Details

sample20.0ms

Algorithm

intervals

Results

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

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 21.2b

Counts

2 → 1

localize11.0ms

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` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

3.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series86.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (* x x) (* y y))
56.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify42.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	308	388
1	1848	330
2	5001	322

prune299.0ms

Filtered

48 candidates to 39 candidates (81.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.3b

Counts

49 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
20.5b	(sqrt (+ (* x x) (* y y)))
20.5b	(sqrt (+ (* x x) (* y y)))
20.6b	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-div`
18×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
12×	`associate-/r*`
9×	`div-inv` `associate-/l/`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 176

Calls

4 calls:

20.0ms	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
4.0ms	(sqrt (+ (* x x) (* y y)))
3.0ms	(sqrt (+ (* x x) (* y y)))
13.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
36.0ms	(sqrt (+ (* x x) (* y y)))
34.0ms	(sqrt (+ (* x x) (* y y)))
80.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

simplify82.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	612	2996
1	2997	2693
2	5002	2692

prune363.0ms

Filtered

188 candidates to 120 candidates (63.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	187	5	192

Merged error: 0.3b

Counts

192 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (/ (* x x) (+ (* x x) (* y y)))) (exp (/ (* y y) (+ (* x x) (* y y)))))
0.0b	(log (/ (exp (/ (* x x) (+ (* x x) (* y y)))) (exp (/ (* y y) (+ (* x x) (* y y))))))
14.8b	(/ (* x x) (+ (* x x) (* y y)))
25.5b	(/ (* y y) (+ (* x x) (* y y)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
24×	`times-frac`
23×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-cbrt-cube`
15×	`add-exp-log`
13×	`log-prod`
9×	`associate-/r*`
6×	`div-exp`
5×	`pow1` `cbrt-undiv` `associate-/l*`
4×	`exp-prod` `associate-/r/` `div-inv` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `rem-log-exp` `prod-exp` `log-pow` `cbrt-unprod` `flip-+` `pow-div`
1×	`log-div`

Counts

4 → 99

Calls

4 calls:

13.0ms	(/ (exp (/ (* x x) (+ (* x x) (* y y)))) (exp (/ (* y y) (+ (* x x) (* y y)))))
12.0ms	(log (/ (exp (/ (* x x) (+ (* x x) (* y y)))) (exp (/ (* y y) (+ (* x x) (* y y))))))
10.0ms	(/ (* x x) (+ (* x x) (* y y)))
7.0ms	(/ (* y y) (+ (* x x) (* y y)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (exp (/ (* x x) (+ (* x x) (* y y)))) (exp (/ (* y y) (+ (* x x) (* y y)))))
102.0ms	(log (/ (exp (/ (* x x) (+ (* x x) (* y y)))) (exp (/ (* y y) (+ (* x x) (* y y))))))
47.0ms	(/ (* x x) (+ (* x x) (* y y)))
43.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify42.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	380	1492
1	1537	1335
2	5002	1296

prune274.0ms

Filtered

111 candidates to 85 candidates (76.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	112	4	116

Merged error: 0.3b

Counts

116 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
14.8b	(/ (* x x) (+ (* x x) (* y y)))
20.5b	(sqrt (+ (* x x) (* y y)))
20.5b	(sqrt (+ (* x x) (* y y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
99×	`times-frac`
64×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
30×	`swap-sqr`
24×	`associate-r` `associate-l`
21×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
12×	`sqrt-div`
10×	`associate-/r/`
9×	`unswap-sqr`
7×	`flip3-+` `flip-+`
6×	`cbrt-undiv` `div-exp`
5×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`add-log-exp`
3×	`associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `-commutative` `pow-prod-up` `associate-/l`

Counts

4 → 164

Calls

4 calls:

23.0ms	(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
6.0ms	(/ (* x x) (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))
4.0ms	(sqrt (+ (* x x) (* y y)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
46.0ms	(/ (* x x) (+ (* x x) (* y y)))
33.0ms	(sqrt (+ (* x x) (* y y)))
37.0ms	(sqrt (+ (* x x) (* y y)))

simplify80.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	638	2303
1	3044	2027
2	5001	1978

prune438.0ms

Filtered

176 candidates to 113 candidates (64.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	175	5	180

Merged error: 0.3b

Counts

180 → 5

regimes75.0ms

Accuracy

71.5% (5.6b remaining)

Error of 6.1b against oracle of 0.5b and baseline of 20.1b

bsearch113.0ms

Steps

Iters	Range		Point
8	3.308964372933633e-168	4.046021815332288e-164	3.3722516347658366e-167
7	3.5062396612508153e-214	7.055199416157192e-213	6.95543461840908e-213
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	41	38
1	41	38

end0.0ms

sample465.0ms

Algorithm

intervals

Results

230.0ms	8000×	body	80	valid
103.0ms	8000×	pre	80	true