Details

Time bar (total: 1.2m)

sample120.0ms

Algorithm
intervals
Results
47.0ms293×body80valid
14.0ms105×body80nan

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5001
52702
4460
3181
281
136
017

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize57.0ms

Local error

Found 4 expressions with local error:

2.4b
(* 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))))
6.0b
(/ (* M D) (* 2.0 d))
10.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite129.0ms

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×*-un-lft-identity add-cube-cbrt
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×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-/l*
Counts
4 → 121
Calls
4 calls:
29.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
11.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
20.0ms
(/ (* M D) (* 2.0 d))
61.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts
4 → 12
Calls
4 calls:
676.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
519.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
35.0ms
(/ (* M D) (* 2.0 d))
1.0s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.3s

Counts
133 → 133
Iterations
IterNodes
done5000
23154
1643
0244

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize37.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)))
5.3b
(/ M (* (/ 2.0 D) d))
5.6b
(/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)
6.4b
(* (pow (/ M (* (/ 2.0 D) d)) 2.0) h)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
55×add-exp-log
21×add-sqr-sqrt
20×add-cbrt-cube
19×div-exp
18×prod-exp
15×*-un-lft-identity
13×add-cube-cbrt
12×associate-*l*
9×unpow-prod-down times-frac
8×pow-exp
6×cbrt-undiv
5×pow1 sqrt-prod
4×expm1-log1p-u associate-/r* cbrt-unprod log1p-expm1-u associate-/l* add-log-exp
3×associate-*r* div-inv unswap-sqr
2×pow-to-exp clear-num frac-2neg sqrt-div associate-*l/ associate-/r/ sqr-pow
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 108
Calls
4 calls:
19.0ms
(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)))
21.0ms
(/ M (* (/ 2.0 D) d))
13.0ms
(/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)
23.0ms
(* (pow (/ M (* (/ 2.0 D) d)) 2.0) h)

series2.7s

Counts
4 → 12
Calls
4 calls:
657.0ms
(sqrt (- 1.0 (/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)))
59.0ms
(/ M (* (/ 2.0 D) d))
958.0ms
(/ (* (pow (/ M (* (/ 2.0 D) d)) 2.0) h) l)
1.0s
(* (pow (/ M (* (/ 2.0 D) d)) 2.0) h)

simplify1.3s

Counts
120 → 120
Iterations
IterNodes
done5000
22835
1595
0245

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize55.0ms

Local error

Found 4 expressions with local error:

4.9b
(* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))
5.3b
(/ M (* (/ 2.0 D) d))
5.3b
(/ (/ M 2.0) (/ d D))
5.6b
(/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)

rewrite470.0ms

Algorithm
rewrite-expression-head
Rules
838×times-frac
410×add-sqr-sqrt
389×*-un-lft-identity add-cube-cbrt
316×add-exp-log
179×unpow-prod-down
178×associate-*r*
149×div-exp
115×prod-exp
67×pow-exp
58×div-inv
36×add-cbrt-cube
17×associate-/r* associate-/l*
15×pow-to-exp cbrt-undiv
7×unswap-sqr
6×cbrt-unprod
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* associate-/r/
2×sqr-pow
1×associate-*l/ *-commutative associate-/l/
Counts
4 → 520
Calls
4 calls:
196.0ms
(* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))
21.0ms
(/ M (* (/ 2.0 D) d))
17.0ms
(/ (/ M 2.0) (/ d D))
167.0ms
(/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)

series2.1s

Counts
4 → 12
Calls
4 calls:
1.0s
(* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))
37.0ms
(/ M (* (/ 2.0 D) d))
35.0ms
(/ (/ M 2.0) (/ d D))
992.0ms
(/ (* (pow (/ M (* (/ 2.0 D) d)) (/ 2.0 2)) (* h (pow (/ (/ M 2.0) (/ d D)) (/ 2.0 2)))) l)

simplify1.9s

Counts
532 → 532
Iterations
IterNodes
done5000
13152
01044

prune5.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.3b

localize59.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ h (/ l (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2))))
5.9b
(/ l (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2)))
6.0b
(/ (/ M (/ 2.0 D)) d)
6.0b
(/ (/ M (/ 2.0 D)) d)

rewrite901.0ms

Algorithm
rewrite-expression-head
Rules
9444×times-frac
3920×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
2176×unpow-prod-down
570×associate-/r*
248×div-inv
94×associate-/l*
64×add-exp-log
57×associate-/r/
43×div-exp
29×add-cbrt-cube
16×cbrt-undiv sqr-pow
8×pow-exp
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×pow-to-exp associate-/l/
Counts
4 → 2699
Calls
4 calls:
230.0ms
(/ h (/ l (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2))))
99.0ms
(/ l (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2)))
19.0ms
(/ (/ M (/ 2.0 D)) d)
25.0ms
(/ (/ M (/ 2.0 D)) d)

series2.7s

Counts
4 → 12
Calls
4 calls:
1.5s
(/ h (/ l (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2))))
1.2s
(/ l (pow (/ (/ M (/ 2.0 D)) d) (/ 2.0 2)))
32.0ms
(/ (/ M (/ 2.0 D)) d)
35.0ms
(/ (/ M (/ 2.0 D)) d)

simplify7.5s

Counts
2711 → 2711
Iterations
IterNodes
done5001
04565

prune34.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.3b

regimes1.0s

Accuracy

0% (1.7b remaining)

Error of 8.6b against oracle of 6.9b and baseline of 8.6b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done29
129
025

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.6s9313×body80valid
325.0ms2984×body80nan