Details

Time bar (total: 11.3s)

sample46.0ms

Algorithm
intervals
Results
15.0ms297×body80valid
5.0ms97×body80nan

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0369
1819
21829
34569
415579
550019
done50019

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.8b
(/ (* M D) (* 2.0 d))
12.9b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite76.0ms

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:
17.0ms
(* 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))
33.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.6s

Counts
4 → 12
Calls
4 calls:
439.0ms
(* 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))))
28.0ms
(/ (* M D) (* 2.0 d))
705.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06301135
127791057
250021054
done50021054

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.6b

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
4.0b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.8b
(/ (* M D) (* 2.0 d))
7.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
609×add-exp-log
325×prod-exp
184×div-exp
75×pow-exp
54×add-cbrt-cube
45×associate-*r*
43×cbrt-unprod
42×times-frac
41×add-sqr-sqrt
36×cbrt-prod
33×add-cube-cbrt *-un-lft-identity
22×cbrt-undiv
15×pow-to-exp
10×associate-*l*
7×pow1 unpow-prod-down
6×unswap-sqr
4×expm1-log1p-u associate-*r/ log1p-expm1-u div-inv add-log-exp
3×sqrt-prod sqr-pow
2×sqrt-div *-commutative
1×frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r* flip-- associate-/l*
Counts
4 → 250
Calls
4 calls:
145.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
9.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
12.0ms
(/ (* M D) (* 2.0 d))
58.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series1.7s

Counts
4 → 12
Calls
4 calls:
706.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
400.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
29.0ms
(/ (* M D) (* 2.0 d))
560.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify57.0ms

Counts
262 → 262
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
014274307
150013768
done50013768

prune806.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize21.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
4.0b
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
70×add-sqr-sqrt
51×times-frac
48×cbrt-prod
40×associate-*r*
32×add-cube-cbrt *-un-lft-identity
31×add-cbrt-cube
30×prod-exp
23×div-exp
15×unswap-sqr
10×unpow-prod-down pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
6×sqr-pow
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 154
Calls
4 calls:
42.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
7.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
12.0ms
(/ (* M D) (* 2.0 d))
15.0ms
(/ (* M D) (* 2.0 d))

series987.0ms

Counts
4 → 12
Calls
4 calls:
527.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
401.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
29.0ms
(/ (* M D) (* 2.0 d))
30.0ms
(/ (* M D) (* 2.0 d))

simplify100.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07762091
137241955
250021950
done50021950

prune775.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize35.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
4.0b
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
4.8b
(/ (* M D) (* 2.0 d))
4.8b
(/ (* M D) (* 2.0 d))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
70×add-sqr-sqrt
51×times-frac
48×cbrt-prod
40×associate-*r*
32×add-cube-cbrt *-un-lft-identity
31×add-cbrt-cube
30×prod-exp
23×div-exp
15×unswap-sqr
10×unpow-prod-down pow-exp cbrt-unprod
9×cbrt-undiv associate-*l*
6×sqr-pow
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×pow-to-exp frac-2neg sqrt-div clear-num associate-/r* associate-/l*
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ *-commutative flip--
Counts
4 → 154
Calls
4 calls:
42.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
7.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
15.0ms
(/ (* M D) (* 2.0 d))
12.0ms
(/ (* M D) (* 2.0 d))

series969.0ms

Counts
4 → 12
Calls
4 calls:
518.0ms
(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l)))
394.0ms
(sqrt (- 1.0 (* (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (cbrt h) (cbrt l))) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l))))) (/ (cbrt (cbrt h)) (cbrt (cbrt l))))) (/ (cbrt h) (cbrt l)))))
28.0ms
(/ (* M D) (* 2.0 d))
29.0ms
(/ (* M D) (* 2.0 d))

simplify108.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07882389
138402241
250022236
done50022236

prune967.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

regimes819.0ms

Accuracy

0% (1.6b remaining)

Error of 8.7b against oracle of 7.1b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04039
14039
done4039

end0.0ms

sample1.2s

Algorithm
intervals
Results
472.0ms9267×body80valid
172.0ms3186×body80nan