Average Error: 2.9 → 2.9
Time: 39.1s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\frac{\frac{x}{\frac{y}{\sin y}}}{z}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\frac{\frac{x}{\frac{y}{\sin y}}}{z}
double f(double x, double y, double z) {
        double r24765534 = x;
        double r24765535 = y;
        double r24765536 = sin(r24765535);
        double r24765537 = r24765536 / r24765535;
        double r24765538 = r24765534 * r24765537;
        double r24765539 = z;
        double r24765540 = r24765538 / r24765539;
        return r24765540;
}
↓
double f(double x, double y, double z) {
        double r24765541 = x;
        double r24765542 = y;
        double r24765543 = sin(r24765542);
        double r24765544 = r24765542 / r24765543;
        double r24765545 = r24765541 / r24765544;
        double r24765546 = z;
        double r24765547 = r24765545 / r24765546;
        return r24765547;
}

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

Original2.9
Target0.3
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Initial program 2.9

    \[\frac{x \cdot \frac{\sin y}{y}}{z}\]
  2. Using strategy rm

  3. Applied clear-num2.9

    \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}}{z}\]
  4. Using strategy rm

  5. Applied un-div-inv2.9

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

  6. Final simplification2.9

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

Reproduce

herbie shell --seed 2019168 
(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))