Details

Time bar (total: 17.3s)

sample57.0ms

Algorithm
intervals
Results
13.0ms202×body80valid
10.0ms24×body2560valid
6.0ms256×pre80true
4.0ms13×body1280valid
3.0ms13×body640valid
1.0ms4×body320valid

simplify92.0ms

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

localize20.0ms

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)))

rewrite177.0ms

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:
39.0ms
(+ (* (* 4.0 p) p) (* x x))
100.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
37.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series275.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(+ (* (* 4.0 p) p) (* x x))
111.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
103.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.2s

Counts
47 → 47
Iterations

Useful iterations: 3 (569.0ms)

IterNodesCost
079761
1203711
2635637
31870612
done5000612

prune270.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize18.0ms

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)))

rewrite223.0ms

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:
97.0ms
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
44.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
47.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
32.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series774.0ms

Counts
4 → 12
Calls
4 calls:
494.0ms
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
93.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
98.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.5s

Counts
71 → 71
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0861203
11991093
24831025
31181978
42752970
done5000968

prune467.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.5b

localize17.0ms

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)))

rewrite355.0ms

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:
177.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
92.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
48.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
482.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
68.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.5s

Counts
137 → 137
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01413702
12882238
28352066
328791948
done50011887

prune522.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize42.0ms

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)))

rewrite280.0ms

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:
167.0ms
(+ 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))))))))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
29.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series763.0ms

Counts
4 → 12
Calls
4 calls:
322.0ms
(+ 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))))))))
76.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
195.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
170.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.0s

Counts
65 → 65
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01421752
13251648
29361478
333181433
done50001400

prune526.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.5b

regimes287.0ms

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

sample2.2s

Algorithm
intervals
Results
631.0ms8000×pre80true
516.0ms5980×body80valid
340.0ms851×body2560valid
296.0ms636×body1280valid
75.0ms299×body640valid
27.0ms151×body320valid
10.0ms83×body160valid