Average Error: 10.8 → 11.0
Time: 19.5s
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 r25522047 = x;
        double r25522048 = y;
        double r25522049 = z;
        double r25522050 = r25522048 * r25522049;
        double r25522051 = r25522047 - r25522050;
        double r25522052 = t;
        double r25522053 = a;
        double r25522054 = r25522053 * r25522049;
        double r25522055 = r25522052 - r25522054;
        double r25522056 = r25522051 / r25522055;
        return r25522056;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25522057 = x;
        double r25522058 = z;
        double r25522059 = y;
        double r25522060 = r25522058 * r25522059;
        double r25522061 = r25522057 - r25522060;
        double r25522062 = 1.0;
        double r25522063 = t;
        double r25522064 = a;
        double r25522065 = r25522064 * r25522058;
        double r25522066 = r25522063 - r25522065;
        double r25522067 = r25522062 / r25522066;
        double r25522068 = r25522061 * r25522067;
        return r25522068;
}

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 +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))))