Details

sample25.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify70.0ms

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: 19.3b

Counts

2 → 2

localize8.0ms

Local error

Found 1 expressions with local error:

19.4b

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 33

Calls

1 calls:

11.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series64.0ms

Counts

1 → 3

Calls

1 calls:

64.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	279	306
1	1480	261
2	5001	254

prune77.0ms

Filtered

36 candidates to 30 candidates (83.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	35	3	38

Merged error: 0.5b

Counts

38 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
0.0b	(/ (- x y) (/ (hypot x y) (+ x y)))
0.0b	(/ (hypot x y) (+ x y))
18.9b	(sqrt (+ (* x x) (* y y)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

1794×	`times-frac`
1230×	`*-un-lft-identity`
977×	`add-sqr-sqrt`
686×	`add-cube-cbrt`
291×	`sqrt-prod`
145×	`distribute-lft-out--` `difference-of-squares`
127×	`distribute-lft-out`
103×	`associate-/l*`
94×	`associate-/r/`
51×	`div-inv`
44×	`flip3-+` `flip-+`
28×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num` `associate-/l/`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `hypot-def`

Counts

4 → 879

Calls

4 calls:

35.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
12.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
5.0ms	(/ (hypot x y) (+ x y))
4.0ms	(sqrt (+ (* x x) (* y y)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
88.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
91.0ms	(/ (hypot x y) (+ x y))
37.0ms	(sqrt (+ (* x x) (* y y)))

simplify194.0ms

Algorithm

egg-herbie

Counts

891 → 891

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	2272	16142
1	5003	14529

prune1.5s

Filtered

891 candidates to 459 candidates (51.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	888	3	891
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	891	3	894

Merged error: 0b

Counts

894 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite90.0ms

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:

26.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
12.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
5.0ms	(/ (hypot x y) (+ x y))

series275.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (/ (- x y) (/ (hypot x y) (+ x y))) (hypot x y))
90.0ms	(/ (- x y) (/ (hypot x y) (+ x y)))
93.0ms	(/ (hypot x y) (+ x y))

simplify120.0ms

Algorithm

egg-herbie

Counts

580 → 580

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1752	8207
1	5001	7913

prune1.0s

Filtered

580 candidates to 372 candidates (64.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	580	0	580
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	580	3	583

Merged error: 0b

Counts

583 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

894×	`times-frac`
603×	`*-un-lft-identity`
475×	`add-sqr-sqrt`
353×	`add-cube-cbrt`
64×	`distribute-lft-out`
61×	`distribute-lft-out--` `difference-of-squares`
43×	`associate-/r/`
42×	`div-inv`
27×	`associate-/l*`
25×	`associate-/r*`
21×	`flip3-+` `flip-+`
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 → 477

Calls

3 calls:

19.0ms	(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
6.0ms	(/ (- x y) (hypot x y))
5.0ms	(/ (hypot x y) (+ x y))

series281.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (/ (- x y) (hypot x y)) (/ (hypot x y) (+ x y)))
92.0ms	(/ (- x y) (hypot x y))
96.0ms	(/ (hypot x y) (+ x y))

simplify155.0ms

Algorithm

egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	1827	7457
1	5001	7288

prune837.0ms

Filtered

486 candidates to 312 candidates (64.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	486	0	486
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	486	3	489

Merged error: 0b

Counts

489 → 3

regimes27.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	7
1	9	7

end0.0ms

sample584.0ms

Algorithm

intervals

Results

294.0ms	8000×	body	80	valid
145.0ms	8000×	pre	80	true