Details

sample29.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify29.0ms

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: 28.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.4b	(- (* x x) (* (* y 4.0) y))
28.1b	(/ (- (* 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))
3.0ms	(- (* x x) (* (* y 4.0) y))
11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* x x) (* (* y 4.0) y))
51.0ms	(- (* x x) (* (* y 4.0) y))
71.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify49.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (40.0ms)

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

prune201.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
1.7b	(/ x (/ (fma x x (* (* y 4.0) y)) x))
16.5b	(/ (fma x x (* (* y 4.0) y)) y)
16.9b	(/ (fma x x (* (* y 4.0) y)) x)

rewrite25.0ms

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:

10.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
5.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.0ms	(/ (fma x x (* (* y 4.0) y)) y)
2.0ms	(/ (fma x x (* (* y 4.0) y)) x)

series268.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
65.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
72.0ms	(/ (fma x x (* (* y 4.0) y)) y)
73.0ms	(/ (fma x x (* (* y 4.0) y)) x)

simplify109.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	613	1740
1	3220	1580
2	5001	1575

prune511.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
1.7b	(/ x (/ (fma x x (* (* y 4.0) y)) x))
7.4b	(/ (pow x 2) y)
16.9b	(/ (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:

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

series236.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
68.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
21.0ms	(/ (pow x 2) y)
80.0ms	(/ (fma x x (* (* y 4.0) y)) x)

simplify103.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (80.0ms)

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

prune823.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
1.7b	(/ x (fma 4.0 (/ (pow y 2) x) x))
5.9b	(/ (pow y 2) x)
7.4b	(/ (pow x 2) y)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

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

series173.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (* y 4.0) (fma 4.0 y (/ (pow x 2) y)))
62.0ms	(/ x (fma 4.0 (/ (pow y 2) x) x))
21.0ms	(/ (pow y 2) x)
22.0ms	(/ (pow x 2) y)

simplify75.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	457	896
1	2096	764
2	5002	762

prune506.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

regimes105.0ms

Accuracy

22.2% (2.7b remaining)

Error of 3.0b against oracle of 0.3b and baseline of 3.7b

bsearch111.0ms

Steps

Iters	Range		Point
9	1.6355955291222859e-227	3.8817003729330007e-221	1.1707538281815936e-226
8	-4.548608944905891e-206	-9.587801766842726e-209	-2.2576090032348994e-207

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	11
1	32	11
2	32	11

end0.0ms

sample765.0ms

Algorithm

intervals

Results

622.0ms

8000×

body

valid