Average Error: 11.2 → 1.0
Time: 13.0s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{\frac{x}{\frac{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}}{\frac{\sqrt[3]{t - z}}{\sqrt[3]{y - z}}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{\frac{x}{\frac{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}}{\frac{\sqrt[3]{t - z}}{\sqrt[3]{y - z}}}
(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))
↓
(FPCore (x y z t)
 :precision binary64
 (/
  (/ x (/ (* (cbrt (- t z)) (cbrt (- t z))) (* (cbrt (- y z)) (cbrt (- y z)))))
  (/ (cbrt (- t z)) (cbrt (- y z)))))
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) {
	return (x / ((cbrt(t - z) * cbrt(t - z)) / (cbrt(y - z) * cbrt(y - z)))) / (cbrt(t - z) / cbrt(y - z));
}

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

Original11.2
Target2.1
Herbie1.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.2

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

  3. Applied associate-/l*_binary64_163912.1

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

  5. Applied add-cube-cbrt_binary64_164813.2

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

  6. Applied add-cube-cbrt_binary64_164812.9

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

  7. Applied times-frac_binary64_164522.9

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

  8. Applied associate-/r*_binary64_163901.0

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

  9. Final simplification1.0

    \[\leadsto \frac{\frac{x}{\frac{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}}{\frac{\sqrt[3]{t - z}}{\sqrt[3]{y - z}}}\]

Reproduce

herbie shell --seed 2021076 
(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)))