Average Error: 2.1 → 0.5
Time: 3.8s
Precision: binary64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + \left(a \cdot \left(\sqrt[3]{z - y} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}}\right)\right) \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + \left(a \cdot \left(\sqrt[3]{z - y} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}}\right)\right) \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)}}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x - ((double) (((double) (y - z)) / ((double) (((double) (((double) (t - z)) + 1.0)) / a))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (a * ((double) (((double) cbrt(((double) (z - y)))) * ((double) (((double) cbrt(((double) (z - y)))) / ((double) (((double) cbrt(((double) (t + ((double) (1.0 - z)))))) * ((double) cbrt(((double) (t + ((double) (1.0 - z)))))))))))))) * ((double) (((double) cbrt(((double) (z - y)))) / ((double) cbrt(((double) (t + ((double) (1.0 - z))))))))))));
}

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

Enter valid numbers for all inputs

Target

Original2.1
Target0.2
Herbie0.5
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{x + a \cdot \frac{z - y}{t + \left(1 - z\right)}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.6

    \[\leadsto x + a \cdot \frac{z - y}{\color{blue}{\left(\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}\right) \cdot \sqrt[3]{t + \left(1 - z\right)}}}\]

  5. Applied add-cube-cbrt0.6

    \[\leadsto x + a \cdot \frac{\color{blue}{\left(\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}\right) \cdot \sqrt[3]{z - y}}}{\left(\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}\right) \cdot \sqrt[3]{t + \left(1 - z\right)}}\]

  6. Applied times-frac0.6

    \[\leadsto x + a \cdot \color{blue}{\left(\frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)}}\right)}\]

  7. Applied associate-*r*0.5

    \[\leadsto x + \color{blue}{\left(a \cdot \frac{\sqrt[3]{z - y} \cdot \sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}}\right) \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)}}}\]

  8. Simplified0.5

    \[\leadsto x + \color{blue}{\left(a \cdot \left(\sqrt[3]{z - y} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}}\right)\right)} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)}}\]

  9. Final simplification0.5

    \[\leadsto x + \left(a \cdot \left(\sqrt[3]{z - y} \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)} \cdot \sqrt[3]{t + \left(1 - z\right)}}\right)\right) \cdot \frac{\sqrt[3]{z - y}}{\sqrt[3]{t + \left(1 - z\right)}}\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))