Average Error: 24.4 → 10.2
Time: 11.0s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.600313077092651 \cdot 10^{94}:\\ \;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;t \le 1.53283743298691262 \cdot 10^{239}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.600313077092651 \cdot 10^{94}:\\
\;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\

\mathbf{elif}\;t \le 1.53283743298691262 \cdot 10^{239}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (z - t)))) / ((double) (a - t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((t <= -4.600313077092651e+94)) {
		VAR = ((double) (y + ((double) (((double) (((double) (x / t)) * z)) - ((double) (y * ((double) (z / t))))))));
	} else {
		double VAR_1;
		if ((t <= 1.5328374329869126e+239)) {
			VAR_1 = ((double) (x + ((double) (((double) (y - x)) * ((double) (((double) (z - t)) / ((double) (a - t))))))));
		} else {
			VAR_1 = ((double) (y + ((double) (((double) (z / t)) * ((double) (x - y))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original24.4
Target9.4
Herbie10.2
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -4.600313077092651e94

    1. Initial program 43.0

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

    2. Simplified20.2

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

    4. Applied *-un-lft-identity20.2

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

    5. Applied add-cube-cbrt20.9

      \[\leadsto x + \left(y - x\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}}}{1 \cdot \left(a - t\right)}\]

    6. Applied times-frac21.0

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}}{1} \cdot \frac{\sqrt[3]{z - t}}{a - t}\right)}\]

    7. Simplified21.0

      \[\leadsto x + \left(y - x\right) \cdot \left(\color{blue}{\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)} \cdot \frac{\sqrt[3]{z - t}}{a - t}\right)\]

    8. Taylor expanded around inf 27.2

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

    9. Simplified18.2

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

    if -4.600313077092651e94 < t < 1.53283743298691262e239

    1. Initial program 17.0

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

    2. Simplified8.0

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

    if 1.53283743298691262e239 < t

    1. Initial program 51.0

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

    2. Simplified26.4

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

    3. Taylor expanded around inf 23.9

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

    4. Simplified11.5

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

  4. Final simplification10.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.600313077092651 \cdot 10^{94}:\\ \;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;t \le 1.53283743298691262 \cdot 10^{239}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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