Details

Time bar (total: 14.2s)

sample75.0ms

Algorithm
intervals
Results
19.0ms206×body80valid
9.0ms17×body1280valid
7.0ms256×pre80true
5.0ms9×body2560valid
4.0ms11×body640valid
2.0ms3×body5120valid
2.0ms6×body320valid
1.0ms4×body160valid

simplify67.0ms

Counts
1 → 1
Iterations
IterNodes
done41
541
440
338
234
127
014

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp pow-prod-down div-inv distribute-lft-out
Counts
4 → 81
Calls
4 calls:
71.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
27.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
80.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
38.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series677.0ms

Counts
4 → 12
Calls
4 calls:
373.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
81.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
126.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
96.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.4s

Counts
93 → 93
Iterations
IterNodes
done5000
33660
2925
1295
0137

prune554.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.7b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
10×pow1
9×add-cbrt-cube
6×sqrt-div add-log-exp
5×unswap-sqr
4×flip3-+ prod-exp flip-+
3×sqrt-pow1 associate-*l* associate-*r/
2×pow1/2 div-exp pow-prod-down associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sum-log 1-exp un-div-inv *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
10.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
94.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
9.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
45.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
320.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
82.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
106.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
84.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.2s

Counts
100 → 100
Iterations
IterNodes
done5000
21479
1420
0161

prune564.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
4.6b
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
16.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
9×times-frac
6×cbrt-prod add-cbrt-cube add-exp-log add-log-exp
4×pow1 cbrt-div
3×associate-/r* flip3-+ flip-+ associate-/l*
2×pow1/3
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv distribute-lft-out
Counts
4 → 65
Calls
4 calls:
7.0ms
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
122.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
16.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series628.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))))
250.0ms
(+ 1.0 (/ (/ x (fabs (cbrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))
169.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
169.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.1s

Counts
77 → 77
Iterations
IterNodes
done5001
21721
1405
0163

prune463.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.7b

localize75.0ms

Local error

Found 4 expressions with local error:

16.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
16.7b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube pow1/3 add-exp-log flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
12.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
12.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
140.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
143.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
140.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.8s

Counts
64 → 64
Iterations
IterNodes
done5001
33621
2543
1149
062

prune520.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

regimes223.0ms

Accuracy

0% (1.7b remaining)

Error of 14.6b against oracle of 12.9b and baseline of 14.6b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done26
126
020

end0.0ms

sample2.0s

Algorithm
intervals
Results
477.0ms8000×pre80true
393.0ms6035×body80valid
356.0ms764×body2560valid
276.0ms596×body1280valid
128.0ms63×body5120valid
90.0ms310×body640valid
28.0ms151×body320valid
10.0ms81×body160valid