Details

Time bar (total: 40.3s)

sample123.0ms

Algorithm
intervals
Results
67.0ms305×body80valid
20.0ms91×body80nan

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
44673
3593
293
136
017

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize36.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))
11.7b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

rewrite257.0ms

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))
19.0ms
(/ (* M D) (* 2 d))
212.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

series406.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
36.0ms
(/ (* M D) (* 2 d))
53.0ms
(/ (* M D) (* 2 d))
135.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))

simplify1.5s

Counts
218 → 218
Iterations
IterNodes
24014
1934
0327

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize47.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
4.0b
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
110×add-exp-log
90×add-cbrt-cube
84×add-sqr-sqrt times-frac
80×cbrt-prod associate-*l*
56×*-un-lft-identity add-cube-cbrt
44×prod-exp cbrt-unprod
34×cbrt-undiv div-exp
10×associate-*r* unswap-sqr
8×pow1
6×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×frac-times clear-num associate-/r* frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
Counts
4 → 218
Calls
4 calls:
54.0ms
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
51.0ms
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
22.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

series636.0ms

Counts
4 → 12
Calls
4 calls:
280.0ms
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
271.0ms
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
40.0ms
(/ (* M D) (* 2 d))
45.0ms
(/ (* M D) (* 2 d))

simplify901.0ms

Counts
230 → 230
Iterations
IterNodes
22560
1542
0191

prune4.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize90.0ms

Local error

Found 4 expressions with local error:

3.1b
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l)))))
4.0b
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
59×add-cbrt-cube
46×add-sqr-sqrt
43×times-frac
40×cbrt-prod associate-*l*
31×*-un-lft-identity add-cube-cbrt
26×prod-exp cbrt-unprod
21×cbrt-undiv div-exp
7×pow1
5×associate-*r* unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 151
Calls
4 calls:
11.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l)))))
56.0ms
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
22.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))

series564.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(sqrt (- 1 (* (* (* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l)))))
280.0ms
(* (/ (cbrt h) (cbrt l)) (/ (* M D) (* 2 d)))
41.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))

simplify1.0s

Counts
163 → 163
Iterations
IterNodes
23021
1638
0232

prune4.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.3b

localize154.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (sqrt (- 1 (* (* (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d)))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l))))) w0)
3.1b
(sqrt (- 1 (* (* (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d)))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l)))))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
7×pow1 sqrt-prod
6×associate-*l*
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×clear-num associate-/r* frac-2neg times-frac flip3-- associate-*l/ div-inv flip-- associate-/l* unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 93
Calls
4 calls:
14.0ms
(* (sqrt (- 1 (* (* (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d)))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l))))) w0)
5.0ms
(sqrt (- 1 (* (* (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d)))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l)))))
21.0ms
(/ (* M D) (* 2 d))
23.0ms
(/ (* M D) (* 2 d))

series643.0ms

Counts
4 → 12
Calls
4 calls:
374.0ms
(* (sqrt (- 1 (* (* (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d)))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l))))) w0)
195.0ms
(sqrt (- 1 (* (* (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (* (cbrt (cbrt l)) (cbrt (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d)))) (* (/ (* (cbrt (cbrt h)) (cbrt (cbrt h))) (cbrt (* (cbrt l) (cbrt l)))) (* (/ (cbrt (cbrt h)) (cbrt (cbrt l))) (/ (* M D) (* 2 d))))) (/ (cbrt h) (cbrt l)))))
30.0ms
(/ (* M D) (* 2 d))
43.0ms
(/ (* M D) (* 2 d))

simplify10.6s

Counts
105 → 105
Iterations
IterNodes
315653
21615
1351
0144

prune3.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.3b

regimes1.9s

Accuracy

12.7% (0.7b remaining)

Error of 7.8b against oracle of 7.1b and baseline of 8.0b

bsearch3.0ms

simplify24.0ms

Iterations
IterNodes
253
153
042

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.8s9339×body80valid
613.0ms3124×body80nan