Details

Time bar (total: 14.9s)

sample76.0ms

Algorithm
intervals
Results
18.0ms202×body80valid
13.0ms24×body2560valid
8.0ms256×pre80true
6.0ms13×body1280valid
5.0ms13×body640valid
1.0ms4×body320valid

simplify51.0ms

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: 11.8b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 add-cube-cbrt
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div sum-log
1×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
Counts
3 → 38
Calls
3 calls:
20.0ms
(+ (* (* 4.0 p) p) (* x x))
87.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
28.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series265.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ (* (* 4.0 p) p) (* x x))
115.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
89.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts
47 → 47
Iterations

Useful iterations: 3 (522.0ms)

IterNodesCost
079761
1203711
2635637
31870612
done5000612

prune211.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×sqrt-div
4×add-exp-log cbrt-prod flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3 distribute-lft-out
Counts
4 → 59
Calls
4 calls:
74.0ms
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
34.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
43.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
27.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series715.0ms

Counts
4 → 12
Calls
4 calls:
499.0ms
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
76.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
70.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
70.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts
71 → 71
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0861203
11991093
24831025
31181978
42752970
done5000968

prune430.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.3b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
20×*-un-lft-identity
18×add-cube-cbrt pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 125
Calls
4 calls:
136.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
93.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
37.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
37.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
86.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
63.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.1s

Counts
137 → 137
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01413702
12882238
28352066
328791948
done50011887

prune366.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize24.0ms

Local error

Found 4 expressions with local error:

7.8b
(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
17.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.1b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
18.1b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log cbrt-div flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×pow1/3 sqrt-div
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
4 → 53
Calls
4 calls:
155.0ms
(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
42.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
23.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
32.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series779.0ms

Counts
4 → 12
Calls
4 calls:
308.0ms
(+ 1.0 (/ x (* (* (sqrt (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
77.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
206.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
188.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
65 → 65
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01421752
13251648
29361478
333181433
done50001400

prune485.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.5b

regimes295.0ms

Accuracy

0% (1.5b remaining)

Error of 14.8b against oracle of 13.3b and baseline of 14.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02547
13247
done3247

end0.0ms

sample2.0s

Algorithm
intervals
Results
807.0ms851×body2560valid
399.0ms5980×body80valid
250.0ms636×body1280valid
142.0ms8000×pre80true
78.0ms299×body640valid
25.0ms151×body320valid
9.0ms83×body160valid