771

Merged error: 18.8b

Counts

771 → 15

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt x) (sqrt 1.0))
0.1b	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.8b	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

490×	`times-frac`
384×	`add-sqr-sqrt`
373×	`*-un-lft-identity`
365×	`add-cube-cbrt`
286×	`prod-diff`
140×	`sqrt-prod`
40×	`div-inv`
22×	`fma-neg`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp` `difference-of-squares`
5×	`distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `hypot-udef` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 414

Calls

4 calls:

1.0ms	(hypot (sqrt x) (sqrt 1.0))
3.0ms	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
4.0ms	(/ 1.0 (sqrt x))
30.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

257.0ms	(hypot (sqrt x) (sqrt 1.0))
404.0ms	(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
45.0ms	(/ 1.0 (sqrt x))
607.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

simplify183.0ms

Algorithm

egg-herbie

Counts

426 → 426

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1262	13797
1	3900	9945
2	5001	9914

prune737.0ms

Filtered

426 candidates to 200 candidates (46.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	424	2	426
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	427	14	441

Merged error: 18.8b

Counts

441 → 14

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
62×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
42×	`prod-diff`
37×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
9×	`pow1`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `hypot-def` `div-inv` `associate-/l*`

Counts

4 → 151

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
22.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
14.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series421.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
261.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify92.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	636	1812
1	2945	1369
2	5002	1271

prune306.0ms

Filtered

163 candidates to 93 candidates (57.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	157	6	163
Fresh	5	7	12
Picked	1	0	1
Done	0	1	1
Total	163	14	177

Merged error: 18.5b

Counts

177 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.4b	(+ x (- 1.0 x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

112×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-cube-cbrt`
11×	`associate-+r+`
9×	`cbrt-undiv` `div-exp` `prod-diff` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `associate-/l*`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `associate-/l/`
2×	`associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `sub-neg` `sqrt-unprod` `diff-log` `div-sub` `*-commutative`

Counts

4 → 156

Calls

4 calls:

20.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
7.0ms	(+ x (- 1.0 x))

series710.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
518.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
58.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify114.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	799	1711
1	4236	1448
2	5001	1435

prune306.0ms

Filtered

168 candidates to 106 candidates (63.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	7	5	12
Picked	1	0	1
Done	0	1	1
Total	173	9	182

Merged error: 0.2b

Counts

182 → 9

regimes40.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	11
1	14	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

273.0ms	8123×	body	80	nan
264.0ms	1825×	body	640	valid
213.0ms	1174×	body	1280	valid
153.0ms	4044×	body	80	valid
68.0ms	649×	body	320	valid
25.0ms	308×	body	160	valid