Average Error: 24.5 → 10.6
Time: 29.6s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -6.186660797876992217305744119765362832497 \cdot 10^{-149}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 1.686242959618626939016913009565689776441 \cdot 10^{-164}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -6.186660797876992217305744119765362832497 \cdot 10^{-149}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

\mathbf{elif}\;a \le 1.686242959618626939016913009565689776441 \cdot 10^{-164}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r516959 = x;
        double r516960 = y;
        double r516961 = r516960 - r516959;
        double r516962 = z;
        double r516963 = t;
        double r516964 = r516962 - r516963;
        double r516965 = r516961 * r516964;
        double r516966 = a;
        double r516967 = r516966 - r516963;
        double r516968 = r516965 / r516967;
        double r516969 = r516959 + r516968;
        return r516969;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r516970 = a;
        double r516971 = -6.186660797876992e-149;
        bool r516972 = r516970 <= r516971;
        double r516973 = x;
        double r516974 = y;
        double r516975 = r516974 - r516973;
        double r516976 = z;
        double r516977 = t;
        double r516978 = r516976 - r516977;
        double r516979 = r516970 - r516977;
        double r516980 = r516978 / r516979;
        double r516981 = r516975 * r516980;
        double r516982 = r516973 + r516981;
        double r516983 = 1.686242959618627e-164;
        bool r516984 = r516970 <= r516983;
        double r516985 = r516973 * r516976;
        double r516986 = r516985 / r516977;
        double r516987 = r516974 + r516986;
        double r516988 = r516976 * r516974;
        double r516989 = r516988 / r516977;
        double r516990 = r516987 - r516989;
        double r516991 = 1.0;
        double r516992 = r516991 / r516978;
        double r516993 = r516979 * r516992;
        double r516994 = r516975 / r516993;
        double r516995 = r516973 + r516994;
        double r516996 = r516984 ? r516990 : r516995;
        double r516997 = r516972 ? r516982 : r516996;
        return r516997;
}

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

Original24.5
Target9.6
Herbie10.6
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -6.186660797876992e-149

    1. Initial program 23.0

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

    3. Applied *-un-lft-identity23.0

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

    4. Applied times-frac10.0

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

    5. Simplified10.0

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

    if -6.186660797876992e-149 < a < 1.686242959618627e-164

    1. Initial program 29.7

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

    2. Taylor expanded around inf 13.8

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

    if 1.686242959618627e-164 < a

    1. Initial program 23.1

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

    3. Applied associate-/l*9.4

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

    5. Applied div-inv9.5

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

  4. Final simplification10.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -6.186660797876992217305744119765362832497 \cdot 10^{-149}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 1.686242959618626939016913009565689776441 \cdot 10^{-164}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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))))