Details

Time bar (total: 38.8s)

sample459.0ms

Algorithm
intervals
Results
220.0ms1212×body80nan
79.0ms395×body80valid

simplify237.0ms

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize36.0ms

Local error

Found 4 expressions with local error:

6.2b
(/ (* M D) (* 2.0 d))
10.4b
(pow (/ d l) (/ 1.0 2.0))
11.1b
(pow (/ d h) (/ 1.0 2.0))
12.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite128.0ms

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:
21.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
13.0ms
(pow (/ d h) (/ 1.0 2.0))
69.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.2s

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (* M D) (* 2.0 d))
89.0ms
(pow (/ d l) (/ 1.0 2.0))
80.0ms
(pow (/ d h) (/ 1.0 2.0))
1.0s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify107.0ms

Counts
171 → 171

prune1.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.2b

localize71.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (* (* (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))))
6.2b
(/ (* M D) (* 2.0 d))
10.4b
(pow (/ d l) (/ 1.0 2.0))
12.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite553.0ms

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×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 → 292
Calls
4 calls:
412.0ms
(* (* (* (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))))
13.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(pow (/ d l) (/ 1.0 2.0))
75.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts
4 → 12
Calls
4 calls:
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))))
45.0ms
(/ (* M D) (* 2.0 d))
88.0ms
(pow (/ d l) (/ 1.0 2.0))
975.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify94.0ms

Counts
304 → 304

prune1.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.9b

localize456.0ms

Local error

Found 4 expressions with local error:

2.4b
(pow (/ d (cbrt h)) (/ 1.0 2.0))
4.6b
(* (* (* (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))))
6.2b
(/ (* M D) (* 2.0 d))
12.9b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
8121×add-exp-log
6369×prod-exp
3426×pow-exp
1900×div-exp
967×pow-to-exp
592×rec-exp 1-exp
55×add-cbrt-cube
37×times-frac
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×cbrt-unprod
22×unpow-prod-down
16×associate-*r*
13×pow-unpow
12×pow1
9×cbrt-undiv cbrt-prod
4×pow-prod-down div-inv add-log-exp
3×associate-*r/ associate-*l/
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l* *-commutative
1×frac-times flip3-- pow-pow frac-2neg clear-num associate-/r* flip-- associate-/l* sqr-pow
Counts
4 → 1525
Calls
4 calls:
17.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
700.0ms
(* (* (* (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))))
23.0ms
(/ (* M D) (* 2.0 d))
99.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.5s

Counts
4 → 12
Calls
4 calls:
269.0ms
(pow (/ d (cbrt h)) (/ 1.0 2.0))
1.2s
(* (* (* (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))))
31.0ms
(/ (* M D) (* 2.0 d))
995.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify541.0ms

Counts
1537 → 1537

prune1.8s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.1b

localize123.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
6.0b
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.2b
(/ (* M D) (* 2.0 d))
7.7b
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
8092×add-exp-log
6361×prod-exp
3419×pow-exp
1884×div-exp
965×pow-to-exp
592×rec-exp 1-exp
60×add-cbrt-cube
29×cbrt-unprod
11×pow1
10×cbrt-undiv
8×add-sqr-sqrt *-un-lft-identity associate-*r*
6×add-cube-cbrt
4×pow-prod-down add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac associate-*r/ associate-*l* clear-num associate-/r* *-commutative div-inv associate-/l*
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 1478
Calls
4 calls:
606.0ms
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
58.0ms
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
21.0ms
(/ (* M D) (* 2.0 d))
68.0ms
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

series3.2s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
1.1s
(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
48.0ms
(/ (* M D) (* 2.0 d))
1.0s
(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify459.0ms

Counts
1490 → 1490

prune932.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.6b

regimes1.5s

Accuracy

-11.6% (8.8b remaining)

Error of 18.2b against oracle of 9.4b and baseline of 17.3b

bsearch2.0s

Steps
ItersRangePoint
9
1.282747705829506e+283
2.0666300332448816e+291
5.320837894328123e+283
7
3.0776510774548433e+215
2.575279917848011e+217
2.520281039428513e+217
7
6.18366793787593e-218
7.065103514836415e-216
1.4473282588936097e-216
8
-2.85483397411846e-212
-8.110272520166952e-215
-8.719035499619317e-213

simplify25.0ms

end0.0ms

sample15.4s

Algorithm
intervals
Results
8.1s37587×body80nan
3.7s12709×body80valid