Average Error: 24.1 → 9.7
Time: 6.5s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -3.9871011799561977 \cdot 10^{+189} \lor \neg \left(t \leq 2.908034067975434 \cdot 10^{+163}\right):\\ \;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -3.9871011799561977 \cdot 10^{+189} \lor \neg \left(t \leq 2.908034067975434 \cdot 10^{+163}\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}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.9871011799561977e+189) (not (<= t 2.908034067975434e+163)))
   (+ y (- (* (/ x t) z) (* y (/ z t))))
   (+ x (* (- y x) (/ (- z t) (- a t))))))
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 tmp;
	if (((t <= -3.9871011799561977e+189) || !(t <= 2.908034067975434e+163))) {
		tmp = ((double) (y + ((double) (((double) ((x / t) * z)) - ((double) (y * (z / t)))))));
	} else {
		tmp = ((double) (x + ((double) (((double) (y - x)) * (((double) (z - t)) / ((double) (a - t)))))));
	}
	return tmp;
}

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

Original24.1
Target9.3
Herbie9.7
\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.98710117995619768e189 or 2.90803406797543381e163 < t

    1. Initial program Error: 48.0 bits

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

    2. SimplifiedError: 23.7 bits

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

    3. Taylor expanded around inf Error: 24.6 bits

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

    4. SimplifiedError: 14.9 bits

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

    if -3.98710117995619768e189 < t < 2.90803406797543381e163

    1. Initial program Error: 16.5 bits

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

    2. SimplifiedError: 8.0 bits

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

  4. Final simplificationError: 9.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9871011799561977 \cdot 10^{+189} \lor \neg \left(t \leq 2.908034067975434 \cdot 10^{+163}\right):\\ \;\;\;\;y + \left(\frac{x}{t} \cdot z - y \cdot \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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))))