Details

Time bar (total: 20.1s)

sample101.0ms

Algorithm
intervals
Results
50.0ms375×body80valid
12.0ms145×body80nan

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (32.0ms)

IterNodesCost
01215
12415
25313
310812
427012
5144212
done500112

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.9b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
10×add-log-exp
8×add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×fma-def
4×div-exp sum-log
3×pow1 expm1-log1p-u flip3-+ times-frac prod-exp associate-/r* flip-+ log1p-expm1-u
2×cbrt-undiv +-commutative associate-/r/
1×pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
3 → 61
Calls
3 calls:
12.0ms
(+ 1.0 (* 10.0 k))
57.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
78.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series347.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(+ 1.0 (* 10.0 k))
53.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
229.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify2.3s

Counts
70 → 70
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01471091
1441953
22441771
done5001761

prune571.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ 10.0 k) k)
1.9b
(/ (* a (pow k m)) (+ 1.0 (* (+ 10.0 k) k)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt *-un-lft-identity
6×add-cube-cbrt
4×pow1 div-exp associate-*l* prod-exp
3×times-frac associate-*r* associate-/r*
2×cbrt-undiv expm1-log1p-u flip3-+ associate-*l/ associate-/r/ cbrt-unprod flip-+ log1p-expm1-u add-log-exp
1×pow-to-exp frac-2neg pow-prod-down pow-exp clear-num *-commutative div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
2 → 50
Calls
2 calls:
47.0ms
(* (+ 10.0 k) k)
35.0ms
(/ (* a (pow k m)) (+ 1.0 (* (+ 10.0 k) k)))

series310.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(* (+ 10.0 k) k)
226.0ms
(/ (* a (pow k m)) (+ 1.0 (* (+ 10.0 k) k)))

simplify1.9s

Counts
56 → 56
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0145828
1400786
22125675
done5001666

prune432.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
1.9b
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
36×times-frac
26×div-exp
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-cbrt-cube
12×prod-exp
8×associate-/r*
7×cbrt-undiv
6×div-inv associate-/l*
5×rec-exp 1-exp
4×pow-to-exp pow-exp
3×pow1
2×expm1-log1p-u frac-2neg clear-num cbrt-unprod log1p-expm1-u add-log-exp
1×pow-flip associate-/r/ inv-pow
Counts
2 → 89
Calls
2 calls:
40.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
20.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

series405.0ms

Counts
2 → 6
Calls
2 calls:
199.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
205.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

simplify1.9s

Counts
95 → 95
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01982007
15161827
223621666
done50001648

prune473.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1.0 a) (pow (/ 1 k) (- m)))
0.3b
(/ 1 (fma (/ k (pow (/ 1 k) (- m))) (/ k a) (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))))
1.1b
(fma (/ k (pow (/ 1 k) (- m))) (/ k a) (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m)))))
1.1b
(fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
518×times-frac
250×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
182×unpow-prod-down
38×add-exp-log
34×div-inv
24×div-exp
20×associate-/r*
16×associate-/l*
14×sqr-pow
11×add-cbrt-cube
8×pow-exp
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×pow-to-exp frac-2neg clear-num associate-/r/ fma-udef
1×neg-sub0 pow-neg pow-flip associate-/l/ inv-pow pow-sub
Counts
4 → 333
Calls
4 calls:
43.0ms
(/ (/ 1.0 a) (pow (/ 1 k) (- m)))
10.0ms
(/ 1 (fma (/ k (pow (/ 1 k) (- m))) (/ k a) (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))))
1.0ms
(fma (/ k (pow (/ 1 k) (- m))) (/ k a) (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m)))))
1.0ms
(fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))

series870.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (/ 1.0 a) (pow (/ 1 k) (- m)))
296.0ms
(/ 1 (fma (/ k (pow (/ 1 k) (- m))) (/ k a) (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))))
259.0ms
(fma (/ k (pow (/ 1 k) (- m))) (/ k a) (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m)))))
188.0ms
(fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))

simplify1.3s

Counts
345 → 345
Iterations

Useful iterations: done (1.3s)

IterNodesCost
06549529
115228555
done50018219

prune2.5s

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes387.0ms

Accuracy

97.8% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.2b

bsearch139.0ms

Steps
ItersRangePoint
10
4.395288122153141e+145
7.086575651892718e+162
1.3820291698720688e+153

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02755
13355
done3355

end0.0ms

sample3.4s

Algorithm
intervals
Results
2.0s11973×body80valid
426.0ms4298×body80nan