Details

sample34.0ms

Algorithm

intervals

Results

7.0ms	71×	body	640	valid
6.0ms	122×	body	80	valid
5.0ms	227×	body	80	nan
4.0ms	31×	body	1280	valid
2.0ms	25×	body	320	valid
0.0ms	7×	body	160	valid

simplify7.0ms

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: 22.0b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

175×	`associate-/r*`
174×	`*-un-lft-identity`
156×	`frac-sub`
148×	`add-sqr-sqrt`
137×	`sqrt-prod`
117×	`add-cube-cbrt`
81×	`associate-/l*`
69×	`times-frac`
27×	`frac-2neg` `clear-num`
20×	`distribute-lft-out`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--`

Counts

4 → 288

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
44.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
79.0ms	(/ 1.0 (sqrt (+ x 1.0)))
45.0ms	(/ 1.0 (sqrt x))
139.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1408	3847
1	5001	3760

prune611.0ms

Filtered

300 candidates to 185 candidates (61.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	281	19	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	282	19	301

Merged error: 21.3b

Counts

301 → 19

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0)))))
0.3b	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
0.3b	(/ 1.0 (sqrt (sqrt x)))
3.1b	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

36257×	`add-sqr-sqrt`
27916×	`sqrt-prod`
14025×	`times-frac`
12522×	`unswap-sqr`
5915×	`difference-of-squares`
3031×	`*-un-lft-identity`
2312×	`sqrt-div`
2113×	`add-cube-cbrt`
1954×	`associate-/r*`
1780×	`associate-r`
1742×	`associate-l`
1692×	`frac-sub`
1580×	`associate-*r/`
1080×	`frac-times`
879×	`associate-/l*`
848×	`associate-/l/`
578×	`flip3-+` `flip-+`
540×	`associate-*l/`
298×	`clear-num`
272×	`distribute-lft-out`
204×	`frac-2neg`
188×	`un-div-inv`
178×	`*-commutative`
140×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
8×	`sqrt-pow1`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`pow1/2`
3×	`cbrt-undiv` `div-exp`
2×	`flip3--` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `sqrt-unprod` `diff-log` `div-sub`

Counts

4 → 8010

Calls

4 calls:

440.0ms	(/ (- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0)))))
12.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
5.0ms	(/ 1.0 (sqrt (sqrt x)))
209.0ms	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

626.0ms	(/ (- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0)))))
126.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
165.0ms	(/ 1.0 (sqrt (sqrt x)))
391.0ms	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

simplify3.0s

Algorithm

egg-herbie

Counts

8022 → 8022

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5001	374550

prune7.7s

Filtered

8022 candidates to 1237 candidates (15.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	8016	6	8022
Fresh	14	4	18
Picked	1	0	1
Done	0	0	0
Total	8031	10	8041

Merged error: 0.1b

Counts

8041 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
0.3b	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
0.3b	(/ 1.0 (sqrt (sqrt x)))
3.1b	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

1661×	`sqrt-prod`
1362×	`add-sqr-sqrt`
1160×	`sqrt-div`
965×	`associate-/r*`
846×	`frac-sub`
792×	`associate-*r/`
595×	`*-un-lft-identity`
540×	`frac-times`
442×	`add-cube-cbrt`
353×	`associate-/l*`
330×	`unswap-sqr`
290×	`flip3-+` `flip-+`
270×	`associate-*l/`
261×	`times-frac`
169×	`difference-of-squares`
149×	`clear-num`
102×	`frac-2neg`
94×	`un-div-inv`
49×	`distribute-lft-out`
22×	`associate-l`
20×	`associate-r`
16×	`pow1` `sqrt-pow1`
10×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
8×	`pow1/2`
6×	`add-log-exp`
4×	`distribute-lft-out--`
2×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `flip--` `div-inv`

Counts

4 → 1174

Calls

4 calls:

12.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
12.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
7.0ms	(/ 1.0 (sqrt (sqrt x)))
203.0ms	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

series798.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
122.0ms	(* (sqrt (sqrt x)) (sqrt (sqrt (+ x 1.0))))
165.0ms	(/ 1.0 (sqrt (sqrt x)))
394.0ms	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

simplify326.0ms

Algorithm

egg-herbie

Counts

1186 → 1186

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5001	40817

prune3.2s

Filtered

1186 candidates to 512 candidates (43.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	1183	3	1186
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	1185	11	1196

Merged error: 0.1b

Counts

1196 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt x))
0.5b	(cbrt (sqrt x))
0.5b	(cbrt (sqrt x))
3.1b	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

rewrite386.0ms

Algorithm

rewrite-expression-head

Rules

1558×	`sqrt-prod`
1298×	`add-sqr-sqrt`
1152×	`sqrt-div`
956×	`associate-/r*`
846×	`frac-sub`
788×	`associate-*r/`
563×	`*-un-lft-identity`
540×	`frac-times`
414×	`add-cube-cbrt`
350×	`associate-/l*`
312×	`unswap-sqr`
288×	`flip3-+` `flip-+`
270×	`associate-*l/`
234×	`times-frac`
169×	`difference-of-squares`
148×	`clear-num`
101×	`frac-2neg`
94×	`un-div-inv`
47×	`distribute-lft-out`
18×	`cbrt-prod`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube` `distribute-lft-out--`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 1073

Calls

4 calls:

2.0ms	(cbrt (sqrt x))
2.0ms	(cbrt (sqrt x))
2.0ms	(cbrt (sqrt x))
206.0ms	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

series845.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (sqrt x))
149.0ms	(cbrt (sqrt x))
148.0ms	(cbrt (sqrt x))
399.0ms	(- (* (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt (+ x 1.0)))) (* (sqrt (sqrt x)) (/ 1.0 (sqrt (sqrt (+ x 1.0))))))

simplify307.0ms

Algorithm

egg-herbie

Counts

1085 → 1085

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5001	40425

prune3.7s

Filtered

1085 candidates to 455 candidates (41.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	1083	2	1085
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	1084	12	1096

Merged error: 0.1b

Counts

1096 → 12

regimes136.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 20.1b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	44
1	44	44

end0.0ms

sample831.0ms

Algorithm

intervals

Results

178.0ms	8087×	body	80	nan
178.0ms	1779×	body	640	valid
141.0ms	1113×	body	1280	valid
105.0ms	4166×	body	80	valid
46.0ms	641×	body	320	valid
18.0ms	301×	body	160	valid