Average Error: 0.1 → 0.1
Time: 12.0s
Precision: 64
\[0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
↓
\[0.9549296585513720181381813745247200131416 \cdot x - {x}^{3} \cdot 0.1290061377327979819096270830414141528308\]
0.9549296585513720181381813745247200131416 \cdot x - 0.1290061377327979819096270830414141528308 \cdot \left(\left(x \cdot x\right) \cdot x\right)
↓
0.9549296585513720181381813745247200131416 \cdot x - {x}^{3} \cdot 0.1290061377327979819096270830414141528308
double f(double x) {
        double r1041996 = 0.954929658551372;
        double r1041997 = x;
        double r1041998 = r1041996 * r1041997;
        double r1041999 = 0.12900613773279798;
        double r1042000 = r1041997 * r1041997;
        double r1042001 = r1042000 * r1041997;
        double r1042002 = r1041999 * r1042001;
        double r1042003 = r1041998 - r1042002;
        return r1042003;
}
↓
double f(double x) {
        double r1042004 = 0.954929658551372;
        double r1042005 = x;
        double r1042006 = r1042004 * r1042005;
        double r1042007 = 3.0;
        double r1042008 = pow(r1042005, r1042007);
        double r1042009 = 0.12900613773279798;
        double r1042010 = r1042008 * r1042009;
        double r1042011 = r1042006 - r1042010;
        return r1042011;
}

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. Using strategy rm

  4. Applied associate-*r*0.1

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

  5. Taylor expanded around 0 0.1

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

  6. Simplified0.1

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

  8. Applied pow10.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - \left(x \cdot \left(x \cdot \color{blue}{{x}^{1}}\right)\right) \cdot 0.1290061377327979819096270830414141528308\]

  9. Applied pow10.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - \left(x \cdot \left(\color{blue}{{x}^{1}} \cdot {x}^{1}\right)\right) \cdot 0.1290061377327979819096270830414141528308\]

  10. Applied pow-prod-up0.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - \left(x \cdot \color{blue}{{x}^{\left(1 + 1\right)}}\right) \cdot 0.1290061377327979819096270830414141528308\]

  11. Applied pow10.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - \left(\color{blue}{{x}^{1}} \cdot {x}^{\left(1 + 1\right)}\right) \cdot 0.1290061377327979819096270830414141528308\]

  12. Applied pow-prod-up0.1

    \[\leadsto 0.9549296585513720181381813745247200131416 \cdot x - \color{blue}{{x}^{\left(1 + \left(1 + 1\right)\right)}} \cdot 0.1290061377327979819096270830414141528308\]

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))