Details

Time bar (total: 33.7s)

sample98.0ms

Algorithm
intervals
Results
40.0ms308×body80valid
16.0ms123×body80nan

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
done5000
3596
295
138
017

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize50.0ms

Local error

Found 4 expressions with local error:

5.3b
(/ (/ (* M D) 2) d)
5.3b
(/ (/ (* M D) 2) d)
5.9b
(sqrt (- 1 (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ l h))))
11.0b
(/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ l h))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
235×add-cbrt-cube add-exp-log
141×cbrt-undiv div-exp
103×times-frac
63×add-sqr-sqrt
56×*-un-lft-identity
51×add-cube-cbrt
50×prod-exp cbrt-unprod
19×associate-/r*
15×associate-/l*
13×div-inv
10×sqrt-prod
6×difference-of-squares
5×pow1 associate-/l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×sqrt-div
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l/ associate-*r/ associate-/r/ flip-- distribute-lft-out--
Counts
4 → 239
Calls
4 calls:
15.0ms
(/ (/ (* M D) 2) d)
21.0ms
(/ (/ (* M D) 2) d)
24.0ms
(sqrt (- 1 (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ l h))))
33.0ms
(/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ l h))

series391.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (/ (* M D) 2) d)
42.0ms
(/ (/ (* M D) 2) d)
198.0ms
(sqrt (- 1 (/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ l h))))
122.0ms
(/ (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) (/ l h))

simplify3.3s

Counts
251 → 251
Iterations
IterNodes
done5000
24478
11075
0386

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.2b

localize62.0ms

Local error

Found 4 expressions with local error:

5.3b
(/ (/ (* M D) 2) d)
5.3b
(/ (/ (* M D) 2) d)
5.5b
(/ (/ (/ (* M D) 2) d) (/ l (cbrt h)))
5.9b
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (/ (* M D) 2) d) (/ l (cbrt h))))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
1774×times-frac
698×add-sqr-sqrt
697×*-un-lft-identity add-cube-cbrt
234×cbrt-prod
129×div-inv
54×add-exp-log
50×add-cbrt-cube
39×associate-/l*
32×cbrt-undiv div-exp
28×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 associate-/l/
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip--
Counts
4 → 748
Calls
4 calls:
22.0ms
(/ (/ (* M D) 2) d)
19.0ms
(/ (/ (* M D) 2) d)
21.0ms
(/ (/ (/ (* M D) 2) d) (/ l (cbrt h)))
5.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (/ (* M D) 2) d) (/ l (cbrt h))))))

series540.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (/ (* M D) 2) d)
45.0ms
(/ (/ (* M D) 2) d)
240.0ms
(/ (/ (/ (* M D) 2) d) (/ l (cbrt h)))
212.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (/ (* M D) 2) d) (/ l (cbrt h))))))

simplify3.5s

Counts
760 → 760
Iterations
IterNodes
done5001
13909
01201

prune7.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.2b

localize97.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h))))
5.3b
(/ (/ (* M D) 2) d)
5.3b
(/ (/ (* M D) 2) d)
5.9b
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (/ (/ (* M D) 2) d) l) (/ 1 (cbrt h))))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
559×times-frac
202×add-sqr-sqrt
201×*-un-lft-identity add-cube-cbrt
140×add-exp-log
89×div-exp
69×div-inv
68×add-cbrt-cube
45×cbrt-undiv
39×associate-/l*
21×prod-exp
13×associate-/r*
9×cbrt-unprod
8×rec-exp 1-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod associate-/l/
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip--
Counts
4 → 382
Calls
4 calls:
43.0ms
(/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h))))
10.0ms
(/ (/ (* M D) 2) d)
10.0ms
(/ (/ (* M D) 2) d)
8.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (/ (/ (* M D) 2) d) l) (/ 1 (cbrt h))))))

series571.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h))))
34.0ms
(/ (/ (* M D) 2) d)
44.0ms
(/ (/ (* M D) 2) d)
245.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (/ (/ (/ (/ (* M D) 2) d) l) (/ 1 (cbrt h))))))

simplify1.8s

Counts
394 → 394
Iterations
IterNodes
done5000
11684
0569

prune3.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.2b

localize109.0ms

Local error

Found 4 expressions with local error:

5.9b
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (* (/ (/ (* (cbrt (/ (* M D) 2)) (cbrt (/ (* M D) 2))) (* (cbrt d) (cbrt d))) (/ (* (cbrt l) (cbrt l)) (* (cbrt (cbrt h)) (cbrt (cbrt h))))) (/ (/ (cbrt (/ (* M D) 2)) (cbrt d)) (/ (cbrt l) (cbrt (cbrt h))))))))
12.9b
(cbrt (/ (* M D) 2))
12.9b
(cbrt (/ (* M D) 2))
12.9b
(cbrt (/ (* M D) 2))

rewrite17.0ms

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:
8.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (* (/ (/ (* (cbrt (/ (* M D) 2)) (cbrt (/ (* M D) 2))) (* (cbrt d) (cbrt d))) (/ (* (cbrt l) (cbrt l)) (* (cbrt (cbrt h)) (cbrt (cbrt h))))) (/ (/ (cbrt (/ (* M D) 2)) (cbrt d)) (/ (cbrt l) (cbrt (cbrt h))))))))
2.0ms
(cbrt (/ (* M D) 2))
3.0ms
(cbrt (/ (* M D) 2))
3.0ms
(cbrt (/ (* M D) 2))

series765.0ms

Counts
4 → 12
Calls
4 calls:
341.0ms
(sqrt (- 1 (* (/ (/ (/ (* M D) 2) d) (/ 1 (* (cbrt h) (cbrt h)))) (* (/ (/ (* (cbrt (/ (* M D) 2)) (cbrt (/ (* M D) 2))) (* (cbrt d) (cbrt d))) (/ (* (cbrt l) (cbrt l)) (* (cbrt (cbrt h)) (cbrt (cbrt h))))) (/ (/ (cbrt (/ (* M D) 2)) (cbrt d)) (/ (cbrt l) (cbrt (cbrt h))))))))
149.0ms
(cbrt (/ (* M D) 2))
145.0ms
(cbrt (/ (* M D) 2))
130.0ms
(cbrt (/ (* M D) 2))

simplify3.0s

Counts
87 → 87
Iterations
IterNodes
done5003
2792
1244
0121

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 8.9b

regimes1.6s

Accuracy

0% (1.3b remaining)

Error of 8.2b against oracle of 6.9b and baseline of 8.2b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.4s9316×body80valid
348.0ms3118×body80nan