Details

sample24.0ms

Algorithm

intervals

Results

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

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	48	15
3	101	15
4	188	15
5	346	15
6	579	15
7	875	15
8	2271	15
done	5000	15

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
22.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite40.0ms

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))
31.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series89.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* x x) (* y y))
63.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify663.0ms

Counts

48 → 48

Iterations

Useful iterations: done (661.0ms)

Iter	Nodes	Cost
0	91	826
1	303	802
2	1443	662
done	5000	655

prune104.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune4.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
0.0b	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
22.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
18×	`unpow-prod-down` `cube-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `times-frac` `add-cbrt-cube`
10×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`associate-/l/`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`pow-unpow` `flip3--` `pow-exp` `associate-/r*` `flip--` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `unpow3` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

8.0ms	(+ (* x x) (* y y))
12.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
25.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
27.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x x) (* y y))
76.0ms	(cbrt (pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3))
74.0ms	(pow (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) 3)
63.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify877.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (299.0ms)

Iter	Nodes	Cost
0	158	2940
1	486	2546
2	2131	2246
done	5000	2246

prune258.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
161×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
9×	`flip3-+` `flip-+`
8×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `flip3--` `div-sub` `sum-log` `flip--`

Counts

3 → 177

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
34.0ms	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
29.0ms	(/ (+ (* x x) (* y y)) (+ x y))

series150.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
59.0ms	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
60.0ms	(/ (+ (* x x) (* y y)) (+ x y))

simplify1.1s

Counts

186 → 186

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	245	4688
1	697	4481
2	2506	4301
done	5000	4282

prune325.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes87.0ms

Accuracy

76.9% (4.9b remaining)

Error of 5.3b against oracle of 0.4b and baseline of 21.7b

bsearch89.0ms

Steps

Iters	Range	Point
10	1.861534858129743e-168	9.788594240831222e-155	6.410512806354982e-156
9	-1.0598232302570995e-148	-8.977338961703427e-154	-3.748181836506679e-150
8	-8.456905247793116e+155	-1.0554603480016106e+153	-3.0099128470371785e+153

Iters

Range

Point

1.861534858129743e-168

9.788594240831222e-155

6.410512806354982e-156

-1.0598232302570995e-148

-8.977338961703427e-154

-3.748181836506679e-150

-8.456905247793116e+155

-1.0554603480016106e+153

-3.0099128470371785e+153

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	52
1	30	35
done	30	35

end0.0ms

sample541.0ms

Algorithm

intervals

Results

246.0ms	8000×	body	80	valid
102.0ms	8000×	pre	80	true