Average Error: 11.9 → 1.0
Time: 3.8s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z} \]
↓
\[\begin{array}{l} t_1 := \sqrt[3]{y - z}\\ t_2 := \sqrt[3]{t - z}\\ \left(x \cdot \frac{t_1 \cdot t_1}{t_2 \cdot t_2}\right) \cdot \frac{t_1}{t_2} \end{array} \]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\begin{array}{l}
t_1 := \sqrt[3]{y - z}\\
t_2 := \sqrt[3]{t - z}\\
\left(x \cdot \frac{t_1 \cdot t_1}{t_2 \cdot t_2}\right) \cdot \frac{t_1}{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 (cbrt (- y z))) (t_2 (cbrt (- t z))))
   (* (* x (/ (* t_1 t_1) (* t_2 t_2))) (/ 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 = cbrt(y - z);
	double t_2 = cbrt(t - z);
	return (x * ((t_1 * t_1) / (t_2 * t_2))) * (t_1 / t_2);
}

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

Original11.9
Target2.1
Herbie1.0
\[\frac{x}{\frac{t - z}{y - z}} \]

Derivation

  1. Initial program 11.9

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

  3. Applied *-un-lft-identity_binary6411.9

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

  4. Applied times-frac_binary642.2

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

  5. Simplified2.2

    \[\leadsto \color{blue}{x} \cdot \frac{y - z}{t - z} \]
  6. Using strategy rm

  7. Applied add-cube-cbrt_binary643.2

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

  8. Applied add-cube-cbrt_binary642.9

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

  9. Applied times-frac_binary642.9

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

  10. Applied associate-*r*_binary641.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2021204 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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