Details

sample32.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify990.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(* (- x y) (+ x y))
23.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite157.0ms

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:

15.0ms	(+ (* x x) (* y y))
82.0ms	(* (- x y) (+ x y))
57.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* x x) (* y y))
71.0ms	(* (- x y) (+ x y))
109.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.1s

Counts: 82 → 82

prune254.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify12.0ms

Counts: 0 → 0

prune6.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

8.6b	(/ (- x y) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))))
23.4b	(cbrt (+ (* x x) (* y y)))
23.4b	(cbrt (+ (* x x) (* y y)))
23.4b	(cbrt (+ (* x x) (* y y)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
13×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod` `add-cube-cbrt` `flip3-+` `flip-+`
8×	`associate-/r/`
7×	`add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`flip3--` `frac-2neg` `div-sub` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `div-inv`

Counts

4 → 75

Calls

4 calls:

49.0ms	(/ (- x y) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))))
10.0ms	(cbrt (+ (* x x) (* y y)))
17.0ms	(cbrt (+ (* x x) (* y y)))
10.0ms	(cbrt (+ (* x x) (* y y)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (- x y) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))))
170.0ms	(cbrt (+ (* x x) (* y y)))
142.0ms	(cbrt (+ (* x x) (* y y)))
135.0ms	(cbrt (+ (* x x) (* y y)))

simplify1.2s

Counts: 87 → 87

prune325.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify11.0ms

Counts: 0 → 0

prune0.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.3b

regimes105.0ms

Accuracy

77.7% (4.6b remaining)

Error of 5.1b against oracle of 0.5b and baseline of 21.1b

bsearch114.0ms

Steps

Iters	Range	Point
7	1.5469854771828655e-166	2.2333130047815493e-164	2.184840803589229e-164
8	-2.1439147322830412e-159	-5.326142386021628e-164	-1.0480049306425092e-161
8	-1.051527773372545e+155	-2.3467814709880217e+151	-1.9464050218174916e+152

Iters

Range

Point

1.5469854771828655e-166

2.2333130047815493e-164

2.184840803589229e-164

-2.1439147322830412e-159

-5.326142386021628e-164

-1.0480049306425092e-161

-1.051527773372545e+155

-2.3467814709880217e+151

-1.9464050218174916e+152

simplify1.1s

end0.0ms

sample1.3s

Algorithm

intervals

Results

735.0ms	8000×	body	80	valid
262.0ms	8000×	pre	80	true