Details

Time bar (total: 11.5s)

sample180.0ms

Algorithm
intervals
Results
34.0ms78×body5120valid
31.0ms493×body80nan
19.0ms48×body2560valid
14.0ms251×body80valid
11.0ms22×body10240exit
10.0ms36×body1280valid
4.0ms16×body640valid
1.0ms5×body320valid
1.0ms5×body160valid

simplify108.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06026
130425
2346225
3500325
done500325

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.4b

localize24.0ms

Local error

Found 4 expressions with local error:

16.6b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.6b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.6b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.8b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite720.0ms

Algorithm
rewrite-expression-head
Rules
211×add-exp-log add-cbrt-cube
117×prod-exp cbrt-unprod
45×cbrt-undiv div-exp
7×*-un-lft-identity
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt fma-def
4×pow1 expm1-log1p-u times-frac log1p-expm1-u div-inv
3×frac-2neg clear-num associate-/r* associate-/l*
2×sqrt-div frac-add
1×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 156
Calls
4 calls:
41.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
41.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
40.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
589.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series559.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
99.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
99.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
262.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify144.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
05942246
138771589
250011584
done50011584

prune610.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.6b

localize5.0ms

Local error

Found 1 expressions with local error:

3.7b
(* (/ c0 (* 2.0 w)) 0)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log add-cbrt-cube
7×associate-*l*
6×add-sqr-sqrt
4×add-cube-cbrt *-un-lft-identity prod-exp cbrt-unprod
3×pow1 times-frac associate-*r*
2×cbrt-undiv div-exp
1×expm1-log1p-u mul0 pow-prod-down associate-*l/ *-commutative log1p-expm1-u div-inv add-log-exp unswap-sqr
Counts
1 → 30
Calls
1 calls:
23.0ms
(* (/ c0 (* 2.0 w)) 0)

series2.0ms

Counts
1 → 3
Calls
1 calls:
2.0ms
(* (/ c0 (* 2.0 w)) 0)

simplify283.0ms

Counts
33 → 33
Iterations

Useful iterations: 2 (280.0ms)

IterNodesCost
017840
1186124
2500114
done500114

prune84.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 30.2b

localize2.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune25.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.2b

localize32.0ms

Local error

Found 4 expressions with local error:

16.6b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.8b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
27.8b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
27.8b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
73×add-exp-log add-cbrt-cube
39×prod-exp cbrt-unprod
15×cbrt-undiv fma-def div-exp
13×*-un-lft-identity
10×add-log-exp
7×add-sqr-sqrt add-cube-cbrt
6×sqrt-div frac-add
4×pow1 expm1-log1p-u times-frac log1p-expm1-u div-inv
3×+-commutative flip3-- flip3-+ sum-log flip-- flip-+ distribute-lft-out
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 108
Calls
4 calls:
41.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
592.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
585.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
598.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series880.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
262.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
263.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
257.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify126.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
05942538
138772127
250012112
done50012112

prune513.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.2b

regimes431.0ms

Accuracy

0% (2.4b remaining)

Error of 33.9b against oracle of 31.5b and baseline of 33.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042
142
done42

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.0s2260×body5120valid
773.0ms13155×body80nan
626.0ms1715×body2560valid
406.0ms6957×body80valid
274.0ms563×body10240exit
271.0ms950×body1280valid
104.0ms466×body640valid
38.0ms218×body320valid
16.0ms113×body160valid