Details

Time bar (total: 20.1s)

sample121.0ms

Algorithm
intervals
Results
63.0ms297×body80valid
25.0ms98×body80nan

simplify447.0ms

Counts
1 → 1
Iterations
IterNodes
done2008
3596
295
138
017

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize60.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (* M D) d)
4.6b
(/ (* M D) d)
4.7b
(sqrt (- 1 (* (/ (/ (/ (* M D) d) 2) (/ l h)) (/ (/ (* M D) d) 2))))
10.1b
(/ (/ (/ (* M D) d) 2) (/ l h))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
985×times-frac
388×add-sqr-sqrt
387×*-un-lft-identity add-cube-cbrt
85×div-inv
46×add-cbrt-cube add-exp-log
27×associate-/l*
26×cbrt-undiv div-exp
19×associate-/r*
5×pow1
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l/
Counts
4 → 460
Calls
4 calls:
19.0ms
(/ (* M D) d)
18.0ms
(/ (* M D) d)
11.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) d) 2) (/ l h)) (/ (/ (* M D) d) 2))))
33.0ms
(/ (/ (/ (* M D) d) 2) (/ l h))

series359.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (* M D) d)
35.0ms
(/ (* M D) d)
184.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) d) 2) (/ l h)) (/ (/ (* M D) d) 2))))
105.0ms
(/ (/ (/ (* M D) d) 2) (/ l h))

simplify785.0ms

Counts
472 → 472
Iterations
IterNodes
done2000
0864

prune4.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize76.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1 (* (* (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) 1) (/ (* (cbrt l) (cbrt l)) 1)) (/ (/ (cbrt (/ (* M D) d)) 2) (/ (cbrt l) h))) (/ (/ (* M D) d) 2))))
17.5b
(cbrt (/ (* M D) d))
17.5b
(cbrt (/ (* M D) d))
17.5b
(cbrt (/ (* M D) d))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×times-frac
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 75
Calls
4 calls:
13.0ms
(sqrt (- 1 (* (* (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) 1) (/ (* (cbrt l) (cbrt l)) 1)) (/ (/ (cbrt (/ (* M D) d)) 2) (/ (cbrt l) h))) (/ (/ (* M D) d) 2))))
5.0ms
(cbrt (/ (* M D) d))
17.0ms
(cbrt (/ (* M D) d))
6.0ms
(cbrt (/ (* M D) d))

series557.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(sqrt (- 1 (* (* (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) 1) (/ (* (cbrt l) (cbrt l)) 1)) (/ (/ (cbrt (/ (* M D) d)) 2) (/ (cbrt l) h))) (/ (/ (* M D) d) 2))))
121.0ms
(cbrt (/ (* M D) d))
111.0ms
(cbrt (/ (* M D) d))
117.0ms
(cbrt (/ (* M D) d))

simplify892.0ms

Counts
87 → 87
Iterations
IterNodes
done2001
2794
1244
0122

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.2b

localize79.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1 (* (* (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) (sqrt 2)) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (cbrt (/ (* M D) d)) (sqrt 2)) (/ l (cbrt h)))) (/ (/ (* M D) d) 2))))
17.5b
(cbrt (/ (* M D) d))
17.5b
(cbrt (/ (* M D) d))
17.5b
(cbrt (/ (* M D) d))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×times-frac
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 75
Calls
4 calls:
9.0ms
(sqrt (- 1 (* (* (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) (sqrt 2)) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (cbrt (/ (* M D) d)) (sqrt 2)) (/ l (cbrt h)))) (/ (/ (* M D) d) 2))))
3.0ms
(cbrt (/ (* M D) d))
2.0ms
(cbrt (/ (* M D) d))
3.0ms
(cbrt (/ (* M D) d))

series1.0s

Counts
4 → 12
Calls
4 calls:
667.0ms
(sqrt (- 1 (* (* (/ (/ (* (cbrt (/ (* M D) d)) (cbrt (/ (* M D) d))) (sqrt 2)) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (cbrt (/ (* M D) d)) (sqrt 2)) (/ l (cbrt h)))) (/ (/ (* M D) d) 2))))
112.0ms
(cbrt (/ (* M D) d))
126.0ms
(cbrt (/ (* M D) d))
131.0ms
(cbrt (/ (* M D) d))

simplify1.1s

Counts
87 → 87
Iterations
IterNodes
done2001
2713
1223
0118

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 8.2b

localize50.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1 (/ (/ (/ (/ (* (/ M d) D) (* (/ (cbrt l) h) 2)) (cbrt l)) (cbrt l)) (/ 2 (* (/ M d) D)))))
5.0b
(* (/ M d) D)
5.0b
(* (/ M d) D)
5.9b
(/ (* (/ M d) D) (* (/ (cbrt l) h) 2))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
55×times-frac
50×add-exp-log
47×add-cbrt-cube
31×*-un-lft-identity
26×associate-*l*
21×add-cube-cbrt
20×sqrt-prod
17×cbrt-undiv div-exp
16×prod-exp cbrt-unprod difference-of-squares
10×cbrt-prod
9×pow1
6×associate-*r*
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×sqrt-div pow-prod-down *-commutative
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 141
Calls
4 calls:
269.0ms
(sqrt (- 1 (/ (/ (/ (/ (* (/ M d) D) (* (/ (cbrt l) h) 2)) (cbrt l)) (cbrt l)) (/ 2 (* (/ M d) D)))))
15.0ms
(* (/ M d) D)
10.0ms
(* (/ M d) D)
25.0ms
(/ (* (/ M d) D) (* (/ (cbrt l) h) 2))

series655.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(sqrt (- 1 (/ (/ (/ (/ (* (/ M d) D) (* (/ (cbrt l) h) 2)) (cbrt l)) (cbrt l)) (/ 2 (* (/ M d) D)))))
30.0ms
(* (/ M d) D)
30.0ms
(* (/ M d) D)
352.0ms
(/ (* (/ M d) D) (* (/ (cbrt l) h) 2))

simplify764.0ms

Counts
153 → 153
Iterations
IterNodes
done2001
1668
0280

prune1.3s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.8b

regimes1.3s

Accuracy

0% (1.2b remaining)

Error of 7.9b against oracle of 6.7b and baseline of 7.9b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done29
129
022

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.1s9286×body80valid
586.0ms3280×body80nan