Average Error: 0.4 → 0.2
Time: 27.9s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[a \cdot 120 + \frac{1}{\frac{\frac{z - t}{60}}{x - y}}\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
a \cdot 120 + \frac{1}{\frac{\frac{z - t}{60}}{x - y}}
double f(double x, double y, double z, double t, double a) {
        double r41861551 = 60.0;
        double r41861552 = x;
        double r41861553 = y;
        double r41861554 = r41861552 - r41861553;
        double r41861555 = r41861551 * r41861554;
        double r41861556 = z;
        double r41861557 = t;
        double r41861558 = r41861556 - r41861557;
        double r41861559 = r41861555 / r41861558;
        double r41861560 = a;
        double r41861561 = 120.0;
        double r41861562 = r41861560 * r41861561;
        double r41861563 = r41861559 + r41861562;
        return r41861563;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r41861564 = a;
        double r41861565 = 120.0;
        double r41861566 = r41861564 * r41861565;
        double r41861567 = 1.0;
        double r41861568 = z;
        double r41861569 = t;
        double r41861570 = r41861568 - r41861569;
        double r41861571 = 60.0;
        double r41861572 = r41861570 / r41861571;
        double r41861573 = x;
        double r41861574 = y;
        double r41861575 = r41861573 - r41861574;
        double r41861576 = r41861572 / r41861575;
        double r41861577 = r41861567 / r41861576;
        double r41861578 = r41861566 + r41861577;
        return r41861578;
}

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

Original0.4
Target0.2
Herbie0.2
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.4

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{60}{z - t}, x - y, a \cdot 120\right)}\]
  3. Using strategy rm

  4. Applied clear-num0.2

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{z - t}{60}}}, x - y, a \cdot 120\right)\]
  5. Using strategy rm

  6. Applied fma-udef0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{z - t}{60}} \cdot \left(x - y\right) + a \cdot 120}\]

  7. Simplified0.1

    \[\leadsto \color{blue}{\frac{x - y}{\frac{z - t}{60}}} + a \cdot 120\]
  8. Using strategy rm

  9. Applied clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z - t}{60}}{x - y}}} + a \cdot 120\]

  10. Final simplification0.2

    \[\leadsto a \cdot 120 + \frac{1}{\frac{\frac{z - t}{60}}{x - y}}\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))