Details

Time bar (total: 31.4s)

sample65.0ms

Algorithm
intervals
Results
23.0ms302×body80valid
9.0ms104×body80nan

simplify2.7s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize57.0ms

Local error

Found 4 expressions with local error:

1.5b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.7b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.1b
(/ (* M D) (* 2.0 d))
11.3b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite80.0ms

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:
16.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
24.0ms
(/ (* M D) (* 2.0 d))
27.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
676.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
520.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
42.0ms
(/ (* M D) (* 2.0 d))
982.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.3s

Counts
133 → 133
Iterations
IterNodes
done5000
23154
1643
0244

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.5b

localize52.0ms

Local error

Found 4 expressions with local error:

4.2b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.7b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
6.1b
(/ (* M D) (* 2.0 d))
6.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
165×add-exp-log
91×prod-exp
40×div-exp
30×add-cbrt-cube
25×pow-exp
21×add-sqr-sqrt
16×associate-*r*
15×*-un-lft-identity add-cube-cbrt
11×times-frac cbrt-unprod
10×associate-*l*
8×rec-exp 1-exp
7×pow1
6×cbrt-undiv unpow-prod-down
5×pow-to-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod div-inv unswap-sqr
2×sqrt-div *-commutative sqr-pow
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*r/ un-div-inv flip-- associate-/l*
Counts
4 → 136
Calls
4 calls:
67.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
11.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
12.0ms
(/ (* M D) (* 2.0 d))
28.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.8s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
589.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
40.0ms
(/ (* M D) (* 2.0 d))
1.1s
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify3.5s

Counts
148 → 148
Iterations
IterNodes
done5001
24546
1786
0277

prune986.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize44.0ms

Local error

Found 4 expressions with local error:

4.2b
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
4.7b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
6.1b
(/ (* M D) (* 2.0 d))
6.1b
(/ (* M D) (* 2.0 d))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
1381×add-exp-log
896×prod-exp
362×div-exp
300×pow-exp
60×pow-to-exp
57×rec-exp 1-exp
49×add-cbrt-cube
20×cbrt-unprod
13×add-sqr-sqrt associate-*r*
12×*-un-lft-identity add-cube-cbrt
11×cbrt-undiv times-frac
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* pow-prod-down associate-*r/ un-div-inv *-commutative flip--
Counts
4 → 324
Calls
4 calls:
145.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
11.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
18.0ms
(/ (* M D) (* 2.0 d))
10.0ms
(/ (* M D) (* 2.0 d))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
590.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
36.0ms
(/ (* M D) (* 2.0 d))
39.0ms
(/ (* M D) (* 2.0 d))

simplify2.3s

Counts
336 → 336
Iterations
IterNodes
done5000
11644
0424

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.5b

localize53.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))))
4.7b
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
6.1b
(/ (* M D) (* 2.0 d))
6.1b
(/ (* M D) (* 2.0 d))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
33×add-cbrt-cube
20×div-exp
19×prod-exp
10×cbrt-undiv
9×cbrt-unprod
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1 associate-/r* times-frac pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod div-inv associate-/l*
2×sqrt-div
1×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 92
Calls
4 calls:
10.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))))
24.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
19.0ms
(/ (* M D) (* 2.0 d))
14.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
598.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l))))
804.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
39.0ms
(/ (* M D) (* 2.0 d))
56.0ms
(/ (* M D) (* 2.0 d))

simplify1.9s

Counts
104 → 104
Iterations
IterNodes
done5002
22326
1484
0183

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

regimes2.5s

Accuracy

0% (1.5b remaining)

Error of 8.7b against oracle of 7.2b and baseline of 8.7b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done30
130
022

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.4s9265×body80valid
488.0ms3173×body80nan