Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

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: 31.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.6b	(- (* x x) (* (* y 4.0) y))
31.0b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite20.0ms

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:

4.0ms	(+ (* x x) (* (* y 4.0) y))
5.0ms	(- (* x x) (* (* y 4.0) y))
9.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series174.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* x x) (* (* y 4.0) y))
53.0ms	(- (* x x) (* (* y 4.0) y))
75.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (42.0ms)

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

prune194.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

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 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune6.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* (* y 4.0) y))
0.0b	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
2.6b	(- (* x x) (* (* y 4.0) y))
31.0b	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `fma-udef` `inv-pow`

Counts

4 → 143

Calls

4 calls:

1.0ms	(fma x x (* (* y 4.0) y))
8.0ms	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
4.0ms	(- (* x x) (* (* y 4.0) y))
6.0ms	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma x x (* (* y 4.0) y))
78.0ms	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
45.0ms	(- (* x x) (* (* y 4.0) y))
78.0ms	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify80.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	449	2045
1	2179	1867
2	5001	1725

prune330.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (- (* x x) (* (* y 4.0) y)))
0.6b	(/ 1 (fma x x (* (* y 4.0) y)))
2.6b	(- (* x x) (* (* y 4.0) y))
30.0b	(/ (/ 1 (fma x x (* (* y 4.0) y))) (/ 1 (- (* x x) (* (* y 4.0) y))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

483×	`times-frac`
230×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
36×	`div-exp`
33×	`div-inv`
31×	`associate-/r/`
21×	`associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-/l*`
16×	`flip3--` `flip--`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 341

Calls

4 calls:

5.0ms	(/ 1 (- (* x x) (* (* y 4.0) y)))
3.0ms	(/ 1 (fma x x (* (* y 4.0) y)))
4.0ms	(- (* x x) (* (* y 4.0) y))
14.0ms	(/ (/ 1 (fma x x (* (* y 4.0) y))) (/ 1 (- (* x x) (* (* y 4.0) y))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (- (* x x) (* (* y 4.0) y)))
50.0ms	(/ 1 (fma x x (* (* y 4.0) y)))
51.0ms	(- (* x x) (* (* y 4.0) y))
80.0ms	(/ (/ 1 (fma x x (* (* y 4.0) y))) (/ 1 (- (* x x) (* (* y 4.0) y))))

simplify91.0ms

Algorithm

egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1380	6275
1	5001	5673

prune652.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes111.0ms

Accuracy

56.6% (13.8b remaining)

Error of 14.1b against oracle of 0.3b and baseline of 32.1b

bsearch193.0ms

Steps

Iters	Range		Point
9	5.41477266608165e+51	6.11744604512166e+58	2.9778125912394635e+57
8	2.914569284707164e-27	7.475162141923425e-25	4.5464237877594004e-26
9	3.6316131954925725e-112	1.441284598851764e-106	1.4128408726374627e-110
6	-1.2969398998702968e-73	-2.2317513318290833e-74	-3.839673263781281e-74
9	-2.4724731267575454e+156	-3.374237180858152e+150	-3.436284107232327e+150

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample364.0ms

Algorithm

intervals

Results

236.0ms

8000×

body

valid