Average Error: 2.6 → 2.7
Time: 14.9s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\frac{\frac{1}{\frac{y}{\sin y}}}{z} \cdot x\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\frac{\frac{1}{\frac{y}{\sin y}}}{z} \cdot x
double f(double x, double y, double z) {
        double r461952 = x;
        double r461953 = y;
        double r461954 = sin(r461953);
        double r461955 = r461954 / r461953;
        double r461956 = r461952 * r461955;
        double r461957 = z;
        double r461958 = r461956 / r461957;
        return r461958;
}
↓
double f(double x, double y, double z) {
        double r461959 = 1.0;
        double r461960 = y;
        double r461961 = sin(r461960);
        double r461962 = r461960 / r461961;
        double r461963 = r461959 / r461962;
        double r461964 = z;
        double r461965 = r461963 / r461964;
        double r461966 = x;
        double r461967 = r461965 * r461966;
        return r461967;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.6
Target0.3
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Initial program 2.6

    \[\frac{x \cdot \frac{\sin y}{y}}{z}\]

  2. Simplified2.6

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

  4. Applied clear-num2.7

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

  5. Final simplification2.7

    \[\leadsto \frac{\frac{1}{\frac{y}{\sin y}}}{z} \cdot x\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))