Details

Time bar (total: 28.3s)

sample54.0ms

Algorithm
intervals
Results
31.0ms369×body80valid
8.0ms106×body80nan

simplify1.1s

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (pow k m) a)
0.0b
(fma k (+ k 10) 1)
2.7b
(/ (* (pow k m) a) (fma k (+ k 10) 1))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt
10×add-cbrt-cube
8×*-un-lft-identity add-cube-cbrt
7×associate-*l*
6×prod-exp
4×unpow-prod-down div-exp
3×expm1-log1p-u pow1 associate-/r* times-frac associate-*r* log1p-expm1-u add-log-exp unswap-sqr
2×pow-to-exp cbrt-undiv pow-exp cbrt-unprod sqr-pow
1×clear-num frac-2neg *-commutative fma-udef div-inv associate-/l*
Counts
3 → 62
Calls
3 calls:
7.0ms
(* (pow k m) a)
0.0ms
(fma k (+ k 10) 1)
9.0ms
(/ (* (pow k m) a) (fma k (+ k 10) 1))

series369.0ms

Counts
3 → 9
Calls
3 calls:
164.0ms
(* (pow k m) a)
31.0ms
(fma k (+ k 10) 1)
174.0ms
(/ (* (pow k m) a) (fma k (+ k 10) 1))

simplify3.2s

Counts
71 → 71
Iterations
IterNodes
35794
21074
1322
0134

prune886.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow k m) (sqrt (fma k (+ k 10) 1)))
0.1b
(* (/ (pow k m) (sqrt (fma k (+ k 10) 1))) (/ a (sqrt (fma k (+ k 10) 1))))
13.8b
(sqrt (fma k (+ k 10) 1))
13.8b
(sqrt (fma k (+ k 10) 1))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
146×add-sqr-sqrt
134×times-frac
76×*-un-lft-identity add-cube-cbrt sqrt-prod
46×associate-*l*
45×unpow-prod-down
33×add-exp-log
22×associate-*r*
21×unswap-sqr
19×sqr-pow
18×add-cbrt-cube
13×div-exp
8×pow1 prod-exp
7×associate-/l*
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×pow-to-exp pow-exp div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 216
Calls
4 calls:
8.0ms
(/ (pow k m) (sqrt (fma k (+ k 10) 1)))
30.0ms
(* (/ (pow k m) (sqrt (fma k (+ k 10) 1))) (/ a (sqrt (fma k (+ k 10) 1))))
2.0ms
(sqrt (fma k (+ k 10) 1))
2.0ms
(sqrt (fma k (+ k 10) 1))

series334.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (pow k m) (sqrt (fma k (+ k 10) 1)))
140.0ms
(* (/ (pow k m) (sqrt (fma k (+ k 10) 1))) (/ a (sqrt (fma k (+ k 10) 1))))
39.0ms
(sqrt (fma k (+ k 10) 1))
40.0ms
(sqrt (fma k (+ k 10) 1))

simplify996.0ms

Counts
228 → 228
Iterations
IterNodes
22476
1806
0290

prune2.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (/ (pow k m) (sqrt (fma k (+ k 10) 1))) (/ 1 (sqrt (sqrt (fma k (+ k 10) 1))))) (/ a (sqrt (sqrt (fma k (+ k 10) 1)))))
13.8b
(sqrt (fma k (+ k 10) 1))
13.8b
(sqrt (fma k (+ k 10) 1))
13.8b
(sqrt (fma k (+ k 10) 1))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
145×add-exp-log
66×prod-exp
57×div-exp
45×add-cbrt-cube
36×sqrt-prod
31×associate-*r*
29×add-sqr-sqrt
27×times-frac
26×*-un-lft-identity add-cube-cbrt
18×cbrt-unprod
13×cbrt-undiv
12×pow1
8×pow-to-exp rec-exp 1-exp pow-exp
6×frac-times associate-*l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*r/
2×un-div-inv
1×associate-*l* *-commutative div-inv
Counts
4 → 142
Calls
4 calls:
60.0ms
(* (* (/ (pow k m) (sqrt (fma k (+ k 10) 1))) (/ 1 (sqrt (sqrt (fma k (+ k 10) 1))))) (/ a (sqrt (sqrt (fma k (+ k 10) 1)))))
1.0ms
(sqrt (fma k (+ k 10) 1))
1.0ms
(sqrt (fma k (+ k 10) 1))
1.0ms
(sqrt (fma k (+ k 10) 1))

series236.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (* (/ (pow k m) (sqrt (fma k (+ k 10) 1))) (/ 1 (sqrt (sqrt (fma k (+ k 10) 1))))) (/ a (sqrt (sqrt (fma k (+ k 10) 1)))))
37.0ms
(sqrt (fma k (+ k 10) 1))
42.0ms
(sqrt (fma k (+ k 10) 1))
40.0ms
(sqrt (fma k (+ k 10) 1))

simplify1.2s

Counts
154 → 154
Iterations
IterNodes
22614
1760
0249

prune2.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 99 (* k k))
1.7b
(* (exp (* (log k) m)) (/ a k))
1.7b
(* (exp (* (log k) m)) (/ a k))
5.5b
(* (/ (* (exp (* (log k) m)) (/ a k)) k) (- (/ 99 (* k k)) (/ 10 k)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
197×add-sqr-sqrt
182×prod-diff
177×*-un-lft-identity
175×add-cube-cbrt
93×distribute-rgt-in distribute-lft-in
44×div-inv
34×associate-*r*
33×add-cbrt-cube
27×add-exp-log
13×associate-*l*
11×prod-exp cbrt-unprod
10×pow1
8×cbrt-undiv div-exp
5×associate-*r/ unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
3×frac-times pow-prod-down *-commutative associate-/l*
2×sub-neg flip3-- frac-sub flip--
1×clear-num associate-/r* frac-2neg associate-*l/ distribute-lft-out--
Counts
4 → 319
Calls
4 calls:
12.0ms
(/ 99 (* k k))
20.0ms
(* (exp (* (log k) m)) (/ a k))
15.0ms
(* (exp (* (log k) m)) (/ a k))
143.0ms
(* (/ (* (exp (* (log k) m)) (/ a k)) k) (- (/ 99 (* k k)) (/ 10 k)))

series672.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 99 (* k k))
174.0ms
(* (exp (* (log k) m)) (/ a k))
181.0ms
(* (exp (* (log k) m)) (/ a k))
269.0ms
(* (/ (* (exp (* (log k) m)) (/ a k)) k) (- (/ 99 (* k k)) (/ 10 k)))

simplify4.6s

Counts
331 → 331
Iterations
IterNodes
26824
11923
0615

prune5.8s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes189.0ms

Accuracy

98.7% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch70.0ms

Steps
ItersRangePoint
6
9.545690680202222e+129
4.384054805801543e+130
1.0815742449266312e+130

simplify10.0ms

Iterations
IterNodes
232
132
026

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.8s12018×body80valid
578.0ms4190×body80nan