Details

Time bar (total: 1.6m)

sample368.0ms

Algorithm
intervals
Results
155.0ms448×body80nan
71.0ms290×body80valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
43017
3618
2155
150
021

prune46.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize74.0ms

Local error

Found 4 expressions with local error:

3.3b
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
4.4b
(/ n (/ Om l))
5.3b
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
19.3b
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
46×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
29×pow1
21×add-cbrt-cube add-exp-log
16×pow-prod-down
13×associate-/r*
8×prod-exp cbrt-unprod
5×sqrt-pow1 fma-udef div-inv
4×distribute-rgt-in expm1-log1p-u distribute-lft-in insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/l*
1×clear-num frac-2neg pow1/2 associate-*r* associate-*l* associate-/r/ *-commutative sqrt-prod
Counts
4 → 130
Calls
4 calls:
0.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
13.0ms
(/ n (/ Om l))
46.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
53.0ms
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
301.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
27.0ms
(/ n (/ Om l))
500.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify947.0ms

Counts
142 → 142
Iterations
IterNodes
22590
1740
0284

prune2.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.2b

localize78.0ms

Local error

Found 4 expressions with local error:

3.3b
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
4.4b
(/ n (/ Om l))
7.1b
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
19.3b
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
47×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
23×pow1
18×add-cbrt-cube add-exp-log
13×associate-/r*
12×pow-prod-down
6×prod-exp cbrt-unprod
5×div-inv
4×expm1-log1p-u sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* fma-udef associate-/l*
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow1/2 associate-*l* associate-/r/ *-commutative sqrt-prod
Counts
4 → 126
Calls
4 calls:
0.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
10.0ms
(/ n (/ Om l))
91.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
73.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

series3.3s

Counts
4 → 12
Calls
4 calls:
354.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
36.0ms
(/ n (/ Om l))
460.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
2.4s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

simplify1.1s

Counts
138 → 138
Iterations
IterNodes
22643
1723
0277

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.0b

localize46.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ (/ Om l) (cbrt n))
3.3b
(fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
7.1b
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
19.3b
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
82×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
42×cbrt-prod
23×pow1
18×add-exp-log
16×add-cbrt-cube
13×associate-/l*
12×pow-prod-down
8×div-inv
6×associate-/r* prod-exp cbrt-unprod
4×expm1-log1p-u sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* fma-udef
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow1/2 associate-*l* *-commutative sqrt-prod associate-/l/
Counts
4 → 168
Calls
4 calls:
16.0ms
(/ (/ Om l) (cbrt n))
0.0ms
(fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
71.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
51.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

series3.5s

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (/ Om l) (cbrt n))
454.0ms
(fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
491.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
2.4s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ Om l) (cbrt n))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

simplify1.0s

Counts
180 → 180
Iterations
IterNodes
22438
1816
0346

prune3.8s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 17.0b

localize93.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l))))
3.3b
(fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
7.1b
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
19.3b
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
7064×times-frac
2277×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
1680×cbrt-prod
964×associate-/r*
375×div-inv
177×add-exp-log
116×div-exp
68×cbrt-undiv
67×add-cbrt-cube
34×prod-exp
23×pow1
22×cbrt-unprod
17×associate-/r/
12×1-exp pow-prod-down
4×expm1-log1p-u sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* fma-udef
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in pow1/2 associate-*l* *-commutative sqrt-prod associate-/l*
Counts
4 → 2048
Calls
4 calls:
31.0ms
(/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l))))
0.0ms
(fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
85.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
73.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

series3.7s

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l))))
344.0ms
(fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
485.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
2.9s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ (* (cbrt n) (cbrt n)) (/ (/ (* (cbrt Om) (cbrt Om)) 1) (/ (cbrt n) (/ (cbrt Om) l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

simplify29.4s

Counts
2060 → 2060
Iterations
IterNodes
115826
04260

prune34.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 17.0b

regimes786.0ms

Accuracy

12.1% (9.8b remaining)

Error of 28.1b against oracle of 18.2b and baseline of 29.4b

bsearch536.0ms

Steps
ItersRangePoint
8
1.775531535574844e+136
2.7010388083314115e+140
1.2796693870036841e+137
10
2.10895001498433e-196
1.1190605292380991e-185
5.193191025670422e-187
9
3.416020371792863e-306
1.1730733401096994e-298
3.546451389182172e-302

simplify23.0ms

Iterations
IterNodes
259
159
050

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.6s14973×body80nan
1.8s9258×body80valid