Average Error: 7.2 → 2.2
Time: 3.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(y \cdot \frac{z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(y \cdot \frac{z}{t \cdot z - x} - \frac{x}{t \cdot z - 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) (y * ((double) (z / ((double) (((double) (t * z)) - x)))))) - ((double) (x / ((double) (((double) (t * z)) - x)))))))) / ((double) (x + 1.0))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

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Target

Original7.2
Target0.3
Herbie2.2
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.2

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

  3. Applied div-sub7.2

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

  5. Applied *-un-lft-identity7.2

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

  6. Applied times-frac2.2

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

  7. Simplified2.2

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

  8. Final simplification2.2

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

Reproduce

herbie shell --seed 2020130 
(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)))