Average Error: 7.6 → 3.1
Time: 4.3s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(\frac{z}{\sqrt[3]{z \cdot t - x} \cdot \sqrt[3]{z \cdot t - x}} \cdot \frac{y}{\sqrt[3]{z \cdot t - x}} - \frac{x}{z \cdot t - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(\frac{z}{\sqrt[3]{z \cdot t - x} \cdot \sqrt[3]{z \cdot t - x}} \cdot \frac{y}{\sqrt[3]{z \cdot t - x}} - \frac{x}{z \cdot t - x}\right)}{x + 1}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x + ((double) (((double) (((double) (y * z)) - x)) / ((double) (((double) (t * z)) - x)))))) / ((double) (x + 1.0))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x + ((double) (((double) (((double) (z / ((double) (((double) cbrt(((double) (((double) (z * t)) - x)))) * ((double) cbrt(((double) (((double) (z * t)) - x)))))))) * ((double) (y / ((double) cbrt(((double) (((double) (z * t)) - x)))))))) - ((double) (x / ((double) (((double) (z * t)) - x)))))))) / ((double) (x + 1.0))));
}

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

Original7.6
Target0.4
Herbie3.1
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.6

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
  2. Using strategy rm

  3. Applied div-sub7.6

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

  4. Simplified4.6

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

  5. Simplified4.6

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

  7. Applied add-cube-cbrt4.9

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

  8. Applied *-un-lft-identity4.9

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

  9. Applied times-frac4.9

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

  10. Applied associate-*r*3.1

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

  11. Simplified3.1

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

  12. Final simplification3.1

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

Reproduce

herbie shell --seed 2020185 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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