Details

sample40.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify271.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.3b	(- (* x x) (* (* y 4.0) y))
30.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

13.0ms	(+ (* x x) (* (* y 4.0) y))
12.0ms	(- (* x x) (* (* y 4.0) y))
26.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (* x x) (* (* y 4.0) y))
50.0ms	(- (* x x) (* (* y 4.0) y))
100.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify1.2s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1203
1	254
0	87

prune303.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

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

prune15.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
21.6b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
23.1b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`associate-/r/` `add-cube-cbrt` `add-log-exp`
7×	`times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`pow1` `prod-exp` `cbrt-unprod` `div-inv`
3×	`distribute-rgt-out--`
2×	`clear-num` `frac-2neg` `associate-/l*` `difference-of-squares`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 79

Calls

4 calls:

12.0ms	(+ (* x x) (* (* y 4.0) y))
110.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
15.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
22.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* x x) (* (* y 4.0) y))
93.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
60.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
76.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify2.4s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	3586
1	453
0	142

prune567.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
0.3b	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
21.6b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
22.8b	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
46×	`times-frac`
38×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
29×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`div-exp`
13×	`prod-exp`
12×	`cbrt-undiv`
11×	`associate-/r*`
8×	`div-inv`
7×	`cbrt-unprod` `associate-/l*`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`rec-exp` `1-exp`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`flip3-+` `flip-+` `distribute-lft-out--` `associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

4 → 129

Calls

4 calls:

132.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
40.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
26.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
70.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))

series343.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))))
92.0ms	(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y)))
76.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
89.0ms	(/ (+ (* x x) (* (* y 4.0) y)) (* (* y 4.0) y))

simplify988.0ms

Counts

141 → 141

Iterations

Iter	Nodes
done	5001
1	660
0	220

prune816.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes366.0ms

Accuracy

60.4% (12.4b remaining)

Error of 12.8b against oracle of 0.4b and baseline of 31.7b

bsearch205.0ms

Steps

Iters	Range		Point
9	3.0455316621450604e+53	6.601528886642014e+60	2.371593609881423e+60
9	2.598286552721665e-80	1.1482561294715716e-71	9.959621465941043e-80
5	-1.1135581929510197e-64	-2.986264416976082e-65	-3.379561403631359e-65
6	-1.2608308818293039e+154	-1.5171851739610474e+153	-2.0417989825890665e+153

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample958.0ms

Algorithm

intervals

Results

645.0ms

8000×

body

valid