Average Error: 7.8 → 0.3
Time: 3.6s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1} - \frac{\frac{x}{t \cdot z - x}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1} - \frac{\frac{x}{t \cdot z - x}}{x + 1}
(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
↓
(FPCore (x y z t)
 :precision binary64
 (- (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0)) (/ (/ x (- (* t z) x)) (+ x 1.0))))
double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
↓
double code(double x, double y, double z, double t) {
	return ((x + (y / (t - (x / z)))) / (x + 1.0)) - ((x / ((t * z) - x)) / (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

Original7.8
Target0.3
Herbie0.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.8

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

  3. Applied div-sub_binary647.8

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

  4. Applied associate-+r-_binary647.8

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

  5. Applied div-sub_binary647.8

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

  6. Simplified7.8

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

  7. Simplified7.8

    \[\leadsto \frac{x + \frac{y \cdot z}{z \cdot t - x}}{x + 1} - \color{blue}{\frac{\frac{x}{z \cdot t - x}}{x + 1}}\]
  8. Using strategy rm

  9. Applied associate-/l*_binary642.3

    \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{z \cdot t - x}{z}}}}{x + 1} - \frac{\frac{x}{z \cdot t - x}}{x + 1}\]
  10. Using strategy rm

  11. Applied div-sub_binary642.3

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

  12. Simplified0.3

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

  13. Final simplification0.3

    \[\leadsto \frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1} - \frac{\frac{x}{t \cdot z - x}}{x + 1}\]

Reproduce

herbie shell --seed 2020231 
(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)))