Details

Time bar (total: 31.9s)

sample128.0ms

Algorithm
intervals
Results
62.0ms302×body80valid
28.0ms137×body80nan

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
44693
3589
293
136
017

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize30.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
5.0b
(/ (* M D) (* 2 d))
5.0b
(/ (* M D) (* 2 d))
11.9b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite216.0ms

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×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 → 194
Calls
4 calls:
4.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
9.0ms
(/ (* M D) (* 2 d))
14.0ms
(/ (* M D) (* 2 d))
177.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series448.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
33.0ms
(/ (* M D) (* 2 d))
47.0ms
(/ (* M D) (* 2 d))
132.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.5s

Counts
206 → 206
Iterations
IterNodes
23923
1954
0318

prune2.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize82.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (/ (* M D) 2) d)
5.2b
(cbrt (* (- 1 (* (/ (/ (* M D) 2) d) (/ (* (/ (/ (* M D) 2) d) h) l))) (sqrt (- 1 (* (/ (/ (* M D) 2) d) (/ (* (/ (/ (* M D) 2) d) h) l))))))
6.0b
(* (/ (/ (* M D) 2) d) h)
6.0b
(* (/ (/ (* M D) 2) d) h)

rewrite481.0ms

Algorithm
rewrite-expression-head
Rules
95×times-frac
61×add-sqr-sqrt
50×*-un-lft-identity associate-*l* add-cube-cbrt
41×add-cbrt-cube add-exp-log
15×cbrt-undiv div-exp
13×div-inv
11×prod-exp cbrt-unprod
8×pow1 cbrt-div
7×associate-/l*
6×flip3-- sqrt-div associate-*r* flip--
4×frac-times associate-*l/ add-log-exp unswap-sqr
3×associate-/r*
2×pow-prod-down associate-*r/ *-commutative
1×cbrt-prod clear-num frac-2neg pow1/3 pow3 rem-cbrt-cube associate-/l/
Counts
4 → 162
Calls
4 calls:
22.0ms
(/ (/ (* M D) 2) d)
386.0ms
(cbrt (* (- 1 (* (/ (/ (* M D) 2) d) (/ (* (/ (/ (* M D) 2) d) h) l))) (sqrt (- 1 (* (/ (/ (* M D) 2) d) (/ (* (/ (/ (* M D) 2) d) h) l))))))
32.0ms
(* (/ (/ (* M D) 2) d) h)
36.0ms
(* (/ (/ (* M D) 2) d) h)

series384.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (/ (* M D) 2) d)
213.0ms
(cbrt (* (- 1 (* (/ (/ (* M D) 2) d) (/ (* (/ (/ (* M D) 2) d) h) l))) (sqrt (- 1 (* (/ (/ (* M D) 2) d) (/ (* (/ (/ (* M D) 2) d) h) l))))))
65.0ms
(* (/ (/ (* M D) 2) d) h)
66.0ms
(* (/ (/ (* M D) 2) d) h)

simplify4.0s

Counts
174 → 174
Iterations
IterNodes
38428
21725
1575
0233

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize127.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (/ (/ (* M D) 2) d) h)
19.5b
(cbrt (* (/ (/ (* M D) 2) d) h))
19.5b
(cbrt (* (/ (/ (* M D) 2) d) h))
19.5b
(cbrt (* (/ (/ (* M D) 2) d) h))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
25×associate-*l*
24×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
18×add-cbrt-cube add-exp-log
6×pow1
5×cbrt-undiv div-exp prod-exp cbrt-unprod
4×associate-*l/ div-inv add-log-exp
3×cbrt-prod cbrt-div pow1/3 associate-*r*
2×unswap-sqr
1×pow-prod-down *-commutative
Counts
4 → 78
Calls
4 calls:
37.0ms
(* (/ (/ (* M D) 2) d) h)
9.0ms
(cbrt (* (/ (/ (* M D) 2) d) h))
9.0ms
(cbrt (* (/ (/ (* M D) 2) d) h))
17.0ms
(cbrt (* (/ (/ (* M D) 2) d) h))

series577.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (/ (/ (* M D) 2) d) h)
188.0ms
(cbrt (* (/ (/ (* M D) 2) d) h))
149.0ms
(cbrt (* (/ (/ (* M D) 2) d) h))
165.0ms
(cbrt (* (/ (/ (* M D) 2) d) h))

simplify3.0s

Counts
90 → 90
Iterations
IterNodes
36188
21303
1433
0174

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize148.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (/ (/ (* M D) 2) d) h)
11.7b
(cbrt (/ (* M D) 2))
11.7b
(cbrt (/ (* M D) 2))
11.7b
(cbrt (/ (* M D) 2))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
30×add-sqr-sqrt
25×*-un-lft-identity associate-*l* add-cube-cbrt
21×cbrt-prod
18×add-cbrt-cube add-exp-log
7×div-inv
6×pow1
5×cbrt-undiv div-exp prod-exp cbrt-unprod
4×add-log-exp
3×cbrt-div pow1/3 associate-*r*
2×unswap-sqr
1×pow-prod-down associate-*l/ *-commutative
Counts
4 → 96
Calls
4 calls:
35.0ms
(* (/ (/ (* M D) 2) d) h)
5.0ms
(cbrt (/ (* M D) 2))
4.0ms
(cbrt (/ (* M D) 2))
4.0ms
(cbrt (/ (* M D) 2))

series497.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (/ (/ (* M D) 2) d) h)
154.0ms
(cbrt (/ (* M D) 2))
142.0ms
(cbrt (/ (* M D) 2))
126.0ms
(cbrt (/ (* M D) 2))

simplify2.6s

Counts
108 → 108
Iterations
IterNodes
35734
21223
1431
0176

prune2.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

regimes1.4s

Accuracy

70.9% (0.7b remaining)

Error of 8.1b against oracle of 7.4b and baseline of 9.7b

bsearch1.0ms

simplify42.0ms

Iterations
IterNodes
272
172
055

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.0s9313×body80valid
571.0ms3155×body80nan