Details

Time bar (total: 15.6s)

sample42.0ms

Algorithm
intervals
Results
8.0ms188×body80valid
8.0ms27×body2560valid
5.0ms21×body1280valid
4.0ms256×pre80true
2.0ms13×body640valid
1.0ms2×body5120valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify45.0ms

Counts
1 → 1
Iterations
IterNodes
done40
440
338
234
127
014

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
25.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms
(+ (* (* 4.0 p) p) (* x x))
65.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
39.0ms
(+ (* (* 4.0 p) p) (* x x))
82.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.3s

Counts
91 → 91
Iterations
IterNodes
done5001
34116
21078
1305
0127

prune484.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* (* p p) 4.0))
0.4b
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
0.4b
(log (exp (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)))
14.0b
(sqrt (+ (* x x) (* (* p p) 4.0)))

rewrite221.0ms

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
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 → 55
Calls
4 calls:
7.0ms
(+ (* x x) (* (* p p) 4.0))
58.0ms
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
149.0ms
(log (exp (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)))
6.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* x x) (* (* p p) 4.0))
92.0ms
(+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)
88.0ms
(log (exp (+ (/ x (sqrt (+ (* x x) (* (* p p) 4.0)))) 1.0)))
56.0ms
(sqrt (+ (* x x) (* (* p p) 4.0)))

simplify1.9s

Counts
67 → 67
Iterations
IterNodes
done5021
32959
2730
1246
0101

prune520.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.6b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp
7×pow1
5×unswap-sqr
4×flip3-+ sqrt-div prod-exp flip-+
3×associate-*l*
2×+-commutative sum-log div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
20.0ms
(+ (* (* 4.0 p) p) (* x x))
70.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
27.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (* (* 4.0 p) p) (* x x))
79.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
114.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
79.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify3.2s

Counts
98 → 98
Iterations
IterNodes
done5007
34656
21273
1420
0151

prune485.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.9b

localize90.0ms

Local error

Found 4 expressions with local error:

2.6b
(+ (* (/ (* x x) (sqrt (+ (* p (* 4.0 p)) (* x x)))) (/ x (+ (* p (* 4.0 p)) (* x x)))) (* 1.0 (* 1.0 1.0)))
14.0b
(sqrt (+ (* p (* 4.0 p)) (* x x)))
14.0b
(sqrt (+ (* p (* 4.0 p)) (* x x)))
14.0b
(sqrt (+ (* p (* 4.0 p)) (* x x)))

rewrite131.0ms

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-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log
Counts
4 → 56
Calls
4 calls:
60.0ms
(+ (* (/ (* x x) (sqrt (+ (* p (* 4.0 p)) (* x x)))) (/ x (+ (* p (* 4.0 p)) (* x x)))) (* 1.0 (* 1.0 1.0)))
25.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
27.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
18.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ (* (/ (* x x) (sqrt (+ (* p (* 4.0 p)) (* x x)))) (/ x (+ (* p (* 4.0 p)) (* x x)))) (* 1.0 (* 1.0 1.0)))
86.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
78.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))
83.0ms
(sqrt (+ (* p (* 4.0 p)) (* x x)))

simplify2.4s

Counts
68 → 68
Iterations
IterNodes
done5002
33089
2693
1199
071

prune379.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

regimes355.0ms

Accuracy

75.3% (0.3b remaining)

Error of 13.9b against oracle of 13.6b and baseline of 15.0b

bsearch2.0ms

simplify8.0ms

Iterations
IterNodes
done39
139
029

end0.0ms

sample1.5s

Algorithm
intervals
Results
406.0ms651×body1280valid
347.0ms5946×body80valid
240.0ms756×body2560valid
222.0ms8000×pre80true
86.0ms322×body640valid
23.0ms182×body320valid
21.0ms61×body5120valid
7.0ms82×body160valid