Details

Time bar (total: 12.5s)

sample88.0ms

Algorithm
intervals
Results
15.0ms195×body80valid
11.0ms21×body2560valid
10.0ms28×body1280valid
6.0ms256×pre80true
1.0ms2×body5120valid
1.0ms6×body320valid
1.0ms4×body640valid

simplify71.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize28.0ms

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
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite233.0ms

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:
90.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
75.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
31.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
33.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series644.0ms

Counts
4 → 12
Calls
4 calls:
382.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
111.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
66.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
85.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts
93 → 93
Iterations

Useful iterations: 3 (814.0ms)

IterNodesCost
01371776
12951594
29241523
335931483
done50001483

prune441.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.7b

localize45.0ms

Local error

Found 4 expressions with local error:

1.4b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
13.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite215.0ms

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:
80.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
54.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
75.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
96.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.1s

Counts
81 → 81
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01111406
13021317
218671189
done50001187

prune551.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.0b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
13.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 94
Calls
4 calls:
36.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
27.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
107.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
76.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify675.0ms

Counts
106 → 106
Iterations

Useful iterations: done (671.0ms)

IterNodesCost
01622389
13642152
214171993
done50001973

prune559.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.7b

localize55.0ms

Local error

Found 4 expressions with local error:

8.0b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (/ x (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
13.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log cbrt-div flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×pow1/3 sqrt-div
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 52
Calls
4 calls:
7.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (/ x (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
41.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
15.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series803.0ms

Counts
4 → 12
Calls
4 calls:
381.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ (/ x (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
104.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
162.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
156.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify787.0ms

Counts
64 → 64
Iterations

Useful iterations: done (785.0ms)

IterNodesCost
01441757
13601650
214121480
done50011408

prune583.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.7b

regimes261.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02252
12952
done2952

end0.0ms

sample2.2s

Algorithm
intervals
Results
556.0ms608×body1280valid
469.0ms5996×body80valid
395.0ms745×body2560valid
242.0ms8000×pre80true
78.0ms334×body640valid
65.0ms59×body5120valid
32.0ms178×body320valid
9.0ms80×body160valid