Average Error: 11.1 → 11.1
Time: 21.6s
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 r29589945 = x;
        double r29589946 = y;
        double r29589947 = z;
        double r29589948 = r29589946 * r29589947;
        double r29589949 = r29589945 - r29589948;
        double r29589950 = t;
        double r29589951 = a;
        double r29589952 = r29589951 * r29589947;
        double r29589953 = r29589950 - r29589952;
        double r29589954 = r29589949 / r29589953;
        return r29589954;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29589955 = x;
        double r29589956 = y;
        double r29589957 = z;
        double r29589958 = r29589956 * r29589957;
        double r29589959 = r29589955 - r29589958;
        double r29589960 = t;
        double r29589961 = a;
        double r29589962 = r29589961 * r29589957;
        double r29589963 = r29589960 - r29589962;
        double r29589964 = r29589959 / r29589963;
        return r29589964;
}

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

Original11.1
Target1.7
Herbie11.1
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958298856956410892592016 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 11.1

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

  3. Applied *-un-lft-identity11.1

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

  4. Applied associate-/r*11.1

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

  5. Simplified11.1

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

  6. Final simplification11.1

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(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))))