Details

Time bar (total: 10.4s)

sample50.0ms

Algorithm
intervals
Results
17.0ms298×body80valid
6.0ms121×body80nan

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21789
34469
415309
550019
done50019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.3b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.9b
(/ (* M D) (* 2.0 d))
8.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite71.0ms

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:
17.0ms
(* 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))))
14.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.8s

Counts
4 → 12
Calls
4 calls:
445.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
393.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(/ (* M D) (* 2.0 d))
921.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Counts
125 → 125
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06091075
12742997
25003994
done5003994

prune371.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize14.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.6b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.5b
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.9b
(/ (* M D) (* 2.0 d))

rewrite67.0ms

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:
11.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
25.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
15.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
12.0ms
(/ (* M D) (* 2.0 d))

series1.9s

Counts
4 → 12
Calls
4 calls:
399.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
754.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
710.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
30.0ms
(/ (* M D) (* 2.0 d))

simplify63.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0560829
12559746
25001744
done5001744

prune329.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.5b
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
5.9b
(/ (* M D) (* 2.0 d))
5.9b
(/ (* M D) (* 2.0 d))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
39×add-cbrt-cube
16×pow-to-exp
14×add-sqr-sqrt
12×cbrt-unprod
11×cbrt-undiv
9×add-cube-cbrt *-un-lft-identity associate-*l*
6×unpow-prod-down times-frac
5×associate-/r*
4×pow1 div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×sqr-pow
1×*-commutative
Counts
4 → 150
Calls
4 calls:
26.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
40.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
15.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
751.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
734.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
29.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(/ (* M D) (* 2.0 d))

simplify82.0ms

Counts
162 → 162
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
08361701
131181278
250011274
done50011274

prune379.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
4.5b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.9b
(/ (* M D) (* 2.0 d))
5.9b
(/ (* M D) (* 2.0 d))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
30×add-cbrt-cube
19×prod-exp
14×add-sqr-sqrt
12×div-exp
9×associate-*l* cbrt-unprod
8×cbrt-undiv add-cube-cbrt *-un-lft-identity
6×unpow-prod-down
5×pow1 pow-exp
4×add-log-exp
3×times-frac associate-*r* sqrt-prod 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--
Counts
4 → 88
Calls
4 calls:
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
16.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))

series1.2s

Counts
4 → 12
Calls
4 calls:
403.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
756.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
34.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(/ (* M D) (* 2.0 d))

simplify55.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0439868
11971763
25001762
done5001762

prune323.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

regimes539.0ms

Accuracy

0% (1.3b remaining)

Error of 8.7b against oracle of 7.4b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03117
13117
done3117

end0.0ms

sample1.2s

Algorithm
intervals
Results
459.0ms9379×body80valid
170.0ms3211×body80nan