Details

sample21.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify25.0ms

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

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.6b	(- (* x x) (* (* y 4.0) y))
28.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite19.0ms

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)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* (* y 4.0) y))
48.0ms	(- (* x x) (* (* y 4.0) y))
69.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (37.0ms)

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

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ x (/ (fma x x (* (* y 4.0) y)) x))
2.4b	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
15.8b	(/ (fma x x (* (* y 4.0) y)) y)
17.4b	(/ (fma x x (* (* y 4.0) y)) x)

rewrite24.0ms

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:

8.0ms	(/ 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)) y)
2.0ms	(/ (fma x x (* (* y 4.0) y)) x)

series249.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ x (/ (fma x x (* (* y 4.0) y)) x))
56.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
68.0ms	(/ (fma x x (* (* y 4.0) y)) y)
70.0ms	(/ (fma x x (* (* y 4.0) y)) x)

simplify102.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (19.0ms)

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

prune467.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ x (fma 4.0 (/ (pow y 2) x) x))
2.4b	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
5.6b	(/ (pow y 2) x)
15.8b	(/ (fma x x (* (* y 4.0) y)) y)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

2.0ms	(/ x (fma 4.0 (/ (pow y 2) x) x))
6.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
4.0ms	(/ (pow y 2) x)
2.0ms	(/ (fma x x (* (* y 4.0) y)) y)

series204.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ x (fma 4.0 (/ (pow y 2) x) x))
56.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
20.0ms	(/ (pow y 2) x)
69.0ms	(/ (fma x x (* (* y 4.0) y)) y)

simplify81.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	515	1177
1	2610	1036
2	5001	1035

prune502.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ y (/ x y))
1.6b	(/ x (fma 4.0 (/ y (/ x y)) x))
2.4b	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
15.8b	(/ (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	(/ y (/ x y))
2.0ms	(/ x (fma 4.0 (/ y (/ x y)) x))
6.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
2.0ms	(/ (fma x x (* (* y 4.0) y)) y)

series214.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ y (/ x y))
56.0ms	(/ x (fma 4.0 (/ y (/ x y)) x))
62.0ms	(/ (* y 4.0) (/ (fma x x (* (* y 4.0) y)) y))
71.0ms	(/ (fma x x (* (* y 4.0) y)) y)

simplify100.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	661	1395
1	3505	1253
2	5002	1253

prune546.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes58.0ms

Accuracy

14.5% (3.3b remaining)

Error of 3.8b against oracle of 0.4b and baseline of 4.3b

bsearch91.0ms

Steps

Iters	Range		Point
10	1.712144304947188e-239	2.2869144983027257e-225	1.9187342776890177e-228
4	-1.2379907160098315e-169	-8.508197600819889e-170	-8.629188524547341e-170

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	15
1	26	15

end0.0ms

sample547.0ms

Algorithm

intervals

Results

414.0ms

8000×

body

valid