Average Error: 7.7 → 1.9
Time: 16.0s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{1}{y - z} \cdot \frac{x}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{1}{y - z} \cdot \frac{x}{t - z}
double f(double x, double y, double z, double t) {
        double r498395 = x;
        double r498396 = y;
        double r498397 = z;
        double r498398 = r498396 - r498397;
        double r498399 = t;
        double r498400 = r498399 - r498397;
        double r498401 = r498398 * r498400;
        double r498402 = r498395 / r498401;
        return r498402;
}
↓
double f(double x, double y, double z, double t) {
        double r498403 = 1.0;
        double r498404 = y;
        double r498405 = z;
        double r498406 = r498404 - r498405;
        double r498407 = r498403 / r498406;
        double r498408 = x;
        double r498409 = t;
        double r498410 = r498409 - r498405;
        double r498411 = r498408 / r498410;
        double r498412 = r498407 * r498411;
        return r498412;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.7
Target8.5
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.7

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity7.7

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

  4. Applied times-frac1.9

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

  5. Final simplification1.9

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z)))))

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