Average Error: 10.3 → 10.3
Time: 18.7s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\frac{x - y \cdot z}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\frac{x - y \cdot z}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r36367649 = x;
        double r36367650 = y;
        double r36367651 = z;
        double r36367652 = r36367650 * r36367651;
        double r36367653 = r36367649 - r36367652;
        double r36367654 = t;
        double r36367655 = a;
        double r36367656 = r36367655 * r36367651;
        double r36367657 = r36367654 - r36367656;
        double r36367658 = r36367653 / r36367657;
        return r36367658;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r36367659 = x;
        double r36367660 = y;
        double r36367661 = z;
        double r36367662 = r36367660 * r36367661;
        double r36367663 = r36367659 - r36367662;
        double r36367664 = t;
        double r36367665 = a;
        double r36367666 = r36367665 * r36367661;
        double r36367667 = r36367664 - r36367666;
        double r36367668 = r36367663 / r36367667;
        return r36367668;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.3
Target1.6
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.3

    \[\frac{x - y \cdot z}{t - a \cdot z}\]
  2. Using strategy rm

  3. Applied div-inv10.4

    \[\leadsto \color{blue}{\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt11.1

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x - y \cdot z} \cdot \sqrt[3]{x - y \cdot z}\right) \cdot \sqrt[3]{x - y \cdot z}\right)} \cdot \frac{1}{t - a \cdot z}\]
  6. Using strategy rm

  7. Applied associate-*r/11.1

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt[3]{x - y \cdot z} \cdot \sqrt[3]{x - y \cdot z}\right) \cdot \sqrt[3]{x - y \cdot z}\right) \cdot 1}{t - a \cdot z}}\]

  8. Simplified10.3

    \[\leadsto \frac{\color{blue}{x - z \cdot y}}{t - a \cdot z}\]

  9. Final simplification10.3

    \[\leadsto \frac{x - y \cdot z}{t - a \cdot z}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"

  :herbie-target
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

  (/ (- x (* y z)) (- t (* a z))))