Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	48	15
3	103	15
4	208	15
5	403	15
6	840	15
7	3699	15
done	5000	15

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

12.0ms	(+ (* x x) (* y y))
45.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series150.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* x x) (* y y))
115.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.1s

Counts

48 → 48

Iterations

Useful iterations: 2 (370.0ms)

Iter	Nodes	Cost
0	91	826
1	336	802
2	2435	666
done	5001	666

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))) (cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
18.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
18.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
18.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-prod`
30×	`add-sqr-sqrt`
24×	`associate-/l/`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac` `add-exp-log`
19×	`add-cbrt-cube`
16×	`flip3-+` `flip-+`
14×	`associate-/r/`
13×	`frac-times`
12×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`associate-/r*` `flip3--` `flip--`
7×	`associate-l/` `associate-r/` `div-inv`
6×	`cbrt-undiv` `pow1/3` `div-exp`
4×	`cbrt-div` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `associate-/l*`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `*-commutative`

Counts

4 → 154

Calls

4 calls:

69.0ms	(* (cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))) (cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
29.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
38.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
26.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(* (cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))) (cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
81.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
104.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
116.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.3s

Counts

166 → 166

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	158	4404
1	428	4167
2	2516	3713
done	5000	3411

prune941.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
17.9b	(/ (+ x y) (+ (* x x) (* y y)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

12.0ms	(+ (* x x) (* y y))
97.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
39.0ms	(/ (+ x y) (+ (* x x) (* y y)))

series233.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (* x x) (* y y))
102.0ms	(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
86.0ms	(/ (+ x y) (+ (* x x) (* y y)))

simplify2.0s

Counts

98 → 98

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	133	1685
1	423	1648
2	2999	1458
done	5000	1454

prune412.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

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

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes190.0ms

Accuracy

73.3% (5.2b remaining)

Error of 5.7b against oracle of 0.5b and baseline of 20.1b

bsearch174.0ms

Steps

Iters	Range	Point
9	1.0539828158360712e-174	4.180108382822779e-169	4.1321470702090296e-169
8	-1.7431458063348651e-140	-8.247834429756668e-144	-2.348476192100428e-141
10	-6.096696810270342e+164	-1.3768668222090048e+153	-1.424347751451892e+153

Iters

Range

Point

1.0539828158360712e-174

4.180108382822779e-169

4.1321470702090296e-169

-1.7431458063348651e-140

-8.247834429756668e-144

-2.348476192100428e-141

-6.096696810270342e+164

-1.3768668222090048e+153

-1.424347751451892e+153

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	114
1	32	65
done	32	65

end0.0ms

sample1.1s

Algorithm

intervals

Results

593.0ms	8000×	body	80	valid
236.0ms	8000×	pre	80	true