Details

Time bar (total: 45.8s)

sample73.0ms

Algorithm
intervals
Results
39.0ms292×body80valid
13.0ms101×body80nan

simplify174.0ms

Calls
1 calls:
Slowest
173.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize24.0ms

Local error

Found 4 expressions with local error:

10.7b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
7.3b
(/ (* M D) (* 2 d))
7.3b
(/ (* M D) (* 2 d))
3.6b
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
26×add-cbrt-cube add-exp-log
11×cbrt-undiv div-exp
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×div-inv
4×expm1-log1p-u pow1 prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod associate-/l* associate-/l/
2×sqrt-div
1×frac-times rem-sqrt-square flip3-- pow1/2 associate-*l/ associate-*r/ associate-/r/ flip--
Calls
4 calls:
Slowest
29.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
7.0ms
(/ (* M D) (* 2 d))
7.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
7.0ms
(/ (* M D) (* 2 d))

series259.0ms

Calls
4 calls:
Slowest
142.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
80.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
20.0ms
(/ (* M D) (* 2 d))
18.0ms
(/ (* M D) (* 2 d))

simplify11.8s

Calls
52 calls:
Slowest
2.0s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
1.1s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
884.0ms
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
579.0ms
(- (+ (log (/ (* M D) (* 2 d))) (log (/ (* M D) (* 2 d)))) (log (/ l h)))
492.0ms
(sqrt (- (pow 1 3) (pow (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h)) 3)))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* M D) (* 2 d))
7.3b
(/ (* M D) (* 2 d))
6.2b
(/ (/ (* M D) (* 2 d)) l)
4.7b
(/ (/ (* M D) (* 2 d)) (/ 1 h))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×times-frac
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt div-inv
13×add-cbrt-cube add-exp-log
12×associate-/l*
6×associate-/r*
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×associate-/l/
1×associate-/r/
Calls
4 calls:
Slowest
14.0ms
(/ (/ (* M D) (* 2 d)) l)
6.0ms
(/ (* M D) (* 2 d))
6.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
6.0ms
(/ (* M D) (* 2 d))

series119.0ms

Calls
4 calls:
Slowest
38.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
38.0ms
(/ (/ (* M D) (* 2 d)) l)
25.0ms
(/ (* M D) (* 2 d))
17.0ms
(/ (* M D) (* 2 d))

simplify8.4s

Calls
78 calls:
Slowest
665.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
528.0ms
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
399.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
397.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
354.0ms
(- (- (log (* M D)) (log (* 2 d))) (log (/ 1 h)))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize27.0ms

Local error

Found 4 expressions with local error:

17.6b
(cbrt (/ (* M D) (* 2 d)))
17.6b
(cbrt (/ (* M D) (* 2 d)))
17.6b
(cbrt (/ (* M D) (* 2 d)))
7.3b
(/ (* M D) (* 2 d))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 times-frac insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3
1×cbrt-undiv clear-num associate-/r* frac-2neg div-exp associate-/l*
Calls
4 calls:
Slowest
3.0ms
(/ (* M D) (* 2 d))
2.0ms
(cbrt (/ (* M D) (* 2 d)))
2.0ms
(cbrt (/ (* M D) (* 2 d)))
2.0ms
(cbrt (/ (* M D) (* 2 d)))

series357.0ms

Calls
4 calls:
Slowest
118.0ms
(cbrt (/ (* M D) (* 2 d)))
110.0ms
(cbrt (/ (* M D) (* 2 d)))
104.0ms
(cbrt (/ (* M D) (* 2 d)))
24.0ms
(/ (* M D) (* 2 d))

simplify4.1s

Calls
34 calls:
Slowest
421.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
354.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 d)) (+ (log (/ 1 M)) (log (/ 1 D)))))))
346.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
309.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 d)) (+ (log (/ 1 M)) (log (/ 1 D)))))))
299.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize41.0ms

Local error

Found 4 expressions with local error:

16.8b
(cbrt (* (* (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))
5.1b
(* (/ M 2) (/ D d))
5.1b
(* (/ M 2) (/ D d))
5.1b
(* (/ M 2) (/ D d))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*r* associate-*l*
10×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
8×frac-times associate-*l/
7×cbrt-div
6×associate-*r/ div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
318.0ms
(cbrt (* (* (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))
5.0ms
(* (/ M 2) (/ D d))
4.0ms
(* (/ M 2) (/ D d))
4.0ms
(* (/ M 2) (/ D d))

series171.0ms

Calls
4 calls:
Slowest
91.0ms
(cbrt (* (* (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))
27.0ms
(* (/ M 2) (/ D d))
27.0ms
(* (/ M 2) (/ D d))
26.0ms
(* (/ M 2) (/ D d))

simplify8.3s

Calls
57 calls:
Slowest
670.0ms
(cbrt (* (* (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))
642.0ms
(cbrt (* (* (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h))))
607.0ms
(cbrt (* (* (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h))) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))
579.0ms
(* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h))
575.0ms
(cbrt (* (* (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l) (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h))) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)))

prune2.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

regimes1.0s

Accuracy

0% (1.3b remaining)

Error of 8.1b against oracle of 6.8b and baseline of 8.1b

bsearch4.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.9s9281×body80valid
601.0ms2962×body80nan