Details

Time bar (total: 38.6s)

sample96.0ms

Algorithm
intervals
Results
48.0ms299×body80valid
27.0ms91×body80nan

simplify129.0ms

Calls
1 calls:
Slowest
129.0ms
(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize35.0ms

Local error

Found 4 expressions with local error:

12.1b
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
6.6b
(/ (* M D) (* 2 d))
6.6b
(/ (* M D) (* 2 d))
4.9b
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

rewrite28.0ms

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
14.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
6.0ms
(/ (* M D) (* 2 d))
5.0ms
(/ (* M D) (* 2 d))
2.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))

series241.0ms

Calls
4 calls:
Slowest
121.0ms
(sqrt (- 1 (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))))
72.0ms
(/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h))
27.0ms
(/ (* M D) (* 2 d))
21.0ms
(/ (* M D) (* 2 d))

simplify12.2s

Calls
52 calls:
Slowest
2.4s
(/ (* (/ (* (* (* 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)))
937.0ms
(/ (* (* (* (/ (* 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)))
858.0ms
(/ (* (* (* (/ (* 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)))
523.0ms
(sqrt (- (pow 1 3) (pow (/ (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ l h)) 3)))
478.0ms
(- (+ (log (/ (* M D) (* 2 d))) (log (/ (* M D) (* 2 d)))) (log (/ l h)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize36.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* M D) (* 2 d))
6.6b
(/ (* M D) (* 2 d))
4.9b
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
4.8b
(/ (/ (* M D) (* 2 d)) l)

rewrite24.0ms

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×pow1 insert-posit16 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
8.0ms
(/ (/ (* M D) (* 2 d)) l)
6.0ms
(/ (* M D) (* 2 d))
6.0ms
(/ (* M D) (* 2 d))
2.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))

series202.0ms

Calls
4 calls:
Slowest
139.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
24.0ms
(/ (/ (* M D) (* 2 d)) l)
19.0ms
(/ (* M D) (* 2 d))
19.0ms
(/ (* M D) (* 2 d))

simplify4.9s

Calls
31 calls:
Slowest
682.0ms
(sqrt (- (pow 1 3) (pow (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))) 3)))
642.0ms
(sqrt (- (* 1 1) (* (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))) (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))))))
487.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
438.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
302.0ms
(sqrt (- 1 (* (/ (/ (* M D) (* 2 d)) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize36.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* M D) (* 2 d))
6.4b
(/ (* 2 d) (* M D))
4.9b
(sqrt (- 1 (* (/ (/ 1 (/ (* 2 d) (* M D))) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
4.8b
(/ (/ 1 (/ (* 2 d) (* M D))) l)

rewrite23.0ms

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×pow1 insert-posit16 div-inv add-log-exp
3×clear-num frac-2neg sqrt-prod
2×cbrt-undiv associate-/r* times-frac sqrt-div div-exp
1×rem-sqrt-square flip3-- pow1/2 associate-/r/ flip-- associate-/l/
Calls
4 calls:
Slowest
7.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) l)
6.0ms
(/ (* M D) (* 2 d))
6.0ms
(/ (* 2 d) (* M D))
2.0ms
(sqrt (- 1 (* (/ (/ 1 (/ (* 2 d) (* M D))) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))

series232.0ms

Calls
4 calls:
Slowest
159.0ms
(sqrt (- 1 (* (/ (/ 1 (/ (* 2 d) (* M D))) l) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
27.0ms
(/ (/ 1 (/ (* 2 d) (* M D))) l)
27.0ms
(/ (* M D) (* 2 d))
19.0ms
(/ (* 2 d) (* M D))

simplify5.2s

Calls
29 calls:
Slowest
515.0ms
(sqrt (- (pow 1 3) (pow (* (/ (/ 1 (/ (* 2 d) (* M D))) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))) 3)))
513.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
509.0ms
(sqrt (- (* 1 1) (* (* (/ (/ 1 (/ (* 2 d) (* M D))) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))) (* (/ (/ 1 (/ (* 2 d) (* M D))) l) (/ (/ (* M D) (* 2 d)) (/ 1 h))))))
449.0ms
(* (cbrt (/ 1 (/ (* 2 d) (* M D)))) (cbrt (/ 1 (/ (* 2 d) (* M D)))))
382.0ms
(/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* (* M D) (* M D)) (* M D)))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize29.0ms

Local error

Found 4 expressions with local error:

6.6b
(/ (* M D) (* 2 d))
6.4b
(/ (* 2 d) (* M D))
5.1b
(* l (/ (* 2 d) (* M D)))
4.9b
(sqrt (- 1 (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×associate-*r*
4×pow1 insert-posit16 add-log-exp
3×times-frac sqrt-prod div-inv
2×cbrt-undiv clear-num associate-/r* frac-2neg sqrt-div div-exp associate-/l*
1×rem-sqrt-square flip3-- pow1/2 associate-*r/ *-commutative flip--
Calls
4 calls:
Slowest
6.0ms
(/ (* 2 d) (* M D))
6.0ms
(/ (* M D) (* 2 d))
2.0ms
(* l (/ (* 2 d) (* M D)))
2.0ms
(sqrt (- 1 (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))

series203.0ms

Calls
4 calls:
Slowest
137.0ms
(sqrt (- 1 (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))
31.0ms
(* l (/ (* 2 d) (* M D)))
19.0ms
(/ (* M D) (* 2 d))
16.0ms
(/ (* 2 d) (* M D))

simplify6.1s

Calls
32 calls:
Slowest
1.0s
(sqrt (- (pow 1 3) (pow (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h))) 3)))
837.0ms
(sqrt (- (* 1 1) (* (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h))) (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h))))))
680.0ms
(* 2 (/ (* l d) (* M D)))
433.0ms
(sqrt (* (cbrt (- 1 (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h))))) (cbrt (- 1 (* (/ 1 (* l (/ (* 2 d) (* M D)))) (/ (/ (* M D) (* 2 d)) (/ 1 h)))))))
433.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.7b

regimes1.1s

Accuracy

0% (1.9b remaining)

Error of 8.8b against oracle of 6.9b and baseline of 8.8b

bsearch4.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.9s9288×body80valid
510.0ms3049×body80nan