Details

Time bar (total: 14.8s)

sample59.0ms

Algorithm
intervals
Results
12.0ms183×body80valid
10.0ms27×body2560valid
8.0ms26×body1280valid
7.0ms256×pre80true
3.0ms11×body640valid
1.0ms6×body320valid
0.0ms2×body160valid
0.0ms1×body5120valid

simplify63.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12717
23417
33817
44017
54117
done4117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
2 → 27
Calls
2 calls:
115.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
39.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series173.0ms

Counts
2 → 6
Calls
2 calls:
101.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.8s

Counts
33 → 33
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
067553
1169508
2456468
31142445
42765443
done5000443

prune207.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

localize33.0ms

Local error

Found 3 expressions with local error:

0.4b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite518.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 log-pow add-log-exp
4×log-prod exp-prod
3×add-exp-log sqrt-prod add-cbrt-cube
2×flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp exp-sum sum-log
Counts
3 → 44
Calls
3 calls:
374.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
114.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
29.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series302.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
91.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
92.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.7s

Counts
53 → 53
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
090918
1196836
2491753
31182730
42755728
done5000728

prune299.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.1b

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)))))
8.6b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite375.0ms

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:
190.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
52.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
50.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
118.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
87.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
89.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.6s

Counts
137 → 137
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01413702
12882238
28352066
328791948
done50011887

prune602.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 15.1b

localize32.0ms

Local error

Found 4 expressions with local error:

8.6b
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.6b
(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.2b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite452.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt
7×pow1
6×sqrt-prod add-log-exp
5×log-pow
4×add-exp-log log-prod exp-prod sqrt-div add-cbrt-cube
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
1×+-commutative rem-log-exp exp-sum sum-log
Counts
4 → 59
Calls
4 calls:
85.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
309.0ms
(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
31.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
88.0ms
(log (exp (+ 1.0 (/ x (* (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))))
66.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
67.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.4s

Counts
71 → 71
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
0911703
11991070
2552975
31525942
44032938
done5001938

prune299.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 15.1b

regimes8.0ms