Details

Time bar (total: 14.9s)

sample72.0ms

Algorithm
intervals
Results
14.0ms256×pre80true
12.0ms188×body80valid
11.0ms27×body2560valid
7.0ms21×body1280valid
3.0ms13×body640valid
1.0ms2×body5120valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify33.0ms

Counts
1 → 1
Iterations
IterNodes
done40
440
338
234
127
014

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
30.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms
(+ (* (* 4.0 p) p) (* x x))
50.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
47.0ms
(+ (* (* 4.0 p) p) (* x x))
99.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.7s

Counts
91 → 91
Iterations
IterNodes
done5001
34116
21078
1305
0127

prune553.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.4b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite362.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×pow1
5×log-pow
4×log-prod exp-prod add-cbrt-cube add-exp-log
3×flip3-+ sqrt-prod flip-+
2×+-commutative sum-log sqrt-div distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp exp-sum
Counts
4 → 55
Calls
4 calls:
19.0ms
(+ (* (* 4.0 p) p) (* x x))
62.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
251.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
28.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* (* 4.0 p) p) (* x x))
87.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
101.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
74.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.3s

Counts
67 → 67
Iterations
IterNodes
done5006
33045
2750
1246
0101

prune418.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp
7×pow1
5×unswap-sqr
4×flip3-+ sqrt-div prod-exp flip-+
3×associate-*l*
2×+-commutative sum-log div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
20.0ms
(+ (* (* 4.0 p) p) (* x x))
85.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
33.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* (* 4.0 p) p) (* x x))
85.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
108.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
80.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.4s

Counts
98 → 98
Iterations
IterNodes
done5007
34656
21273
1420
0151

prune425.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.9b

localize64.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (* (/ (* x x) (sqrt (+ (* p (* 4.0 p)) (* x x)))) (/ x (+ (* p (* 4.0 p)) (* x x)))) (* 1.0 (* 1.0 1.0)))
14.0b
(sqrt (+ (* p (* 4.0 p)) (* x x)))
14.0b
(sqrt (+ (* p (* 4.0 p)) (* x x)))
14.0b
(sqrt (+ (* p (* 4.0 p)) (* x x)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-+ add-cbrt-cube add-exp-log flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log
Counts
4 → 56
Calls
4 calls:
37.0ms
(+ (* (/ (* x x) (sqrt (+ (* p (* 4.0 p)) (* x x)))) (/ x (+ (* p (* 4.0 p)) (* x x)))) (* 1.0 (* 1.0 1.0)))
15.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
15.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
15.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ (* (/ (* x x) (sqrt (+ (* p (* 4.0 p)) (* x x)))) (/ x (+ (* p (* 4.0 p)) (* x x)))) (* 1.0 (* 1.0 1.0)))
59.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
55.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
58.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))

simplify1.7s

Counts
68 → 68
Iterations
IterNodes
done5002
33089
2693
1199
071

prune385.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

regimes359.0ms

Accuracy

75.3% (0.3b remaining)

Error of 13.9b against oracle of 13.6b and baseline of 15.0b

bsearch2.0ms

simplify8.0ms

Iterations
IterNodes
done39
139
029

end0.0ms

sample1.6s

Algorithm
intervals
Results
401.0ms5946×body80valid
275.0ms182×body320valid
239.0ms756×body2560valid
175.0ms651×body1280valid
160.0ms8000×pre80true
85.0ms322×body640valid
23.0ms61×body5120valid
7.0ms82×body160valid