Details

Time bar (total: 9.2m)

sample218.0ms

Algorithm
intervals
Results
103.0ms498×body80nan
58.0ms292×body80valid

simplify232.0ms

Calls
1 calls:
Slowest
231.0ms
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.7b

localize83.0ms

Local error

Found 4 expressions with local error:

20.1b
(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
7.5b
(/ (* l l) Om)
6.3b
(* (* (/ l Om) (/ l Om)) (- U U*))
6.1b
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite26.7s

Algorithm
rewrite-expression-head
Rules
890×frac-times
593×add-sqr-sqrt
399×*-un-lft-identity
385×add-cube-cbrt
381×associate-/l*
369×associate-*r/
363×associate-/r*
256×associate-*l/
205×flip3-- flip--
191×associate-*r*
149×times-frac
147×associate-*l*
127×clear-num
121×frac-2neg
100×unswap-sqr
55×distribute-rgt-in distribute-lft-in
54×prod-diff
52×add-cbrt-cube add-exp-log
46×swap-sqr sqrt-prod
28×pow1
25×prod-exp cbrt-unprod
16×*-commutative
15×pow-prod-down
13×difference-of-squares
12×un-div-inv
10×cbrt-undiv div-exp
9×div-inv
6×sub-neg
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
2×sqrt-div
1×pow1/2
Calls
4 calls:
Slowest
26.3s
(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
276.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
96.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))
25.0ms
(/ (* l l) Om)

series2.7s

Calls
4 calls:
Slowest
2.4s
(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
165.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
103.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))
35.0ms
(/ (* l l) Om)

simplify3.7m

Calls
1233 calls:
Slowest
906.0ms
(* (* (sqrt l) 1) (- (* U U) (* U* U*)))
829.0ms
(* (* Om (- Om)) (+ (* U U) (+ (* U* U*) (* U U*))))
778.0ms
(* (* (sqrt Om) (/ Om (cbrt l))) (+ U U*))
672.0ms
(* (* (fma (- (sqrt U*)) (sqrt U*) (* (sqrt U*) (sqrt U*))) (* (/ l Om) (/ l Om))) n)
657.0ms
(* (* (* n n) n) (* (* (/ (* (* l l) l) (* (* Om Om) Om)) (/ (* (* l l) l) (* (* Om Om) Om))) (* (* (- U U*) (- U U*)) (- U U*))))

prune20.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.7b

localize73.0ms

Local error

Found 4 expressions with local error:

15.9b
(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
7.5b
(/ (* l l) Om)
6.3b
(* (* (/ l Om) (/ l Om)) (- U U*))
6.1b
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite8.6s

Algorithm
rewrite-expression-head
Rules
890×frac-times
589×add-sqr-sqrt
398×*-un-lft-identity
384×add-cube-cbrt
381×associate-/l*
367×associate-*r/
363×associate-/r*
256×associate-*l/
205×flip3-- flip--
156×associate-*r*
149×times-frac
147×associate-*l*
127×clear-num
121×frac-2neg
97×unswap-sqr
55×distribute-rgt-in distribute-lft-in
54×prod-diff
52×add-cbrt-cube add-exp-log
46×swap-sqr
40×sqrt-prod
25×prod-exp cbrt-unprod
24×pow1
15×*-commutative
13×difference-of-squares
12×pow-prod-down un-div-inv
10×cbrt-undiv div-exp
9×div-inv
7×cbrt-prod
6×sub-neg
5×rem-sqrt-square
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
3×sqrt-pow1
2×sqrt-div
1×pow1/2
Calls
4 calls:
Slowest
8.1s
(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
293.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
83.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))
13.0ms
(/ (* l l) Om)

series9.3s

Calls
4 calls:
Slowest
9.0s
(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
174.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
89.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))
41.0ms
(/ (* l l) Om)

simplify3.7m

Calls
1227 calls:
Slowest
1.0s
(* (* (/ l Om) (* (cbrt l) (cbrt l))) (- (pow U 3) (pow U* 3)))
842.0ms
(* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (- (pow U 3) (pow U* 3)))
739.0ms
(* (* (/ l (* (cbrt Om) (cbrt Om))) 1) (- (* U U) (* U* U*)))
702.0ms
(* (* (* (/ l Om) (/ l Om)) (fma (- U*) 1 (* U* 1))) n)
693.0ms
(* (* (* n n) n) (* (* (/ (* (* l l) l) (* (* Om Om) Om)) (/ (* (* l l) l) (* (* Om Om) Om))) (* (* (- U U*) (- U U*)) (- U U*))))

prune23.9s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 13.2b

localize89.0ms

Local error

Found 4 expressions with local error:

15.9b
(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
6.3b
(* (* (/ l Om) (/ l Om)) (- U U*))
6.1b
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
3.6b
(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))

rewrite9.7s

Algorithm
rewrite-expression-head
Rules
1454×add-sqr-sqrt
890×frac-times
748×*-un-lft-identity
718×add-cube-cbrt
670×associate-*r*
564×prod-diff
523×associate-*l*
422×times-frac
369×associate-*r/
366×associate-/l*
360×associate-/r*
357×unswap-sqr
313×distribute-rgt-in distribute-lft-in
256×associate-*l/
206×flip3-- flip--
138×swap-sqr
126×clear-num
120×frac-2neg
49×add-cbrt-cube add-exp-log
43×*-commutative
40×sqrt-prod
32×div-inv
30×difference-of-squares
26×pow1
25×prod-exp cbrt-unprod
13×pow-prod-down
12×un-div-inv distribute-lft-out--
8×cbrt-undiv sub-neg div-exp
7×cbrt-prod
5×rem-sqrt-square
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1
2×sqrt-div associate--l+ fma-udef
1×pow1/2
Calls
4 calls:
Slowest
7.7s
(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
1.6s
(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))
292.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
111.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

series9.9s

Calls
4 calls:
Slowest
9.1s
(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
511.0ms
(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))
156.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
111.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))