Average Error: 7.3 → 0.4
Time: 4.8s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\frac{1}{x + 1}}{\frac{1}{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\frac{1}{x + 1}}{\frac{1}{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}}
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) (1.0 / ((double) (x + 1.0)))) / ((double) (1.0 / ((double) (x + ((double) (((double) (y / ((double) (t - ((double) (x / z)))))) - ((double) (x / ((double) (((double) (t * z)) - x))))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Target

Original7.3
Target0.3
Herbie0.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.3

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

  3. Applied div-sub7.3

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

  4. Simplified2.3

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

  5. Simplified2.3

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

  7. Applied clear-num2.4

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

  8. Simplified0.4

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

  10. Applied div-inv0.5

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

  11. Applied associate-/r*0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020184 
(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)))