Details

Time bar (total: 40.2s)

sample339.0ms

Algorithm
intervals
Results
75.0ms429×body80nan
56.0ms254×body80valid
55.0ms75×body5120valid
44.0ms59×body2560valid
14.0ms17×body10240exit
11.0ms26×body1280valid
5.0ms14×body640valid
2.0ms9×body320valid
1.0ms5×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02152
16052
230350
3343550
done500045

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.4b

localize27.0ms

Local error

Found 4 expressions with local error:

17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.6b
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.1s

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:
59.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
59.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
62.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
862.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series704.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
114.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
142.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
317.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify845.0ms

Counts
168 → 168
Iterations

Useful iterations: done (835.0ms)

IterNodesCost
01614866
16194432
done50003209

prune634.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 30.0b

localize9.0ms

Local error

Found 1 expressions with local error:

4.9b
(* (/ c0 (* 2.0 w)) 0)

rewrite45.0ms

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:
43.0ms
(* (/ c0 (* 2.0 w)) 0)

series3.0ms

Counts
1 → 3
Calls
1 calls:
3.0ms
(* (/ c0 (* 2.0 w)) 0)

simplify1.4s

Counts
33 → 33
Iterations

Useful iterations: 2 (175.0ms)

IterNodesCost
069299
118890
287342
done500042

prune159.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 28.7b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune66.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 28.7b

localize109.0ms

Local error

Found 4 expressions with local error:

17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
20.7b
(/ (+ (pow (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) 3) (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (- (fma (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) (* (/ (* (pow d 2) c0) (* (* w h) D)) (/ (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) D))))
37.9b
(+ (pow (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) 3) (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))

rewrite515.0ms

Algorithm
rewrite-expression-head
Rules
144×add-exp-log add-cbrt-cube
78×prod-exp cbrt-unprod
71×*-un-lft-identity
31×cbrt-undiv div-exp
29×times-frac
25×distribute-lft-out
24×unpow-prod-down cube-prod
21×add-sqr-sqrt add-cube-cbrt
14×fma-def
11×associate-/l*
8×cube-div
6×add-log-exp
5×associate-/r* sum-cubes
4×pow1 expm1-log1p-u sqrt-div associate-*r/ frac-add log1p-expm1-u associate-/l/
3×flip3-- frac-2neg clear-num flip-- div-inv
2×flip3-+ sqrt-prod associate-/r/ flip-+
1×+-commutative cube-mult unpow3 sum-log sqr-pow
Counts
4 → 184
Calls
4 calls:
66.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
58.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
287.0ms
(/ (+ (pow (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) 3) (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (- (fma (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) (* (/ (* (pow d 2) c0) (* (* w h) D)) (/ (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) D))))
92.0ms
(+ (pow (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) 3) (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))

series14.0s

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
134.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
4.2s
(/ (+ (pow (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) 3) (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (- (fma (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) (* (/ (* (pow d 2) c0) (* (* w h) D)) (/ (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) D))))
9.5s
(+ (pow (sqrt (* (fma (/ c0 (* w h)) (/ (* d d) (* D D)) M) (- (/ (* c0 (* d d)) (* (* w h) (* D D))) M))) 3) (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3))

simplify799.0ms

Counts
196 → 196
Iterations

Useful iterations: done (783.0ms)

IterNodesCost
027017808
191616977
done500115731

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 28.7b

regimes1.1s

Accuracy

0% (2.8b remaining)

Error of 33.8b against oracle of 31.0b and baseline of 33.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033
done33

end0.0ms

sample15.0s

Algorithm
intervals
Results
3.0s1735×body2560valid
2.9s13429×body80nan
2.7s2263×body5120valid
1.1s915×body1280valid
1.1s6820×body80valid
753.0ms608×body10240exit
730.0ms462×body640valid
264.0ms133×body160valid
121.0ms237×body320valid