Details

Time bar (total: 13.2s)

sample68.0ms

Algorithm
intervals
Results
14.0ms188×body80valid
11.0ms23×body2560valid
8.0ms20×body1280valid
6.0ms256×pre80true
5.0ms14×body640valid
2.0ms7×body320valid
1.0ms3×body160valid
0.0ms1×body5120valid

simplify57.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.2b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-log-exp
7×*-un-lft-identity
6×add-sqr-sqrt
5×add-cube-cbrt
4×flip3-+ add-cbrt-cube sqrt-div add-exp-log sqrt-prod flip-+
3×sqrt-pow1
2×+-commutative sum-log pow1/2 associate-*r/
1×rem-sqrt-square pow-prod-down distribute-lft-out
Counts
4 → 51
Calls
4 calls:
14.0ms
(+ (* (* 4.0 p) p) (* x x))
79.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
94.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
20.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (* (* 4.0 p) p) (* x x))
412.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
114.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify653.0ms

Counts
63 → 63
Iterations

Useful iterations: done (650.0ms)

IterNodesCost
0991088
12561002
21081921
done5000905

prune498.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.3b

localize51.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
5×distribute-lft-out
4×unpow-prod-down flip3-+ add-cbrt-cube cube-prod add-exp-log flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log sum-cubes
Counts
4 → 62
Calls
4 calls:
165.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
35.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
20.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
82.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
82.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts
74 → 74
Iterations

Useful iterations: 3 (762.0ms)

IterNodesCost
0751289
11981144
27361072
335721041
done50001041

prune624.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.3b

localize416.0ms

Local error

Found 4 expressions with local error:

1.2b
(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite637.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
12×add-sqr-sqrt
10×log-pow
9×exp-prod add-cube-cbrt sqrt-prod
8×pow1
6×sqrt-div
5×distribute-lft-out
4×log-prod unpow-prod-down add-cbrt-cube cube-prod add-exp-log add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×rem-log-exp exp-sum sum-cubes
Counts
4 → 67
Calls
4 calls:
558.0ms
(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
30.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
73.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
65.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify861.0ms

Counts
79 → 79
Iterations

Useful iterations: 3 (289.0ms)

IterNodesCost
0881310
11871149
24881058
314611027
done50011027

prune678.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.3b

localize63.0ms

Local error

Found 4 expressions with local error:

12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.4b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
13.4b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
20.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
19.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
146.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
142.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts
68 → 68
Iterations

Useful iterations: done (1.7s)

IterNodesCost
0781114
11731038
2603958
33775906
done5000894

prune599.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

regimes487.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03270
14070
done4070

end0.0ms

sample1.7s

Algorithm
intervals
Results
498.0ms796×body2560valid
370.0ms5963×body80valid
247.0ms8000×pre80true
211.0ms615×body1280valid
58.0ms323×body640valid
24.0ms163×body320valid
20.0ms54×body5120valid
8.0ms86×body160valid