Average Error: 33.9 → 0.4
Time: 30.5s
Precision: 64
\[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]
↓
\[\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y} \cdot \left(\frac{1}{y} \cdot x\right)\]
\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}
↓
\frac{z}{t} \cdot \frac{z}{t} + \frac{x}{y} \cdot \left(\frac{1}{y} \cdot x\right)
double f(double x, double y, double z, double t) {
        double r447453 = x;
        double r447454 = r447453 * r447453;
        double r447455 = y;
        double r447456 = r447455 * r447455;
        double r447457 = r447454 / r447456;
        double r447458 = z;
        double r447459 = r447458 * r447458;
        double r447460 = t;
        double r447461 = r447460 * r447460;
        double r447462 = r447459 / r447461;
        double r447463 = r447457 + r447462;
        return r447463;
}
↓
double f(double x, double y, double z, double t) {
        double r447464 = z;
        double r447465 = t;
        double r447466 = r447464 / r447465;
        double r447467 = r447466 * r447466;
        double r447468 = x;
        double r447469 = y;
        double r447470 = r447468 / r447469;
        double r447471 = 1.0;
        double r447472 = r447471 / r447469;
        double r447473 = r447472 * r447468;
        double r447474 = r447470 * r447473;
        double r447475 = r447467 + r447474;
        return r447475;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

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Target

Original33.9
Target0.4
Herbie0.4
\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2}\]

Derivation

  1. Initial program 33.9

    \[\frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t}\]

  2. Simplified13.5

    \[\leadsto \color{blue}{\frac{x}{\frac{y \cdot y}{x}} + \frac{z}{t} \cdot \frac{z}{t}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity13.5

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

  5. Applied times-frac4.2

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

  6. Applied associate-/r*0.4

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

  7. Simplified0.4

    \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{\frac{y}{x}} + \frac{z}{t} \cdot \frac{z}{t}\]
  8. Using strategy rm

  9. Applied div-inv0.4

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

  10. Applied div-inv0.4

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

  11. Applied times-frac0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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