Average Error: 2.8 → 0.1
Time: 3.7s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{1 \cdot \left(1.12837916709551256 \cdot \frac{e^{z}}{y} - x\right)}\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{1 \cdot \left(1.12837916709551256 \cdot \frac{e^{z}}{y} - x\right)}
double f(double x, double y, double z) {
        double r407104 = x;
        double r407105 = y;
        double r407106 = 1.1283791670955126;
        double r407107 = z;
        double r407108 = exp(r407107);
        double r407109 = r407106 * r407108;
        double r407110 = r407104 * r407105;
        double r407111 = r407109 - r407110;
        double r407112 = r407105 / r407111;
        double r407113 = r407104 + r407112;
        return r407113;
}
↓
double f(double x, double y, double z) {
        double r407114 = x;
        double r407115 = 1.0;
        double r407116 = 1.1283791670955126;
        double r407117 = z;
        double r407118 = exp(r407117);
        double r407119 = y;
        double r407120 = r407118 / r407119;
        double r407121 = r407116 * r407120;
        double r407122 = r407121 - r407114;
        double r407123 = r407115 * r407122;
        double r407124 = r407115 / r407123;
        double r407125 = r407114 + r407124;
        return r407125;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.8
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

    \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.8

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity2.8

    \[\leadsto x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{\color{blue}{1 \cdot y}}}\]

  6. Applied *-un-lft-identity2.8

    \[\leadsto x + \frac{1}{\frac{\color{blue}{1 \cdot \left(1.12837916709551256 \cdot e^{z} - x \cdot y\right)}}{1 \cdot y}}\]

  7. Applied times-frac2.8

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]

  8. Simplified2.8

    \[\leadsto x + \frac{1}{\color{blue}{1} \cdot \frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}\]

  9. Simplified0.1

    \[\leadsto x + \frac{1}{1 \cdot \color{blue}{\left(1.12837916709551256 \cdot \frac{e^{z}}{y} - x\right)}}\]

  10. Final simplification0.1

    \[\leadsto x + \frac{1}{1 \cdot \left(1.12837916709551256 \cdot \frac{e^{z}}{y} - x\right)}\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))