Details

sample15.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	9
1	36	9
2	68	9
3	117	9
4	174	9
5	195	9
6	197	9
7	197	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize7.0ms

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)))

rewrite17.0ms

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` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

3.0ms	(+ (* x x) (* (* y 4.0) y))
2.0ms	(- (* x x) (* (* y 4.0) y))
11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* (* y 4.0) y))
41.0ms	(- (* x x) (* (* y 4.0) y))
64.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify41.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	234	680
1	1007	622
2	5001	620

prune143.0ms

Pruning

5 alts after pruning (5 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

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune7.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
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)))

rewrite37.0ms

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` `add-log-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `diff-log` `sum-log` `inv-pow`

Counts

4 → 138

Calls

4 calls:

14.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
3.0ms	(+ (* x x) (* (* y 4.0) y))
3.0ms	(- (* x x) (* (* y 4.0) y))
12.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
36.0ms	(+ (* x x) (* (* y 4.0) y))
43.0ms	(- (* x x) (* (* y 4.0) y))
59.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify72.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	461	2225
1	2326	2037
2	5002	1901

prune235.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ 1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
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)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

447×	`times-frac`
211×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
53×	`associate-/r*`
49×	`add-exp-log`
36×	`div-exp`
31×	`associate-/r/`
18×	`div-inv`
15×	`add-cbrt-cube`
14×	`flip3-+` `flip-+`
13×	`rec-exp` `1-exp`
8×	`add-log-exp`
7×	`cbrt-undiv`
6×	`pow1` `associate-/l*`
4×	`pow-flip`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/` `inv-pow`
1×	`+-commutative` `sub-neg` `diff-log` `div-sub` `sum-log` `remove-double-div`

Counts

4 → 298

Calls

4 calls:

22.0ms	(/ 1 (/ 1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
3.0ms	(+ (* x x) (* (* y 4.0) y))
3.0ms	(- (* x x) (* (* y 4.0) y))
10.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1 (/ 1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
36.0ms	(+ (* x x) (* (* y 4.0) y))
44.0ms	(- (* x x) (* (* y 4.0) y))
59.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify85.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1163	5803
1	5001	4963

prune430.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes141.0ms

Accuracy

56.6% (13.8b remaining)

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

bsearch165.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	50
1	40	50

end0.0ms

sample350.0ms

Algorithm

intervals

Results

221.0ms

8000×

body

valid