Average Error: 10.5 → 10.5
Time: 9.8s
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 r4114 = x;
        double r4115 = y;
        double r4116 = z;
        double r4117 = r4115 * r4116;
        double r4118 = r4114 - r4117;
        double r4119 = t;
        double r4120 = a;
        double r4121 = r4120 * r4116;
        double r4122 = r4119 - r4121;
        double r4123 = r4118 / r4122;
        return r4123;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r4124 = x;
        double r4125 = y;
        double r4126 = z;
        double r4127 = r4125 * r4126;
        double r4128 = r4124 - r4127;
        double r4129 = t;
        double r4130 = a;
        double r4131 = r4130 * r4126;
        double r4132 = r4129 - r4131;
        double r4133 = r4128 / r4132;
        return r4133;
}

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

Original10.5
Target1.9
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;z \lt -32113435955957344:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \lt 3.51395223729782958 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - a \cdot z} - \frac{y}{\frac{t}{z} - a}\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  2. Final simplification10.5

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

Reproduce

herbie shell --seed 2020025 
(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))))