Details

sample27.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify187.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize19.0ms

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)))

rewrite710.0ms

Algorithm

rewrite-expression-head

Rules

533×	`add-sqr-sqrt`
482×	`*-un-lft-identity`
333×	`associate-l`
216×	`times-frac`
198×	`unswap-sqr`
165×	`difference-of-squares`
156×	`distribute-lft-out`
66×	`distribute-lft-out--`
38×	`add-cube-cbrt`
33×	`swap-sqr` `*-commutative`
24×	`associate-/l*`
9×	`associate-/r*`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `insert-posit16`
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 → 319

Calls

3 calls:

87.0ms	(+ (* x x) (* (* y 4.0) y))
121.0ms	(- (* x x) (* (* y 4.0) y))
477.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series214.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (* x x) (* (* y 4.0) y))
58.0ms	(- (* x x) (* (* y 4.0) y))
103.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify1.7s

Counts

328 → 328

Iterations

Iter	Nodes
done	5000
2	1370
1	444
0	181

prune603.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize0.0ms

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

prune14.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize26.0ms

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)))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

3635×	`*-un-lft-identity`
2955×	`associate-l`
1206×	`distribute-lft-out`
1141×	`associate-/l*`
983×	`times-frac`
974×	`add-sqr-sqrt`
918×	`frac-sub`
683×	`associate-/r*`
523×	`add-cube-cbrt`
354×	`associate-r`
307×	`distribute-lft-out--`
214×	`unswap-sqr`
136×	`swap-sqr`
122×	`*-commutative`
67×	`sub-div`
65×	`frac-2neg`
63×	`clear-num`
24×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/` `add-log-exp`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`pow1` `prod-exp` `cbrt-unprod` `insert-posit16` `div-inv`
3×	`distribute-rgt-out--`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 1774

Calls

4 calls:

67.0ms	(+ (* x x) (* (* y 4.0) y))
2.8s	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
179.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
227.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* x x) (* (* y 4.0) y))
102.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
82.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
70.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify2.4s

Counts

1786 → 1786

Iterations

Iter	Nodes
done	5001
0	1836

prune3.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize53.0ms

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)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

1128×	`*-un-lft-identity`
879×	`associate-l`
608×	`times-frac`
426×	`distribute-lft-out`
417×	`add-sqr-sqrt`
276×	`add-cube-cbrt`
150×	`associate-r`
141×	`sqrt-prod`
91×	`swap-sqr`
71×	`unswap-sqr`
67×	`associate-/l*`
51×	`*-commutative`
36×	`associate-/r*`
27×	`sqrt-div`
23×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/`
7×	`cbrt-undiv` `div-exp`
6×	`rem-sqrt-square`
5×	`pow1` `prod-exp` `cbrt-unprod`
4×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `insert-posit16` `div-inv` `add-log-exp`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 784

Calls

4 calls:

317.0ms	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
212.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
200.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
234.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (/ (* x x) (+ (* x x) (* (* y 4.0) y))))
76.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
73.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
96.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify2.3s

Counts

796 → 796

Iterations

Iter	Nodes
done	5001
2	2665
1	980
0	427

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes199.0ms

Accuracy

62.6% (11.6b remaining)

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

bsearch205.0ms

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

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample1.0s

Algorithm

intervals

Results

792.0ms

8000×

body

valid