Details

Time bar (total: 29.5s)

sample113.0ms

Algorithm
intervals
Results
65.0ms384×body80valid
21.0ms136×body80nan

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
62068
5649
4212
394
250
124
012

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1 (* 10 k)) (* k k))
0.0b
(* a (pow k m))
1.2b
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
14×add-sqr-sqrt
10×add-cbrt-cube
9×*-un-lft-identity add-cube-cbrt
8×add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×expm1-log1p-u pow1 associate-/r* sum-log fma-def times-frac associate-*l* insert-posit16 log1p-expm1-u unswap-sqr
2×pow-to-exp cbrt-undiv flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ clear-num frac-2neg *-commutative div-inv associate-/l*
Counts
3 → 75
Calls
3 calls:
39.0ms
(+ (+ 1 (* 10 k)) (* k k))
18.0ms
(* a (pow k m))
25.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

series292.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (+ 1 (* 10 k)) (* k k))
102.0ms
(* a (pow k m))
159.0ms
(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

simplify3.2s

Counts
84 → 84
Iterations
IterNodes
36592
21426
1410
0159

prune404.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma k (+ k 10) 1)
0.3b
(/ (pow k m) (/ (fma k (+ k 10) 1) a))
0.6b
(expm1 (log1p (/ (pow k m) (/ (fma k (+ k 10) 1) a))))
3.6b
(/ (fma k (+ k 10) 1) a)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
96×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
42×unpow-prod-down
19×add-exp-log
16×associate-/r*
14×sqr-pow
11×add-cbrt-cube
10×div-exp div-inv associate-/l*
4×expm1-log1p-u pow1 cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp clear-num frac-2neg pow-exp
1×expm1-log1p associate-/r/ fma-udef expm1-udef
Counts
4 → 186
Calls
4 calls:
0.0ms
(fma k (+ k 10) 1)
17.0ms
(/ (pow k m) (/ (fma k (+ k 10) 1) a))
0.0ms
(expm1 (log1p (/ (pow k m) (/ (fma k (+ k 10) 1) a))))
9.0ms
(/ (fma k (+ k 10) 1) a)

series395.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(fma k (+ k 10) 1)
154.0ms
(/ (pow k m) (/ (fma k (+ k 10) 1) a))
164.0ms
(expm1 (log1p (/ (pow k m) (/ (fma k (+ k 10) 1) a))))
46.0ms
(/ (fma k (+ k 10) 1) a)

simplify2.0s

Counts
198 → 198
Iterations
IterNodes
22333
1792
0335

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k))))
0.3b
(/ 10 (/ a k))
0.6b
(expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k))))))
1.3b
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
195×*-un-lft-identity
153×times-frac
71×add-sqr-sqrt add-cube-cbrt
66×distribute-lft-out
24×unpow-prod-down
20×associate-/r*
16×div-inv
14×add-exp-log
11×add-cbrt-cube
10×associate-/l*
9×add-log-exp
8×frac-add sqr-pow
6×fma-def div-exp associate-/r/
4×expm1-log1p-u pow1 cbrt-undiv flip3-+ flip-+ insert-posit16 log1p-expm1-u
3×sum-log
2×clear-num frac-2neg
1×pow-to-exp +-commutative associate-+l+ expm1-log1p pow-exp expm1-udef
Counts
4 → 199
Calls
4 calls:
150.0ms
(/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k))))
6.0ms
(/ 10 (/ a k))
0.0ms
(expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k))))))
104.0ms
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k))))
28.0ms
(/ 10 (/ a k))
139.0ms
(expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k))))))
47.0ms
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))

simplify1.3s

Counts
211 → 211
Iterations
IterNodes
22600
1837
0352

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))
1.3b
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))
6.6b
(sqrt (expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))))))
6.6b
(sqrt (expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))))))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×distribute-lft-out
14×add-log-exp
12×fma-def
10×add-sqr-sqrt times-frac
8×frac-add add-cube-cbrt
6×pow1 sum-log sqrt-prod
4×expm1-log1p-u flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u div-inv
2×+-commutative rem-sqrt-square associate-+l+ sqrt-pow1 pow1/2
Counts
4 → 90
Calls
4 calls:
117.0ms
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))
120.0ms
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))
2.0ms
(sqrt (expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))))))
3.0ms
(sqrt (expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))))))

series700.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))
45.0ms
(+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))
322.0ms
(sqrt (expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))))))
293.0ms
(sqrt (expm1 (log1p (/ (pow k m) (+ (+ (/ k (/ a k)) (/ 1 a)) (/ 10 (/ a k)))))))

simplify11.6s

Counts
102 → 102
Iterations
IterNodes
36058
21420
1414
0145

prune817.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes247.0ms

Accuracy

91.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 2.0b

bsearch120.0ms

Steps
ItersRangePoint
8
1.3481016745397874e+138
8.814273209687855e+141
8.663816625552649e+141

simplify9.0ms

Iterations
IterNodes
230
130
024

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.8s11956×body80valid
999.0ms4252×body80nan