Average Error: 25.2 → 8.5
Time: 6.8s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -8.236707572209711538125694934855866174229 \cdot 10^{-288}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -8.236707572209711538125694934855866174229 \cdot 10^{-288}:\\
\;\;\;\;x + \frac{y - x}{\frac{a}{z - t} - \frac{t}{z - t}}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r557687 = x;
        double r557688 = y;
        double r557689 = r557688 - r557687;
        double r557690 = z;
        double r557691 = t;
        double r557692 = r557690 - r557691;
        double r557693 = r557689 * r557692;
        double r557694 = a;
        double r557695 = r557694 - r557691;
        double r557696 = r557693 / r557695;
        double r557697 = r557687 + r557696;
        return r557697;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r557698 = x;
        double r557699 = y;
        double r557700 = r557699 - r557698;
        double r557701 = z;
        double r557702 = t;
        double r557703 = r557701 - r557702;
        double r557704 = r557700 * r557703;
        double r557705 = a;
        double r557706 = r557705 - r557702;
        double r557707 = r557704 / r557706;
        double r557708 = r557698 + r557707;
        double r557709 = -8.236707572209712e-288;
        bool r557710 = r557708 <= r557709;
        double r557711 = r557705 / r557703;
        double r557712 = r557702 / r557703;
        double r557713 = r557711 - r557712;
        double r557714 = r557700 / r557713;
        double r557715 = r557698 + r557714;
        double r557716 = 0.0;
        bool r557717 = r557708 <= r557716;
        double r557718 = r557698 * r557701;
        double r557719 = r557718 / r557702;
        double r557720 = r557699 + r557719;
        double r557721 = r557701 * r557699;
        double r557722 = r557721 / r557702;
        double r557723 = r557720 - r557722;
        double r557724 = r557703 / r557706;
        double r557725 = r557700 * r557724;
        double r557726 = r557698 + r557725;
        double r557727 = r557717 ? r557723 : r557726;
        double r557728 = r557710 ? r557715 : r557727;
        return r557728;
}

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

Original25.2
Target9.4
Herbie8.5
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (/ (* (- y x) (- z t)) (- a t))) < -8.236707572209712e-288

    1. Initial program 21.4

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

    3. Applied associate-/l*7.3

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-sub7.3

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

    if -8.236707572209712e-288 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 0.0

    1. Initial program 59.7

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

    2. Taylor expanded around inf 17.6

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

    if 0.0 < (+ x (/ (* (- y x) (- z t)) (- a t)))

    1. Initial program 22.9

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

    3. Applied *-un-lft-identity22.9

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

    4. Applied times-frac8.2

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

    5. Simplified8.2

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

  4. Final simplification8.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -8.236707572209711538125694934855866174229 \cdot 10^{-288}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z - t} - \frac{t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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) (/ (- z t) (- a t)))) (if (< a 3.7744031700831742e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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