Details

Time bar (total: 19.8s)

sample109.0ms

Algorithm
intervals
Results
28.0ms202×body80valid
21.0ms16×body1280valid
19.0ms21×body2560valid
13.0ms256×pre80true
5.0ms9×body640valid
2.0ms5×body320valid
1.0ms1×body5120valid
1.0ms2×body160valid

simplify26.0ms

Counts
1 → 1
Iterations
IterNodes
542
442
340
236
129
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5))
0.0b
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
0.4b
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
13×sqrt-prod
12×add-sqr-sqrt
10×add-cube-cbrt
9×add-cbrt-cube add-exp-log
6×pow1 associate-/r* times-frac sqrt-div add-log-exp
4×flip3-+ flip-+ insert-posit16
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r/ distribute-lft-out
1×+-commutative clear-num sum-log frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
69.0ms
(sqrt (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5))
28.0ms
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
45.0ms
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
7.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series563.0ms

Counts
4 → 12
Calls
4 calls:
292.0ms
(sqrt (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5))
105.0ms
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
102.0ms
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
63.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.3s

Counts
88 → 88
Iterations
IterNodes
33186
2882
1289
0125

prune914.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.8b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
0.2b
(log (exp (sqrt (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5))))
0.4b
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
13×add-sqr-sqrt sqrt-prod
12×add-cube-cbrt
9×add-cbrt-cube add-exp-log
8×log-pow
7×exp-prod
6×pow1 associate-/r* times-frac add-log-exp
4×sqrt-div insert-posit16
3×log-prod flip3-+ flip-+
2×cbrt-undiv div-exp associate-/r/ distribute-lft-out
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 rem-log-exp prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
14.0ms
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
114.0ms
(log (exp (sqrt (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5))))
47.0ms
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
312.0ms
(log (exp (sqrt (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5))))
94.0ms
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
47.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.2s

Counts
91 → 91
Iterations
IterNodes
32918
2868
1308
0142

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (* (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5) (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)) (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)))
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))
17.0b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
30×flip3-+ flip-+
28×frac-times
26×cbrt-div
14×associate-*l/
10×add-sqr-sqrt
9×sqrt-prod
8×associate-*r/
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 85
Calls
4 calls:
284.0ms
(cbrt (* (* (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5) (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)) (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
13.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
21.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series307.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(cbrt (* (* (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5) (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)) (+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)))
57.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
54.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
74.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify6.0s

Counts
97 → 97
Iterations
IterNodes
310032
21972
1462
0157

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.8b

localize101.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (* (/ 0.5 (sqrt (+ (* x x) (* (* p 4) p)))) x) 0.5)
17.0b
(sqrt (+ (* x x) (* (* p 4) p)))
17.0b
(sqrt (+ (* x x) (* (* p 4) p)))
17.0b
(sqrt (+ (* x x) (* (* p 4) p)))

rewrite46.0ms

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×add-cbrt-cube add-exp-log insert-posit16
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sub-neg flip3-- diff-log flip--
Counts
4 → 61
Calls
4 calls:
15.0ms
(- (* (/ 0.5 (sqrt (+ (* x x) (* (* p 4) p)))) x) 0.5)
6.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
10.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
13.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (* (/ 0.5 (sqrt (+ (* x x) (* (* p 4) p)))) x) 0.5)
65.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
55.0ms
(sqrt (+ (* x x) (* (* p 4) p)))
58.0ms
(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.2s

Counts
73 → 73
Iterations
IterNodes
43279
31247
2439
1162
071

prune983.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.7b

regimes158.0ms

Accuracy

0% (1.3b remaining)

Error of 14.5b against oracle of 13.2b and baseline of 14.5b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
238
138
028

end0.0ms

sample2.5s

Algorithm
intervals
Results
605.0ms5992×body80valid
544.0ms8000×pre80true
522.0ms738×body2560valid
411.0ms672×body1280valid
164.0ms293×body640valid
45.0ms174×body320valid
35.0ms54×body5120valid
13.0ms77×body160valid