Average Error: 0.2 → 0.1
Time: 1.9s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot 0.9549296585513720181381813745247200131416 + \left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot 0.9549296585513720181381813745247200131416 + \left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)
double f(double x) {
        double r37097 = 0.954929658551372;
        double r37098 = x;
        double r37099 = r37097 * r37098;
        double r37100 = 0.12900613773279798;
        double r37101 = r37098 * r37098;
        double r37102 = r37101 * r37098;
        double r37103 = r37100 * r37102;
        double r37104 = r37099 - r37103;
        return r37104;
}
↓
double f(double x) {
        double r37105 = x;
        double r37106 = 0.954929658551372;
        double r37107 = r37105 * r37106;
        double r37108 = 0.12900613773279798;
        double r37109 = 3.0;
        double r37110 = pow(r37105, r37109);
        double r37111 = r37108 * r37110;
        double r37112 = -r37111;
        double r37113 = r37107 + r37112;
        return r37113;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot \left(x \cdot x\right)\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

    \[\leadsto x \cdot 0.9549296585513720181381813745247200131416 + \color{blue}{\left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)}\]

  7. Final simplification0.1

    \[\leadsto x \cdot 0.9549296585513720181381813745247200131416 + \left(-0.1290061377327979819096270830414141528308 \cdot {x}^{3}\right)\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))