Average Error: 10.2 → 10.3
Time: 4.4s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r742678 = x;
        double r742679 = y;
        double r742680 = z;
        double r742681 = r742679 * r742680;
        double r742682 = r742678 - r742681;
        double r742683 = t;
        double r742684 = a;
        double r742685 = r742684 * r742680;
        double r742686 = r742683 - r742685;
        double r742687 = r742682 / r742686;
        return r742687;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r742688 = x;
        double r742689 = y;
        double r742690 = z;
        double r742691 = r742689 * r742690;
        double r742692 = r742688 - r742691;
        double r742693 = 1.0;
        double r742694 = t;
        double r742695 = a;
        double r742696 = r742695 * r742690;
        double r742697 = r742694 - r742696;
        double r742698 = r742693 / r742697;
        double r742699 = r742692 * r742698;
        return r742699;
}

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

Original10.2
Target1.7
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.2

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

  3. Applied div-inv10.3

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

  4. Final simplification10.3

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

Reproduce

herbie shell --seed 2020039 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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