Details

Time bar (total: 6.2s)

sample41.0ms

Algorithm
intervals
Results
18.0ms381×body80valid
4.0ms126×body80nan

simplify104.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015
done50015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma k 10.0 1.0)
0.1b
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.3b
(fma k k (fma k 10.0 1.0))
3.6b
(/ (fma k k (fma k 10.0 1.0)) a)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
96×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
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×pow1 cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num fma-udef
1×associate-/r/
Counts
4 → 181
Calls
4 calls:
0.0ms
(fma k 10.0 1.0)
12.0ms
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.0ms
(fma k k (fma k 10.0 1.0))
5.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

series225.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma k 10.0 1.0)
114.0ms
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
22.0ms
(fma k k (fma k 10.0 1.0))
51.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

simplify85.0ms

Counts
193 → 193
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07151922
132801854
250021852
done50021852

prune542.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.2b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
7×associate-*r*
6×fma-def prod-exp
4×pow1 expm1-log1p-u unpow-prod-down div-exp sum-log log1p-expm1-u
3×flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
2×cbrt-undiv +-commutative pow-to-exp pow-exp associate-/r/ cbrt-unprod sqr-pow
1×associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
5.0ms
(+ 1.0 (* 10.0 k))
11.0ms
(* a (pow k m))
25.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
31.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ 1.0 (* 10.0 k))
66.0ms
(* a (pow k m))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
127.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify59.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0477629
12275544
25001524
done5001524

prune277.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.5b
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
6.9b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))
7.1b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
8.1b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
19×times-frac associate-/r*
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×unpow-prod-down div-exp
8×exp-neg distribute-rgt-neg-out associate-/l/
6×cube-prod associate-*r/ prod-exp add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u pow-to-exp mul-1-neg log-rec pow-exp un-div-inv log1p-expm1-u sqr-pow
2×cube-mult frac-2neg unpow3 clear-num cbrt-unprod div-inv associate-/l*
1×sub-neg flip3-- fma-neg diff-log prod-diff frac-sub flip-- fma-udef
Counts
4 → 115
Calls
4 calls:
0.0ms
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
66.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))
36.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
32.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))

series532.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
170.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))
82.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
87.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))

simplify98.0ms

Counts
127 → 127
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06231864
131711567
250011493
done50011493

prune572.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

8.1b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
8.1b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
9.0b
(sqrt (fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))))
9.0b
(sqrt (fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity times-frac associate-/r* add-cbrt-cube
12×unpow-prod-down div-exp
8×exp-neg distribute-rgt-neg-out associate-/l/
6×pow1 prod-exp sqrt-prod
4×cbrt-undiv expm1-log1p-u pow-to-exp mul-1-neg associate-*r/ log-rec pow-exp un-div-inv log1p-expm1-u add-log-exp sqr-pow
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 108
Calls
4 calls:
34.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
32.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
1.0ms
(sqrt (fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))))
2.0ms
(sqrt (fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))))

series999.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
88.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
418.0ms
(sqrt (fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))))
413.0ms
(sqrt (fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))))

simplify82.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04431904
119071708
250011648
done50011648

prune693.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes148.0ms

Accuracy

93.9% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 2.2b

bsearch14.0ms

Steps
ItersRangePoint
2
1.2784432988208537e+99
1.53471152700023e+99
1.3745438843881196e+99

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04232
14832
24832
done4832

end0.0ms

sample1.1s

Algorithm
intervals
Results
458.0ms11858×body80valid
145.0ms4362×body80nan