Details

Time bar (total: 14.9s)

sample70.0ms

Algorithm
intervals
Results
15.0ms34×body2560valid
13.0ms185×body80valid
7.0ms20×body1280valid
7.0ms256×pre80true
2.0ms7×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify79.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
96.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
52.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
30.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
362.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
79.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
96.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
68.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify3.1s

Counts
93 → 93
Iterations

Useful iterations: 4 (1.8s)

IterNodesCost
01371776
12821594
26981499
316441483
442611479
done50011479

prune360.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize20.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0)
4.9b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
10×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt
7×sqrt-prod
6×pow1 add-log-exp
5×times-frac
4×sqrt-div
3×flip3-+ associate-/r* flip-+ difference-of-squares
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r/
1×sub-neg flip3-- frac-2neg diff-log prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out--
Counts
4 → 69
Calls
4 calls:
222.0ms
(- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0)
33.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
42.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0)
72.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
68.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts
81 → 81
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01121386
12621302
28321156
332511130
done50001124

prune418.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize27.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity sqrt-prod add-cbrt-cube
7×pow1
6×sqrt-div
4×flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/r*
2×cbrt-undiv div-exp associate-/r/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 68
Calls
4 calls:
34.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
26.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts
80 → 80
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0791257
11961145
27061039
329941003
done5001995

prune462.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.7b

localize31.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.7b
(+ (/ x (exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)

rewrite234.0ms

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:
24.0ms
(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)))
161.0ms
(+ (/ x (exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)

series256.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
80.0ms
(+ (/ x (exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))) 1.0)

simplify1.9s

Counts
69 → 69
Iterations

Useful iterations: 4 (835.0ms)

IterNodesCost
0681121
1170987
2452923
31125869
42667863
done5000863

prune474.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.7b

regimes283.0ms

Accuracy

0% (0.5b remaining)

Error of 13.2b against oracle of 12.8b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12419
done2419

end0.0ms

sample1.0s

Algorithm
intervals
Results
244.0ms6050×body80valid
214.0ms835×body2560valid
118.0ms8000×pre80true
112.0ms568×body1280valid
52.0ms316×body640valid
19.0ms161×body320valid
6.0ms70×body160valid