Details

sample48.0ms

Algorithm

intervals

Results

33.0ms

256×

body

valid

simplify249.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	177
7	177
6	168
5	143
4	100
3	59
2	34
1	17
0	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.4b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite57.0ms

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` `insert-posit16` `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 → 58

Calls

3 calls:

7.0ms	(+ (* x x) (* (* y 4.0) y))
7.0ms	(- (* x x) (* (* y 4.0) y))
41.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* x x) (* (* y 4.0) y))
46.0ms	(- (* x x) (* (* y 4.0) y))
85.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify3.2s

Counts

67 → 67

Iterations

Iter	Nodes
done	5059
3	3850
2	861
1	249
0	90

prune285.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

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

prune9.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize22.0ms

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))))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite181.0ms

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` `insert-posit16` `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 → 83

Calls

4 calls:

13.0ms	(+ (* x x) (* (* y 4.0) y))
105.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
24.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
37.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x x) (* (* y 4.0) y))
78.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
66.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
73.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify1.4s

Counts

95 → 95

Iterations

Iter	Nodes
done	5002
2	1839
1	455
0	146

prune443.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

10.5b	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.8b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
21.9b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
13×	`times-frac`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-/r*` `sqrt-prod`
8×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
5×	`pow1` `prod-exp` `cbrt-unprod`
4×	`flip3-+` `flip-+` `insert-posit16` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l*`
2×	`rem-sqrt-square`
1×	`sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 96

Calls

4 calls:

10.0ms	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
15.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
18.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
23.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
85.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
84.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
79.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify1.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	1483
1	373
0	130

prune577.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes223.0ms

Accuracy

62.6% (11.6b remaining)

Error of 12.0b against oracle of 0.4b and baseline of 31.4b

bsearch180.0ms

Steps

Iters	Range		Point
6	1.0558091000171249e+107	1.6495200433389913e+108	1.6131348038947783e+108
5	1.6035341286232548e-95	3.474093194158715e-95	2.0369408682057436e-95
9	-2.6910417602547767e-130	-2.4810864431677805e-136	-2.981255488591297e-134
7	-6.914140684613533e+154	-5.409346264960912e+152	-6.641800154736106e+153

simplify10.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample1.2s

Algorithm

intervals

Results

993.0ms

8000×

body

valid