Details

Time bar (total: 52.3s)

sample561.0ms

Algorithm
intervals
Results
334.0ms1293×body80nan
123.0ms396×body80valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5001
31261
2198
158
022

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.6b

localize81.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.7b
(pow (/ d l) (/ 1 2))
11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.0b
(pow (/ d h) (/ 1 2))

rewrite117.0ms

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:
42.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.0ms
(pow (/ d l) (/ 1 2))
55.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0ms
(pow (/ d h) (/ 1 2))

series648.0ms

Counts
4 → 12
Calls
4 calls:
365.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
86.0ms
(pow (/ d l) (/ 1 2))
104.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
93.0ms
(pow (/ d h) (/ 1 2))

simplify2.9s

Counts
220 → 220
Iterations
IterNodes
done5004
24156
11276
0438

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.3b

localize76.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ (* M D) (* 2 d))
6.1b
(* (* (* (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))))
10.7b
(pow (/ d l) (/ 1 2))
11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite276.0ms

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:
22.0ms
(/ (* M D) (* 2 d))
190.0ms
(* (* (* (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))))
11.0ms
(pow (/ d l) (/ 1 2))
45.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series1.5s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ (* M D) (* 2 d))
1.2s
(* (* (* (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))))
82.0ms
(pow (/ d l) (/ 1 2))
105.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify2.5s

Counts
199 → 199
Iterations
IterNodes
done5000
11404
0475

prune1.5s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 8.2b

localize116.0ms

Local error

Found 4 expressions with local error:

1.9b
(sqrt (/ d (cbrt l)))
4.4b
(/ (* M D) (* 2 d))
6.1b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
11.0b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite441.0ms

Algorithm
rewrite-expression-head
Rules
305×add-exp-log
163×prod-exp
93×div-exp
55×add-cbrt-cube
40×pow-exp
37×sqrt-div
30×add-sqr-sqrt frac-times times-frac associate-*r/
27×cbrt-unprod
25×pow1 *-un-lft-identity add-cube-cbrt
22×sqrt-prod
19×associate-*l/
16×associate-*r*
14×rec-exp 1-exp pow-prod-down
10×cbrt-prod
9×cbrt-undiv
8×pow-to-exp flip3-- flip--
4×insert-posit16 add-log-exp
3×rem-sqrt-square div-inv
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 associate-/l*
Counts
4 → 204
Calls
4 calls:
6.0ms
(sqrt (/ d (cbrt l)))
19.0ms
(/ (* M D) (* 2 d))
323.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
85.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series2.8s

Counts
4 → 12
Calls
4 calls:
219.0ms
(sqrt (/ d (cbrt l)))
34.0ms
(/ (* M D) (* 2 d))
2.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
132.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify4.2s

Counts
216 → 216
Iterations
IterNodes
done5000
11667
0583

prune2.1s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 6.3b

localize95.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ M (/ (* d 2) D))
4.9b
(/ M (/ (* d 2) D))
6.1b
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))))
6.9b
(* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
477×add-exp-log
370×add-cbrt-cube
271×prod-exp cbrt-unprod
137×cbrt-undiv div-exp
84×times-frac
50×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
47×pow1
38×associate-*r/
36×sqrt-div
34×frac-times
32×pow-prod-down
29×associate-*l/
25×associate-*r*
14×associate-/r*
11×div-inv
9×cbrt-prod
8×flip3-- flip--
6×associate-/l*
4×insert-posit16 add-log-exp
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in associate-*l* associate-/r/ *-commutative
Counts
4 → 306
Calls
4 calls:
7.0ms
(/ M (/ (* d 2) D))
12.0ms
(/ M (/ (* d 2) D))
361.0ms
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))))
1.5s
(* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))

series2.6s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ M (/ (* d 2) D))
49.0ms
(/ M (/ (* d 2) D))
2.3s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))))
164.0ms
(* (* 1/2 (* (* (/ M (/ (* d 2) D)) (cbrt h)) (* (/ M (/ (* d 2) D)) (cbrt h)))) (/ (cbrt h) l))

simplify3.9s

Counts
318 → 318
Iterations
IterNodes
done5001
12126
0677

prune2.6s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.5b

regimes2.2s

Accuracy

3.1% (5.7b remaining)

Error of 13.2b against oracle of 7.5b and baseline of 13.4b

bsearch3.0ms

simplify60.0ms

Iterations
IterNodes
done110
1110
082

end0.0ms

sample16.2s

Algorithm
intervals
Results
10.5s37793×body80nan
3.6s12766×body80valid