Average Error: 0.2 → 0.1
Time: 20.9s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[x \cdot 0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
x \cdot 0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}
double f(double x) {
        double r20953 = 0.954929658551372;
        double r20954 = x;
        double r20955 = r20953 * r20954;
        double r20956 = 0.12900613773279798;
        double r20957 = r20954 * r20954;
        double r20958 = r20957 * r20954;
        double r20959 = r20956 * r20958;
        double r20960 = r20955 - r20959;
        return r20960;
}
↓
double f(double x) {
        double r20961 = x;
        double r20962 = 0.954929658551372;
        double r20963 = r20961 * r20962;
        double r20964 = 0.12900613773279798;
        double r20965 = 3.0;
        double r20966 = pow(r20961, r20965);
        double r20967 = r20964 * r20966;
        double r20968 = r20963 - r20967;
        return r20968;
}

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. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}}\]

  4. Simplified0.1

    \[\leadsto \color{blue}{x \cdot 0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}}\]

  5. Final simplification0.1

    \[\leadsto x \cdot 0.9549296585513720181381813745247200131416 - 0.1290061377327979819096270830414141528308 \cdot {x}^{3}\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  :precision binary64
  (- (* 0.95492965855137202 x) (* 0.129006137732797982 (* (* x x) x))))