Details

sample35.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify243.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	202
7	202
6	198
5	169
4	116
3	67
2	35
1	17
0	9

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* y y))
0.0b	(* 4.0 (* y y))
4.2b	(- (* x x) (* 4.0 (* y y)))
30.1b	(/ (- (* x x) (* 4.0 (* y y))) (+ (* x x) (* 4.0 (* y y))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
14×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `associate-r` `associate-/r/` `*-commutative` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 82

Calls

4 calls:

17.0ms	(* 4.0 (* y y))
21.0ms	(* 4.0 (* y y))
7.0ms	(- (* x x) (* 4.0 (* y y)))
28.0ms	(/ (- (* x x) (* 4.0 (* y y))) (+ (* x x) (* 4.0 (* y y))))

series222.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 4.0 (* y y))
51.0ms	(* 4.0 (* y y))
56.0ms	(- (* x x) (* 4.0 (* y y)))
67.0ms	(/ (- (* x x) (* 4.0 (* y y))) (+ (* x x) (* 4.0 (* y y))))

simplify1.1s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	1789
1	315
0	107

prune411.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ x (/ (+ (* x x) (* (* 4.0 y) y)) x))
2.2b	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
17.2b	(/ (+ (* x x) (* (* 4.0 y) y)) x)
18.0b	(/ (+ (* x x) (* (* 4.0 y) y)) y)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

124×	`times-frac`
76×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
32×	`associate-/r*`
25×	`add-cbrt-cube` `add-exp-log`
11×	`cbrt-undiv` `div-exp`
10×	`div-inv` `associate-/l*`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp` `associate-/l/`
2×	`flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`

Counts

4 → 174

Calls

4 calls:

14.0ms	(/ x (/ (+ (* x x) (* (* 4.0 y) y)) x))
15.0ms	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
24.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) x)
44.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) y)

series293.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ x (/ (+ (* x x) (* (* 4.0 y) y)) x))
72.0ms	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
79.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) x)
61.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) y)

simplify462.0ms

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
1	764
0	272

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b	(/ x (+ (* (/ (* y y) x) 4.0) x))
2.2b	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
6.3b	(/ (* y y) x)
18.0b	(/ (+ (* x x) (* (* 4.0 y) y)) y)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
36×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
22×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
6×	`div-inv`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
3×	`prod-exp` `associate-/r/` `cbrt-unprod`
2×	`flip3-+` `flip-+` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

43.0ms	(/ x (+ (* (/ (* y y) x) 4.0) x))
31.0ms	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
8.0ms	(/ (* y y) x)
35.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) y)

series277.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ x (+ (* (/ (* y y) x) 4.0) x))
75.0ms	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
35.0ms	(/ (* y y) x)
96.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) y)

simplify413.0ms

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
1	649
0	219

prune779.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* 4.0 y) y))
0.0b	(/ 1 (/ (+ (* x x) (* (* 4.0 y) y)) (- (* x x) (* (* 4.0 y) y))))
4.2b	(- (* x x) (* (* 4.0 y) y))
30.1b	(/ (+ (* x x) (* (* 4.0 y) y)) (- (* x x) (* (* 4.0 y) y)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 138

Calls

4 calls:

12.0ms	(+ (* x x) (* (* 4.0 y) y))
21.0ms	(/ 1 (/ (+ (* x x) (* (* 4.0 y) y)) (- (* x x) (* (* 4.0 y) y))))
6.0ms	(- (* x x) (* (* 4.0 y) y))
47.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) (- (* x x) (* (* 4.0 y) y)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* x x) (* (* 4.0 y) y))
107.0ms	(/ 1 (/ (+ (* x x) (* (* 4.0 y) y)) (- (* x x) (* (* 4.0 y) y))))
62.0ms	(- (* x x) (* (* 4.0 y) y))
96.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) (- (* x x) (* (* 4.0 y) y)))

simplify1.3s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	3133
1	534
0	192

prune628.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes306.0ms

Accuracy

79% (3.8b remaining)

Error of 4.2b against oracle of 0.3b and baseline of 18.6b

bsearch249.0ms

Steps

Iters	Range		Point
11	3.550984960573557e+103	3.1447189754541467e+124	3.1088232252357084e+124
7	5.398636740828856e-182	4.9739715934540585e-180	4.876101206523021e-180
8	-1.2665164637226831e-155	-2.6235253916143137e-159	-2.6777867496852493e-159
10	-2.715343385846948e+153	-1.066572806747229e+141	-2.6816105046843377e+153

simplify5.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

974.0ms

8000×

body

valid