Details

Time bar (total: 2.4m)

sample1.2s

Algorithm
intervals
Results
941.0ms1407×body80nan
128.0ms411×body80valid

simplify6.9s

Counts
1 → 1
Iterations
IterNodes
done5003
43939
3645
2170
154
022

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize111.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (* (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))))
12.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.8b
(pow (/ d h) (/ 1.0 2.0))
13.3b
(pow (/ d l) (/ 1.0 2.0))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
205×add-exp-log
107×prod-exp
55×div-exp
45×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-exp
30×add-cbrt-cube
26×unpow-prod-down pow-unpow
16×associate-*r*
14×pow-to-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×add-log-exp
3×associate-*r/ associate-*l/
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 → 176
Calls
4 calls:
107.0ms
(* (* (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
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
16.0ms
(pow (/ d h) (/ 1.0 2.0))
15.0ms
(pow (/ d l) (/ 1.0 2.0))

series3.0s

Counts
4 → 12
Calls
4 calls:
1.3s
(* (* (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))))
1.5s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
123.0ms
(pow (/ d h) (/ 1.0 2.0))
124.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify5.0s

Counts
188 → 188
Iterations
IterNodes
done5004
24443
11342
0440

prune2.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.2b

localize209.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
6.4b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
12.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.3b
(pow (/ d l) (/ 1.0 2.0))

rewrite755.0ms

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:
27.0ms
(/ (* M D) (* 2.0 d))
537.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
108.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
17.0ms
(pow (/ d l) (/ 1.0 2.0))

series3.1s

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (* M D) (* 2.0 d))
1.4s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
1.5s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
118.0ms
(pow (/ d l) (/ 1.0 2.0))

simplify3.3s

Counts
272 → 272
Iterations
IterNodes
done5000
11598
0547

prune2.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 10.2b

localize310.0ms

Local error

Found 4 expressions with local error:

2.6b
(pow (/ d (cbrt l)) (/ 1.0 2.0))
3.8b
(/ (* M D) (* 2.0 d))
6.4b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
12.7b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
6965×add-exp-log
5245×prod-exp
2614×pow-exp
1626×div-exp
789×pow-to-exp
232×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 → 1229
Calls
4 calls:
23.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
30.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
94.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series4.2s

Counts
4 → 12
Calls
4 calls:
410.0ms
(pow (/ d (cbrt l)) (/ 1.0 2.0))
69.0ms
(/ (* M D) (* 2.0 d))
2.1s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
1.6s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify25.5s

Counts
1241 → 1241
Iterations
IterNodes
done5001
14400
01493

prune3.2s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.5b

localize341.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* M D) (* 2.0 d))
4.8b
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.4b
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)))
7.7b
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
6964×add-exp-log
5245×prod-exp
2612×pow-exp
1626×div-exp
788×pow-to-exp
232×rec-exp 1-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 → 1192
Calls
4 calls:
26.0ms
(/ (* M D) (* 2.0 d))
100.0ms
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
992.0ms
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)))
103.0ms
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

series5.2s

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (* M D) (* 2.0 d))
1.6s
(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
2.0s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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)))
1.5s
(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

simplify43.1s

Counts
1204 → 1204
Iterations
IterNodes
done5003
13461
01376

prune1.9s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.0b

regimes4.5s

Accuracy

-5.2% (6.8b remaining)

Error of 15.7b against oracle of 8.9b and baseline of 15.3b

bsearch1.7s

Steps
ItersRangePoint
4
2.137943356240003e+146
3.2866166890404634e+146
3.1071364807903915e+146
7
2.266942447605223e-76
5.979089740469276e-75
8.69469409831458e-76
7
-5.285703722799295e-200
-2.7860630370664197e-201
-1.7590984635087784e-200

simplify52.0ms

Iterations
IterNodes
done73
173
056

end0.0ms

sample23.7s

Algorithm
intervals
Results
14.0s39051×body80nan
6.2s12887×body80valid