Details

Time bar (total: 45.2s)

sample273.0ms

Algorithm
intervals
Results
122.0ms473×body80nan
96.0ms300×body80valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
43017
3618
2155
150
021

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.9b

localize34.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ n (/ Om l))
4.5b
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
6.8b
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
19.1b
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite95.0ms

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 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 → 126
Calls
4 calls:
11.0ms
(/ n (/ Om l))
0.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
48.0ms
(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
30.0ms
(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:
32.0ms
(/ n (/ Om l))
361.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
518.0ms
(* (* 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)))))

simplify1.4s

Counts
138 → 138
Iterations
IterNodes
22646
1720
0280

prune2.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.3b

localize35.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ n (/ Om l))
4.5b
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
7.5b
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
19.1b
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite89.0ms

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 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 → 122
Calls
4 calls:
5.0ms
(/ n (/ Om l))
0.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
47.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
35.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

series2.9s

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ n (/ Om l))
317.0ms
(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
425.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
2.1s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

simplify838.0ms

Counts
134 → 134
Iterations
IterNodes
22560
1721
0273

prune2.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 16.8b

localize47.0ms

Local error

Found 4 expressions with local error:

7.5b
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
7.5b
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
19.1b
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
19.1b
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
42×pow1
24×pow-prod-down
22×add-cbrt-cube add-exp-log
12×prod-exp cbrt-unprod
8×sqrt-pow1
6×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
2×distribute-rgt-in distribute-lft-in pow1/2 associate-*l* *-commutative sqrt-prod
Counts
4 → 80
Calls
4 calls:
54.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
41.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
46.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
44.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

series5.1s

Counts
4 → 12
Calls
4 calls:
440.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
498.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
2.1s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.1s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

simplify4.9s

Counts
92 → 92
Iterations
IterNodes
38502
21473
1343
0121

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 16.8b

localize56.0ms

Local error

Found 4 expressions with local error:

19.1b
(sqrt (* (* (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
20.7b
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
20.7b
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
20.7b
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
15×sqrt-pow1
12×pow1/3
9×pow-prod-up
6×pow-plus
5×pow-prod-down
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt log1p-expm1-u add-log-exp
3×cbrt-prod pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 59
Calls
4 calls:
103.0ms
(sqrt (* (* (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
60.0ms
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
33.0ms
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
43.0ms
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

series5.0s

Counts
4 → 12
Calls
4 calls:
2.8s
(sqrt (* (* (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
828.0ms
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
675.0ms
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
736.0ms
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

simplify838.0ms

Counts
71 → 71
Iterations
IterNodes
32472
2744
1283
0131

prune1.4s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 16.8b

regimes990.0ms

Accuracy

29.9% (8.0b remaining)

Error of 26.4b against oracle of 18.4b and baseline of 29.9b

bsearch522.0ms

Steps
ItersRangePoint
5
1.3731110314963724e+134
3.3072949375599235e+134
1.6146438901602828e+134
6
4.104476132045785e-159
5.52927876224082e-158
3.943826962444769e-158
8
3.251403580285843e-305
3.6574182083595513e-301
3.311625067513457e-305

simplify16.0ms

Iterations
IterNodes
243
143
034

end0.0ms

sample8.9s

Algorithm
intervals
Results
4.7s14546×body80nan
3.0s9210×body80valid