Details

Time bar (total: 42.2s)

sample217.0ms

Algorithm
intervals
Results
92.0ms428×body80nan
60.0ms304×body80valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
43017
3618
2155
150
021

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.7b

localize37.0ms

Local error

Found 4 expressions with local error:

4.8b
(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
4.8b
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
7.2b
(/ n (/ Om l))
20.0b
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
31×pow1
23×add-cbrt-cube add-exp-log
17×pow-prod-down
13×associate-/r*
9×prod-exp cbrt-unprod
6×fma-udef
5×distribute-rgt-in distribute-lft-in sqrt-pow1 div-inv
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×*-commutative
1×clear-num frac-2neg pow1/2 associate-/r/ sqrt-prod unswap-sqr
Counts
4 → 142
Calls
4 calls:
7.0ms
(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
36.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
6.0ms
(/ n (/ Om l))
19.0ms
(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:
409.0ms
(* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
456.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
29.0ms
(/ n (/ Om l))
2.4s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify1.1s

Counts
154 → 154
Iterations
IterNodes
22618
1747
0291

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.9b

localize66.0ms

Local error

Found 4 expressions with local error:

7.2b
(/ n (/ Om l))
7.2b
(/ n (/ Om l))
20.0b
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
20.0b
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
88×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×pow1
26×associate-/r*
16×pow-prod-down
14×add-cbrt-cube add-exp-log
10×sqrt-pow1 div-inv
6×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg pow1/2 associate-/r/ sqrt-prod
Counts
4 → 180
Calls
4 calls:
6.0ms
(/ n (/ Om l))
6.0ms
(/ n (/ Om l))
31.0ms
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
21.0ms
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series5.2s

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ n (/ Om l))
42.0ms
(/ n (/ Om l))
2.6s
(sqrt (* (* 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)))))

simplify2.0s

Counts
192 → 192
Iterations
IterNodes
35072
21445
1473
0201

prune2.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 21.9b

localize117.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
7.2b
(/ n (/ Om l))
20.0b
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
20.0b
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (cbrt l) (cbrt l)) (/ n (/ Om (cbrt l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
46×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
42×pow1
24×pow-prod-down
21×add-cbrt-cube add-exp-log
13×associate-/r*
10×sqrt-pow1
8×prod-exp cbrt-unprod
5×div-inv
4×distribute-rgt-in expm1-log1p-u distribute-lft-in fma-udef insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×pow1/2 sqrt-prod
1×clear-num frac-2neg associate-*r* associate-*l* associate-/r/ *-commutative
Counts
4 → 136
Calls
4 calls:
24.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
6.0ms
(/ n (/ Om l))
19.0ms
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
25.0ms
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (cbrt l) (cbrt l)) (/ n (/ Om (cbrt l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series5.6s

Counts
4 → 12
Calls
4 calls:
497.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
36.0ms
(/ n (/ Om l))
2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (cbrt l) (cbrt l)) (/ n (/ Om (cbrt l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify1.0s

Counts
148 → 148
Iterations
IterNodes
22722
1750
0287

prune2.0s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 21.9b

localize76.0ms

Local error

Found 4 expressions with local error:

4.2b
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
4.8b
(* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
7.2b
(/ n (/ Om l))
20.0b
(sqrt (* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
87×pow1
75×times-frac
62×pow-prod-down
50×add-exp-log
46×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
38×add-cbrt-cube
31×prod-exp cbrt-unprod
13×associate-/r*
12×distribute-rgt-in distribute-lft-in
11×sqrt-pow1
9×fma-udef
5×div-inv
4×expm1-log1p-u 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 → 158
Calls
4 calls:
0.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
159.0ms
(* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
7.0ms
(/ n (/ Om l))
96.0ms
(sqrt (* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))

series3.9s

Counts
4 → 12
Calls
4 calls:
689.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
526.0ms
(* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
34.0ms
(/ n (/ Om l))
2.6s
(sqrt (* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))

simplify1.7s

Counts
170 → 170
Iterations
IterNodes
23905
1992
0342

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 21.9b

regimes1.1s

Accuracy

40.3% (5.5b remaining)

Error of 25.7b against oracle of 20.2b and baseline of 29.4b

bsearch239.0ms

Steps
ItersRangePoint
7
-1.1161865709419737e-308
1.6416820990279393e-306
1.4828608859501e-310

simplify11.0ms

Iterations
IterNodes
246
146
038

end0.0ms

sample8.4s

Algorithm
intervals
Results
4.3s14975×body80nan
2.3s9155×body80valid