Details

Time bar (total: 17.2s)

sample73.0ms

Algorithm
intervals
Results
27.0ms369×body80valid
18.0ms122×body80nan

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
01215
12415
25313
310812
427012
5144212
done500112

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.8b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite111.0ms

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:
12.0ms
(+ 1.0 (* 10.0 k))
24.0ms
(* a (pow k m))
34.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
36.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ 1.0 (* 10.0 k))
85.0ms
(* a (pow k m))
28.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
159.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.7s

Counts
100 → 100
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01791340
14991186
22549990
done5000977

prune460.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma k (+ 10.0 k) 1.0)
0.1b
(/ (pow k m) (fma k (+ 10.0 k) 1.0))
1.8b
(* a (/ (pow k m) (fma k (+ 10.0 k) 1.0)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
44×add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
25×associate-*r*
22×unpow-prod-down
18×add-exp-log
10×add-cbrt-cube
8×sqr-pow
7×associate-/l*
6×div-exp
5×pow1
4×prod-exp unswap-sqr
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×cbrt-undiv pow-to-exp pow-exp cbrt-unprod div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative fma-udef
Counts
3 → 107
Calls
3 calls:
1.0ms
(fma k (+ 10.0 k) 1.0)
24.0ms
(/ (pow k m) (fma k (+ 10.0 k) 1.0))
36.0ms
(* a (/ (pow k m) (fma k (+ 10.0 k) 1.0)))

series306.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(fma k (+ 10.0 k) 1.0)
96.0ms
(/ (pow k m) (fma k (+ 10.0 k) 1.0))
173.0ms
(* a (/ (pow k m) (fma k (+ 10.0 k) 1.0)))

simplify1.2s

Counts
116 → 116
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02092042
15151955
222191831
done50011823

prune633.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

4.7b
(fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m)))))))
7.7b
(fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))
9.7b
(/ (pow k 3) (pow (/ 1 k) (- m)))
15.3b
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
328×times-frac
229×unpow-prod-down
166×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
87×add-exp-log
54×cube-prod
51×div-exp
37×pow-exp
33×sqr-pow
24×associate-/r*
19×pow-to-exp
18×cube-mult unpow3 prod-exp
15×div-inv
13×associate-/l*
11×add-cbrt-cube
6×rec-exp 1-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv
2×neg-sub0 pow-neg frac-2neg associate-*l/ clear-num associate-/r/ fma-udef associate-/l/ pow-sub
1×cbrt-unprod
Counts
4 → 338
Calls
4 calls:
0.0ms
(fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m)))))))
0.0ms
(fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))
43.0ms
(/ (pow k 3) (pow (/ 1 k) (- m)))
19.0ms
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))

series1.3s

Counts
4 → 12
Calls
4 calls:
258.0ms
(fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m)))))))
238.0ms
(fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))
553.0ms
(/ (pow k 3) (pow (/ 1 k) (- m)))
214.0ms
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))

simplify684.0ms

Counts
350 → 350
Iterations

Useful iterations: done (665.0ms)

IterNodesCost
05227963
110506598
done50016284

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))))
9.8b
(sqrt (fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))))
15.3b
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))
15.3b
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
110×add-exp-log
54×div-exp
38×pow-exp
36×prod-exp
20×pow-to-exp
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity times-frac associate-/r* add-cbrt-cube
12×unpow-prod-down
6×pow1 rec-exp 1-exp sqrt-prod
4×cbrt-undiv expm1-log1p-u associate-*l/ log1p-expm1-u associate-/l/ add-log-exp sqr-pow
2×neg-sub0 pow-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod div-inv associate-/l* pow-sub
Counts
4 → 134
Calls
4 calls:
2.0ms
(sqrt (fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))))
2.0ms
(sqrt (fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))))
36.0ms
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))
35.0ms
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))

series1.4s

Counts
4 → 12
Calls
4 calls:
510.0ms
(sqrt (fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))))
514.0ms
(sqrt (fma (/ (pow (/ 1 k) (- m)) k) (/ a k) (fma (/ (* (pow (/ 1 k) (- m)) a) (pow k 4)) 99.0 (- (/ (* 10.0 a) (/ (pow k 3) (pow (/ 1 k) (- m))))))))
153.0ms
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))
174.0ms
(/ (* (pow (/ 1 k) (- m)) a) (pow k 4))

simplify1.7s

Counts
146 → 146
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02023566
15033214
227433002
done50012780

prune1.2s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes181.0ms

Accuracy

96.1% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch90.0ms

Steps
ItersRangePoint
7
1.2018855207213504e+129
6.098651889528118e+130
2.2032230850129666e+130

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03460
14460
25060
done5060

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.2s11911×body80valid
720.0ms4296×body80nan