Details

Time bar (total: 29.7s)

sample225.0ms

Algorithm
intervals
Results
41.0ms66×body5120valid
32.0ms416×body80nan
28.0ms57×body2560valid
17.0ms229×body80valid
17.0ms28×body10240exit
13.0ms31×body1280valid
8.0ms15×body640valid
1.0ms6×body320valid
1.0ms4×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02152
16052
229550
3326950
done500045

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.6b

localize31.0ms

Local error

Found 4 expressions with local error:

19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.0b
(/ (* c0 (* d d)) (* (* w h) (* D D)))
25.2b
(+ (/ (* 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:
50.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
75.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
61.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
868.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
123.0ms
(/ (* c0 (* d d)) (* (* w h) (* D D)))
116.0ms
(/ (* 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))))

simplify2.0s

Counts
168 → 168
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01614866
14844432
231242971
done50022933

prune556.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 32.2b

localize8.0ms

Local error

Found 1 expressions with local error:

6.2b
(* (/ c0 (* 2.0 w)) 0)

rewrite44.0ms

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:
42.0ms
(* (/ c0 (* 2.0 w)) 0)

series3.0ms

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

simplify3.2s

Counts
33 → 33
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
069299
116078
247242
3212242
done500142

prune113.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.5b
(* (cbrt c0) (cbrt c0))
0.6b
(cbrt c0)
0.6b
(cbrt c0)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod
21×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×pow1
8×pow1/3
6×swap-sqr associate-*r* associate-*l*
5×add-exp-log
4×unswap-sqr
3×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
3 → 68
Calls
3 calls:
15.0ms
(* (cbrt c0) (cbrt c0))
1.0ms
(cbrt c0)
1.0ms
(cbrt c0)

series668.0ms

Counts
3 → 9
Calls
3 calls:
276.0ms
(* (cbrt c0) (cbrt c0))
216.0ms
(cbrt c0)
176.0ms
(cbrt c0)

simplify5.4s

Counts
77 → 77
Iterations

Useful iterations: done (5.4s)

IterNodesCost
065483
1119380
2327362
31104347
44523342
done5001334

prune374.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 30.5b

localize57.0ms

Local error

Found 4 expressions with local error:

8.4b
(/ d (* D D))
14.4b
(sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M))))
24.0b
(fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))
48.0b
(fma (/ (* c0 d) (* w h)) (/ d (* D D)) (sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac sqrt-prod associate-/l*
2×cbrt-undiv div-exp fma-udef
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 58
Calls
4 calls:
22.0ms
(/ d (* D D))
4.0ms
(sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M))))
1.0ms
(fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))
1.0ms
(fma (/ (* c0 d) (* w h)) (/ d (* D D)) (sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ d (* D D))
344.0ms
(sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M))))
470.0ms
(fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))
367.0ms
(fma (/ (* c0 d) (* w h)) (/ d (* D D)) (sqrt (fma (* (/ d D) (pow (/ d D) 3)) (* (/ c0 (* w h)) (/ c0 (* w h))) (- (* M M)))))

simplify3.0s

Counts
70 → 70
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01151563
12531492
28021174
345421172
done50001172

prune540.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 29.7b

regimes766.0ms

Accuracy

0% (3.1b remaining)

Error of 33.2b against oracle of 30.1b and baseline of 33.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
189
done89

end0.0ms

sample7.6s

Algorithm
intervals
Results
1.7s2317×body5120valid
1.2s12746×body80nan
973.0ms1704×body2560valid
601.0ms6570×body80valid
452.0ms961×body1280valid
436.0ms577×body10240exit
146.0ms411×body640valid
61.0ms233×body320valid
24.0ms124×body160valid