Details

sample24.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	40	9
2	78	9
3	134	9
4	200	9
5	233	9
6	239	9
7	239	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.5b	(- (* x x) (* (* y 4.0) y))
32.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

3.0ms	(+ (* x x) (* (* y 4.0) y))
4.0ms	(- (* x x) (* (* y 4.0) y))
11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* (* y 4.0) y))
42.0ms	(- (* x x) (* (* y 4.0) y))
64.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	254	719
1	1175	657
2	5001	641

prune167.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize0.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b	(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.9b	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
17.3b	(/ (fma x x (* (* y 4.0) y)) x)
19.7b	(/ (fma x x (* (* y 4.0) y)) y)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac`
76×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`associate-/r*`
25×	`add-exp-log` `add-cbrt-cube`
11×	`cbrt-undiv` `div-exp`
10×	`div-inv` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`

Counts

4 → 178

Calls

4 calls:

5.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
6.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
2.0ms	(/ (fma x x (* (* y 4.0) y)) x)
2.0ms	(/ (fma x x (* (* y 4.0) y)) y)

series246.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
53.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
70.0ms	(/ (fma x x (* (* y 4.0) y)) x)
65.0ms	(/ (fma x x (* (* y 4.0) y)) y)

simplify91.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	613	1740
1	3204	1580
2	5002	1580

prune423.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.5b	(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.9b	(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
5.7b	(/ (pow x 2) y)
17.3b	(/ (fma x x (* (* y 4.0) y)) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

111×	`times-frac`
73×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
21×	`add-exp-log`
18×	`add-cbrt-cube`
15×	`associate-/l*`
12×	`unpow-prod-down`
9×	`div-exp`
8×	`div-inv`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod`

Counts

4 → 175

Calls

4 calls:

5.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
3.0ms	(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
4.0ms	(/ (pow x 2) y)
2.0ms	(/ (fma x x (* (* y 4.0) y)) x)

series219.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
66.0ms	(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
19.0ms	(/ (pow x 2) y)
71.0ms	(/ (fma x x (* (* y 4.0) y)) x)

simplify91.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	582	1433
1	3097	1281
2	5001	1279

prune530.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes197.0ms

Accuracy

68.9% (5.4b remaining)

Error of 5.7b against oracle of 0.3b and baseline of 17.5b

bsearch88.0ms

Steps

Iters	Range		Point
9	3.187575323954816e+149	1.1937552692612344e+157	1.3249836726640813e+154
9	-3.02364926008494e+163	-5.0703513731044795e+156	-5.297341487908735e+156

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	11
1	28	11

end0.0ms

sample552.0ms

Algorithm

intervals

Results

422.0ms

8000×

body

valid