Average Error: 9.2 → 0.9
Time: 14.4s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
↓
\[\frac{\frac{\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}\]
\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}
↓
\frac{\frac{\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}
double f(double x, double y, double z) {
        double r33287446 = x;
        double r33287447 = y;
        double r33287448 = z;
        double r33287449 = r33287447 - r33287448;
        double r33287450 = 1.0;
        double r33287451 = r33287449 + r33287450;
        double r33287452 = r33287446 * r33287451;
        double r33287453 = r33287452 / r33287448;
        return r33287453;
}
↓
double f(double x, double y, double z) {
        double r33287454 = x;
        double r33287455 = z;
        double r33287456 = cbrt(r33287455);
        double r33287457 = 1.0;
        double r33287458 = y;
        double r33287459 = r33287458 - r33287455;
        double r33287460 = r33287457 + r33287459;
        double r33287461 = cbrt(r33287460);
        double r33287462 = r33287456 / r33287461;
        double r33287463 = r33287454 / r33287462;
        double r33287464 = r33287463 / r33287462;
        double r33287465 = r33287464 / r33287462;
        return r33287465;
}

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

Original9.2
Target0.4
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;x \lt -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1.0\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 9.2

    \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
  2. Using strategy rm

  3. Applied associate-/l*3.1

    \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt3.9

    \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(\sqrt[3]{\left(y - z\right) + 1.0} \cdot \sqrt[3]{\left(y - z\right) + 1.0}\right) \cdot \sqrt[3]{\left(y - z\right) + 1.0}}}}\]

  6. Applied add-cube-cbrt3.8

    \[\leadsto \frac{x}{\frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{\left(\sqrt[3]{\left(y - z\right) + 1.0} \cdot \sqrt[3]{\left(y - z\right) + 1.0}\right) \cdot \sqrt[3]{\left(y - z\right) + 1.0}}}\]

  7. Applied times-frac3.8

    \[\leadsto \frac{x}{\color{blue}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1.0} \cdot \sqrt[3]{\left(y - z\right) + 1.0}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1.0}}}}\]

  8. Applied associate-/r*1.2

    \[\leadsto \color{blue}{\frac{\frac{x}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1.0} \cdot \sqrt[3]{\left(y - z\right) + 1.0}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1.0}}}}\]

  9. Simplified0.9

    \[\leadsto \frac{\color{blue}{\frac{\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1.0}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1.0}}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{\left(y - z\right) + 1.0}}}\]

  10. Final simplification0.9

    \[\leadsto \frac{\frac{\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}}{\frac{\sqrt[3]{z}}{\sqrt[3]{1.0 + \left(y - z\right)}}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))