Details

Time bar (total: 21.1s)

sample92.0ms

Algorithm
intervals
Results
36.0ms306×body80valid
10.0ms105×body80nan

simplify1.0s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.4b
(/ (* M D) (* 2.0 d))
9.2b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
18.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
21.0ms
(/ (* M D) (* 2.0 d))
66.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
646.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
557.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
50.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.1s

Counts
125 → 125

prune653.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize18.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.5b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b
(/ (* M D) (* 2.0 d))

rewrite138.0ms

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×add-cube-cbrt pow-exp
9×associate-*l*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/l* sqr-pow
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
26.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
23.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
52.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
33.0ms
(/ (* M D) (* 2.0 d))

series2.6s

Counts
4 → 12
Calls
4 calls:
991.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
551.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
52.0ms
(/ (* M D) (* 2.0 d))

simplify975.0ms

Counts
108 → 108

prune461.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize21.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.4b
(/ (* M D) (* 2.0 d))
5.4b
(/ (* M D) (* 2.0 d))
6.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
16×add-sqr-sqrt
12×div-exp
10×*-un-lft-identity
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt
6×unpow-prod-down
5×pow1 pow-exp sqrt-prod
4×add-log-exp
3×times-frac associate-*r* div-inv unswap-sqr
2×frac-2neg sqrt-div clear-num associate-/r* associate-/l* sqr-pow
1×pow-to-exp rem-sqrt-square flip3-- sqrt-pow1 pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
15.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
21.0ms
(/ (* M D) (* 2.0 d))
13.0ms
(/ (* M D) (* 2.0 d))
32.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.5s

Counts
4 → 12
Calls
4 calls:
489.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
40.0ms
(/ (* M D) (* 2.0 d))
51.0ms
(/ (* M D) (* 2.0 d))
924.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify746.0ms

Counts
102 → 102

prune554.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

localize31.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
4.5b
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
4.6b
(* (/ M 2.0) (/ D d))
5.1b
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
41×add-sqr-sqrt
26×prod-exp
25×*-un-lft-identity times-frac
23×add-cube-cbrt add-cbrt-cube
20×div-exp
18×associate-*l*
16×associate-*r*
10×pow-exp
7×pow1
6×cbrt-undiv cbrt-unprod unswap-sqr
5×sqrt-prod
4×add-log-exp
3×associate-/r* div-inv
2×pow-to-exp sqrt-div *-commutative sqr-pow
1×frac-times unpow-prod-down rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num flip-- associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 120
Calls
4 calls:
29.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
31.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
26.0ms
(* (/ M 2.0) (/ D d))
20.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

series2.4s

Counts
4 → 12
Calls
4 calls:
880.0ms
(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)
526.0ms
(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
30.0ms
(* (/ M 2.0) (/ D d))
921.0ms
(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)

simplify1.1s

Counts
132 → 132

prune519.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

regimes1.4s

Accuracy

-142.2% (5.0b remaining)

Error of 12.4b against oracle of 7.3b and baseline of 9.4b

bsearch3.0ms

simplify1.0s

end0.0ms

sample2.1s

Algorithm
intervals
Results
949.0ms9336×body80valid
324.0ms3103×body80nan