Average Error: 6.9 → 0.7
Time: 5.7s
Precision: binary64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
↓
\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ t_2 := \frac{\frac{x}{y - z}}{t - z}\\ \mathbf{if}\;t_1 \leq -1.0594107857469512 \cdot 10^{+298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 1.0247681833563597 \cdot 10^{+222}:\\ \;\;\;\;\frac{x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\begin{array}{l}
t_1 := \left(y - z\right) \cdot \left(t - z\right)\\
t_2 := \frac{\frac{x}{y - z}}{t - z}\\
\mathbf{if}\;t_1 \leq -1.0594107857469512 \cdot 10^{+298}:\\
\;\;\;\;t_2\\

\mathbf{elif}\;t_1 \leq 1.0247681833563597 \cdot 10^{+222}:\\
\;\;\;\;\frac{x}{t_1}\\

\mathbf{else}:\\
\;\;\;\;t_2\\


\end{array}

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))) (t_2 (/ (/ x (- y z)) (- t z))))
   (if (<= t_1 -1.0594107857469512e+298)
     t_2
     (if (<= t_1 1.0247681833563597e+222) (/ x t_1) t_2))))
double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}
↓
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double t_2 = (x / (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -1.0594107857469512e+298) {
		tmp = t_2;
	} else if (t_1 <= 1.0247681833563597e+222) {
		tmp = x / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

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

Original6.9
Target7.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -1.0594107857469512e298 or 1.0247681833563597e222 < (*.f64 (-.f64 y z) (-.f64 t z))

    1. Initial program 12.9

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

    2. Applied associate-/r*_binary640.1

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

    if -1.0594107857469512e298 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.0247681833563597e222

    1. Initial program 1.3

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

    2. Applied pow1_binary641.3

      \[\leadsto \color{blue}{{\left(\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\right)}^{1}} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -1.0594107857469512 \cdot 10^{+298}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 1.0247681833563597 \cdot 10^{+222}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \end{array} \]

Reproduce

herbie shell --seed 2022125 
(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 (/ 1.0 (* (- y z) (- t z)))))

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