Details

Time bar (total: 14.6s)

sample91.0ms

Algorithm
intervals
Results
36.0ms376×body80valid
14.0ms157×body80nan

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
01215
12415
25313
310812
427012
5144212
done500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
14×add-sqr-sqrt
10×add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
8×add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 expm1-log1p-u fma-def times-frac associate-*l* associate-/r* sum-log log1p-expm1-u unswap-sqr
2×cbrt-undiv pow-to-exp flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
3 → 72
Calls
3 calls:
30.0ms
(* a (pow k m))
54.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
64.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series303.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(* a (pow k m))
21.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
190.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.3s

Counts
81 → 81
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01611204
14391140
22143885
done5000872

prune379.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (pow k m))
0.1b
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
2.6b
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
56×add-exp-log
36×times-frac
29×add-sqr-sqrt
26×div-exp
24×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
15×prod-exp
8×associate-/r*
7×cbrt-undiv associate-*r*
6×div-inv associate-/l*
5×pow-to-exp rec-exp 1-exp pow-exp
4×pow1 unpow-prod-down
3×expm1-log1p-u associate-*l* cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num sqr-pow
1×pow-flip associate-/r/ *-commutative inv-pow
Counts
3 → 116
Calls
3 calls:
20.0ms
(* a (pow k m))
19.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
17.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

series411.0ms

Counts
3 → 9
Calls
3 calls:
89.0ms
(* a (pow k m))
133.0ms
(/ 1 (/ (fma k (+ 10.0 k) 1.0) (* a (pow k m))))
190.0ms
(/ (fma k (+ 10.0 k) 1.0) (* a (pow k m)))

simplify1.4s

Counts
125 → 125
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02302256
15862060
225991887
done50011864

prune390.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow k m) (sqrt (fma k (+ 10.0 k) 1.0)))
0.1b
(* (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (/ (pow k m) (sqrt (fma k (+ 10.0 k) 1.0))))
14.7b
(sqrt (fma k (+ 10.0 k) 1.0))
14.7b
(sqrt (fma k (+ 10.0 k) 1.0))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
146×add-sqr-sqrt
134×times-frac
76×add-cube-cbrt *-un-lft-identity sqrt-prod
46×associate-*r*
45×unpow-prod-down
33×add-exp-log
22×associate-*l*
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 frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 216
Calls
4 calls:
11.0ms
(/ (pow k m) (sqrt (fma k (+ 10.0 k) 1.0)))
69.0ms
(* (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (/ (pow k m) (sqrt (fma k (+ 10.0 k) 1.0))))
3.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
2.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

series474.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (pow k m) (sqrt (fma k (+ 10.0 k) 1.0)))
201.0ms
(* (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (/ (pow k m) (sqrt (fma k (+ 10.0 k) 1.0))))
55.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
57.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

simplify499.0ms

Counts
228 → 228
Iterations

Useful iterations: done (491.0ms)

IterNodesCost
03115578
18725205
done50004979

prune920.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1.0 a) (pow (/ 1 k) (- m)))
0.1b
(/ 1 (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))))
2.4b
(fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m)))))
3.1b
(fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))

rewrite90.0ms

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:
49.0ms
(/ (/ 1.0 a) (pow (/ 1 k) (- m)))
11.0ms
(/ 1 (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))))
1.0ms
(fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m)))))
1.0ms
(fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ 1.0 a) (pow (/ 1 k) (- m)))
239.0ms
(/ 1 (fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))))
199.0ms
(fma (/ 10.0 (pow (/ 1 k) (- m))) (/ k a) (fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m)))))
228.0ms
(fma (/ k a) (/ k (pow (/ 1 k) (- m))) (/ (/ 1.0 a) (pow (/ 1 k) (- m))))

simplify878.0ms

Counts
345 → 345
Iterations

Useful iterations: done (852.0ms)

IterNodesCost
06589529
115298557
done50018222

prune1.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

91.6% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.1b

bsearch58.0ms

Steps
ItersRangePoint
6
2116652649.122401
27336059735.119156
20048275272.014378

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02654
13054
done3054

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.1s11820×body80valid
825.0ms4127×body80nan