Details

Time bar (total: 16.6s)

sample84.0ms

Algorithm
intervals
Results
19.0ms182×body80valid
19.0ms27×body2560valid
18.0ms30×body1280valid
10.0ms256×pre80true
2.0ms8×body320valid
1.0ms3×body640valid
1.0ms5×body160valid
1.0ms1×body5120valid

simplify41.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
0.0b
(+ (* x x) (* (* p p) 4))
1.7b
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
15.0b
(sqrt (+ (* x x) (* (* p p) 4)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 56
Calls
4 calls:
36.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
23.0ms
(+ (* x x) (* (* p p) 4))
23.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
48.0ms
(+ (* x x) (* (* p p) 4))
103.0ms
(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
74.0ms
(sqrt (+ (* x x) (* (* p p) 4)))

simplify1.3s

Counts
68 → 68
Iterations
IterNodes
33141
2774
1235
097

prune754.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x))
1.7b
(+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))
1.7b
(log (exp (+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))))
15.0b
(sqrt (+ (* x x) (* (* 4 p) p)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
86×*-un-lft-identity
83×add-sqr-sqrt
82×add-cube-cbrt
39×sqrt-prod
22×associate-/r*
9×add-cbrt-cube add-exp-log
6×pow1 add-log-exp
5×log-pow div-inv
4×log-prod exp-prod insert-posit16
3×cbrt-undiv div-exp associate-/l*
2×flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 rem-log-exp exp-sum associate-/r/
Counts
4 → 154
Calls
4 calls:
11.0ms
(/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x))
18.0ms
(+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))
75.0ms
(log (exp (+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))))
13.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x))
108.0ms
(+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))
86.0ms
(log (exp (+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))))
62.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

simplify2.0s

Counts
166 → 166
Iterations
IterNodes
34655
21571
1641
0268

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(exp (log (+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5)))
1.1b
(log (+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5))
5.3b
(+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5)
15.0b
(sqrt (+ (* x x) (* 4 (* p p))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×log-prod add-log-exp
5×add-exp-log
4×log-div exp-prod flip3-+ add-cbrt-cube flip-+ insert-posit16
3×exp-sum sqrt-prod
2×exp-diff sqrt-div log-pow
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp rem-exp-log
Counts
4 → 61
Calls
4 calls:
23.0ms
(exp (log (+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5)))
12.0ms
(log (+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5))
12.0ms
(+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5)
7.0ms
(sqrt (+ (* x x) (* 4 (* p p))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(exp (log (+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5)))
174.0ms
(log (+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5))
90.0ms
(+ (* (/ 0.5 (sqrt (+ (* x x) (* 4 (* p p))))) x) 0.5)
79.0ms
(sqrt (+ (* x x) (* 4 (* p p))))

simplify2.6s

Counts
73 → 73
Iterations
IterNodes
44522
31748
2634
1246
0114

prune844.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.4b

localize91.0ms

Local error

Found 4 expressions with local error:

1.7b
(log (exp (+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))))
15.0b
(sqrt (+ (* x x) (* (* 4 p) p)))
15.0b
(sqrt (+ (* x x) (* (* 4 p) p)))
15.0b
(sqrt (+ (* x x) (* (* 4 p) p)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
9×add-cube-cbrt sqrt-prod
8×pow1
6×sqrt-div
5×log-pow
4×log-prod exp-prod add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×rem-log-exp exp-sum distribute-lft-out
Counts
4 → 66
Calls
4 calls:
75.0ms
(log (exp (+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))))
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
6.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(log (exp (+ 0.5 (/ 0.5 (/ (sqrt (+ (* x x) (* (* 4 p) p))) x)))))
54.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
55.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))
46.0ms
(sqrt (+ (* x x) (* (* 4 p) p)))

simplify764.0ms

Counts
78 → 78
Iterations
IterNodes
42076
3869
2343
1142
078

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.4b

regimes222.0ms

Accuracy

0% (3.5b remaining)

Error of 13.6b against oracle of 10.1b and baseline of 13.6b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
223
123
018

end0.0ms

sample2.5s

Algorithm
intervals
Results
882.0ms5969×body80valid
579.0ms775×body2560valid
326.0ms634×body1280valid
310.0ms8000×pre80true
144.0ms291×body640valid
69.0ms180×body320valid
45.0ms67×body5120valid
15.0ms84×body160valid