Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify2.7s

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite37.0ms

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))
28.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series92.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ (* x x) (* y y))
65.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify873.0ms

Counts

48 → 48

Iterations

Useful iterations: done (871.0ms)

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

prune105.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
18.8b	(/ (+ (* x x) (* y y)) (+ x y))

rewrite85.0ms

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

series154.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* x x) (* y y))
66.0ms	(/ (- 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

prune340.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (/ (+ (* x x) (* y y)) (+ x y)))
18.8b	(/ (+ (* x x) (* y y)) (+ x y))
18.8b	(/ (+ (* x x) (* y y)) (+ x y))
18.8b	(/ (+ (* x x) (* y y)) (+ x y))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
48×	`times-frac`
39×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`cbrt-prod`
15×	`distribute-lft-out`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`associate-/l/`
4×	`pow1` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`cbrt-div` `pow1/3`

Counts

4 → 132

Calls

4 calls:

8.0ms	(cbrt (/ (+ (* x x) (* y y)) (+ x y)))
30.0ms	(/ (+ (* x x) (* y y)) (+ x y))
33.0ms	(/ (+ (* x x) (* y y)) (+ x y))
31.0ms	(/ (+ (* x x) (* y y)) (+ x y))

series335.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (/ (+ (* x x) (* y y)) (+ x y)))
60.0ms	(/ (+ (* x x) (* y y)) (+ x y))
62.0ms	(/ (+ (* x x) (* y y)) (+ x y))
62.0ms	(/ (+ (* x x) (* y y)) (+ x y))

simplify1.1s

Counts

144 → 144

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	128	2642
1	281	2551
2	757	2389
3	1936	2386
done	5000	2384

prune450.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

localize5.0ms

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

prune0.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.4b

regimes82.0ms

Accuracy

76.3% (4.6b remaining)

Error of 5.2b against oracle of 0.6b and baseline of 20.2b

bsearch72.0ms

Steps

Iters	Range	Point
6	9.517071470764056e-169	1.244017797499222e-167	1.2196978986578245e-167
8	-2.155163838538853e-155	-8.651262834478996e-160	-6.692220829649749e-158
8	-6.481059119392077e+156	-4.5338274440125526e+153	-1.1330412481698895e+154

Iters

Range

Point

9.517071470764056e-169

1.244017797499222e-167

1.2196978986578245e-167

-2.155163838538853e-155

-8.651262834478996e-160

-6.692220829649749e-158

-6.481059119392077e+156

-4.5338274440125526e+153

-1.1330412481698895e+154

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	21	50
1	29	36
done	29	36

end0.0ms

sample495.0ms

Algorithm

intervals

Results

215.0ms	8000×	body	80	valid
101.0ms	8000×	pre	80	true