Average Error: 24.2 → 9.5
Time: 7.2s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -1.1045848138808895 \cdot 10^{+163} \lor \neg \left(t \leq 8.905955603016087 \cdot 10^{+185}\right):\\ \;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -1.1045848138808895 \cdot 10^{+163} \lor \neg \left(t \leq 8.905955603016087 \cdot 10^{+185}\right):\\
\;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((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 <= -1.1045848138808895e+163) || !(t <= 8.905955603016087e+185))) {
		VAR = ((double) (y + ((double) (((double) ((x / t) * z)) - ((double) (y * (z / t)))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y - x)) * (((double) (z - t)) / ((double) (a - t)))))));
	}
	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

Original24.2
Target9.5
Herbie9.5
\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.10458481388088954e163 or 8.90595560301608662e185 < t

    1. Initial program 49.3

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

    2. Simplified23.5

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

    3. Taylor expanded around inf 25.1

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

    4. Simplified14.9

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

    if -1.10458481388088954e163 < t < 8.90595560301608662e185

    1. Initial program 16.0

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

    2. Simplified7.8

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

  4. Final simplification9.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1045848138808895 \cdot 10^{+163} \lor \neg \left(t \leq 8.905955603016087 \cdot 10^{+185}\right):\\ \;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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))))