Details

Time bar (total: 14.7s)

sample74.0ms

Algorithm
intervals
Results
15.0ms4×body5120valid
14.0ms32×body2560valid
12.0ms185×body80valid
7.0ms256×pre80true
5.0ms17×body1280valid
3.0ms10×body640valid
1.0ms4×body320valid
1.0ms4×body160valid

simplify68.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite192.0ms

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:
35.0ms
(+ (* (* 4.0 p) p) (* x x))
37.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
68.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
48.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ (* (* 4.0 p) p) (* x x))
63.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
122.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
90.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts
91 → 91

prune494.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
0.0b
(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
1.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite459.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt
8×unpow-prod-down cube-prod
6×pow1 add-log-exp
5×add-exp-log add-cbrt-cube distribute-lft-out
4×cube-div flip3-+ flip-+
3×pow-unpow sqrt-prod
2×cube-mult cbrt-div sqrt-div unpow3 sqr-pow
1×+-commutative pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 pow1/3 pow-exp sum-log rem-cbrt-cube rem-cube-cbrt
Counts
4 → 79
Calls
4 calls:
117.0ms
(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
175.0ms
(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
118.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
46.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)
131.0ms
(cbrt (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
131.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
68.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify627.0ms

Counts
91 → 91

prune489.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(exp (log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)))
1.3b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.9b
(log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
11.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite507.0ms

Algorithm
rewrite-expression-head
Rules
28×log-prod
22×*-un-lft-identity
14×exp-sum
13×add-sqr-sqrt
12×add-cube-cbrt
8×unpow-prod-down cube-prod
6×add-exp-log add-log-exp
5×pow1 distribute-lft-out
4×cube-div log-div exp-prod flip3-+ add-cbrt-cube flip-+
3×rem-log-exp sqrt-prod
2×cube-mult exp-diff sqrt-div unpow3 log-pow sqr-pow
1×+-commutative pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp sum-log rem-exp-log
Counts
4 → 82
Calls
4 calls:
159.0ms
(exp (log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)))
93.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
220.0ms
(log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
29.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series958.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(exp (log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3)))
144.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
475.0ms
(log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
90.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify607.0ms

Counts
94 → 94

prune533.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.7b

localize53.0ms

Local error

Found 4 expressions with local error:

2.9b
(log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
11.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod *-un-lft-identity
13×add-sqr-sqrt
10×add-cube-cbrt
9×sqrt-prod
7×pow1
6×add-exp-log sqrt-div
4×unpow-prod-down flip3-+ cube-prod add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp
2×cube-div log-div distribute-lft-out
1×cube-mult pow-to-exp unpow3 pow-exp log-pow sqr-pow
Counts
4 → 72
Calls
4 calls:
143.0ms
(log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
39.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
47.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series612.0ms

Counts
4 → 12
Calls
4 calls:
377.0ms
(log (pow (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
89.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.5s

Counts
84 → 84

prune667.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.7b

regimes587.0ms

Accuracy

0% (1.1b remaining)

Error of 13.1b against oracle of 12.0b and baseline of 13.1b

bsearch0.0ms

simplify600.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
757.0ms758×body2560valid
532.0ms6052×body80valid
276.0ms8000×pre80true
246.0ms633×body1280valid
76.0ms292×body640valid
30.0ms61×body5120valid
29.0ms128×body320valid
9.0ms76×body160valid