Details

Time bar (total: 27.6s)

sample85.0ms

Algorithm
intervals
Results
32.0ms299×body80valid
9.0ms87×body80nan

simplify5.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01718
13618
28118
317618
442218
5117418
6457018
done500018

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.3b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b
(/ (* M D) (* 2.0 d))
10.7b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite125.0ms

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:
29.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
8.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
20.0ms
(/ (* M D) (* 2.0 d))
58.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
622.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
463.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
39.0ms
(/ (* M D) (* 2.0 d))
1.2s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.1s

Counts
125 → 125
Iterations

Useful iterations: 2 (364.0ms)

IterNodesCost
02362311
15772083
222621927
done50001927

prune417.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.4b

localize33.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
4.5b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.3b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.7b
(/ (* M D) (* 2.0 d))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv flip-- associate-/l*
Counts
4 → 128
Calls
4 calls:
7.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
26.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
41.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
18.0ms
(/ (* M D) (* 2.0 d))

series2.6s

Counts
4 → 12
Calls
4 calls:
513.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
935.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
40.0ms
(/ (* M D) (* 2.0 d))

simplify1.3s

Counts
140 → 140
Iterations

Useful iterations: 2 (478.0ms)

IterNodesCost
02692521
16522089
224821883
done50001883

prune464.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize39.0ms

Local error

Found 4 expressions with local error:

5.3b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
5.4b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))

rewrite309.0ms

Algorithm
rewrite-expression-head
Rules
1402×add-exp-log
907×prod-exp
366×div-exp
305×pow-exp
61×pow-to-exp
57×rec-exp 1-exp
51×add-cbrt-cube
21×cbrt-unprod
19×add-sqr-sqrt
16×associate-*r*
14×add-cube-cbrt *-un-lft-identity
12×times-frac
11×cbrt-undiv
10×associate-*l*
6×pow1 unpow-prod-down
4×div-inv add-log-exp
3×unswap-sqr
2×frac-2neg clear-num associate-/r* *-commutative associate-/l* sqr-pow
1×associate-*r/ pow-prod-down un-div-inv
Counts
4 → 332
Calls
4 calls:
184.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
38.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
19.0ms
(/ (* M D) (* 2.0 d))
20.0ms
(/ (* M D) (* 2.0 d))

series2.0s

Counts
4 → 12
Calls
4 calls:
934.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
944.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
33.0ms
(/ (* M D) (* 2.0 d))
41.0ms
(/ (* M D) (* 2.0 d))

simplify1.5s

Counts
344 → 344
Iterations

Useful iterations: 2 (660.0ms)

IterNodesCost
044110490
18726098
229355622
done50015622

prune550.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize45.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) (/ 1 l))))
5.3b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) (/ 1 l))
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (* M D) (* 2.0 d))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
3341×add-exp-log
2396×prod-exp
714×div-exp
600×pow-exp
120×pow-to-exp
113×rec-exp 1-exp
63×add-cbrt-cube
38×cbrt-unprod
13×cbrt-undiv add-sqr-sqrt associate-*r*
12×add-cube-cbrt *-un-lft-identity
11×times-frac
7×pow1
4×add-log-exp
3×sqrt-prod div-inv
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ associate-*l* pow-prod-down un-div-inv *-commutative flip--
Counts
4 → 544
Calls
4 calls:
5.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) (/ 1 l))))
1.3s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) (/ 1 l))
15.0ms
(/ (* M D) (* 2.0 d))
23.0ms
(/ (* M D) (* 2.0 d))

series1.6s

Counts
4 → 12
Calls
4 calls:
622.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) (/ 1 l))))
869.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt h))) (/ 1 l))
60.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))

simplify2.3s

Counts
556 → 556
Iterations

Useful iterations: done (2.2s)

IterNodesCost
066623115
1112618795
2338511216
done50009607

prune446.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.2b

regimes1.1s

Accuracy

-15% (2.7b remaining)

Error of 10.0b against oracle of 7.3b and baseline of 9.6b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04372
15572
done5572

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.5s9262×body80valid
317.0ms3211×body80nan