Average Error: 2.2 → 1.0
Time: 17.2s
Precision: binary64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}} \cdot \left(\frac{\sqrt[3]{x - y}}{\sqrt[3]{z - y}} \cdot t\right)\]
\frac{x - y}{z - y} \cdot t
↓
\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)
(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))
↓
(FPCore (x y z t)
 :precision binary64
 (*
  (/ (* (cbrt (- x y)) (cbrt (- x y))) (* (cbrt (- z y)) (cbrt (- z y))))
  (* (/ (cbrt (- x y)) (cbrt (- z y))) 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) {
	return ((cbrt(x - y) * cbrt(x - y)) / (cbrt(z - y) * cbrt(z - y))) * ((cbrt(x - y) / cbrt(z - y)) * 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
Herbie1.0
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.2

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

  3. Applied add-cube-cbrt_binary64_164813.3

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

  4. Applied add-cube-cbrt_binary64_164812.9

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

  5. Applied times-frac_binary64_164522.9

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

  6. Applied associate-*l*_binary64_163871.0

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

  7. Final simplification1.0

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

Reproduce

herbie shell --seed 2021076 
(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))