Details

Time bar (total: 41.6s)

sample362.0ms

Algorithm
intervals
Results
106.0ms70×body5120valid
64.0ms51×body2560valid
52.0ms379×body80nan
29.0ms41×body1280valid
29.0ms201×body80valid
22.0ms18×body10240exit
5.0ms9×body640valid
3.0ms7×body320valid
1.0ms4×body160valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5207
32972
2280
159
021

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.7b

localize51.0ms

Local error

Found 4 expressions with local error:

15.8b
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
26.3b
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
199×add-cbrt-cube add-exp-log
81×prod-exp cbrt-unprod
72×cbrt-undiv div-exp
11×associate-*r/
9×associate-/l/
8×sqrt-div frac-add
7×frac-times
6×*-un-lft-identity add-log-exp
5×associate-*l/
4×add-sqr-sqrt pow1 flip3-+ add-cube-cbrt flip-+ insert-posit16
3×clear-num associate-/r* frac-2neg times-frac flip3-- div-inv flip-- associate-/l*
1×+-commutative sum-log distribute-lft-out
Counts
4 → 156
Calls
4 calls:
46.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
63.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
72.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
78.0ms
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series1.2s

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
90.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
101.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
905.0ms
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify2.7s

Counts
168 → 168
Iterations
IterNodes
done5049
23555
1665
0215

prune979.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 49.9b

localize98.0ms

Local error

Found 4 expressions with local error:

15.8b
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
26.3b
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
26.3b
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
134×add-cbrt-cube add-exp-log
54×prod-exp cbrt-unprod
48×cbrt-undiv div-exp
16×sqrt-div frac-add
10×frac-times associate-*r/
8×*-un-lft-identity flip3-+ flip-+ add-log-exp
6×flip3-- associate-*l/ flip-- associate-/l/
4×add-sqr-sqrt pow1 add-cube-cbrt insert-posit16
2×+-commutative clear-num associate-/r* sum-log frac-2neg times-frac div-inv distribute-lft-out associate-/l*
Counts
4 → 132
Calls
4 calls:
67.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
50.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
100.0ms
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
97.0ms
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series2.0s

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
93.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
891.0ms
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))
937.0ms
(+ (sqrt (* (+ M (/ (* (* c0 (/ d D)) (/ d D)) (* w h))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify2.8s

Counts
144 → 144
Iterations
IterNodes
done5049
23555
1665
0215

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 49.9b

localize59.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
15.8b
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
15.8b
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
29.6b
(+ (sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
134×add-cbrt-cube add-exp-log
54×prod-exp cbrt-unprod
48×cbrt-undiv div-exp
16×sqrt-div
10×frac-times associate-*r/
8×frac-add
7×pow1 flip3-+ flip-+
6×*-un-lft-identity flip3-- associate-*l/ flip-- add-log-exp associate-/l/
4×add-sqr-sqrt add-cube-cbrt insert-posit16
2×clear-num associate-/r* frac-2neg sqrt-pow1 times-frac div-inv associate-/l*
1×+-commutative sum-log pow1/2 pow-prod-down sqrt-prod distribute-lft-out
Counts
4 → 131
Calls
4 calls:
102.0ms
(sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
69.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
48.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
115.0ms
(+ (sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

series1.9s

Counts
4 → 12
Calls
4 calls:
805.0ms
(sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M)))
125.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
102.0ms
(/ (* (* c0 (/ d D)) (/ d D)) (* w h))
914.0ms
(+ (sqrt (* (+ M (/ (* c0 (/ d D)) (/ (* w h) (/ d D)))) (- (/ (* (* c0 (/ d D)) (/ d D)) (* w h)) M))) (/ (* (* c0 (/ d D)) (/ d D)) (* w h)))

simplify3.0s

Counts
143 → 143
Iterations
IterNodes
done5001
23734
1706
0227

prune914.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 45.6b

localize49.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* c0 (/ d D)) w)
7.0b
(- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M))
14.3b
(sqrt (- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M)))
26.3b
(+ (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (sqrt (- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube add-exp-log
8×add-sqr-sqrt sqrt-div add-log-exp
7×*-un-lft-identity add-cube-cbrt
6×frac-add
5×pow1 flip3-- flip--
4×cbrt-undiv div-exp sqrt-prod insert-posit16
3×associate-/r* times-frac associate-*r/
2×frac-times associate-*l/ prod-exp cbrt-unprod difference-of-squares
1×+-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+ div-inv associate-/l* associate-/l/
Counts
4 → 74
Calls
4 calls:
26.0ms
(/ (* c0 (/ d D)) w)
268.0ms
(- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M))
483.0ms
(sqrt (- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M)))
660.0ms
(+ (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (sqrt (- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M))))

series940.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (* c0 (/ d D)) w)
323.0ms
(- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M))
292.0ms
(sqrt (- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M)))
295.0ms
(+ (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (sqrt (- (* (* (/ (/ d D) h) (/ (* c0 (/ d D)) w)) (* (/ (/ d D) h) (/ (* c0 (/ d D)) w))) (* M M))))

simplify1.7s

Counts
86 → 86
Iterations
IterNodes
done5000
22096
1519
0186

prune729.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 21.4b

regimes1.8s

Accuracy

0.2% (12.4b remaining)

Error of 33.7b against oracle of 21.4b and baseline of 33.7b

bsearch793.0ms

Steps
ItersRangePoint
9
1.543960985167607e-18
4.309827058074858e-09
2.9331498702830513e-09
8
-1.39518314170493e-34
-3.656145425498872e-37
-1.3791872014049456e-34
8
-7.898649155445275e+34
-1.1663228295461918e+31
-1.1915796734409398e+31

simplify20.0ms

Iterations
IterNodes
done63
163
049

end0.0ms

sample14.0s

Algorithm
intervals
Results
3.4s2263×body5120valid
3.4s13010×body80nan
2.4s1817×body2560valid
1.2s6718×body80valid
1.1s877×body1280valid
782.0ms616×body10240exit
273.0ms443×body640valid
120.0ms229×body320valid
28.0ms118×body160valid