Details

Time bar (total: 30.9s)

sample83.0ms

Algorithm
intervals
Results
46.0ms305×body80valid
12.0ms91×body80nan

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
44693
3589
293
136
017

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize30.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))
11.7b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
368×add-cbrt-cube add-exp-log
190×prod-exp cbrt-unprod
114×cbrt-undiv div-exp
16×add-sqr-sqrt
13×associate-*r*
12×*-un-lft-identity times-frac add-cube-cbrt
10×pow1
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×pow-prod-down associate-*r/ sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 198
Calls
4 calls:
4.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
12.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
193.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series409.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
52.0ms
(/ (* M D) (* 2 d))
41.0ms
(/ (* M D) (* 2 d))
132.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.4s

Counts
210 → 210
Iterations
IterNodes
23936
1957
0321

prune3.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize64.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
4.0b
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
110×add-exp-log
90×add-cbrt-cube
84×add-sqr-sqrt times-frac
80×cbrt-prod associate-*r*
56×*-un-lft-identity add-cube-cbrt
44×prod-exp cbrt-unprod
34×cbrt-undiv div-exp
10×associate-*l* unswap-sqr
8×pow1
6×div-inv
4×insert-posit16 add-log-exp
2×frac-times clear-num associate-/r* frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
Counts
4 → 210
Calls
4 calls:
60.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
52.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
11.0ms
(/ (* M D) (* 2 d))
14.0ms
(/ (* M D) (* 2 d))

series410.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
149.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
37.0ms
(/ (* M D) (* 2 d))
54.0ms
(/ (* M D) (* 2 d))

simplify1.2s

Counts
222 → 222
Iterations
IterNodes
23435
1706
0236

prune4.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize104.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
4.0b
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
59×add-cbrt-cube
46×add-sqr-sqrt
43×times-frac
40×cbrt-prod associate-*r*
31×*-un-lft-identity add-cube-cbrt
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
7×pow1
5×associate-*l* unswap-sqr
4×insert-posit16 div-inv add-log-exp
3×sqrt-prod
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 143
Calls
4 calls:
8.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
61.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
18.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))

series508.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
169.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
47.0ms
(/ (* M D) (* 2 d))
47.0ms
(/ (* M D) (* 2 d))

simplify1.4s

Counts
155 → 155
Iterations
IterNodes
23871
1790
0272

prune4.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

localize124.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))))
3.1b
(sqrt (- 1 (* (* (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) 1)) (/ (cbrt (cbrt h)) (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
97×add-exp-log
77×add-cbrt-cube
40×prod-exp cbrt-unprod
30×cbrt-undiv div-exp
14×add-sqr-sqrt
9×times-frac
8×*-un-lft-identity associate-*r* add-cube-cbrt
7×pow1
5×associate-*l*
4×insert-posit16 div-inv add-log-exp
3×sqrt-prod unswap-sqr
2×cbrt-prod clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 119
Calls
4 calls:
66.0ms
(* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))))
4.0ms
(sqrt (- 1 (* (* (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) 1)) (/ (cbrt (cbrt h)) (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
11.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))

series472.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))))
192.0ms
(sqrt (- 1 (* (* (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) 1)) (/ (cbrt (cbrt h)) (cbrt l))) (* (* (/ (* M D) (* 2 d)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
40.0ms
(/ (* M D) (* 2 d))
38.0ms
(/ (* M D) (* 2 d))

simplify1.5s

Counts
131 → 131
Iterations
IterNodes
23275
1657
0225

prune3.9s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.8b

regimes1.6s

Accuracy

17.2% (1.0b remaining)

Error of 7.7b against oracle of 6.7b and baseline of 8.0b

bsearch2.0ms

simplify70.0ms

Iterations
IterNodes
278
178
059

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.8s9339×body80valid
600.0ms3124×body80nan