Average Error: 6.3 → 1.9
Time: 1.5m
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\frac{z - x}{\frac{t}{y}} + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\frac{z - x}{\frac{t}{y}} + x
double f(double x, double y, double z, double t) {
        double r256159 = x;
        double r256160 = y;
        double r256161 = z;
        double r256162 = r256161 - r256159;
        double r256163 = r256160 * r256162;
        double r256164 = t;
        double r256165 = r256163 / r256164;
        double r256166 = r256159 + r256165;
        return r256166;
}
↓
double f(double x, double y, double z, double t) {
        double r256167 = z;
        double r256168 = x;
        double r256169 = r256167 - r256168;
        double r256170 = t;
        double r256171 = y;
        double r256172 = r256170 / r256171;
        double r256173 = r256169 / r256172;
        double r256174 = r256173 + r256168;
        return r256174;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.3
Target2.0
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if y < -7.329715074495526

    1. Initial program 14.7

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

    3. Applied associate-/l*2.0

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

    if -7.329715074495526 < y < 4.102782586155086e+55

    1. Initial program 1.2

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

    3. Applied div-inv1.2

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

    if 4.102782586155086e+55 < y

    1. Initial program 19.5

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

    3. Applied clear-num19.5

      \[\leadsto x + \color{blue}{\frac{1}{\frac{t}{y \cdot \left(z - x\right)}}}\]
    4. Using strategy rm

    5. Applied associate-/r*3.8

      \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity3.8

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

    8. Applied *-un-lft-identity3.8

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

    9. Applied *-un-lft-identity3.8

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

    10. Applied times-frac3.8

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

    11. Applied times-frac3.8

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

    12. Applied *-un-lft-identity3.8

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

    13. Applied times-frac3.8

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

    14. Simplified3.8

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

    15. Simplified3.7

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

  4. Final simplification1.9

    \[\leadsto \frac{z - x}{\frac{t}{y}} + x\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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