Average Error: 0.0 → 0.4
Time: 20.2s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\left(x + t \cdot \left(y - z\right)\right) + \left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \left(\sqrt[3]{-x} \cdot \left(y - z\right)\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\left(x + t \cdot \left(y - z\right)\right) + \left(\sqrt[3]{-x} \cdot \sqrt[3]{-x}\right) \cdot \left(\sqrt[3]{-x} \cdot \left(y - z\right)\right)
double f(double x, double y, double z, double t) {
        double r952174 = x;
        double r952175 = y;
        double r952176 = z;
        double r952177 = r952175 - r952176;
        double r952178 = t;
        double r952179 = r952178 - r952174;
        double r952180 = r952177 * r952179;
        double r952181 = r952174 + r952180;
        return r952181;
}
↓
double f(double x, double y, double z, double t) {
        double r952182 = x;
        double r952183 = t;
        double r952184 = y;
        double r952185 = z;
        double r952186 = r952184 - r952185;
        double r952187 = r952183 * r952186;
        double r952188 = r952182 + r952187;
        double r952189 = -r952182;
        double r952190 = cbrt(r952189);
        double r952191 = r952190 * r952190;
        double r952192 = r952190 * r952186;
        double r952193 = r952191 * r952192;
        double r952194 = r952188 + r952193;
        return r952194;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.4
\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]

Derivation

  1. Initial program 0.0

    \[x + \left(y - z\right) \cdot \left(t - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(t + \left(-x\right)\right)}\]

  4. Applied distribute-rgt-in0.0

    \[\leadsto x + \color{blue}{\left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)}\]

  5. Applied associate-+r+0.0

    \[\leadsto \color{blue}{\left(x + t \cdot \left(y - z\right)\right) + \left(-x\right) \cdot \left(y - z\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.4

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

  8. Applied associate-*l*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))