Details

Time bar (total: 12.2s)

sample57.0ms

Algorithm
intervals
Results
23.0ms196×body80valid
8.0ms27×body2560valid
4.0ms256×pre80true
4.0ms17×body1280valid
1.0ms8×body640valid
0.0ms1×body5120valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

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×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
28.0ms
(+ (* (* 4.0 p) p) (* x x))
46.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
84.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
39.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (* (* 4.0 p) p) (* x x))
69.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
114.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
86.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify836.0ms

Counts
91 → 91
Iterations

Useful iterations: done (832.0ms)

IterNodesCost
01281657
13071506
214361422
done50001406

prune362.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite233.0ms

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×add-exp-log unpow-prod-down flip3-+ cube-prod add-cbrt-cube flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log sum-cubes
Counts
4 → 62
Calls
4 calls:
145.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
80.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts
74 → 74
Iterations

Useful iterations: 3 (707.0ms)

IterNodesCost
0751289
11981144
27361072
336051041
done50011041

prune509.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.6b

localize65.0ms

Local error

Found 4 expressions with local error:

1.0b
(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite849.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
12×add-sqr-sqrt
10×log-pow
9×add-cube-cbrt exp-prod sqrt-prod
8×pow1
6×sqrt-div
5×distribute-lft-out
4×add-exp-log unpow-prod-down log-prod cube-prod add-cbrt-cube 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:
730.0ms
(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
40.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
32.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
43.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
67.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
84.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify877.0ms

Counts
79 → 79
Iterations

Useful iterations: 3 (268.0ms)

IterNodesCost
0881310
11871149
24881058
314401027
done50001027

prune435.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.6b

localize40.0ms

Local error

Found 4 expressions with local error:

5.1b
(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sqrt-prod
10×add-cube-cbrt *-un-lft-identity
9×pow1
8×sqrt-div
6×log-prod exp-prod exp-sum
4×add-exp-log sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square log-pow
2×log-div exp-diff
1×rem-exp-log
Counts
4 → 67
Calls
4 calls:
22.0ms
(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
24.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
32.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series238.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(exp (log (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
79 → 79
Iterations

Useful iterations: 4 (933.0ms)

IterNodesCost
0811225
11491047
2357959
3949919
42578901
done5000901

prune470.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.6b

regimes319.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03095
13995
done3995

end0.0ms

sample1.8s

Algorithm
intervals
Results
596.0ms719×body2560valid
426.0ms6025×body80valid
196.0ms638×body1280valid
153.0ms8000×pre80true
65.0ms322×body640valid
54.0ms50×body5120valid
24.0ms169×body320valid
7.0ms77×body160valid