Average Error: 23.3 → 23.3
Time: 6.9s
Precision: 64
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
↓
\[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + {\left(z \cdot \left(b - y\right)\right)}^{1}}\]
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}
↓
\frac{x \cdot y + z \cdot \left(t - a\right)}{y + {\left(z \cdot \left(b - y\right)\right)}^{1}}
double f(double x, double y, double z, double t, double a, double b) {
        double r781071 = x;
        double r781072 = y;
        double r781073 = r781071 * r781072;
        double r781074 = z;
        double r781075 = t;
        double r781076 = a;
        double r781077 = r781075 - r781076;
        double r781078 = r781074 * r781077;
        double r781079 = r781073 + r781078;
        double r781080 = b;
        double r781081 = r781080 - r781072;
        double r781082 = r781074 * r781081;
        double r781083 = r781072 + r781082;
        double r781084 = r781079 / r781083;
        return r781084;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r781085 = x;
        double r781086 = y;
        double r781087 = r781085 * r781086;
        double r781088 = z;
        double r781089 = t;
        double r781090 = a;
        double r781091 = r781089 - r781090;
        double r781092 = r781088 * r781091;
        double r781093 = r781087 + r781092;
        double r781094 = b;
        double r781095 = r781094 - r781086;
        double r781096 = r781088 * r781095;
        double r781097 = 1.0;
        double r781098 = pow(r781096, r781097);
        double r781099 = r781086 + r781098;
        double r781100 = r781093 / r781099;
        return r781100;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original23.3
Target17.8
Herbie23.3
\[\frac{z \cdot t + y \cdot x}{y + z \cdot \left(b - y\right)} - \frac{a}{\left(b - y\right) + \frac{y}{z}}\]

Derivation

  1. Initial program 23.3

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

  3. Applied pow123.3

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

  4. Applied pow123.3

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

  5. Applied pow-prod-down23.3

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

  6. Final simplification23.3

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

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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