Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1355	7
7	5001	7

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: 21.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
20.9b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

285×	`*-un-lft-identity`
120×	`times-frac`
113×	`associate-l`
94×	`distribute-lft-out`
81×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`associate-r`
34×	`swap-sqr`
15×	`associate-/l*`
9×	`*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
8×	`associate-/r*` `associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`frac-times` `add-log-exp`
3×	`flip3--` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv`

Counts

2 → 183

Calls

2 calls:

18.0ms	(+ (* x x) (* y y))
28.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series92.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* x x) (* y y))
65.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify86.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	552	1904
1	2882	1846
2	5001	1844

prune183.0ms

Filtered

189 candidates to 80 candidates (42.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	6	190

Merged error: 0.2b

Counts

190 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (+ x y) (sqrt (+ (* x x) (* y y)))) (/ (- x y) (sqrt (+ (* x x) (* y y)))))
20.2b	(sqrt (+ (* x x) (* y y)))
20.2b	(sqrt (+ (* x x) (* y y)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

1064×	`*-un-lft-identity`
484×	`associate-/r*`
478×	`sqrt-prod`
420×	`frac-times`
340×	`distribute-lft-out`
295×	`add-sqr-sqrt`
286×	`associate-l`
199×	`add-cube-cbrt` `associate-/l*`
155×	`times-frac`
118×	`swap-sqr`
88×	`associate-/l/`
61×	`associate-r`
45×	`clear-num`
44×	`frac-2neg`
33×	`distribute-lft-out--`
32×	`difference-of-squares`
28×	`flip3-+` `flip-+`
21×	`flip3--` `associate-*r/` `flip--`
20×	`associate-*l/`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r/`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`un-div-inv` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 716

Calls

4 calls:

25.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
99.0ms	(* (/ (+ x y) (sqrt (+ (* x x) (* y y)))) (/ (- x y) (sqrt (+ (* x x) (* y y)))))
17.0ms	(sqrt (+ (* x x) (* y y)))
15.0ms	(sqrt (+ (* x x) (* y y)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (+ x y) (sqrt (+ (* x x) (* y y))))
61.0ms	(* (/ (+ x y) (sqrt (+ (* x x) (* y y)))) (/ (- x y) (sqrt (+ (* x x) (* y y)))))
39.0ms	(sqrt (+ (* x x) (* y y)))
36.0ms	(sqrt (+ (* x x) (* y y)))

simplify141.0ms

Algorithm

egg-herbie

Counts

728 → 728

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1769	9517
1	5001	9240

prune559.0ms

Filtered

728 candidates to 232 candidates (31.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	728	0	728
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	728	6	734

Merged error: 0.2b

Counts

734 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
0.0b	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
20.9b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

792×	`*-un-lft-identity`
360×	`times-frac`
313×	`associate-l`
260×	`distribute-lft-out`
252×	`exp-prod`
228×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
127×	`log-pow`
100×	`associate-r`
94×	`swap-sqr`
25×	`*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
15×	`associate-/l*`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`associate-/r*` `associate-/l/`
7×	`flip3-+` `flip-+` `add-log-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`frac-times`
3×	`log-prod` `flip3--` `flip--` `div-inv`
2×	`cbrt-undiv` `associate-r/` `div-exp` `rem-log-exp` `associate-l/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `rem-exp-log`

Counts

4 → 456

Calls

4 calls:

15.0ms	(+ (* x x) (* y y))
44.0ms	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
42.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
28.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* x x) (* y y))
80.0ms	(exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
65.0ms	(log (exp (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
69.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify114.0ms

Algorithm

egg-herbie

Counts

468 → 468

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	689	3532
1	3123	3391
2	5001	3379

prune636.0ms

Filtered

468 candidates to 172 candidates (36.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	465	3	468
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	468	6	474

Merged error: 0.2b

Counts

474 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

12.9b	(/ (+ (* x x) (* y y)) (cbrt (* (- x y) (+ x y))))
20.8b	(cbrt (* (- x y) (+ x y)))
20.8b	(cbrt (* (- x y) (+ x y)))
20.8b	(cbrt (* (- x y) (+ x y)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

344×	`*-un-lft-identity`
180×	`cbrt-prod`
144×	`times-frac`
136×	`associate-l`
116×	`add-sqr-sqrt`
107×	`distribute-lft-out`
68×	`add-cube-cbrt`
48×	`associate-r`
38×	`swap-sqr`
32×	`cbrt-div`
18×	`associate-/r*`
16×	`frac-times`
13×	`flip3-+` `flip-+`
12×	`flip3--` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
8×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l*`
7×	`add-cbrt-cube`
6×	`add-exp-log`
4×	`pow1` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `associate-/l/`
1×	`frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 286

Calls

4 calls:

30.0ms	(/ (+ (* x x) (* y y)) (cbrt (* (- x y) (+ x y))))
10.0ms	(cbrt (* (- x y) (+ x y)))
12.0ms	(cbrt (* (- x y) (+ x y)))
9.0ms	(cbrt (* (- x y) (+ x y)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(/ (+ (* x x) (* y y)) (cbrt (* (- x y) (+ x y))))
155.0ms	(cbrt (* (- x y) (+ x y)))
151.0ms	(cbrt (* (- x y) (+ x y)))
156.0ms	(cbrt (* (- x y) (+ x y)))

simplify105.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	623	3573
1	2416	3503
2	5003	3432

prune614.0ms

Filtered

298 candidates to 163 candidates (54.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	298	6	304

Merged error: 0.2b

Counts

304 → 6

regimes113.0ms

Accuracy

76.5% (4.6b remaining)

Error of 5.1b against oracle of 0.5b and baseline of 20.0b

bsearch96.0ms

Steps

Iters	Range	Point
8	2.5243384552883467e-180	3.1207004374649646e-177	3.081095278491971e-177
10	-9.555436698065281e-158	-1.442907561800155e-167	-2.4149536997492782e-160
9	-1.5548261699289447e+154	-9.01623960660628e+145	-3.7202401672427106e+146

Iters

Range

Point

2.5243384552883467e-180

3.1207004374649646e-177

3.081095278491971e-177

-9.555436698065281e-158

-1.442907561800155e-167

-2.4149536997492782e-160

-1.5548261699289447e+154

-9.01623960660628e+145

-3.7202401672427106e+146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	20
1	32	20

end0.0ms

sample511.0ms

Algorithm

intervals

Results

236.0ms	8000×	body	80	valid
126.0ms	8000×	pre	80	true