Average Error: 1.8 → 1.6
Time: 5.2s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -2.996781646434753 \cdot 10^{+66} \lor \neg \left(t \leq 9.598855295195375 \cdot 10^{-207}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -2.996781646434753 \cdot 10^{+66} \lor \neg \left(t \leq 9.598855295195375 \cdot 10^{-207}\right):\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.996781646434753e+66) (not (<= t 9.598855295195375e-207)))
   (+ x (/ (- y x) (/ t z)))
   (+ x (/ (* (- y x) z) t))))
double code(double x, double y, double z, double t) {
	return x + ((y - x) * (z / t));
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.996781646434753e+66) || !(t <= 9.598855295195375e-207)) {
		tmp = x + ((y - x) / (t / z));
	} else {
		tmp = x + (((y - x) * z) / t);
	}
	return tmp;
}

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
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.99678164643475287e66 or 9.59885529519537526e-207 < t

    1. Initial program 1.2

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

    3. Applied associate-*r/_binary64_158457.6

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

    5. Applied associate-/l*_binary64_158481.2

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

    if -2.99678164643475287e66 < t < 9.59885529519537526e-207

    1. Initial program 3.2

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

    3. Applied associate-*r/_binary64_158452.5

      \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot z}{t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.996781646434753 \cdot 10^{+66} \lor \neg \left(t \leq 9.598855295195375 \cdot 10^{-207}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020289 
(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))))