Details

sample26.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
4.0ms	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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
17.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite41.0ms

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))
26.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series145.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(+ (* x x) (* y y))
96.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
2	2435
1	336
0	91

prune280.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(/ 1 (/ (+ (* x x) (* y y)) (* (+ x y) (- x y))))
17.1b	(/ (+ (* x x) (* y y)) (* (+ x y) (- x y)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
41×	`associate-/r/`
29×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
20×	`frac-times`
17×	`flip3-+` `add-cbrt-cube` `flip-+`
16×	`associate-/r*`
15×	`flip3--` `flip--`
14×	`div-exp`
10×	`associate-l/` `associate-r/`
7×	`cbrt-undiv`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `prod-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `sum-log` `pow-flip` `inv-pow`

Counts

3 → 130

Calls

3 calls:

7.0ms	(+ (* x x) (* y y))
54.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (+ x y) (- x y))))
46.0ms	(/ (+ (* x x) (* y y)) (* (+ x y) (- x y)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
81.0ms	(/ 1 (/ (+ (* x x) (* y y)) (* (+ x y) (- x y))))
94.0ms	(/ (+ (* x x) (* y y)) (* (+ x y) (- x y)))

simplify1.9s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	4295
1	644
0	220

prune550.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize1.0ms

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

prune12.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (+ y x) (+ y x)) (- x y))
0.2b	(* (* (/ 1 (+ (* y y) (* x x))) (* (* (+ y x) (+ y x)) (- x y))) (/ 1 (+ y x)))
0.6b	(/ 1 (+ (* y y) (* x x)))
28.5b	(* (/ 1 (+ (* y y) (* x x))) (* (* (+ y x) (+ y x)) (- x y)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

327×	`frac-times`
277×	`add-exp-log`
175×	`prod-exp`
154×	`associate-*l/`
135×	`associate-*r/`
129×	`flip3-+` `flip-+`
97×	`add-cbrt-cube`
63×	`flip3--` `flip--`
58×	`div-exp`
53×	`cbrt-unprod`
36×	`*-un-lft-identity`
33×	`pow1`
31×	`add-sqr-sqrt`
30×	`times-frac`
29×	`rec-exp` `1-exp`
28×	`add-cube-cbrt`
24×	`associate-r`
19×	`pow-prod-down`
17×	`cbrt-undiv` `associate-l`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`sub-neg` `associate-/r/`
4×	`add-log-exp`
3×	`associate-/r` `-commutative` `div-inv` `distribute-lft-out` `associate-/l*`
1×	`clear-num` `frac-2neg` `un-div-inv` `pow-flip` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 395

Calls

4 calls:

78.0ms	(* (* (+ y x) (+ y x)) (- x y))
781.0ms	(* (* (/ 1 (+ (* y y) (* x x))) (* (* (+ y x) (+ y x)) (- x y))) (/ 1 (+ y x)))
11.0ms	(/ 1 (+ (* y y) (* x x)))
249.0ms	(* (/ 1 (+ (* y y) (* x x))) (* (* (+ y x) (+ y x)) (- x y)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* (+ y x) (+ y x)) (- x y))
115.0ms	(* (* (/ 1 (+ (* y y) (* x x))) (* (* (+ y x) (+ y x)) (- x y))) (/ 1 (+ y x)))
52.0ms	(/ 1 (+ (* y y) (* x x)))
155.0ms	(* (/ 1 (+ (* y y) (* x x))) (* (* (+ y x) (+ y x)) (- x y)))

simplify1.5s

Counts

407 → 407

Iterations

Iter	Nodes
done	5001
1	2465
0	558

prune2.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.6b

regimes187.0ms

Accuracy

77.6% (4.5b remaining)

Error of 4.9b against oracle of 0.4b and baseline of 20.3b

bsearch105.0ms

Steps

Iters	Range	Point
9	5.406303382120601e-192	8.906821559558098e-187	8.82873352566288e-187
7	-2.6597031830043453e-160	-5.902380441646539e-162	-5.832122554270737e-161
7	-4.00956143299081e+154	-3.349244442405179e+152	-6.684928343955356e+152

Iters

Range

Point

5.406303382120601e-192

8.906821559558098e-187

8.82873352566288e-187

-2.6597031830043453e-160

-5.902380441646539e-162

-5.832122554270737e-161

-4.00956143299081e+154

-3.349244442405179e+152

-6.684928343955356e+152

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

996.0ms	8000×	body	80	valid
221.0ms	8000×	pre	80	true