Details

Time bar (total: 32.2s)

sample113.0ms

Algorithm
intervals
Results
46.0ms293×body80valid
13.0ms105×body80nan

simplify2.1s

Counts
1 → 1
Iterations
IterNodes
done5001
52638
4446
3177
281
136
017

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize31.0ms

Local error

Found 4 expressions with local error:

4.5b
(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
5.6b
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
6.0b
(/ (* M D) (* 2.0 d))
6.4b
(* h (pow (/ (* M D) (* 2.0 d)) 2.0))

rewrite80.0ms

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×pow-exp add-cube-cbrt
9×associate-*r*
6×cbrt-undiv unpow-prod-down cbrt-unprod
5×pow1 times-frac sqrt-prod
4×associate-/r* add-log-exp
3×associate-*l* div-inv unswap-sqr
2×pow-to-exp clear-num frac-2neg sqrt-div associate-/l* sqr-pow
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 96
Calls
4 calls:
9.0ms
(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
12.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
13.0ms
(/ (* M D) (* 2.0 d))
40.0ms
(* h (pow (/ (* M D) (* 2.0 d)) 2.0))

series2.4s

Counts
4 → 12
Calls
4 calls:
403.0ms
(sqrt (- 1.0 (/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)))
846.0ms
(/ (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) l)
33.0ms
(/ (* M D) (* 2.0 d))
1.2s
(* h (pow (/ (* M D) (* 2.0 d)) 2.0))

simplify1.5s

Counts
108 → 108
Iterations
IterNodes
done5001
22601
1552
0222

prune838.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.4b

localize53.0ms

Local error

Found 4 expressions with local error:

4.9b
(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
5.4b
(* (/ M 2.0) (/ D d))
5.6b
(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
6.0b
(/ (* M D) (* 2.0 d))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
373×add-exp-log
184×prod-exp
129×div-exp
80×pow-exp
39×add-cbrt-cube
37×add-sqr-sqrt
26×times-frac
22×*-un-lft-identity add-cube-cbrt
18×associate-*r*
16×pow-to-exp associate-*l*
12×cbrt-unprod
11×cbrt-undiv
6×pow1 unswap-sqr
4×associate-/r* div-inv add-log-exp
2×clear-num frac-2neg *-commutative associate-/l* sqr-pow
1×frac-times unpow-prod-down pow-prod-down associate-*l/ associate-*r/
Counts
4 → 174
Calls
4 calls:
20.0ms
(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
22.0ms
(* (/ M 2.0) (/ D d))
50.0ms
(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
10.0ms
(/ (* M D) (* 2.0 d))

series2.0s

Counts
4 → 12
Calls
4 calls:
1.1s
(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
33.0ms
(* (/ M 2.0) (/ D d))
825.0ms
(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)
39.0ms
(/ (* M D) (* 2.0 d))

simplify597.0ms

Counts
186 → 186
Iterations
IterNodes
done5001
11147
0368

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize77.0ms

Local error

Found 4 expressions with local error:

4.4b
(* h (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l)))
4.5b
(sqrt (- 1.0 (* (/ (* h (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l))) (cbrt l)) (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l)))))
5.4b
(* M (/ D d))
5.4b
(* M (/ D d))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
110×times-frac
96×associate-*r*
92×add-sqr-sqrt
63×*-un-lft-identity add-cube-cbrt
44×unpow-prod-down
39×add-exp-log
36×cbrt-prod
18×add-cbrt-cube
13×prod-exp
12×div-exp
11×pow1 unswap-sqr
9×associate-*l* div-inv
8×sqr-pow
6×cbrt-unprod
4×pow-exp add-log-exp
3×cbrt-undiv pow-prod-down associate-*r/ *-commutative sqrt-prod
2×sqrt-div
1×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 178
Calls
4 calls:
44.0ms
(* h (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l)))
5.0ms
(sqrt (- 1.0 (* (/ (* h (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l))) (cbrt l)) (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l)))))
17.0ms
(* M (/ D d))
11.0ms
(* M (/ D d))

series1.1s

Counts
4 → 12
Calls
4 calls:
570.0ms
(* h (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l)))
509.0ms
(sqrt (- 1.0 (* (/ (* h (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l))) (cbrt l)) (/ (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)) (cbrt l)))))
36.0ms
(* M (/ D d))
26.0ms
(* M (/ D d))

simplify2.2s

Counts
190 → 190
Iterations
IterNodes
done5000
24058
1943
0365

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize179.0ms

Local error

Found 4 expressions with local error:

5.4b
(* M (/ D d))
16.0b
(cbrt (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)))
16.0b
(cbrt (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
16.0b
(cbrt (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×cbrt-prod
17×*-un-lft-identity add-cube-cbrt
13×times-frac associate-*r*
9×unpow-prod-down add-cbrt-cube add-exp-log
6×pow1
4×add-log-exp
3×pow1/3 associate-*l* sqr-pow
2×prod-exp cbrt-unprod div-inv unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative
Counts
4 → 77
Calls
4 calls:
13.0ms
(* M (/ D d))
3.0ms
(cbrt (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)))
2.0ms
(cbrt (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
2.0ms
(cbrt (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))

series7.0s

Counts
4 → 12
Calls
4 calls:
35.0ms
(* M (/ D d))
2.4s
(cbrt (pow (/ (* M (/ D d)) 2.0) (/ 2.0 2)))
2.5s
(cbrt (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
2.1s
(cbrt (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))

simplify1.9s

Counts
89 → 89
Iterations
IterNodes
done5000
22210
1888
0339

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

regimes1.8s

Accuracy

0% (1.2b remaining)

Error of 8.1b against oracle of 6.9b and baseline of 8.1b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.0s9313×body80valid
310.0ms2984×body80nan