Details

Time bar (total: 6.1s)

sample15.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify117.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0919
11719
23519
37019
411919
516719
618719
718819
done18819

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize7.0ms

Local error

Found 2 expressions with local error:

2.8b
(- (* x x) (* (* y 4.0) y))
31.7b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
3.0ms
(- (* x x) (* (* y 4.0) y))
13.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series102.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(- (* x x) (* (* y 4.0) y))
59.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.9s

Counts
50 → 50
Iterations

Useful iterations: 3 (439.0ms)

IterNodesCost
0821196
12191174
29401060
347721056
done50001056

prune126.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune6.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
22.1b
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
23.7b
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
9×*-un-lft-identity
8×associate-/r/
7×add-cube-cbrt times-frac
6×associate-/r*
5×cbrt-undiv div-exp add-log-exp
4×flip3-+ prod-exp cbrt-unprod flip-+ div-inv
3×pow1 distribute-rgt-out--
2×frac-2neg clear-num associate-/l* difference-of-squares
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
3 → 68
Calls
3 calls:
35.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
6.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
11.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series177.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
51.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
53.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify546.0ms

Counts
77 → 77
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
01301924
13751812
215991590
done50001590

prune159.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (log (exp (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))))
2.0b
(log (exp (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))))
22.1b
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
23.7b
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
15×*-un-lft-identity
12×add-cube-cbrt
11×log-pow
10×times-frac
9×exp-prod
6×pow1 log-prod associate-/r* associate-/r/
5×cbrt-undiv div-exp add-log-exp
4×prod-exp cbrt-unprod
3×flip3-+ flip-+ div-inv associate--r+
2×frac-2neg clear-num associate-/l* distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- diff-log rem-log-exp flip--
Counts
4 → 88
Calls
4 calls:
51.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (log (exp (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))))
10.0ms
(log (exp (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))))
10.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
10.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (log (exp (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))))
53.0ms
(log (exp (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))))
55.0ms
(/ (* x x) (+ (* x x) (* (* y 4.0) y)))
55.0ms
(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))

simplify562.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (127.0ms)

IterNodesCost
01602419
14042181
216321945
done50001945

prune231.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes141.0ms

Accuracy

57.9% (13.2b remaining)

Error of 13.6b against oracle of 0.4b and baseline of 31.7b

bsearch208.0ms

Steps
ItersRangePoint
9
4.283497980630725e+128
1.2086931281044804e+136
4.367447801126625e+128
8
4.2706539415928307e+104
2.1878188410446244e+107
2.1620145518824135e+107
9
1.855235282084144e+33
6.217793645765005e+41
4.011625031578035e+38
6
2231369.5462890854
28638621.607503247
28161126.972837694
8
6.0695211452904165e-58
2.2556006266800907e-55
1.1196094733529732e-55
7
-2.4883474419946845e-96
-1.2073393430268885e-97
-1.3841596065667632e-97
6
-3.1442305190809916e+143
-5.062787100137526e+142
-7.710738992849757e+142

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
036128
141128
done41128

end0.0ms

sample358.0ms

Algorithm
intervals
Results
231.0ms8000×body80valid