Average Error: 2.2 → 2.4
Time: 4.8s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 3.29194830615707638 \cdot 10^{-308} \lor \neg \left(z \le 2.88733508478686524 \cdot 10^{205}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt{z} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt{z}}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le 3.29194830615707638 \cdot 10^{-308} \lor \neg \left(z \le 2.88733508478686524 \cdot 10^{205}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

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

\end{array}
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 temp;
	if (((z <= 3.2919483061570764e-308) || !(z <= 2.8873350847868652e+205))) {
		temp = (x + ((y - x) * (z / t)));
	} else {
		temp = (x + ((sqrt(z) * (y - x)) * (sqrt(z) / t)));
	}
	return temp;
}

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

Original2.2
Target2.5
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < 3.2919483061570764e-308 or 2.8873350847868652e+205 < z

    1. Initial program 2.6

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

    if 3.2919483061570764e-308 < z < 2.8873350847868652e+205

    1. Initial program 1.8

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

    3. Applied *-un-lft-identity1.8

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

    4. Applied add-sqr-sqrt2.0

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

    5. Applied times-frac2.0

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

    6. Applied associate-*r*2.3

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

    7. Simplified2.3

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 3.29194830615707638 \cdot 10^{-308} \lor \neg \left(z \le 2.88733508478686524 \cdot 10^{205}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt{z} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt{z}}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)) -1013646692435.887) (+ 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))))