Details

Time bar (total: 27.2s)

sample89.0ms

Algorithm
intervals
Results
22.0ms196×body80valid
17.0ms23×body2560valid
9.0ms256×pre80true
8.0ms18×body640valid
7.0ms12×body1280valid
2.0ms6×body320valid
0.0ms1×body160valid

simplify169.0ms

Counts
1 → 1
Iterations
IterNodes
done40
440
338
234
127
014

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize124.0ms

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))))
0.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite493.0ms

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×associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×flip3-+ flip-+ insert-posit16
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp pow-prod-down div-inv distribute-lft-out
Counts
4 → 85
Calls
4 calls:
175.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
85.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
155.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
67.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series896.0ms

Counts
4 → 12
Calls
4 calls:
515.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
134.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
157.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
90.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify5.3s

Counts
97 → 97
Iterations
IterNodes
done5001
32590
2839
1299
0141

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

localize246.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
4.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×pow1 associate-/r* times-frac sqrt-prod
4×cbrt-undiv flip3-+ sqrt-div div-exp associate-/r/ flip-+ insert-posit16 add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
80.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
70.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
74.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
48.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
91.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
81.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
83.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.7s

Counts
92 → 92
Iterations
IterNodes
done5001
21074
1235
081

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.2b

localize276.0ms

Local error

Found 4 expressions with local error:

4.2b
(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
4.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
21×add-sqr-sqrt add-cbrt-cube
16×*-un-lft-identity
15×associate-*r* add-cube-cbrt
14×times-frac
13×prod-exp
11×pow1
7×cbrt-unprod
6×div-exp sqrt-prod
4×cbrt-undiv flip3-+ sqrt-div associate-/r/ flip-+ insert-posit16 add-log-exp
3×associate-/r* pow-prod-down unswap-sqr
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp div-inv
1×clear-num frac-2neg associate-*l* associate-*r/ un-div-inv *-commutative associate-/l*
Counts
4 → 100
Calls
4 calls:
180.0ms
(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
92.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
47.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
66.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (* x x) (/ 1 (+ (* (* 4.0 p) p) (* x x))))
74.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
82.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify4.2s

Counts
112 → 112
Iterations
IterNodes
done5363
22297
1450
0146

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

localize204.0ms

Local error

Found 4 expressions with local error:

2.6b
(/ x (/ (+ (* (* 4.0 p) p) (* x x)) x))
4.5b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
15.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
52×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
16×associate-/r*
14×add-cbrt-cube add-exp-log
6×pow1 sqrt-prod div-inv
5×cbrt-undiv div-exp
4×sqrt-div insert-posit16 associate-/l* add-log-exp
3×flip3-+ associate-/r/ flip-+
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×prod-exp cbrt-unprod
Counts
4 → 127
Calls
4 calls:
56.0ms
(/ x (/ (+ (* (* 4.0 p) p) (* x x)) x))
64.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
46.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
46.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ x (/ (+ (* (* 4.0 p) p) (* x x)) x))
67.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
71.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.7s

Counts
139 → 139
Iterations
IterNodes
done5023
22128
1568
0207

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

regimes746.0ms

Accuracy

0% (0.7b remaining)

Error of 13.8b against oracle of 13.0b and baseline of 13.8b

bsearch0.0ms

simplify15.0ms

Iterations
IterNodes
done33
133
024

end0.0ms

sample2.0s

Algorithm
intervals
Results
501.0ms6029×body80valid
362.0ms325×body640valid
321.0ms745×body2560valid
289.0ms8000×pre80true
224.0ms620×body1280valid
31.0ms157×body320valid
29.0ms59×body5120valid
8.0ms65×body160valid