Average Error: 24.7 → 9.4
Time: 9.5s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4.7882633144150225 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right) \land x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 1.1897674420967624 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\

\mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4.7882633144150225 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right) \land x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 1.1897674420967624 \cdot 10^{+306}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y z) (- t x)) (- a z))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* (- y z) (- t x)) (- a z))) (- INFINITY))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (if (or (<= (+ x (/ (* (- y z) (- t x)) (- a z))) -4.7882633144150225e-279)
           (and (not (<= (+ x (/ (* (- y z) (- t x)) (- a z))) 0.0))
                (<=
                 (+ x (/ (* (- y z) (- t x)) (- a z)))
                 1.1897674420967624e+306)))
     (+ x (/ (* (- y z) (- t x)) (- a z)))
     (+ t (* y (- (/ x z) (/ t z)))))))
double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * (t - x)) / (a - z));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + (((y - z) * (t - x)) / (a - z))) <= -((double) INFINITY)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else if (((x + (((y - z) * (t - x)) / (a - z))) <= -4.7882633144150225e-279) || (!((x + (((y - z) * (t - x)) / (a - z))) <= 0.0) && ((x + (((y - z) * (t - x)) / (a - z))) <= 1.1897674420967624e+306))) {
		tmp = x + (((y - z) * (t - x)) / (a - z));
	} else {
		tmp = t + (y * ((x / z) - (t / z)));
	}
	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

Original24.7
Target11.4
Herbie9.4
\[\begin{array}{l} \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{z} \cdot \left(t - x\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity_binary64_1678764.0

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

    4. Applied times-frac_binary64_1679318.3

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

    5. Simplified18.3

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

    if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.7882633144150225e-279 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1.1897674420967624e306

    1. Initial program 1.9

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

    if -4.7882633144150225e-279 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0 or 1.1897674420967624e306 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

    1. Initial program 61.9

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

    2. Taylor expanded around inf 32.2

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

    3. Simplified24.2

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

  4. Final simplification9.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -4.7882633144150225 \cdot 10^{-279} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right) \land x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 1.1897674420967624 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020355 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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