Details

Time bar (total: 50.8s)

sample554.0ms

Algorithm
intervals
Results
270.0ms1301×body80nan
135.0ms427×body80valid

simplify895.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
3720
2174
154
022

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.7b

localize87.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
9.4b
(pow (/ d h) (/ 1.0 2.0))
14.8b
(pow (/ d l) (/ 1.0 2.0))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
42×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
40×pow-exp
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 190
Calls
4 calls:
59.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
7.0ms
(pow (/ d h) (/ 1.0 2.0))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
65.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
964.0ms
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
110.0ms
(pow (/ d h) (/ 1.0 2.0))
100.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify687.0ms

Counts
202 → 202
Iterations
IterNodes
done5001
11468
0460

prune1.9s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.9b

localize146.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (* M D) (* 2.0 d))
5.6b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.8b
(pow (/ d l) (/ 1.0 2.0))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite483.0ms

Algorithm
rewrite-expression-head
Rules
818×add-exp-log
567×prod-exp
280×pow-exp
187×div-exp
94×pow-to-exp
46×add-cbrt-cube
32×rec-exp 1-exp
28×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
13×pow-unpow unpow-prod-down
9×pow1 cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg associate-*l* pow-prod-down *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 306
Calls
4 calls:
10.0ms
(/ (* M D) (* 2.0 d))
376.0ms
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
7.0ms
(pow (/ d l) (/ 1.0 2.0))
59.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (* M D) (* 2.0 d))
1.3s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
92.0ms
(pow (/ d l) (/ 1.0 2.0))
973.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.1s

Counts
318 → 318
Iterations
IterNodes
done5001
12038
0629

prune2.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.4b

localize200.0ms

Local error

Found 4 expressions with local error:

3.4b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.1b
(/ (* M D) (* 2.0 d))
5.6b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (/ 1 (cbrt l)) (cbrt l)) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
6521×add-exp-log
4653×prod-exp
2614×pow-exp
1922×div-exp
789×pow-to-exp
380×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
34×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-prod cbrt-undiv
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg associate-*l* *-commutative
1×frac-times clear-num associate-/r* pow-pow frac-2neg flip3-- flip-- associate-/l* sqr-pow
Counts
4 → 1243
Calls
4 calls:
9.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
10.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (/ 1 (cbrt l)) (cbrt l)) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
70.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series3.1s

Counts
4 → 12
Calls
4 calls:
278.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
47.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (/ 1 (cbrt l)) (cbrt l)) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.4s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.0s

Counts
1255 → 1255
Iterations
IterNodes
done5001
01514

prune2.9s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.3b

localize182.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
4.4b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l)))
5.1b
(/ (* M D) (* 2.0 d))
5.6b
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (/ 1 (cbrt l)) (cbrt l)) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
6903×add-exp-log
4877×prod-exp
2652×pow-exp
2028×div-exp
796×pow-to-exp
380×rec-exp 1-exp
88×add-cbrt-cube
63×cbrt-unprod
24×cbrt-undiv
14×pow1
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×prod-diff pow-prod-down
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u associate-*r* associate-*l/ log1p-expm1-u add-log-exp
2×clear-num associate-/r* sub-neg frac-2neg times-frac associate-*l* associate-*r/ *-commutative div-inv associate-/l*
1×flip3-- flip-- associate-/l/
Counts
4 → 1273
Calls
4 calls:
101.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
66.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l)))
10.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (/ 1 (cbrt l)) (cbrt l)) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))

series3.1s

Counts
4 → 12
Calls
4 calls:
774.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h)))
903.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l)))
60.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (/ 1 (cbrt l)) (cbrt l)) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt h) (cbrt h))) (* (cbrt l) (cbrt l))) (/ (cbrt h) (cbrt l)))))

simplify972.0ms

Counts
1285 → 1285
Iterations
IterNodes
done5000
01472

prune2.4s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 7.0b

regimes3.1s

Accuracy

7.3% (7.4b remaining)

Error of 15.3b against oracle of 7.9b and baseline of 15.9b

bsearch734.0ms

Steps
ItersRangePoint
5
3.739078058005972e+23
1.2884358372882108e+24
1.0241610527241071e+24
8
-1.3764254372615653e+34
-3.2063577882571644e+30
-3.790337651398802e+31

simplify18.0ms

Iterations
IterNodes
done93
193
071

end0.0ms

sample17.3s

Algorithm
intervals
Results
10.4s38741×body80nan
4.1s12885×body80valid