Average Error: 10.9 → 2.2
Time: 4.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{z - t}{\sqrt[3]{z - a}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\sqrt[3]{z - a} \cdot \sqrt[3]{z - a}} \cdot \frac{z - t}{\sqrt[3]{z - a}}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (+ x (* (/ y (* (cbrt (- z a)) (cbrt (- z a)))) (/ (- z t) (cbrt (- z a))))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (z - a)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) ((y / ((double) (((double) cbrt(((double) (z - a)))) * ((double) cbrt(((double) (z - a))))))) * (((double) (z - t)) / ((double) cbrt(((double) (z - a)))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

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Target

Original10.9
Target1.1
Herbie2.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied add-cube-cbrt_binary6411.3

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

  4. Applied times-frac_binary642.2

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

  5. Final simplification2.2

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

Reproduce

herbie shell --seed 2020205 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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