Details

sample47.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify2.4s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite44.0ms

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

series134.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(+ (* x x) (* y y))
96.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
2	2435
1	336
0	91

prune213.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))) (cbrt (/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))))
17.8b	(/ (+ (* x x) (* y y)) (+ y x))
17.8b	(/ (+ (* x x) (* y y)) (+ y x))
17.8b	(/ (+ (* x x) (* y y)) (+ y x))

rewrite487.0ms

Algorithm

rewrite-expression-head

Rules

949×	`*-un-lft-identity`
948×	`times-frac`
567×	`add-sqr-sqrt`
560×	`cbrt-prod`
343×	`add-cube-cbrt`
176×	`swap-sqr`
132×	`distribute-lft-out--`
126×	`distribute-lft-out`
98×	`associate-r` `associate-l`
84×	`difference-of-squares`
58×	`associate-/r/`
31×	`div-inv`
30×	`flip3-+` `flip-+`
16×	`unswap-sqr`
12×	`associate-/r*` `add-exp-log`
11×	`pow1`
10×	`add-cbrt-cube`
9×	`associate-/l*`
6×	`pow1/3` `associate-/l/`
4×	`cbrt-div` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 514

Calls

4 calls:

351.0ms	(* (cbrt (/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))) (cbrt (/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))))
29.0ms	(/ (+ (* x x) (* y y)) (+ y x))
27.0ms	(/ (+ (* x x) (* y y)) (+ y x))
25.0ms	(/ (+ (* x x) (* y y)) (+ y x))

series540.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(* (cbrt (/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))) (cbrt (/ (- x y) (/ (+ (* x x) (* y y)) (+ y x)))))
108.0ms	(/ (+ (* x x) (* y y)) (+ y x))
80.0ms	(/ (+ (* x x) (* y y)) (+ y x))
85.0ms	(/ (+ (* x x) (* y y)) (+ y x))

simplify730.0ms

Counts

526 → 526

Iterations

Iter	Nodes
done	5000
1	1173
0	598

prune2.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite112.0ms

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:

13.0ms	(+ (* x x) (* y y))
61.0ms	(* (- x y) (/ (+ y x) (+ (* x x) (* y y))))
33.0ms	(/ (+ y x) (+ (* x x) (* y y)))

series185.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (* x x) (* y y))
89.0ms	(* (- x y) (/ (+ y x) (+ (* x x) (* y y))))
55.0ms	(/ (+ y x) (+ (* x x) (* y y)))

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	2948
1	423
0	136

prune452.0ms

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

Iter	Nodes
done	0
0	0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes115.0ms

Accuracy

72.9% (5.3b remaining)

Error of 5.8b against oracle of 0.5b and baseline of 20.1b

bsearch136.0ms

Steps

Iters	Range	Point
9	1.0539828158360712e-174	4.180108382822779e-169	4.1321470702090296e-169
8	-1.7431458063348651e-140	-8.247834429756668e-144	-1.4421997174909255e-141
10	-6.096696810270342e+164	-1.3768668222090048e+153	-1.3314221285400745e+154

Iters

Range

Point

1.0539828158360712e-174

4.180108382822779e-169

4.1321470702090296e-169

-1.7431458063348651e-140

-8.247834429756668e-144

-1.4421997174909255e-141

-6.096696810270342e+164

-1.3768668222090048e+153

-1.3314221285400745e+154

simplify20.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

987.0ms	8000×	body	80	valid
214.0ms	8000×	pre	80	true