Details

Time bar (total: 39.1s)

sample90.0ms

Algorithm
intervals
Results
37.0ms302×body80valid
9.0ms68×body80nan

simplify2.1s

Counts
1 → 1
Iterations
IterNodes
done5001
52638
4446
3177
281
136
017

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.2b

localize30.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
5.0b
(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
5.6b
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
5.7b
(/ (* M D) (* 2.0 d))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
26×prod-exp
23×add-cbrt-cube
20×div-exp
18×add-sqr-sqrt
12×*-un-lft-identity
10×pow-exp add-cube-cbrt
9×associate-*r*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*l* div-inv unswap-sqr
2×pow-to-exp clear-num frac-2neg sqrt-div associate-/l* sqr-pow
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
19.0ms
(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
29.0ms
(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
12.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
14.0ms
(/ (* M D) (* 2.0 d))

series2.4s

Counts
4 → 12
Calls
4 calls:
444.0ms
(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
1.0s
(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
889.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
55.0ms
(/ (* M D) (* 2.0 d))

simplify1.4s

Counts
108 → 108
Iterations
IterNodes
done5000
22624
1551
0222

prune805.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.6b

localize65.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* (* h (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (/ M (/ 2.0 D)) d)
6.0b
(* h (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2)))

rewrite467.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
360×add-sqr-sqrt
343×*-un-lft-identity add-cube-cbrt
317×add-exp-log
140×unpow-prod-down associate-*r*
136×div-exp
129×prod-exp
67×pow-exp
46×associate-/l*
36×add-cbrt-cube
32×div-inv
15×pow-to-exp
13×cbrt-undiv
8×cbrt-unprod
7×associate-/r* associate-/r/
6×unswap-sqr
4×pow1 add-log-exp
3×clear-num frac-2neg associate-*l*
2×sqr-pow
1×*-commutative associate-/l/
Counts
4 → 451
Calls
4 calls:
205.0ms
(/ (* (* h (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
9.0ms
(/ (* M D) (* 2.0 d))
17.0ms
(/ (/ M (/ 2.0 D)) d)
171.0ms
(* h (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2)))

series2.1s

Counts
4 → 12
Calls
4 calls:
860.0ms
(/ (* (* h (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
49.0ms
(/ (* M D) (* 2.0 d))
52.0ms
(/ (/ M (/ 2.0 D)) d)
1.1s
(* h (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2)))

simplify1.5s

Counts
463 → 463
Iterations
IterNodes
done5001
12652
0967

prune5.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.3b

localize76.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (* (* (* h (pow (/ 1 (sqrt 2.0)) (/ 2.0 2))) (pow (/ (/ M (/ (sqrt 2.0) D)) d) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
5.7b
(/ (* M D) (* 2.0 d))
5.7b
(/ (/ M (/ (sqrt 2.0) D)) d)
6.1b
(* (* h (pow (/ 1 (sqrt 2.0)) (/ 2.0 2))) (pow (/ (/ M (/ (sqrt 2.0) D)) d) (/ 2.0 2)))

rewrite954.0ms

Algorithm
rewrite-expression-head
Rules
2177×add-exp-log
1270×times-frac
1101×prod-exp
916×div-exp
631×pow-exp
585×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
221×associate-*r*
217×unpow-prod-down
189×sqrt-prod
147×pow-to-exp
73×associate-/l*
48×rec-exp 1-exp
44×add-cbrt-cube
32×div-inv
14×cbrt-undiv
13×cbrt-unprod
7×associate-/r* associate-/r/
4×pow1 add-log-exp
3×clear-num frac-2neg
1×associate-*l* *-commutative sqr-pow associate-/l/
Counts
4 → 922
Calls
4 calls:
477.0ms
(/ (* (* (* h (pow (/ 1 (sqrt 2.0)) (/ 2.0 2))) (pow (/ (/ M (/ (sqrt 2.0) D)) d) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
19.0ms
(/ (* M D) (* 2.0 d))
54.0ms
(/ (/ M (/ (sqrt 2.0) D)) d)
276.0ms
(* (* h (pow (/ 1 (sqrt 2.0)) (/ 2.0 2))) (pow (/ (/ M (/ (sqrt 2.0) D)) d) (/ 2.0 2)))

series3.3s

Counts
4 → 12
Calls
4 calls:
1.7s
(/ (* (* (* h (pow (/ 1 (sqrt 2.0)) (/ 2.0 2))) (pow (/ (/ M (/ (sqrt 2.0) D)) d) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
49.0ms
(/ (* M D) (* 2.0 d))
160.0ms
(/ (/ M (/ (sqrt 2.0) D)) d)
1.4s
(* (* h (pow (/ 1 (sqrt 2.0)) (/ 2.0 2))) (pow (/ (/ M (/ (sqrt 2.0) D)) d) (/ 2.0 2)))

simplify1.9s

Counts
934 → 934
Iterations
IterNodes
done5001
14990
01551

prune6.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize120.0ms

Local error

Found 4 expressions with local error:

4.7b
(/ (* (cbrt l) (cbrt l)) (pow (* (/ M (sqrt 2.0)) (/ D d)) (/ 2.0 2)))
4.9b
(* (/ M 2.0) (/ D d))
5.0b
(* (/ M (sqrt 2.0)) (/ D d))
5.3b
(/ (* (pow (/ 1 (sqrt 2.0)) (/ 2.0 2)) h) (/ (* (cbrt l) (cbrt l)) (pow (* (/ M (sqrt 2.0)) (/ D d)) (/ 2.0 2))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
622×add-exp-log
319×div-exp
218×prod-exp
140×pow-exp
80×times-frac
75×add-sqr-sqrt
48×add-cbrt-cube
44×*-un-lft-identity add-cube-cbrt
35×associate-*l*
31×pow-to-exp
26×associate-*r*
20×cbrt-undiv
15×rec-exp 1-exp
14×associate-/r* cbrt-unprod
11×sqrt-prod
10×unswap-sqr
8×pow1 div-inv
4×unpow-prod-down add-log-exp sqr-pow
2×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
1×associate-/r/
Counts
4 → 289
Calls
4 calls:
27.0ms
(/ (* (cbrt l) (cbrt l)) (pow (* (/ M (sqrt 2.0)) (/ D d)) (/ 2.0 2)))
21.0ms
(* (/ M 2.0) (/ D d))
23.0ms
(* (/ M (sqrt 2.0)) (/ D d))
36.0ms
(/ (* (pow (/ 1 (sqrt 2.0)) (/ 2.0 2)) h) (/ (* (cbrt l) (cbrt l)) (pow (* (/ M (sqrt 2.0)) (/ D d)) (/ 2.0 2))))

series2.1s

Counts
4 → 12
Calls
4 calls:
861.0ms
(/ (* (cbrt l) (cbrt l)) (pow (* (/ M (sqrt 2.0)) (/ D d)) (/ 2.0 2)))
57.0ms
(* (/ M 2.0) (/ D d))
142.0ms
(* (/ M (sqrt 2.0)) (/ D d))
1.1s
(/ (* (pow (/ 1 (sqrt 2.0)) (/ 2.0 2)) h) (/ (* (cbrt l) (cbrt l)) (pow (* (/ M (sqrt 2.0)) (/ D d)) (/ 2.0 2))))

simplify972.0ms

Counts
301 → 301
Iterations
IterNodes
done5000
11585
0434

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.3b

regimes710.0ms

Accuracy

19.1% (2.1b remaining)

Error of 9.3b against oracle of 7.1b and baseline of 9.8b

bsearch326.0ms

Steps
ItersRangePoint
10
6.489369345543714e+28
1.667766485067598e+43
1.3142528216400636e+41
9
-1.547090166699088e-237
-8.249421660369221e-246
-8.061268150334176e-242

simplify18.0ms

Iterations
IterNodes
done70
370
268
166
053

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.5s9319×body80valid
479.0ms3144×body80nan