Details

Time bar (total: 32.5s)

sample125.0ms

Algorithm
intervals
Results
65.0ms313×body80valid
22.0ms104×body80nan

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
44693
3589
293
136
017

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize25.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
5.1b
(/ (* M D) (* 2 d))
5.1b
(/ (* M D) (* 2 d))
10.0b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite211.0ms

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:
4.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
13.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
177.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series383.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
35.0ms
(/ (* M D) (* 2 d))
49.0ms
(/ (* M D) (* 2 d))
107.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.4s

Counts
210 → 210
Iterations
IterNodes
23936
1957
0321

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.3b

localize60.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
4.7b
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
5.1b
(/ (* M D) (* 2 d))
5.1b
(/ (* M D) (* 2 d))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
59×add-cbrt-cube
46×add-sqr-sqrt
43×times-frac
40×cbrt-prod associate-*r*
31×*-un-lft-identity add-cube-cbrt
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
7×pow1
5×associate-*l* unswap-sqr
4×insert-posit16 div-inv add-log-exp
3×sqrt-prod
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 143
Calls
4 calls:
32.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
4.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
23.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))

series388.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))
163.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* 2 d)) (/ (cbrt h) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
31.0ms
(/ (* M D) (* 2 d))
42.0ms
(/ (* M D) (* 2 d))

simplify1.1s

Counts
155 → 155
Iterations
IterNodes
23713
1792
0269

prune3.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize117.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (* M D) (* 2 d))
5.1b
(/ (* M D) (* 2 d))
5.1b
(/ (* M D) (* 2 d))
5.1b
(/ (* M D) (* 2 d))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
52×add-cbrt-cube add-exp-log
16×cbrt-undiv div-exp prod-exp cbrt-unprod
4×add-sqr-sqrt pow1 clear-num associate-/r* frac-2neg *-un-lft-identity times-frac add-cube-cbrt insert-posit16 div-inv associate-/l* add-log-exp
Counts
4 → 88
Calls
4 calls:
22.0ms
(/ (* M D) (* 2 d))
22.0ms
(/ (* M D) (* 2 d))
23.0ms
(/ (* M D) (* 2 d))
17.0ms
(/ (* M D) (* 2 d))

series140.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (* M D) (* 2 d))
29.0ms
(/ (* M D) (* 2 d))
33.0ms
(/ (* M D) (* 2 d))
36.0ms
(/ (* M D) (* 2 d))

simplify2.5s

Counts
100 → 100
Iterations
IterNodes
36436
2836
1159
057

prune2.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.1b

localize82.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (* M 1/2) (/ d D))
5.0b
(/ (* M 1/2) (/ d D))
5.0b
(/ (* M 1/2) (/ d D))
6.2b
(cbrt (* (- 1 (* (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l)))))) (sqrt (- 1 (* (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l)))))))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
93×times-frac
47×add-sqr-sqrt
46×*-un-lft-identity add-cube-cbrt
40×add-cbrt-cube add-exp-log
39×associate-/r*
18×cbrt-undiv div-exp
9×div-inv
8×cbrt-div
6×flip3-- sqrt-div prod-exp cbrt-unprod flip--
4×frac-times pow1 insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/r/ associate-/l*
2×associate-*l/ associate-*r/
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 160
Calls
4 calls:
19.0ms
(/ (* M 1/2) (/ d D))
24.0ms
(/ (* M 1/2) (/ d D))
20.0ms
(/ (* M 1/2) (/ d D))
13.0ms
(cbrt (* (- 1 (* (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l)))))) (sqrt (- 1 (* (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l)))))))))

series409.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (* M 1/2) (/ d D))
30.0ms
(/ (* M 1/2) (/ d D))
48.0ms
(/ (* M 1/2) (/ d D))
300.0ms
(cbrt (* (- 1 (* (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l)))))) (sqrt (- 1 (* (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l))) (* (/ (cbrt h) (cbrt l)) (* (/ (* M 1/2) (/ d D)) (/ (cbrt h) (cbrt l)))))))))

simplify5.4s

Counts
172 → 172
Iterations
IterNodes
38377
21475
1446
0187

prune3.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.6b

regimes1.8s

Accuracy

0% (1.1b remaining)

Error of 7.9b against oracle of 6.8b and baseline of 7.9b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
225
125
020

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.3s9360×body80valid
620.0ms3141×body80nan