Details

sample26.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify52.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
21.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `flip3-+` `flip-+` `associate-/l/`
7×	`add-cube-cbrt`
6×	`flip3--` `flip--`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-r/` `associate-r` `associate-l/`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

10.0ms	(+ (* x x) (* y y))
41.0ms	(* (- x y) (+ x y))
32.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
44.0ms	(* (- x y) (+ x y))
71.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify54.0ms

Counts: 82 → 82

prune178.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
20.4b	(sqrt (+ (* x x) (* y y)))
20.4b	(sqrt (+ (* x x) (* y y)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
96×	`times-frac`
95×	`*-un-lft-identity`
57×	`add-cube-cbrt` `sqrt-prod`
36×	`associate-l`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `associate-/r/` `distribute-lft-out`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 183

Calls

4 calls:

44.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
137.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
8.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
67.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
37.0ms	(sqrt (+ (* x x) (* y y)))
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify64.0ms

Counts: 195 → 195

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

20.4b	(sqrt (+ (* x x) (* y y)))
20.4b	(sqrt (+ (* x x) (* y y)))
20.4b	(sqrt (+ (* x x) (* y y)))
20.4b	(sqrt (+ (* x x) (* y y)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

8.0ms	(sqrt (+ (* x x) (* y y)))
8.0ms	(sqrt (+ (* x x) (* y y)))
8.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ (* x x) (* y y)))
37.0ms	(sqrt (+ (* x x) (* y y)))
37.0ms	(sqrt (+ (* x x) (* y y)))
41.0ms	(sqrt (+ (* x x) (* y y)))

simplify127.0ms

Counts: 72 → 72

prune266.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

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

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes57.0ms

Accuracy

73.3% (5.3b remaining)

Error of 5.8b against oracle of 0.5b and baseline of 20.2b

bsearch84.0ms

Steps

Iters	Range	Point
9	7.317544829255995e-171	8.172128628284949e-165	8.086849682588499e-165
3	-7.225648132123047e-146	-5.344245046864215e-146	-6.402534282322308e-146
10	-2.4132847384386213e+159	-3.218335132667145e+145	-1.3267065753407922e+154

Iters

Range

Point

7.317544829255995e-171

8.172128628284949e-165

8.086849682588499e-165

-7.225648132123047e-146

-5.344245046864215e-146

-6.402534282322308e-146

-2.4132847384386213e+159

-3.218335132667145e+145

-1.3267065753407922e+154

simplify1.0ms

end0.0ms

sample768.0ms

Algorithm

intervals

Results

373.0ms	8000×	body	80	valid
175.0ms	8000×	pre	80	true