Details

Time bar (total: 11.1s)

sample54.0ms

Algorithm
intervals
Results
11.0ms195×body80valid
8.0ms22×body2560valid
7.0ms25×body1280valid
5.0ms256×pre80true
2.0ms8×body640valid
1.0ms4×body320valid
0.0ms2×body160valid

simplify49.0ms

Counts
1 → 1
Iterations
IterNodes
done41
541
440
338
234
127
014

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize30.0ms

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)))))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite212.0ms

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:
26.0ms
(+ (* (* 4.0 p) p) (* x x))
86.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
20.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* (* 4.0 p) p) (* x x))
342.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
98.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
93.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify604.0ms

Counts
63 → 63
Iterations
IterNodes
done5000
21081
1256
099

prune401.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0))) 3))
0.5b
(pow (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0))) 3)
0.9b
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
13.8b
(sqrt (+ (* x x) (* (* p p) 4.0)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
13×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
9×pow1
8×unpow-prod-down cube-prod
7×sqrt-prod
6×sqrt-div add-log-exp
5×add-cbrt-cube add-exp-log
4×cube-div pow-pow flip3-+ associate-*r/ flip-+
3×pow-unpow sqrt-pow1
2×cube-mult cbrt-div pow1/2 unpow3 sqr-pow
1×pow-to-exp +-commutative rem-sqrt-square sum-log pow1/3 pow-prod-down pow-exp rem-cbrt-cube sqrt-pow2 distribute-lft-out rem-cube-cbrt
Counts
4 → 83
Calls
4 calls:
4.0ms
(cbrt (pow (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0))) 3))
32.0ms
(pow (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0))) 3)
57.0ms
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
10.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
377.0ms
(cbrt (pow (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0))) 3))
599.0ms
(pow (sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0))) 3)
102.0ms
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
74.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

simplify1.1s

Counts
95 → 95
Iterations
IterNodes
done5000
21806
1412
0142

prune520.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* p p) 4.0)
0.0b
(sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)))
0.9b
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
13.8b
(sqrt (+ (* x x) (* (* p p) 4.0)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity
6×add-cube-cbrt add-log-exp
4×sqrt-div pow-prod-down sqrt-prod
3×sqrt-pow1 flip3-+ associate-*r* prod-exp cbrt-unprod flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square sum-log associate-*l* *-commutative distribute-lft-out unswap-sqr
Counts
4 → 59
Calls
4 calls:
30.0ms
(* (* p p) 4.0)
35.0ms
(sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)))
74.0ms
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
7.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (* p p) 4.0)
390.0ms
(sqrt (* 0.5 (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)))
124.0ms
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
63.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

simplify603.0ms

Counts
71 → 71
Iterations
IterNodes
done5000
21263
1286
0116

prune355.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 3))
13.8b
(sqrt (+ (* x x) (* (* p p) 4.0)))
13.8b
(sqrt (+ (* x x) (* (* p p) 4.0)))
13.8b
(sqrt (+ (* x x) (* (* p p) 4.0)))

rewrite92.0ms

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:
70.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 3))
7.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))
7.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))
7.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 3))
60.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))
56.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))
65.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

simplify1.6s

Counts
74 → 74
Iterations
IterNodes
done5000
33846
2735
1196
075

prune425.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.8b

regimes219.0ms

Accuracy

0% (0.3b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done18
118
014

end0.0ms

sample1.8s

Algorithm
intervals
Results
627.0ms6015×body80valid
383.0ms741×body2560valid
229.0ms639×body1280valid
180.0ms8000×pre80true
102.0ms301×body640valid
28.0ms59×body5120valid
23.0ms153×body320valid
9.0ms92×body160valid