Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify52.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
21.7b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

8.0ms	(+ (* x x) (* y y))
29.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series109.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x x) (* y y))
76.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify41.0ms

Counts: 48 → 48

prune125.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
21.7b	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
41×	`associate-/r/`
29×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`frac-times`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
16×	`associate-/r*`
15×	`flip3--` `flip--`
14×	`div-exp`
10×	`associate-r/` `associate-l/`
7×	`cbrt-undiv`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `prod-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 130

Calls

3 calls:

9.0ms	(+ (* x x) (* y y))
39.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
42.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series166.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
68.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
69.0ms	(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify88.0ms

Counts: 139 → 139

prune258.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
21.4b	(sqrt (+ (* x x) (* y y)))
21.4b	(sqrt (+ (* x x) (* y y)))
21.5b	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-div`
18×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
12×	`associate-/r*`
9×	`div-inv` `associate-/l/`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 176

Calls

4 calls:

46.0ms	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
13.0ms	(sqrt (+ (* x x) (* y y)))
8.0ms	(sqrt (+ (* x x) (* y y)))
30.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

series242.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
39.0ms	(sqrt (+ (* x x) (* y y)))
45.0ms	(sqrt (+ (* x x) (* y y)))
86.0ms	(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

simplify75.0ms

Counts: 188 → 188

prune414.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Counts: 0 → 0

prune0.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes64.0ms

Accuracy

77.4% (4.5b remaining)

Error of 5.0b against oracle of 0.5b and baseline of 20.4b

bsearch79.0ms

Steps

Iters	Range	Point
6	1.520145198895703e-167	2.1557865162740726e-166	2.1155504904828537e-166
7	-5.771560909560032e-159	-2.816861526094086e-161	-7.718474411270338e-160
9	-1.411670626970749e+155	-1.4567969182990413e+150	-5.000545272256956e+152

Iters

Range

Point

1.520145198895703e-167

2.1557865162740726e-166

2.1155504904828537e-166

-5.771560909560032e-159

-2.816861526094086e-161

-7.718474411270338e-160

-1.411670626970749e+155

-1.4567969182990413e+150

-5.000545272256956e+152

simplify1.0ms

end0.0ms

sample840.0ms

Algorithm

intervals

Results

445.0ms	8000×	body	80	valid
170.0ms	8000×	pre	80	true