Details

Time bar (total: 47.3s)

sample83.0ms

Algorithm
intervals
Results
41.0ms292×body80valid
15.0ms101×body80nan

simplify143.0ms

Calls
1 calls:
Slowest
143.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize42.0ms

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))))

rewrite36.0ms

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×pow1 prod-exp cbrt-unprod insert-posit16 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
13.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
6.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

series245.0ms

Calls
4 calls:
Slowest
138.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
69.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
22.0ms
(/ (* M D) (* 2 d))
16.0ms
(/ (* M D) (* 2 d))

simplify12.6s

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)))
1.0s
(/ (* (* (* (/ (* 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)))
934.0ms
(/ (* (* (* (/ (* 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)))
573.0ms
(* (/ (* M D) (* 2 d)) (* M D))
573.0ms
(- (+ (log (/ (* M D) (* 2 d))) (log (/ (* M D) (* 2 d)))) (log (/ l h)))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize18.0ms

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))

rewrite22.0ms

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×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×associate-/l/
1×associate-/r/
Calls
4 calls:
Slowest
8.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
5.0ms
(/ (/ (* M D) (* 2 d)) l)
3.0ms
(/ (* M D) (* 2 d))
3.0ms
(/ (* M D) (* 2 d))

series152.0ms

Calls
4 calls:
Slowest
52.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
42.0ms
(/ (/ (* M D) (* 2 d)) l)
31.0ms
(/ (* M D) (* 2 d))
26.0ms
(/ (* M D) (* 2 d))

simplify9.9s

Calls
78 calls:
Slowest
818.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
573.0ms
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
460.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
408.0ms
(- (- (log (* M D)) (log (* 2 d))) (log (/ 1 h)))
388.0ms
(/ (/ (* M D) (* 2 d)) (sqrt (/ 1 h)))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize23.0ms

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))

rewrite7.0ms

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×pow1 times-frac insert-posit16 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))
1.0ms
(cbrt (/ (* M D) (* 2 d)))
1.0ms
(cbrt (/ (* M D) (* 2 d)))
1.0ms
(cbrt (/ (* M D) (* 2 d)))

series398.0ms

Calls
4 calls:
Slowest
145.0ms
(cbrt (/ (* M D) (* 2 d)))
123.0ms
(cbrt (/ (* M D) (* 2 d)))
113.0ms
(cbrt (/ (* M D) (* 2 d)))
17.0ms
(/ (* M D) (* 2 d))

simplify3.6s

Calls
34 calls:
Slowest
412.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
293.0ms
(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
291.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 d)) (+ (log (/ 1 M)) (log (/ 1 D)))))))
290.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 d)) (+ (log (/ 1 M)) (log (/ 1 D)))))))
273.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (log (/ 1 d)) (+ (log (/ 1 M)) (log (/ 1 D)))))))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize35.0ms

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))

rewrite326.0ms

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×insert-posit16 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
314.0ms
(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)))
4.0ms
(* (/ M 2) (/ D d))
4.0ms
(* (/ M 2) (/ D d))
4.0ms
(* (/ M 2) (/ D d))

series115.0ms

Calls
4 calls:
Slowest
58.0ms
(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)))
25.0ms
(* (/ M 2) (/ D d))
16.0ms
(* (/ M 2) (/ D d))
16.0ms
(* (/ M 2) (/ D d))

simplify9.2s

Calls
57 calls:
Slowest
944.0ms
(* (* (* (/ M 2) (/ M 2)) (/ M 2)) (* (* (/ D d) (/ D d)) (/ D d)))
737.0ms
(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))))
685.0ms
(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)))
625.0ms
(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)))
603.0ms
(* (* (* (/ M 2) (/ M 2)) (/ M 2)) (* (* (/ D d) (/ D d)) (/ D d)))

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

regimes1.1s

Accuracy

0% (1.3b remaining)

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

bsearch7.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.8s9281×body80valid
660.0ms2962×body80nan