Details

Time bar (total: 15.7s)

sample79.0ms

Algorithm
intervals
Results
18.0ms195×body80valid
16.0ms26×body2560valid
8.0ms256×pre80true
8.0ms16×body1280valid
3.0ms10×body320valid
2.0ms5×body640valid
1.0ms4×body160valid

simplify91.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

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))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite226.0ms

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:
20.0ms
(+ (* (* 4.0 p) p) (* x x))
41.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
113.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
47.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(+ (* (* 4.0 p) p) (* x x))
76.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
111.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
91.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts
91 → 91
Iterations

Useful iterations: 3 (591.0ms)

IterNodesCost
01281657
12771506
27731400
320621385
done50001385

prune387.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.9b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.4b
(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite230.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt log-prod
7×pow1
6×add-log-exp
5×add-exp-log
4×log-div exp-prod flip3-+ exp-sum add-cbrt-cube flip-+
3×sqrt-prod distribute-lft-out
2×exp-diff sqrt-div log-pow
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log rem-exp-log
Counts
4 → 60
Calls
4 calls:
61.0ms
(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
64.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms
(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
99.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
215.0ms
(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
66.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.3s

Counts
72 → 72
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01101434
12311313
25511163
312881114
430861106
done50011105

prune361.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize35.0ms

Local error

Found 4 expressions with local error:

2.4b
(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (- (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0)))))
4.0b
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite396.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
35×log-prod
30×times-frac
23×add-sqr-sqrt
21×add-cube-cbrt
15×distribute-lft-out
12×add-exp-log unpow-prod-down cube-prod
9×add-cbrt-cube
7×pow1
6×sqrt-prod associate-/r/
4×sqrt-div add-log-exp
3×flip3-+ div-exp associate-/r* sum-cubes flip-+
2×cbrt-undiv rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ rem-log-exp frac-sub flip-- div-inv
1×log-div frac-2neg prod-exp clear-num log-pow cbrt-unprod associate-/l*
Counts
4 → 99
Calls
4 calls:
269.0ms
(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (- (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0)))))
36.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
32.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series752.0ms

Counts
4 → 12
Calls
4 calls:
533.0ms
(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (- (/ (* x x) (+ (* (* 4.0 p) p) (* x x))) (* 1.0 (- (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 1.0)))))
76.0ms
(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
70.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify864.0ms

Counts
111 → 111
Iterations

Useful iterations: done (859.0ms)

IterNodesCost
02175118
15304887
216344628
done50004276

prune546.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

localize32.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
26.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
33.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
64.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify3.6s

Counts
72 → 72
Iterations

Useful iterations: 4 (577.0ms)

IterNodesCost
0421060
1100936
2279888
3723848
41565840
54270840
done5001840

prune548.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.3b

regimes124.0ms

Accuracy

0% (3.6b remaining)

Error of 13.3b against oracle of 9.7b and baseline of 13.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
027109
133109
done33109

end0.0ms

sample1.7s

Algorithm
intervals
Results
632.0ms850×body2560valid
387.0ms5977×body80valid
201.0ms8000×pre80true
193.0ms638×body1280valid
85.0ms284×body640valid
24.0ms165×body320valid
8.0ms86×body160valid