Details

Time bar (total: 8.1s)

sample33.0ms

Algorithm
intervals
Results
7.0ms201×body80valid
5.0ms24×body2560valid
4.0ms256×pre80true
3.0ms14×body1280valid
1.0ms7×body640valid
1.0ms8×body320valid
0.0ms2×body160valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23317
33717
43917
54017
done4017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

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))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite53.0ms

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×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms
(+ (* (* 4.0 p) p) (* x x))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series220.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
32.0ms
(+ (* (* 4.0 p) p) (* x x))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts
91 → 91
Iterations

Useful iterations: 3 (450.0ms)

IterNodesCost
01281657
12791506
28491400
337461385
done50011385

prune274.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.3b

localize13.0ms

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)))))
3.1b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

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 div-exp sum-log associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
8.0ms
(+ (* (* 4.0 p) p) (* x x))
32.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series220.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (* 4.0 p) p) (* x x))
57.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify631.0ms

Counts
98 → 98
Iterations

Useful iterations: done (628.0ms)

IterNodesCost
01521717
13871427
212231271
done50001269

prune258.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
4 → 54
Calls
4 calls:
23.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
9.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
68.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.1s

Counts
66 → 66
Iterations

Useful iterations: 4 (437.0ms)

IterNodesCost
0671106
11691016
2430936
31115890
42600886
done5000886

prune261.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity sqrt-prod
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×add-exp-log flip3-+ add-cbrt-cube flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log distribute-lft-out
Counts
4 → 57
Calls
4 calls:
23.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
9.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
49.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.1s

Counts
69 → 69
Iterations

Useful iterations: 4 (428.0ms)

IterNodesCost
0671083
1169976
2430912
31115869
42600863
done5000863

prune250.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

regimes219.0ms

Accuracy

0% (0.4b remaining)

Error of 13.1b against oracle of 12.7b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
12419
done2419

end0.0ms

sample989.0ms

Algorithm
intervals
Results
342.0ms795×body2560valid
209.0ms6089×body80valid
110.0ms8000×pre80true
104.0ms604×body1280valid
45.0ms292×body640valid
16.0ms143×body320valid
5.0ms77×body160valid