Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify199.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* y y))
0.0b	(* 4.0 (* y y))
3.3b	(- (* x x) (* 4.0 (* y y)))
29.1b	(/ (- (* x x) (* 4.0 (* y y))) (+ (* x x) (* 4.0 (* y y))))

rewrite90.0ms

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:

21.0ms	(* 4.0 (* y y))
21.0ms	(* 4.0 (* y y))
11.0ms	(- (* x x) (* 4.0 (* y y)))
34.0ms	(/ (- (* x x) (* 4.0 (* y y))) (+ (* x x) (* 4.0 (* y y))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 4.0 (* y y))
27.0ms	(* 4.0 (* y y))
48.0ms	(- (* x x) (* 4.0 (* y y)))
98.0ms	(/ (- (* x x) (* 4.0 (* y y))) (+ (* x x) (* 4.0 (* y y))))

simplify936.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	1789
1	315
0	107

prune507.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x (/ (+ (* x x) (* (* 4.0 y) y)) x))
2.1b	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
15.2b	(/ (+ (* x x) (* (* 4.0 y) y)) x)
15.7b	(/ (+ (* x x) (* (* 4.0 y) y)) y)

rewrite86.0ms

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:

12.0ms	(/ x (/ (+ (* x x) (* (* 4.0 y) y)) x))
18.0ms	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
29.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) x)
21.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) y)

series362.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ x (/ (+ (* x x) (* (* 4.0 y) y)) x))
91.0ms	(/ (* 4.0 y) (/ (+ (* x x) (* (* 4.0 y) y)) y))
95.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) x)
86.0ms	(/ (+ (* x x) (* (* 4.0 y) y)) y)

simplify405.0ms

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
1	764
0	272

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y))) 3))
0.0b	(pow (/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y))) 3)
3.3b	(- (* x x) (* (* 4.0 y) y))
29.1b	(/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
36×	`cbrt-prod`
30×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cube-div` `cube-mult` `cbrt-undiv` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `rem-cube-cbrt` `sqr-pow` `associate-/l/`
1×	`pow-to-exp` `cbrt-div` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `rem-cbrt-cube`

Counts

4 → 140

Calls

4 calls:

15.0ms	(cbrt (pow (/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y))) 3))
26.0ms	(pow (/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y))) 3)
7.0ms	(- (* x x) (* (* 4.0 y) y))
20.0ms	(/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (pow (/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y))) 3))
94.0ms	(pow (/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y))) 3)
53.0ms	(- (* x x) (* (* 4.0 y) y))
80.0ms	(/ (- (* x x) (* (* 4.0 y) y)) (+ (* x x) (* (* 4.0 y) y)))

simplify2.0s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	3981
1	617
0	166

prune627.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize4.0ms

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: 0.6b

regimes292.0ms

Accuracy

59% (12.5b remaining)

Error of 12.8b against oracle of 0.3b and baseline of 30.7b

bsearch1.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample936.0ms

Algorithm

intervals

Results

745.0ms

8000×

body

valid