Average Error: 0.1 → 0.1
Time: 21.9s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot \left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot \left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)
double f(double x) {
        double r25938 = 0.954929658551372;
        double r25939 = x;
        double r25940 = r25938 * r25939;
        double r25941 = 0.12900613773279798;
        double r25942 = r25939 * r25939;
        double r25943 = r25942 * r25939;
        double r25944 = r25941 * r25943;
        double r25945 = r25940 - r25944;
        return r25945;
}
↓
double f(double x) {
        double r25946 = x;
        double r25947 = 0.954929658551372;
        double r25948 = 0.12900613773279798;
        double r25949 = r25946 * r25946;
        double r25950 = r25948 * r25949;
        double r25951 = r25947 - r25950;
        double r25952 = r25946 * r25951;
        return r25952;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)}\]

  3. Final simplification0.1

    \[\leadsto x \cdot \left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))