Details

Time bar (total: 13.9s)

sample82.0ms

Algorithm
intervals
Results
29.0ms27×body2560valid
17.0ms192×body80valid
11.0ms26×body1280valid
8.0ms256×pre80true
1.0ms4×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
540
440
338
234
127
014

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))
0.0b
(* (* p p) 4)
0.9b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
17.1b
(sqrt (+ (* x x) (* (* p p) 4)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
27×associate-*r*
20×*-un-lft-identity times-frac add-cube-cbrt
14×add-cbrt-cube add-exp-log
13×sqrt-prod
12×pow1
6×add-log-exp
5×prod-exp cbrt-unprod
4×sqrt-div associate-*l* pow-prod-down insert-posit16 unswap-sqr
3×flip3-+ flip-+
2×associate-/r/ *-commutative
1×cbrt-undiv +-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 div-exp associate-*r/ div-inv
Counts
4 → 93
Calls
4 calls:
24.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))
15.0ms
(* (* p p) 4)
28.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))
47.0ms
(* (* p p) 4)
110.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
58.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

simplify1.8s

Counts
105 → 105
Iterations
IterNodes
33762
21162
1429
0169

prune498.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* (* 4 p) p))
0.0b
(* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))
0.9b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p))))) 0.5)
17.1b
(sqrt (+ (* x x) (* (* 4 p) p)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×associate-*r*
20×times-frac
19×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×pow1
4×flip3-+ sqrt-div flip-+ insert-posit16
3×associate-*l* unswap-sqr
2×+-commutative sum-log prod-exp associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*r/ *-commutative div-inv
Counts
4 → 85
Calls
4 calls:
8.0ms
(+ (* x x) (* (* 4 p) p))
27.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))
12.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p))))) 0.5)
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* x x) (* (* 4 p) p))
81.0ms
(* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))
100.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p))))) 0.5)
59.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

simplify2.1s

Counts
97 → 97
Iterations
IterNodes
35109
21247
1393
0150

prune423.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.0b

localize53.0ms

Local error

Found 4 expressions with local error:

17.1b
(sqrt (+ (* x x) (* (* 4 p) p)))
17.1b
(sqrt (+ (* x x) (* (* 4 p) p)))
17.1b
(sqrt (+ (* x x) (* (* 4 p) p)))
18.8b
(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*r/
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 cbrt-div *-un-lft-identity add-cube-cbrt
6×sqrt-div
5×frac-times associate-*l/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 66
Calls
4 calls:
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
350.0ms
(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))))

series323.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
72.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
57.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
130.0ms
(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* 4 p) p)))))))

simplify1.4s

Counts
78 → 78
Iterations
IterNodes
42877
31130
2441
1176
079

prune457.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 14.0b

localize81.0ms

Local error

Found 4 expressions with local error:

15.4b
(/ (* (* x x) x) (+ (* x x) (* (* 4 p) p)))
17.1b
(sqrt (+ (* x x) (* (* 4 p) p)))
17.1b
(sqrt (+ (* x x) (* (* 4 p) p)))
17.1b
(sqrt (+ (* x x) (* (* 4 p) p)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
7×pow1
6×sqrt-div
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×cbrt-undiv rem-sqrt-square associate-/r* sqrt-pow1 times-frac pow1/2 div-exp prod-exp cbrt-unprod
2×associate-/r/
1×clear-num frac-2neg div-inv associate-/l*
Counts
4 → 74
Calls
4 calls:
23.0ms
(/ (* (* x x) x) (+ (* x x) (* (* 4 p) p)))
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
13.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (* (* x x) x) (+ (* x x) (* (* 4 p) p)))
66.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
56.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
50.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

simplify1.4s

Counts
86 → 86
Iterations
IterNodes
33799
2882
1233
087

prune593.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.0b

regimes225.0ms

Accuracy

0% (0.4b remaining)

Error of 13.3b against oracle of 12.9b and baseline of 13.3b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
232
132
023

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.2s6068×body80valid
606.0ms743×body2560valid
361.0ms586×body1280valid
350.0ms8000×pre80true
128.0ms306×body640valid
78.0ms167×body320valid
40.0ms49×body5120valid
17.0ms81×body160valid