Average Error: 11.7 → 2.2
Time: 3.6s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)
(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))
↓
(FPCore (x y z t) :precision binary64 (* x (- (/ y (- t z)) (/ z (- t z)))))
double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}
↓
double code(double x, double y, double z, double t) {
	return x * ((y / (t - z)) - (z / (t - z)));
}

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

Original11.7
Target2.2
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.7

    \[\frac{x \cdot \left(y - z\right)}{t - z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity_binary64_1610511.7

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

  4. Applied times-frac_binary64_161112.2

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

  5. Simplified2.2

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

  7. Applied div-sub_binary64_161102.2

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

  8. Final simplification2.2

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

Reproduce

herbie shell --seed 2020355 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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