Details

Time bar (total: 53.2s)

sample419.0ms

Algorithm
intervals
Results
251.0ms1101×body80nan
96.0ms402×body80valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done5001
31261
2198
158
022

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize58.0ms

Local error

Found 4 expressions with local error:

7.5b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
12.2b
(pow (/ d h) (/ 1 2))
14.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
15.5b
(pow (/ d l) (/ 1 2))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 208
Calls
4 calls:
58.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0ms
(pow (/ d h) (/ 1 2))
67.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
18.0ms
(pow (/ d l) (/ 1 2))

series627.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
79.0ms
(pow (/ d h) (/ 1 2))
103.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
92.0ms
(pow (/ d l) (/ 1 2))

simplify2.9s

Counts
220 → 220
Iterations
IterNodes
done5022
24182
11276
0438

prune1.4s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 14.0b

localize90.0ms

Local error

Found 4 expressions with local error:

3.2b
(/ (* M D) (* 2 d))
7.5b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
14.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
15.5b
(pow (/ d l) (/ 1 2))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
320×add-exp-log
171×prod-exp
96×div-exp
46×add-cbrt-cube pow-exp
28×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
11×pow-to-exp
9×pow1 cbrt-undiv
7×associate-*l/
6×associate-*r/
4×insert-posit16 div-inv add-log-exp
3×frac-times sqrt-div
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- associate-*l* pow-prod-down *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 187
Calls
4 calls:
13.0ms
(/ (* M D) (* 2 d))
216.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
69.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
27.0ms
(pow (/ d l) (/ 1 2))

series1.7s

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* M D) (* 2 d))
1.5s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
106.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
77.0ms
(pow (/ d l) (/ 1 2))

simplify2.6s

Counts
199 → 199
Iterations
IterNodes
done5003
11385
0475

prune1.5s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 13.0b

localize92.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
4.4b
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
7.5b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))) (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
15.5b
(pow (/ d l) (/ 1 2))

rewrite503.0ms

Algorithm
rewrite-expression-head
Rules
176×times-frac
163×add-sqr-sqrt
101×add-exp-log
97×*-un-lft-identity add-cube-cbrt
88×cbrt-prod
83×associate-*r*
61×add-cbrt-cube
53×associate-*l*
41×prod-exp
31×div-exp
28×cbrt-undiv
26×cbrt-unprod
20×unswap-sqr
13×pow-unpow unpow-prod-down
12×div-inv
11×pow1
7×associate-*r/
6×associate-*l/ pow-exp
4×frac-times insert-posit16 add-log-exp
3×pow-to-exp sqrt-div pow-prod-down *-commutative
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- associate-/r/ flip--
1×pow-pow sqr-pow
Counts
4 → 284
Calls
4 calls:
72.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
74.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
330.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))) (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
13.0ms
(pow (/ d l) (/ 1 2))

series1.9s

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
149.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
1.5s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))) (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
72.0ms
(pow (/ d l) (/ 1 2))

simplify2.5s

Counts
296 → 296
Iterations
IterNodes
done5000
11631
0520

prune4.4s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 8.2b

localize113.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ M (/ (* d 2) D))
4.4b
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
4.4b
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
7.5b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))) (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
191×times-frac
165×add-sqr-sqrt
99×*-un-lft-identity add-cube-cbrt
95×add-exp-log
88×cbrt-prod
84×sqrt-div
83×frac-times associate-*r*
79×add-cbrt-cube
67×associate-*r/
53×associate-*l*
50×associate-*l/
34×prod-exp cbrt-unprod
33×cbrt-undiv div-exp
26×pow1
20×unswap-sqr
16×flip3-- flip--
15×pow-prod-down div-inv
7×associate-/r*
4×insert-posit16 add-log-exp
3×associate-/r/ *-commutative associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in
1×clear-num frac-2neg
Counts
4 → 338
Calls
4 calls:
13.0ms
(/ M (/ (* d 2) D))
50.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
70.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
1.2s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))) (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ M (/ (* d 2) D))
150.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
156.0ms
(* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l)))
1.3s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l)))) (sqrt (/ (cbrt d) (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))) (* (/ M (/ (* d 2) D)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

simplify3.2s

Counts
350 → 350
Iterations
IterNodes
done5002
11906
0569

prune4.6s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 7.5b

regimes3.6s

Accuracy

0% (2.8b remaining)

Error of 10.1b against oracle of 7.3b and baseline of 10.1b

bsearch0.0ms

simplify17.0ms

Iterations
IterNodes
done39
139
030

end0.0ms

sample16.3s

Algorithm
intervals
Results
10.2s38005×body80nan
4.0s12701×body80valid