Details

Time bar (total: 2.4m)

sample241.0ms

Algorithm
intervals
Results
120.0ms505×body80nan
75.0ms303×body80valid

simplify880.0ms

Counts
1 → 1

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize63.0ms

Local error

Found 4 expressions with local error:

19.0b
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
7.3b
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
7.0b
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
6.9b
(/ Om (* l l))

rewrite487.0ms

Algorithm
rewrite-expression-head
Rules
1844×times-frac
803×add-sqr-sqrt
774×*-un-lft-identity
772×add-cube-cbrt
580×associate-*l*
98×div-inv
47×add-cbrt-cube add-exp-log
26×associate-*r/
25×pow1
17×cbrt-undiv div-exp
14×distribute-rgt-in distribute-lft-in prod-exp associate-/r/ cbrt-unprod
13×pow-prod-down
7×unswap-sqr
6×associate-*r*
4×sqrt-pow1 flip3-- sqrt-div frac-add insert-posit16 flip-- add-log-exp
3×associate-/l*
2×frac-times sub-neg flip3-+ *-commutative flip-+
1×clear-num associate-/r* frac-2neg pow1/2 associate-*l/ sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 696
Calls
4 calls:
Slowest
214.0ms
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
195.0ms
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
39.0ms
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
6.0ms
(/ Om (* l l))

series2.6s

Counts
4 → 12
Calls
4 calls:
Slowest
2.0s
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
428.0ms
(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
136.0ms
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
29.0ms
(/ Om (* l l))

simplify1.8s

Counts
708 → 708

prune14.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.7b

localize54.0ms

Local error

Found 4 expressions with local error:

19.0b
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
7.5b
(* (/ (* -2 n) (/ (/ Om l) l)) (* U 2))
7.3b
(* (* U 2) (* n (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
7.0b
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
1950×times-frac
838×add-sqr-sqrt
808×*-un-lft-identity
806×add-cube-cbrt
626×associate-*l*
110×add-cbrt-cube add-exp-log
102×div-inv
42×prod-exp cbrt-unprod
39×cbrt-undiv div-exp
24×pow1
15×associate-/r/
12×pow-prod-down
10×distribute-rgt-in distribute-lft-in associate-*r/
7×associate-*r* unswap-sqr
6×sub-neg
4×flip3-- sqrt-div associate-*l/ insert-posit16 flip-- add-log-exp
3×*-commutative sqrt-prod
2×frac-times frac-add
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 762
Calls
4 calls:
Slowest
77.0ms
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
62.0ms
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
61.0ms
(* (* U 2) (* n (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
37.0ms
(* (/ (* -2 n) (/ (/ Om l) l)) (* U 2))

series4.9s

Counts
4 → 12
Calls
4 calls:
Slowest
4.3s
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
421.0ms
(* (* U 2) (* n (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))
157.0ms
(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
94.0ms
(* (/ (* -2 n) (/ (/ Om l) l)) (* U 2))

simplify2.7s

Counts
774 → 774

prune17.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 19.9b

localize120.0ms

Local error

Found 4 expressions with local error:

19.0b
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
8.7b
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
7.5b
(* (/ (* -2 n) (/ (/ Om l) l)) (* U 2))
7.3b
(* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
3266×times-frac
1406×add-sqr-sqrt
1352×*-un-lft-identity
1346×add-cube-cbrt
977×associate-*l*
354×cbrt-prod
134×add-exp-log
129×div-inv
108×add-cbrt-cube
54×div-exp
48×prod-exp
42×cbrt-unprod
39×cbrt-undiv
24×pow1
15×associate-/r/
13×unswap-sqr
12×pow-prod-down
10×distribute-rgt-in distribute-lft-in associate-*r/
7×associate-*r*
6×sub-neg
4×flip3-- sqrt-div associate-*l/ insert-posit16 flip-- add-log-exp
3×rec-exp 1-exp *-commutative sqrt-prod
2×frac-times frac-add
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 1125
Calls
4 calls:
Slowest
97.0ms
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
66.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
57.0ms
(* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))
46.0ms
(* (/ (* -2 n) (/ (/ Om l) l)) (* U 2))

series5.8s

Counts
4 → 12
Calls
4 calls:
Slowest
4.7s
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
550.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
542.0ms
(* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))
97.0ms
(* (/ (* -2 n) (/ (/ Om l) l)) (* U 2))

simplify3.9s

Counts
1137 → 1137

prune31.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.4b

localize131.0ms

Local error

Found 4 expressions with local error:

19.0b
(sqrt (+ (* (/ -2 (/ 1 (* (cbrt l) (cbrt l)))) (* (/ n (/ (/ Om l) (cbrt l))) (* U 2))) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
8.7b
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
8.5b
(* (/ n (/ (/ Om l) (cbrt l))) (* U 2))
7.3b
(* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))

rewrite485.0ms

Algorithm
rewrite-expression-head
Rules
3799×times-frac
1660×add-sqr-sqrt
1606×*-un-lft-identity
1600×add-cube-cbrt
1180×associate-*l*
471×cbrt-prod
146×div-inv
101×add-exp-log
71×add-cbrt-cube
42×div-exp
33×prod-exp
27×cbrt-undiv cbrt-unprod
24×pow1
20×associate-*r/
15×associate-/r/
13×unswap-sqr
12×pow-prod-down
10×distribute-rgt-in distribute-lft-in
8×sqrt-div associate-*l/
7×associate-*r*
6×sub-neg flip3-- frac-add flip--
4×frac-times insert-posit16 add-log-exp
3×rec-exp 1-exp *-commutative sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 1320
Calls
4 calls:
Slowest
240.0ms
(sqrt (+ (* (/ -2 (/ 1 (* (cbrt l) (cbrt l)))) (* (/ n (/ (/ Om l) (cbrt l))) (* U 2))) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
58.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
40.0ms
(* (/ n (/ (/ Om l) (cbrt l))) (* U 2))
40.0ms
(* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))

series2.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (+ (* (/ -2 (/ 1 (* (cbrt l) (cbrt l)))) (* (/ n (/ (/ Om l) (cbrt l))) (* U 2))) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
568.0ms
(* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))
447.0ms
(* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))
316.0ms
(* (/ n (/ (/ Om l) (cbrt l))) (* U 2))

simplify4.7s

Counts
1332 → 1332

prune37.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.7b

regimes2.0s

Accuracy

37.8% (5.5b remaining)

Error of 24.4b against oracle of 18.9b and baseline of 27.7b

bsearch42.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.0s14747×body80nan
2.5s9218×body80valid