Average Error: 25.0 → 10.7
Time: 5.4s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -6.169776304608411520157249671206390746068 \cdot 10^{-256}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 1.769639326006987274457462695533275354439 \cdot 10^{-255}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -6.169776304608411520157249671206390746068 \cdot 10^{-256}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

\mathbf{elif}\;a \le 1.769639326006987274457462695533275354439 \cdot 10^{-255}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r651617 = x;
        double r651618 = y;
        double r651619 = r651618 - r651617;
        double r651620 = z;
        double r651621 = t;
        double r651622 = r651620 - r651621;
        double r651623 = r651619 * r651622;
        double r651624 = a;
        double r651625 = r651624 - r651621;
        double r651626 = r651623 / r651625;
        double r651627 = r651617 + r651626;
        return r651627;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r651628 = a;
        double r651629 = -6.169776304608412e-256;
        bool r651630 = r651628 <= r651629;
        double r651631 = x;
        double r651632 = y;
        double r651633 = r651632 - r651631;
        double r651634 = z;
        double r651635 = t;
        double r651636 = r651634 - r651635;
        double r651637 = r651628 - r651635;
        double r651638 = r651636 / r651637;
        double r651639 = r651633 * r651638;
        double r651640 = r651631 + r651639;
        double r651641 = 1.7696393260069873e-255;
        bool r651642 = r651628 <= r651641;
        double r651643 = r651631 * r651634;
        double r651644 = r651643 / r651635;
        double r651645 = r651632 + r651644;
        double r651646 = r651634 * r651632;
        double r651647 = r651646 / r651635;
        double r651648 = r651645 - r651647;
        double r651649 = 1.0;
        double r651650 = r651649 / r651637;
        double r651651 = r651636 * r651650;
        double r651652 = r651633 * r651651;
        double r651653 = r651631 + r651652;
        double r651654 = r651642 ? r651648 : r651653;
        double r651655 = r651630 ? r651640 : r651654;
        return r651655;
}

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

Original25.0
Target9.3
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -6.169776304608412e-256

    1. Initial program 24.4

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

    3. Applied *-un-lft-identity24.4

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

    4. Applied times-frac11.2

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

    5. Simplified11.2

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

    if -6.169776304608412e-256 < a < 1.7696393260069873e-255

    1. Initial program 32.4

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

    2. Taylor expanded around inf 7.6

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

    if 1.7696393260069873e-255 < a

    1. Initial program 24.4

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

    3. Applied *-un-lft-identity24.4

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

    4. Applied times-frac10.6

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

    5. Simplified10.6

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

    7. Applied div-inv10.6

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{1}{a - t}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -6.169776304608411520157249671206390746068 \cdot 10^{-256}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 1.769639326006987274457462695533275354439 \cdot 10^{-255}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 
(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 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

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