Details

Time bar (total: 13.6s)

sample44.0ms

Algorithm
intervals
Results
16.0ms306×body80valid
6.0ms104×body80nan

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28018
317218
440518
5124718
6495518
done500018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.4b
(/ (* M D) (* 2.0 d))
11.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
8.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
406.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
364.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms
(/ (* M D) (* 2.0 d))
684.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify657.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (198.0ms)

IterNodesCost
02362311
16102083
224151927
done50001927

prune393.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

3.6b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.4b
(/ (* M D) (* 2.0 d))
6.4b
(/ (* M D) (* 2.0 d))
8.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
33×add-cbrt-cube
30×prod-exp
28×add-sqr-sqrt
23×div-exp
15×times-frac
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
10×pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
7×unpow-prod-down
6×unswap-sqr
5×pow1
4×div-inv add-log-exp
3×sqrt-prod sqr-pow
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 110
Calls
4 calls:
2.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.1s

Counts
4 → 12
Calls
4 calls:
364.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
32.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(/ (* M D) (* 2.0 d))
700.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify618.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (181.0ms)

IterNodesCost
02112420
15792019
223081799
done50011799

prune425.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize17.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.4b
(/ (* M D) (* 2.0 d))
6.4b
(/ (* M D) (* 2.0 d))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
79×add-exp-log
35×add-cbrt-cube
30×prod-exp
24×div-exp
14×add-sqr-sqrt
10×cbrt-undiv pow-exp cbrt-unprod
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×pow-to-exp sqr-pow
1×*-commutative
Counts
4 → 100
Calls
4 calls:
10.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
4.0ms
(/ (* M D) (* 2.0 d))
4.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
733.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
700.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
28.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(/ (* M D) (* 2.0 d))

simplify773.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (155.0ms)

IterNodesCost
01881746
15021640
221571398
done50001398

prune373.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize27.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (* M D) (* 2.0 d))
17.6b
(cbrt (/ (* M D) (* 2.0 d)))
17.6b
(cbrt (/ (* M D) (* 2.0 d)))
17.6b
(cbrt (/ (* M D) (* 2.0 d)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log add-cbrt-cube
15×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv times-frac div-exp prod-exp cbrt-unprod div-inv add-log-exp
3×cbrt-div pow1/3
1×frac-2neg clear-num associate-/r* associate-/l*
Counts
4 → 63
Calls
4 calls:
4.0ms
(/ (* M D) (* 2.0 d))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))
3.0ms
(cbrt (/ (* M D) (* 2.0 d)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (* M D) (* 2.0 d))
102.0ms
(cbrt (/ (* M D) (* 2.0 d)))
102.0ms
(cbrt (/ (* M D) (* 2.0 d)))
105.0ms
(cbrt (/ (* M D) (* 2.0 d)))

simplify448.0ms

Counts
75 → 75
Iterations

Useful iterations: done (445.0ms)

IterNodesCost
0102944
1246921
21064797
done5001794

prune379.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.3b

regimes753.0ms

Accuracy

-56.7% (2.4b remaining)

Error of 9.7b against oracle of 7.3b and baseline of 8.8b

bsearch54.0ms

Steps
ItersRangePoint
0
-6.0706316482279e-314
-1.976262583365e-323
-3.0353158251021e-314
6
-4.4879316068299356e+294
-6.981255098223496e+293
-4.434769257142831e+294

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03252
14249
done4249

end0.0ms

sample1.2s

Algorithm
intervals
Results
512.0ms9329×body80valid
178.0ms3112×body80nan