Average Error: 2.2 → 1.1
Time: 6.5s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t \]
↓
\[\begin{array}{l} t_1 := \sqrt[3]{x - y}\\ t_2 := \sqrt[3]{z - y}\\ \frac{t_1 \cdot t_1}{t_2 \cdot t_2} \cdot \left(\frac{t_1}{t_2} \cdot t\right) \end{array} \]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
t_1 := \sqrt[3]{x - y}\\
t_2 := \sqrt[3]{z - y}\\
\frac{t_1 \cdot t_1}{t_2 \cdot t_2} \cdot \left(\frac{t_1}{t_2} \cdot t\right)
\end{array}

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))
↓
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (cbrt (- x y))) (t_2 (cbrt (- z y))))
   (* (/ (* t_1 t_1) (* t_2 t_2)) (* (/ t_1 t_2) t))))
double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}
↓
double code(double x, double y, double z, double t) {
	double t_1 = cbrt(x - y);
	double t_2 = cbrt(z - y);
	return ((t_1 * t_1) / (t_2 * t_2)) * ((t_1 / t_2) * t);
}

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

Original2.2
Target2.2
Herbie1.1
\[\frac{t}{\frac{z - y}{x - y}} \]

Derivation

  1. Initial program 2.2

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

  2. Applied add-cube-cbrt_binary643.2

    \[\leadsto \frac{x - y}{\color{blue}{\left(\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}\right) \cdot \sqrt[3]{z - y}}} \cdot t \]

  3. Applied add-cube-cbrt_binary642.9

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}\right) \cdot \sqrt[3]{x - y}}}{\left(\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}\right) \cdot \sqrt[3]{z - y}} \cdot t \]

  4. Applied times-frac_binary642.9

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}} \cdot \frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}}\right)} \cdot t \]

  5. Applied associate-*l*_binary641.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}} \cdot \left(\frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}} \cdot t\right)} \]

  6. Final simplification1.1

    \[\leadsto \frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}} \cdot \left(\frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}} \cdot t\right) \]

Reproduce

herbie shell --seed 2022076 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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