Details

Time bar (total: 8.6m)

sample110.0ms

Algorithm
intervals
Results
56.0ms314×body80valid
22.0ms90×body80nan

simplify168.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
168.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize54.0ms

Local error

Found 4 expressions with local error:

12.9b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* (/ (* 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×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:
Slowest
169.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
12.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
6.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))

series353.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(sqrt (- 1 (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))))
99.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ h l))
45.0ms
(/ (* M D) (* 2 d))
29.0ms
(/ (* M D) (* 2 d))

simplify51.6s

Counts
172 → 210
Calls
172 calls:
Slowest
2.9s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.9s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.6s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.5s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.4s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))

prune3.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

localize70.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
4.9b
(/ (* M D) (* 2 d))
4.9b
(/ (* M D) (* 2 d))
4.7b
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
1021×add-exp-log
813×add-cbrt-cube
567×prod-exp cbrt-unprod
312×cbrt-undiv div-exp
10×pow1
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×frac-times associate-*r* associate-*l/
4×times-frac 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 → 346
Calls
4 calls:
Slowest
170.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
20.0ms
(/ (* M D) (* 2 d))
18.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(sqrt (- 1 (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
199.0ms
(* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))
41.0ms
(/ (* M D) (* 2 d))
31.0ms
(/ (* M D) (* 2 d))

simplify1.7m

Counts
321 → 358
Calls
321 calls:
Slowest
3.0s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (/ (* h h) (* l l)))
2.9s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* h h) (* l l)))
2.5s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (/ (* h h) (* l l)))
2.4s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* h h) (* l l)))
1.7s
(sqrt (- (* 1 1) (* (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))) (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l))))))

prune7.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.4b

localize81.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
6.6b
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
4.7b
(sqrt (- 1 (* (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))) (/ (cbrt h) (cbrt l)))))
2.5b
(* (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))) (/ (cbrt h) (cbrt l)))

rewrite384.0ms

Algorithm
rewrite-expression-head
Rules
1861×add-exp-log
1407×add-cbrt-cube
983×cbrt-undiv div-exp
654×prod-exp cbrt-unprod
392×times-frac
180×add-sqr-sqrt
170×*-un-lft-identity add-cube-cbrt
88×associate-/r*
40×cbrt-prod associate-*r*
19×div-inv
10×pow1
6×associate-/r/
5×frac-times associate-*l/ associate-*r/ unswap-sqr
4×insert-posit16 add-log-exp
3×pow-prod-down sqrt-prod
2×clear-num frac-2neg sqrt-div associate-/l* associate-/l/
1×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* *-commutative flip--
Counts
4 → 724
Calls
4 calls:
Slowest
242.0ms
(* (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))) (/ (cbrt h) (cbrt l)))
29.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
29.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
8.0ms
(sqrt (- 1 (* (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))) (/ (cbrt h) (cbrt l)))))

series885.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
249.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
228.0ms
(sqrt (- 1 (* (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))) (/ (cbrt h) (cbrt l)))))
217.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
190.0ms
(* (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))) (/ (cbrt h) (cbrt l)))

simplify3.9m

Counts
788 → 736
Calls
788 calls:
Slowest
3.1s
(* (* (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))
2.9s
(* (* (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))) (/ h l))
2.4s
(* (* (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d)))) (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (/ (* (* 2 2) 2) (* (* (/ D d) (/ D d)) (/ D d))))) (/ h l))
2.4s
(* (* (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (/ (* (* 2 2) 2) (* (* (/ D d) (/ D d)) (/ D d)))) (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (/ (* (* 2 2) 2) (* (* (/ D d) (/ D d)) (/ D d))))) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))
2.4s
(* (* (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))

prune16.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

localize56.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
6.6b
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
4.7b
(sqrt (- 1 (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l))))))
2.5b
(* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
502×times-frac
221×add-sqr-sqrt
206×*-un-lft-identity add-cube-cbrt
180×add-exp-log
136×add-cbrt-cube
94×cbrt-undiv div-exp
88×associate-/r*
49×associate-*l*
44×prod-exp cbrt-unprod
40×cbrt-prod associate-*r*
24×div-inv
8×associate-/r/
7×pow1
5×unswap-sqr
4×insert-posit16 add-log-exp
3×associate-*r/ sqrt-prod
2×clear-num frac-2neg sqrt-div associate-/l* associate-/l/
1×frac-times rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 403
Calls
4 calls:
Slowest
72.0ms
(* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l)))
38.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
30.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
8.0ms
(sqrt (- 1 (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l))))))

series985.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
339.0ms
(* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l)))
236.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
213.0ms
(/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d)))
197.0ms
(sqrt (- 1 (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l))))))

simplify1.4m

Counts
464 → 415
Calls
464 calls:
Slowest
1.4s
(* (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d)))) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))
1.3s
(* (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))
1.2s
(sqrt (- (* 1 1) (* (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l)))) (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l)))))))
1.2s
(sqrt (- (pow 1 3) (pow (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (* (/ (* M (/ (cbrt h) (cbrt l))) (/ 2 (/ D d))) (/ (cbrt h) (cbrt l)))) 3)))
1.2s
(* (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))

prune9.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.6b

regimes2.4s

Accuracy

0% (1.4b remaining)

Error of 7.8b against oracle of 6.5b and baseline of 7.8b

bsearch4.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.9s9328×body80valid
650.0ms3043×body80nan