Details

Time bar (total: 41.1s)

sample522.0ms

Algorithm
intervals
Results
254.0ms1341×body80nan
126.0ms417×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02235
15435
217435
371035
done500035

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.4b

localize35.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (* M D) (* 2.0 d))
9.2b
(pow (/ d l) (/ 1.0 2.0))
10.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.3b
(pow (/ d h) (/ 1.0 2.0))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
78×prod-exp
51×div-exp
46×times-frac
39×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
26×unpow-prod-down pow-unpow
24×pow-exp
14×cbrt-unprod
13×associate-*r*
9×cbrt-undiv
8×pow1
6×pow-to-exp div-inv
4×add-log-exp
3×associate-*l/
2×pow-pow sqr-pow
1×frac-times frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 159
Calls
4 calls:
13.0ms
(/ (* M D) (* 2.0 d))
11.0ms
(pow (/ d l) (/ 1.0 2.0))
78.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
24.0ms
(pow (/ d h) (/ 1.0 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (* M D) (* 2.0 d))
77.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
121.0ms
(pow (/ d h) (/ 1.0 2.0))

simplify571.0ms

Counts
171 → 171
Iterations

Useful iterations: done (560.0ms)

IterNodesCost
03842847
112432638
done50002324

prune903.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.0b

localize84.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
4.9b
(/ (* M D) (* 2.0 d))
9.2b
(pow (/ d l) (/ 1.0 2.0))
10.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite595.0ms

Algorithm
rewrite-expression-head
Rules
738×add-exp-log
487×prod-exp
216×pow-exp
171×div-exp
78×pow-to-exp
46×add-cbrt-cube
28×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×cbrt-unprod
16×associate-*r*
13×unpow-prod-down pow-unpow
9×pow1 cbrt-undiv
4×div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* pow-prod-down *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 260
Calls
4 calls:
457.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
16.0ms
(/ (* M D) (* 2.0 d))
8.0ms
(pow (/ d l) (/ 1.0 2.0))
78.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
901.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
49.0ms
(/ (* M D) (* 2.0 d))
120.0ms
(pow (/ d l) (/ 1.0 2.0))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify871.0ms

Counts
272 → 272
Iterations

Useful iterations: done (858.0ms)

IterNodesCost
055111028
1177510141
done50008532

prune1.2s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.9b

localize86.0ms

Local error

Found 4 expressions with local error:

4.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)))
4.9b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
9.2b
(pow (/ d l) (/ 1.0 2.0))

rewrite899.0ms

Algorithm
rewrite-expression-head
Rules
658×add-exp-log
450×prod-exp
206×pow-exp
141×div-exp
76×pow-to-exp
34×add-cbrt-cube
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×times-frac
15×cbrt-unprod
13×unpow-prod-down pow-unpow
9×pow1
8×associate-*r*
5×cbrt-undiv
4×add-log-exp
3×div-inv
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ associate-*l* pow-prod-down associate-*l/ *-commutative
1×flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 232
Calls
4 calls:
477.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)))
14.0ms
(/ (* M D) (* 2.0 d))
381.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
8.0ms
(pow (/ d l) (/ 1.0 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
820.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)))
34.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
74.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify718.0ms

Counts
244 → 244
Iterations

Useful iterations: done (704.0ms)

IterNodesCost
051610313
116029535
done50018289

prune1.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.4b

localize78.0ms

Local error

Found 4 expressions with local error:

4.0b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
4.4b
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
4.9b
(/ (* M D) (* 2.0 d))
5.5b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

rewrite982.0ms

Algorithm
rewrite-expression-head
Rules
3060×add-exp-log
2393×prod-exp
1062×pow-exp
557×div-exp
423×pow-to-exp
57×add-cbrt-cube
27×cbrt-unprod
11×pow1
10×cbrt-undiv add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt associate-*r*
4×times-frac pow-prod-down associate-*l/ associate-/r* add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in associate-*r/ associate-*l* clear-num *-commutative div-inv associate-/l*
1×flip3-- flip-- associate-/l/ distribute-lft-out-- difference-of-squares
Counts
4 → 612
Calls
4 calls:
67.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
718.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
17.0ms
(/ (* M D) (* 2.0 d))
82.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

series3.8s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
1.5s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (* (cbrt d) (cbrt d)) (/ 1.0 2.0)) (pow (/ (cbrt d) l) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)))
53.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)

simplify1.5s

Counts
624 → 624
Iterations

Useful iterations: done (1.5s)

IterNodesCost
077839714
1284234629
done500029251

prune927.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 7.2b

regimes2.0s

Accuracy

0% (5.9b remaining)

Error of 16.4b against oracle of 10.5b and baseline of 16.4b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03164
13864
done3864

end0.0ms

sample17.4s

Algorithm
intervals
Results
9.4s38038×body80nan
4.3s12698×body80valid