Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Average Error: 24.6 → 11.6

Time: 16.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -3.543954312374929 \cdot 10^{-257}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 2.94699012045890585 \cdot 10^{-116}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}{\frac{\sqrt[3]{a - t}}{z - t}}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r726073 = x;
        double r726074 = y;
        double r726075 = r726074 - r726073;
        double r726076 = z;
        double r726077 = t;
        double r726078 = r726076 - r726077;
        double r726079 = r726075 * r726078;
        double r726080 = a;
        double r726081 = r726080 - r726077;
        double r726082 = r726079 / r726081;
        double r726083 = r726073 + r726082;
        return r726083;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r726084 = a;
        double r726085 = -3.543954312374929e-257;
        bool r726086 = r726084 <= r726085;
        double r726087 = x;
        double r726088 = y;
        double r726089 = r726088 - r726087;
        double r726090 = z;
        double r726091 = t;
        double r726092 = r726090 - r726091;
        double r726093 = r726084 - r726091;
        double r726094 = r726092 / r726093;
        double r726095 = r726089 * r726094;
        double r726096 = r726087 + r726095;
        double r726097 = 2.946990120458906e-116;
        bool r726098 = r726084 <= r726097;
        double r726099 = r726087 * r726090;
        double r726100 = r726099 / r726091;
        double r726101 = r726088 + r726100;
        double r726102 = r726090 * r726088;
        double r726103 = r726102 / r726091;
        double r726104 = r726101 - r726103;
        double r726105 = cbrt(r726093);
        double r726106 = r726105 * r726105;
        double r726107 = r726089 / r726106;
        double r726108 = r726105 / r726092;
        double r726109 = r726107 / r726108;
        double r726110 = r726087 + r726109;
        double r726111 = r726098 ? r726104 : r726110;
        double r726112 = r726086 ? r726096 : r726111;
        return r726112;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	24.6
Target	9.3
Herbie	11.6

\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if a < -3.543954312374929e-257

   1. Initial program 23.5

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

   3. Applied *-un-lft-identity 23.5

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

   4. Applied times-frac 11.5

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

   5. Simplified 11.5

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

   if -3.543954312374929e-257 < a < 2.946990120458906e-116

   1. Initial program 29.9

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

   2. Taylor expanded around inf 14.8

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

   if 2.946990120458906e-116 < a

   1. Initial program 23.7

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

   3. Applied associate-/l* 8.8

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

   5. Applied *-un-lft-identity 8.8

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

   6. Applied add-cube-cbrt 9.4

      \[\leadsto x + \frac{y - x}{\frac{\color{blue}{\left(\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}\right) \cdot \sqrt[3]{a - t}}}{1 \cdot \left(z - t\right)}}\]

   7. Applied times-frac 9.4

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1} \cdot \frac{\sqrt[3]{a - t}}{z - t}}}\]

   8. Applied associate-/r* 10.3

      \[\leadsto x + \color{blue}{\frac{\frac{y - x}{\frac{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}{1}}}{\frac{\sqrt[3]{a - t}}{z - t}}}\]

   9. Simplified 10.3

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

4. Final simplification 11.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.543954312374929 \cdot 10^{-257}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 2.94699012045890585 \cdot 10^{-116}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - x}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}}{\frac{\sqrt[3]{a - t}}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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))))