Average Error: 11.8 → 2.1
Time: 5.9s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z} \]
↓
\[\frac{x}{\frac{t - z}{y - z}} \]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x}{\frac{t - z}{y - z}}

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))
↓
(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y 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 / ((t - z) / (y - 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

Original11.8
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}} \]

Derivation

  1. Initial program 11.8

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

  2. Applied associate-/l*_binary642.1

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

  3. Final simplification2.1

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

Reproduce

herbie shell --seed 2022077 
(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)))