Average Error: 10.8 → 11.0
Time: 18.3s
Precision: 64
\[\frac{x - y \cdot z}{t - a \cdot z}\]
↓
\[\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}\]
\frac{x - y \cdot z}{t - a \cdot z}
↓
\left(x - z \cdot y\right) \cdot \frac{1}{t - a \cdot z}
double f(double x, double y, double z, double t, double a) {
        double r35221644 = x;
        double r35221645 = y;
        double r35221646 = z;
        double r35221647 = r35221645 * r35221646;
        double r35221648 = r35221644 - r35221647;
        double r35221649 = t;
        double r35221650 = a;
        double r35221651 = r35221650 * r35221646;
        double r35221652 = r35221649 - r35221651;
        double r35221653 = r35221648 / r35221652;
        return r35221653;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r35221654 = x;
        double r35221655 = z;
        double r35221656 = y;
        double r35221657 = r35221655 * r35221656;
        double r35221658 = r35221654 - r35221657;
        double r35221659 = 1.0;
        double r35221660 = t;
        double r35221661 = a;
        double r35221662 = r35221661 * r35221655;
        double r35221663 = r35221660 - r35221662;
        double r35221664 = r35221659 / r35221663;
        double r35221665 = r35221658 * r35221664;
        return r35221665;
}

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

Original10.8
Target1.7
Herbie11.0
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  3. Applied div-inv11.0

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

  4. Final simplification11.0

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

Reproduce

herbie shell --seed 2019172 
(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))))