Details

Time bar (total: 16.8s)

sample106.0ms

Algorithm
intervals
Results
31.0ms27×body2560valid
25.0ms195×body80valid
11.0ms256×pre80true
9.0ms16×body1280valid
4.0ms5×body5120valid
3.0ms7×body320valid
1.0ms3×body640valid
1.0ms3×body160valid

simplify28.0ms

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: 12.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
0.0b
(+ (* x x) (* p (* 4 p)))
0.7b
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
16.1b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
8×add-log-exp
6×associate-/r* times-frac
5×pow1
4×flip3-+ sqrt-div flip-+ insert-posit16
2×cbrt-undiv +-commutative sum-log div-exp associate-/r/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv distribute-lft-out associate-/l*
Counts
4 → 71
Calls
4 calls:
14.0ms
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
11.0ms
(+ (* x x) (* p (* 4 p)))
34.0ms
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series258.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
40.0ms
(+ (* x x) (* p (* 4 p)))
97.0ms
(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
52.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify2.0s

Counts
83 → 83
Iterations
IterNodes
34812
21040
1312
0121

prune994.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* p (* 4 p)))
0.2b
(* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))
3.6b
(+ (* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
16.1b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×associate-*r*
19×add-sqr-sqrt
18×*-un-lft-identity times-frac add-cube-cbrt
16×add-cbrt-cube
12×prod-exp sqrt-prod
10×pow1
8×add-log-exp
6×cbrt-unprod
4×flip3-+ sqrt-div div-exp flip-+ insert-posit16
3×pow-prod-down
2×cbrt-undiv +-commutative rec-exp sum-log 1-exp associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 90
Calls
4 calls:
17.0ms
(+ (* x x) (* p (* 4 p)))
42.0ms
(* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))
26.0ms
(+ (* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
18.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ (* x x) (* p (* 4 p)))
74.0ms
(* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p))))))
106.0ms
(+ (* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
74.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify3.1s

Counts
102 → 102
Iterations
IterNodes
35641
21478
1470
0162

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 4 (* p p)) (* x x))
0.7b
(+ (/ (* x 0.5) (sqrt (+ (* 4 (* p p)) (* x x)))) 0.5)
0.8b
(log (exp (+ (/ (* x 0.5) (sqrt (+ (* 4 (* p p)) (* x x)))) 0.5)))
16.1b
(sqrt (+ (* 4 (* p p)) (* x x)))

rewrite525.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×pow1
5×log-pow
4×log-prod exp-prod add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ sqrt-prod flip-+
2×+-commutative sum-log sqrt-div distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp exp-sum
Counts
4 → 59
Calls
4 calls:
28.0ms
(+ (* 4 (* p p)) (* x x))
152.0ms
(+ (/ (* x 0.5) (sqrt (+ (* 4 (* p p)) (* x x)))) 0.5)
317.0ms
(log (exp (+ (/ (* x 0.5) (sqrt (+ (* 4 (* p p)) (* x x)))) 0.5)))
27.0ms
(sqrt (+ (* 4 (* p p)) (* x x)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(+ (* 4 (* p p)) (* x x))
111.0ms
(+ (/ (* x 0.5) (sqrt (+ (* 4 (* p p)) (* x x)))) 0.5)
101.0ms
(log (exp (+ (/ (* x 0.5) (sqrt (+ (* 4 (* p p)) (* x x)))) 0.5)))
82.0ms
(sqrt (+ (* 4 (* p p)) (* x x)))

simplify1.0s

Counts
71 → 71
Iterations
IterNodes
32775
2749
1255
0105

prune744.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.8b

localize62.0ms

Local error

Found 4 expressions with local error:

3.6b
(+ (* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
16.1b
(sqrt (+ (* x x) (* p (* 4 p))))
16.1b
(sqrt (+ (* x x) (* p (* 4 p))))
16.1b
(sqrt (+ (* x x) (* p (* 4 p))))

rewrite56.0ms

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×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log
Counts
4 → 60
Calls
4 calls:
25.0ms
(+ (* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
6.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
12.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(+ (* (* 0.5 x) (/ 1 (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
74.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
66.0ms
(sqrt (+ (* x x) (* p (* 4 p))))
71.0ms
(sqrt (+ (* x x) (* p (* 4 p))))

simplify690.0ms

Counts
72 → 72
Iterations
IterNodes
32001
2555
1181
070

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.8b

regimes85.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 13.0b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
219
119
015

end0.0ms

sample3.2s

Algorithm
intervals
Results
858.0ms6020×body80valid
722.0ms8000×pre80true
657.0ms751×body2560valid
407.0ms634×body1280valid
139.0ms305×body640valid
95.0ms68×body5120valid
76.0ms152×body320valid
43.0ms70×body160valid