Average Error: 24.3 → 12.6
Time: 13.3s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.017349515652042311145981409869525810825 \cdot 10^{-103}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;a \le -1.05656481426195461736762491417520109376 \cdot 10^{-182}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{elif}\;a \le -5.244444911381475218279391153195092082915 \cdot 10^{-267}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;a \le 1.146658007406096389473970469097263702452 \cdot 10^{-6}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\frac{1}{\frac{a - t}{z}} - \frac{t}{a - t}\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.017349515652042311145981409869525810825 \cdot 10^{-103}:\\
\;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\

\mathbf{elif}\;a \le -1.05656481426195461736762491417520109376 \cdot 10^{-182}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

\mathbf{elif}\;a \le -5.244444911381475218279391153195092082915 \cdot 10^{-267}:\\
\;\;\;\;x + \frac{y - x}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\sqrt[3]{a - t}}\\

\mathbf{elif}\;a \le 1.146658007406096389473970469097263702452 \cdot 10^{-6}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r490221 = x;
        double r490222 = y;
        double r490223 = r490222 - r490221;
        double r490224 = z;
        double r490225 = t;
        double r490226 = r490224 - r490225;
        double r490227 = r490223 * r490226;
        double r490228 = a;
        double r490229 = r490228 - r490225;
        double r490230 = r490227 / r490229;
        double r490231 = r490221 + r490230;
        return r490231;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r490232 = a;
        double r490233 = -1.0173495156520423e-103;
        bool r490234 = r490232 <= r490233;
        double r490235 = x;
        double r490236 = y;
        double r490237 = r490236 - r490235;
        double r490238 = z;
        double r490239 = t;
        double r490240 = r490238 - r490239;
        double r490241 = 1.0;
        double r490242 = r490232 - r490239;
        double r490243 = r490241 / r490242;
        double r490244 = r490240 * r490243;
        double r490245 = r490237 * r490244;
        double r490246 = r490235 + r490245;
        double r490247 = -1.0565648142619546e-182;
        bool r490248 = r490232 <= r490247;
        double r490249 = r490235 * r490238;
        double r490250 = r490249 / r490239;
        double r490251 = r490236 + r490250;
        double r490252 = r490238 * r490236;
        double r490253 = r490252 / r490239;
        double r490254 = r490251 - r490253;
        double r490255 = -5.244444911381475e-267;
        bool r490256 = r490232 <= r490255;
        double r490257 = cbrt(r490242);
        double r490258 = r490257 * r490257;
        double r490259 = r490237 / r490258;
        double r490260 = r490240 / r490257;
        double r490261 = r490259 * r490260;
        double r490262 = r490235 + r490261;
        double r490263 = 1.1466580074060964e-06;
        bool r490264 = r490232 <= r490263;
        double r490265 = r490242 / r490238;
        double r490266 = r490241 / r490265;
        double r490267 = r490239 / r490242;
        double r490268 = r490266 - r490267;
        double r490269 = r490237 * r490268;
        double r490270 = r490235 + r490269;
        double r490271 = r490264 ? r490254 : r490270;
        double r490272 = r490256 ? r490262 : r490271;
        double r490273 = r490248 ? r490254 : r490272;
        double r490274 = r490234 ? r490246 : r490273;
        return r490274;
}

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

Original24.3
Target9.1
Herbie12.6
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if a < -1.0173495156520423e-103

    1. Initial program 22.3

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

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

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

    4. Applied times-frac8.6

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

    5. Simplified8.6

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

    7. 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 -1.0173495156520423e-103 < a < -1.0565648142619546e-182 or -5.244444911381475e-267 < a < 1.1466580074060964e-06

    1. Initial program 27.9

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

    2. Taylor expanded around inf 20.3

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

    if -1.0565648142619546e-182 < a < -5.244444911381475e-267

    1. Initial program 28.3

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

    3. Applied add-cube-cbrt29.0

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

    4. Applied times-frac22.2

      \[\leadsto x + \color{blue}{\frac{y - x}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\sqrt[3]{a - t}}}\]

    if 1.1466580074060964e-06 < a

    1. Initial program 22.1

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

    3. Applied *-un-lft-identity22.1

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

    4. Applied times-frac6.7

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

    5. Simplified6.7

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

    7. Applied div-sub6.7

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

    9. Applied clear-num6.7

      \[\leadsto x + \left(y - x\right) \cdot \left(\color{blue}{\frac{1}{\frac{a - t}{z}}} - \frac{t}{a - t}\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification12.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.017349515652042311145981409869525810825 \cdot 10^{-103}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \mathbf{elif}\;a \le -1.05656481426195461736762491417520109376 \cdot 10^{-182}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{elif}\;a \le -5.244444911381475218279391153195092082915 \cdot 10^{-267}:\\ \;\;\;\;x + \frac{y - x}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}} \cdot \frac{z - t}{\sqrt[3]{a - t}}\\ \mathbf{elif}\;a \le 1.146658007406096389473970469097263702452 \cdot 10^{-6}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\frac{1}{\frac{a - t}{z}} - \frac{t}{a - t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019297 
(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))))