Details

sample21.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	6
1	52	6
2	117	6
3	240	6
4	478	6
5	947	6
6	1844	6
7	5001	6

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 20.9b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
21.0b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `associate-/r/` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 47

Calls

2 calls:

4.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series93.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* x x) (* y y))
66.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify48.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	322	380
1	1875	324
2	5001	308

prune133.0ms

Filtered

53 candidates to 43 candidates (81.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Merged error: 0.3b

Counts

55 → 4

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Merged error: 0.3b

Counts

4 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(/ (- x y) (/ (hypot x y) (+ x y)))
20.5b	(sqrt (+ (* x x) (* y y)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
163×	`*-un-lft-identity`
120×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`div-inv` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `div-sub` `sum-log` `flip--` `hypot-def`

Counts

4 → 200

Calls

4 calls:

4.0ms	(+ (* x x) (* y y))
5.0ms	(/ (hypot x y) (+ x y))
12.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x x) (* y y))
92.0ms	(/ (hypot x y) (+ x y))
89.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
41.0ms	(sqrt (+ (* x x) (* y y)))

simplify100.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	753	1885
1	3494	1809
2	5001	1803

prune520.0ms

Filtered

212 candidates to 150 candidates (70.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	212	4	216

Merged error: 0.0b

Counts

216 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(/ (- x y) (/ (hypot x y) (+ x y)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

1059×	`times-frac`
757×	`*-un-lft-identity`
593×	`add-sqr-sqrt`
411×	`add-cube-cbrt`
103×	`associate-/l*`
91×	`distribute-lft-out--` `difference-of-squares`
82×	`distribute-lft-out`
59×	`associate-/r/`
33×	`div-inv`
27×	`flip3-+` `flip-+`
25×	`associate-/r*`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `div-sub` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `flip--`

Counts

3 → 571

Calls

3 calls:

25.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
5.0ms	(/ (hypot x y) (+ x y))
16.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))

series276.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
92.0ms	(/ (hypot x y) (+ x y))
91.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))

simplify120.0ms

Algorithm

egg-herbie

Counts

580 → 580

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1752	8207
1	5001	7913

prune1.3s

Filtered

580 candidates to 373 candidates (64.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	579	1	580
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	580	4	584

Merged error: 0b

Counts

584 → 4

regimes135.0ms

Accuracy

70.2% (5.9b remaining)

Error of 6.2b against oracle of 0.2b and baseline of 20.2b

bsearch148.0ms

Steps

Iters	Range		Point
8	3.308964372933633e-168	4.046021815332288e-164	3.7703083762849e-166
8	1.1727994473914191e-228	1.2123816733011987e-225	1.1991678665601801e-225
8	-5.540009797186545e-149	-8.992206990105925e-152	-1.2162082839611001e-151
9	-3.7151424973443123e+161	-1.322407815397355e+153	-1.3453816967374705e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	31
1	31	31

end0.0ms

sample502.0ms

Algorithm

intervals

Results

257.0ms	8000×	body	80	valid
107.0ms	8000×	pre	80	true