Details

Time bar (total: 43.7s)

sample138.0ms

Algorithm
intervals
Results
85.0ms299×body80valid
24.0ms107×body80nan

simplify204.0ms

Calls
1 calls:
Slowest
203.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize46.0ms

Local error

Found 4 expressions with local error:

10.2b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
5.8b
(/ (* M D) (* 2 d))
5.8b
(/ (* M D) (* 2 d))
4.9b
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

rewrite33.0ms

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
12.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
7.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
7.0ms
(/ (* M D) (* 2 d))
5.0ms
(/ (* M D) (* 2 d))

series429.0ms

Calls
4 calls:
Slowest
225.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
107.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
50.0ms
(/ (* M D) (* 2 d))
46.0ms
(/ (* M D) (* 2 d))

simplify12.3s

Calls
52 calls:
Slowest
2.3s
(/ (* (/ (* (* (* 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)))
996.0ms
(/ (* (* (* (/ (* 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)))
649.0ms
(- (+ (log (/ (* M D) (* 2 d))) (log (/ (* M D) (* 2 d)))) (log (/ l h)))
574.0ms
(sqrt (- (pow 1 3) (pow (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h)) 3)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.1b

localize24.0ms

Local error

Found 4 expressions with local error:

6.1b
(/ (/ (* M D) (* 2 d)) (/ 1 h))
5.8b
(/ (* M D) (* 2 d))
5.8b
(/ (* M D) (* 2 d))
5.0b
(/ (/ (* M D) (* 2 d)) l)

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×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
6.0ms
(/ (/ (* 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))

series153.0ms

Calls
4 calls:
Slowest
54.0ms
(/ (/ (* M D) (* 2 d)) (/ 1 h))
40.0ms
(/ (/ (* M D) (* 2 d)) l)
31.0ms
(/ (* M D) (* 2 d))
28.0ms
(/ (* M D) (* 2 d))

simplify10.0s

Calls
78 calls:
Slowest
996.0ms
(/ (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
679.0ms
(/ (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (* (* (/ 1 h) (/ 1 h)) (/ 1 h)))
426.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
402.0ms
(- (- (log (* M D)) (log (* 2 d))) (log (/ 1 h)))
390.0ms
(* 1/2 (/ (* M (* D h)) d))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.1b

localize20.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* M D) (* 2 d))
5.8b
(/ (* M D) (* 2 d))
5.0b
(/ (/ (* M D) (* 2 d)) l)
4.9b
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (/ (* M D) (* 2 d)) (* (cbrt (/ 1 h)) (cbrt (/ 1 h)))) (cbrt (/ 1 h))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
8×add-cbrt-cube add-exp-log
7×add-sqr-sqrt associate-/l*
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u div-inv add-log-exp
3×clear-num frac-2neg times-frac sqrt-prod
2×cbrt-undiv associate-/r* sqrt-div div-exp
1×rem-sqrt-square flip3-- pow1/2 flip-- associate-/l/
Calls
4 calls:
Slowest
11.0ms
(/ (/ (* M D) (* 2 d)) l)
6.0ms
(/ (* M D) (* 2 d))
4.0ms
(/ (* M D) (* 2 d))
4.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (/ (* M D) (* 2 d)) (* (cbrt (/ 1 h)) (cbrt (/ 1 h)))) (cbrt (/ 1 h))))))

series371.0ms

Calls
4 calls:
Slowest
245.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (/ (* M D) (* 2 d)) (* (cbrt (/ 1 h)) (cbrt (/ 1 h)))) (cbrt (/ 1 h))))))
50.0ms
(/ (/ (* M D) (* 2 d)) l)
46.0ms
(/ (* M D) (* 2 d))
30.0ms
(/ (* M D) (* 2 d))

simplify5.1s

Calls
31 calls:
Slowest
784.0ms
(sqrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (/ (* M D) (* 2 d)) (* (cbrt (/ 1 h)) (cbrt (/ 1 h)))) (cbrt (/ 1 h)))) 3)))
592.0ms
(sqrt (- (* 1 1) (* (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (/ (* M D) (* 2 d)) (* (cbrt (/ 1 h)) (cbrt (/ 1 h)))) (cbrt (/ 1 h)))) (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (/ (* M D) (* 2 d)) (* (cbrt (/ 1 h)) (cbrt (/ 1 h)))) (cbrt (/ 1 h)))))))
426.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
415.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
355.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (/ (* M D) (* 2 d)) (* (cbrt (/ 1 h)) (cbrt (/ 1 h)))) (cbrt (/ 1 h))))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.1b

localize22.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* M D) (* 2 d))
5.8b
(/ (* M D) (* 2 d))
4.9b
(sqrt (- 1 (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h))))
4.1b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
8×add-cbrt-cube add-exp-log
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg sqrt-prod div-inv associate-/l* associate-/l/
2×cbrt-undiv associate-/r* times-frac sqrt-div div-exp
1×frac-times rem-sqrt-square flip3-- pow1/2 associate-*l/ associate-*r/ flip--
Calls
4 calls:
Slowest
21.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l)
8.0ms
(sqrt (- 1 (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h))))
6.0ms
(/ (* M D) (* 2 d))
6.0ms
(/ (* M D) (* 2 d))

series385.0ms

Calls
4 calls:
Slowest
198.0ms
(sqrt (- 1 (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h))))
89.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l)
52.0ms
(/ (* M D) (* 2 d))
46.0ms
(/ (* M D) (* 2 d))

simplify4.0s

Calls
30 calls:
Slowest
443.0ms
(sqrt (- (pow 1 3) (pow (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h)) 3)))
442.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
401.0ms
(sqrt (- (* 1 1) (* (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h)) (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h)))))
397.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
259.0ms
(sqrt (* (cbrt (- 1 (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h)))) (cbrt (- 1 (/ (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) l) (/ 1 h))))))

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.9b

regimes1.2s

Accuracy

0% (1.4b remaining)

Error of 8.5b against oracle of 7.1b and baseline of 8.5b

bsearch8.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s9327×body80valid
967.0ms3239×body80nan