Details

Time bar (total: 1.1m)

sample122.0ms

Algorithm
intervals
Results
69.0ms289×body80valid
21.0ms107×body80nan

simplify711.0ms

Counts
1 → 1
Iterations
IterNodes
done2071
42071
3592
295
138
017

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize30.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
5.7b
(/ (* M D) (* 2 d))
5.7b
(/ (* M D) (* 2 d))
10.7b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
368×add-cbrt-cube add-exp-log
190×prod-exp cbrt-unprod
114×cbrt-undiv div-exp
16×add-sqr-sqrt
13×associate-*r*
12×*-un-lft-identity times-frac add-cube-cbrt
10×pow1
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×pow-prod-down associate-*r/ sqrt-prod div-inv
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 198
Calls
4 calls:
8.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
19.0ms
(/ (* M D) (* 2 d))
17.0ms
(/ (* M D) (* 2 d))
126.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series669.0ms

Counts
4 → 12
Calls
4 calls:
513.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
29.0ms
(/ (* M D) (* 2 d))
39.0ms
(/ (* M D) (* 2 d))
88.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify928.0ms

Counts
210 → 210
Iterations
IterNodes
done2000
22000
1961
0321

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize91.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
3.5b
(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
6.3b
(/ M (/ 2 (/ D d)))
6.3b
(/ M (/ 2 (/ D d)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
1616×times-frac
896×add-sqr-sqrt
724×*-un-lft-identity add-cube-cbrt
274×associate-*r*
104×cbrt-prod
88×associate-/r*
86×add-exp-log
80×associate-*l*
70×add-cbrt-cube
62×div-inv
44×cbrt-undiv div-exp
40×unswap-sqr
18×associate-/r/
16×prod-exp cbrt-unprod
8×pow1
6×associate-/l*
4×insert-posit16 add-log-exp
2×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 846
Calls
4 calls:
46.0ms
(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
25.0ms
(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
8.0ms
(/ M (/ 2 (/ D d)))
11.0ms
(/ M (/ 2 (/ D d)))

series632.0ms

Counts
4 → 12
Calls
4 calls:
289.0ms
(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
247.0ms
(* (/ (cbrt h) (cbrt l)) (/ M (/ 2 (/ D d))))
49.0ms
(/ M (/ 2 (/ D d)))
47.0ms
(/ M (/ 2 (/ D d)))

simplify1.9s

Counts
858 → 858
Iterations
IterNodes
done2001
12001
0724

prune18.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

localize86.0ms

Local error

Found 4 expressions with local error:

6.3b
(/ M (/ 2 (/ D d)))
14.4b
(cbrt (/ 2 (/ D d)))
14.4b
(cbrt (/ 2 (/ D d)))
14.4b
(cbrt (/ 2 (/ D d)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
594×times-frac
294×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
132×cbrt-prod
44×associate-/r*
29×div-inv
13×add-cbrt-cube add-exp-log
8×associate-/r/
6×cbrt-undiv div-exp
4×pow1 insert-posit16 add-log-exp
3×cbrt-div pow1/3 associate-/l*
1×clear-num frac-2neg
Counts
4 → 359
Calls
4 calls:
8.0ms
(/ M (/ 2 (/ D d)))
2.0ms
(cbrt (/ 2 (/ D d)))
4.0ms
(cbrt (/ 2 (/ D d)))
4.0ms
(cbrt (/ 2 (/ D d)))

series689.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ M (/ 2 (/ D d)))
97.0ms
(cbrt (/ 2 (/ D d)))
401.0ms
(cbrt (/ 2 (/ D d)))
145.0ms
(cbrt (/ 2 (/ D d)))

simplify1.4s

Counts
371 → 371
Iterations
IterNodes
done2000
22000
11387
0555

prune8.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

localize162.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (/ (cbrt h) (cbrt l)) (* (/ 1 (/ (sqrt 2) (/ 1 (* (cbrt d) (cbrt d))))) (/ M (/ (sqrt 2) (/ D (cbrt d))))))
14.4b
(cbrt (/ 2 (/ D d)))
14.4b
(cbrt (/ 2 (/ D d)))
14.4b
(cbrt (/ 2 (/ D d)))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
1361×add-exp-log
793×div-exp
474×prod-exp
234×times-frac
221×add-cbrt-cube
168×cbrt-prod
153×cbrt-undiv
134×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
112×rec-exp 1-exp
90×cbrt-unprod
40×associate-*l*
13×div-inv
9×pow1
5×frac-times associate-*r/
4×insert-posit16 add-log-exp
3×cbrt-div pow1/3 pow-prod-down associate-*l/ associate-/r/
1×associate-*r* *-commutative
Counts
4 → 465
Calls
4 calls:
248.0ms
(* (/ (cbrt h) (cbrt l)) (* (/ 1 (/ (sqrt 2) (/ 1 (* (cbrt d) (cbrt d))))) (/ M (/ (sqrt 2) (/ D (cbrt d))))))
3.0ms
(cbrt (/ 2 (/ D d)))
4.0ms
(cbrt (/ 2 (/ D d)))
4.0ms
(cbrt (/ 2 (/ D d)))

series1.2s

Counts
4 → 12
Calls
4 calls:
795.0ms
(* (/ (cbrt h) (cbrt l)) (* (/ 1 (/ (sqrt 2) (/ 1 (* (cbrt d) (cbrt d))))) (/ M (/ (sqrt 2) (/ D (cbrt d))))))
123.0ms
(cbrt (/ 2 (/ D d)))
126.0ms
(cbrt (/ 2 (/ D d)))
131.0ms
(cbrt (/ 2 (/ D d)))

simplify3.2s

Counts
477 → 477
Iterations
IterNodes
done2001
22001
11982
0792

prune15.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.3b

regimes1.8s

Accuracy

0% (1.4b remaining)

Error of 7.8b against oracle of 6.4b and baseline of 7.8b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done34
134
026

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.0s9290×body80valid
757.0ms3330×body80nan