Details

Time bar (total: 51.3s)

sample133.0ms

Algorithm
intervals
Results
72.0ms295×body80valid
24.0ms110×body80nan

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
44673
3593
293
136
017

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize36.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.4b
(/ (* M D) (* 2 d))
4.4b
(/ (* M D) (* 2 d))
8.6b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite210.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 206
Calls
4 calls:
6.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
11.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
176.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series368.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
28.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))
116.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.4s

Counts
218 → 218
Iterations
IterNodes
24014
1934
0327

prune3.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.4b

localize46.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))))
4.4b
(/ (* M D) (* 2 d))
4.4b
(/ (* M D) (* 2 d))
5.3b
(* (* (* (/ (* M D) (* 2 d)) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))

rewrite695.0ms

Algorithm
rewrite-expression-head
Rules
597×add-exp-log
440×add-cbrt-cube
370×prod-exp cbrt-unprod
141×cbrt-undiv div-exp
24×add-sqr-sqrt
23×pow1
22×times-frac associate-*r*
18×*-un-lft-identity add-cube-cbrt
13×pow-prod-down associate-*l/
10×cbrt-prod
5×frac-times
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/ sqrt-prod div-inv unswap-sqr
2×clear-num associate-/r* frac-2neg sqrt-div associate-/l*
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 263
Calls
4 calls:
11.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))))
23.0ms
(/ (* M D) (* 2 d))
24.0ms
(/ (* M D) (* 2 d))
620.0ms
(* (* (* (/ (* M D) (* 2 d)) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))

series548.0ms

Counts
4 → 12
Calls
4 calls:
276.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))))
48.0ms
(/ (* M D) (* 2 d))
54.0ms
(/ (* M D) (* 2 d))
170.0ms
(* (* (* (/ (* M D) (* 2 d)) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))

simplify3.2s

Counts
275 → 275
Iterations
IterNodes
25295
11257
0432

prune4.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.7b

localize63.0ms

Local error

Found 4 expressions with local error:

4.7b
(cbrt (/ (cbrt h) l))
4.7b
(cbrt (/ (cbrt h) l))
7.2b
(* (* (cbrt h) (/ M 2)) (/ D d))
7.2b
(* (* (cbrt h) (/ M 2)) (/ D d))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
62×cbrt-prod
54×times-frac
46×add-exp-log
44×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
38×add-cbrt-cube
26×associate-*r*
20×prod-exp cbrt-unprod
14×pow1
10×cbrt-undiv div-exp
6×pow-prod-down associate-*r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×frac-times cbrt-div pow1/3 associate-*l* associate-*l/ *-commutative
Counts
4 → 152
Calls
4 calls:
3.0ms
(cbrt (/ (cbrt h) l))
3.0ms
(cbrt (/ (cbrt h) l))
47.0ms
(* (* (cbrt h) (/ M 2)) (/ D d))
41.0ms
(* (* (cbrt h) (/ M 2)) (/ D d))

series844.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(cbrt (/ (cbrt h) l))
238.0ms
(cbrt (/ (cbrt h) l))
175.0ms
(* (* (cbrt h) (/ M 2)) (/ D d))
190.0ms
(* (* (cbrt h) (/ M 2)) (/ D d))

simplify5.3s

Counts
164 → 164
Iterations
IterNodes
37297
21620
1490
0211

prune3.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.7b

localize72.0ms

Local error

Found 4 expressions with local error:

4.3b
(sqrt (- 1 (* (* (* (* (* M D) (/ 1 (* 2 d))) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))))
4.4b
(/ (* M D) (* 2 d))
4.5b
(* (* M D) (/ 1 (* 2 d)))
5.3b
(* (* (* (* (* M D) (/ 1 (* 2 d))) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
1706×add-exp-log
1209×prod-exp
637×add-cbrt-cube
569×cbrt-unprod
333×div-exp
169×cbrt-undiv
52×pow1 rec-exp 1-exp
36×pow-prod-down
29×associate-*r*
23×associate-*l/
22×times-frac
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
9×cbrt-prod frac-times
8×associate-*r/
5×un-div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod div-inv
2×sqrt-div associate-*l* *-commutative
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 flip3-- pow1/2 flip-- associate-/l*
Counts
4 → 431
Calls
4 calls:
13.0ms
(sqrt (- 1 (* (* (* (* (* M D) (/ 1 (* 2 d))) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))))
23.0ms
(/ (* M D) (* 2 d))
44.0ms
(* (* M D) (/ 1 (* 2 d)))
1.9s
(* (* (* (* (* M D) (/ 1 (* 2 d))) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))

series465.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(sqrt (- 1 (* (* (* (* (* M D) (/ 1 (* 2 d))) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))))
36.0ms
(/ (* M D) (* 2 d))
43.0ms
(* (* M D) (/ 1 (* 2 d)))
151.0ms
(* (* (* (* (* M D) (/ 1 (* 2 d))) (cbrt h)) (* (/ (* M D) (* 2 d)) (cbrt h))) (/ (cbrt h) l))

simplify9.3s

Counts
443 → 443
Iterations
IterNodes
210123
11988
0736

prune8.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.7b

regimes1.9s

Accuracy

19.5% (2.4b remaining)

Error of 9.1b against oracle of 6.7b and baseline of 9.7b

bsearch2.0ms

simplify21.0ms

Iterations
IterNodes
253
153
039

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.8s9335×body80valid
583.0ms3071×body80nan