Details

Time bar (total: 10.6s)

sample47.0ms

Algorithm
intervals
Results
15.0ms298×body80valid
6.0ms121×body80nan

simplify53.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019
done50019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize18.0ms

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))

rewrite73.0ms

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×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 frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 121
Calls
4 calls:
20.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
7.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
12.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
453.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
406.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
29.0ms
(/ (* M D) (* 2.0 d))
721.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06301135
127791057
250021054
done50021054

prune427.0ms

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))

rewrite74.0ms

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×expm1-log1p-u associate-/r* log1p-expm1-u 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 → 104
Calls
4 calls:
16.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
15.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
15.0ms
(/ (* M D) (* 2.0 d))

series1.9s

Counts
4 → 12
Calls
4 calls:
394.0ms
(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
742.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
716.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
30.0ms
(/ (* M D) (* 2.0 d))

simplify69.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0576881
12585798
25001796
done5001796

prune372.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize21.0ms

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))

rewrite100.0ms

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 expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg associate-*r* clear-num associate-/l* unswap-sqr
2×sqr-pow
1×*-commutative
Counts
4 → 158
Calls
4 calls:
23.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
42.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
12.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))

series1.5s

Counts
4 → 12
Calls
4 calls:
754.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
717.0ms
(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
30.0ms
(/ (* M D) (* 2.0 d))
34.0ms
(/ (* M D) (* 2.0 d))

simplify82.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08821759
131701336
250021332
done50021332

prune414.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize17.0ms

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))

rewrite61.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 96
Calls
4 calls:
7.0ms
(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)
12.0ms
(/ (* M D) (* 2.0 d))
16.0ms
(/ (* M D) (* 2.0 d))

series1.4s

Counts
4 → 12
Calls
4 calls:
408.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l))))
952.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
29.0ms
(/ (* M D) (* 2.0 d))
33.0ms
(/ (* M D) (* 2.0 d))

simplify57.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0453929
11999824
25001823
done5001823

prune357.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

regimes536.0ms

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
474.0ms9379×body80valid
173.0ms3211×body80nan