Average Error: 1.8 → 1.8
Time: 3.0s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[x + \frac{y - x}{\frac{t}{z}}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
x + \frac{y - x}{\frac{t}{z}}
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
↓
(FPCore (x y z t) :precision binary64 (+ x (/ (- y x) (/ t z))))
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y - x)) * (z / t)))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + (((double) (y - x)) / (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

Original1.8
Target2.0
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < -0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Initial program Error: 1.8 bits

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

  3. Applied associate-*r/Error: 6.2 bits

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

  5. Applied associate-/l*Error: 1.8 bits

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

  6. Final simplificationError: 1.8 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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