Details

Time bar (total: 14.1s)

sample54.0ms

Algorithm
intervals
Results
10.0ms185×body80valid
8.0ms28×body1280valid
8.0ms23×body2560valid
5.0ms256×pre80true
2.0ms11×body640valid
1.0ms6×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify62.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite162.0ms

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:
17.0ms
(+ (* (* 4.0 p) p) (* x x))
31.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
36.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (* (* 4.0 p) p) (* x x))
81.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
90.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify733.0ms

Counts
91 → 91
Iterations

Useful iterations: done (729.0ms)

IterNodesCost
01281657
13071506
214361422
done50001406

prune304.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
5×distribute-lft-out
4×add-exp-log unpow-prod-down flip3-+ cube-prod add-cbrt-cube flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log sum-cubes
Counts
4 → 62
Calls
4 calls:
167.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
27.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
34.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
93.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
85.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts
74 → 74
Iterations

Useful iterations: 3 (724.0ms)

IterNodesCost
0751289
11981144
27361072
336051041
done50011041

prune480.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.7b

localize50.0ms

Local error

Found 4 expressions with local error:

13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
34.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
28.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
45.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
83.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
71.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
71.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts
72 → 72
Iterations

Useful iterations: 4 (907.0ms)

IterNodesCost
0421060
1100936
2290888
3833848
42241840
done5001840

prune757.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.7b

localize77.0ms

Local error

Found 4 expressions with local error:

13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
34.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
78.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
84.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts
72 → 72
Iterations

Useful iterations: 4 (836.0ms)

IterNodesCost
0421060
1100936
2290888
3833848
42241840
done5001840

prune716.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.7b

regimes496.0ms

Accuracy

0% (0.5b remaining)

Error of 13.8b against oracle of 13.3b and baseline of 13.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12419
done2419

end0.0ms

sample2.2s

Algorithm
intervals
Results
494.0ms5975×body80valid
367.0ms778×body2560valid
336.0ms54×body5120valid
277.0ms8000×pre80true
250.0ms671×body1280valid
78.0ms316×body640valid
27.0ms139×body320valid
8.0ms67×body160valid