Average Error: 24.9 → 9.6
Time: 5.8s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -8.8111473127541213 \cdot 10^{-122} \lor \neg \left(a \le 7.09279336725498623 \cdot 10^{-98}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(z \cdot \frac{x}{t} - y \cdot \frac{z}{t}\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -8.8111473127541213 \cdot 10^{-122} \lor \neg \left(a \le 7.09279336725498623 \cdot 10^{-98}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\

\mathbf{else}:\\
\;\;\;\;y + \left(z \cdot \frac{x}{t} - y \cdot \frac{z}{t}\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 (((a <= -8.811147312754121e-122) || !(a <= 7.092793367254986e-98))) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * ((double) (((double) (z - t)) * ((double) (1.0 / ((double) (a - t))))))))));
	} else {
		VAR = ((double) (y + ((double) (((double) (z * ((double) (x / t)))) - ((double) (y * ((double) (z / 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

Original24.9
Target9.4
Herbie9.6
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -8.8111473127541213e-122 or 7.09279336725498623e-98 < a

    1. Initial program 23.2

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

    2. Simplified8.7

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

    4. Applied div-inv8.7

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

    if -8.8111473127541213e-122 < a < 7.09279336725498623e-98

    1. Initial program 29.1

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

    2. Simplified20.0

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

    3. Taylor expanded around inf 15.5

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

    4. Simplified11.9

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

  4. Final simplification9.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -8.8111473127541213 \cdot 10^{-122} \lor \neg \left(a \le 7.09279336725498623 \cdot 10^{-98}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(z \cdot \frac{x}{t} - y \cdot \frac{z}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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))))