Average Error: 2.8 → 3.0
Time: 12.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\frac{x}{\frac{z}{\frac{\sin y}{y}}}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\frac{x}{\frac{z}{\frac{\sin y}{y}}}
double f(double x, double y, double z) {
        double r348201 = x;
        double r348202 = y;
        double r348203 = sin(r348202);
        double r348204 = r348203 / r348202;
        double r348205 = r348201 * r348204;
        double r348206 = z;
        double r348207 = r348205 / r348206;
        return r348207;
}
↓
double f(double x, double y, double z) {
        double r348208 = x;
        double r348209 = z;
        double r348210 = y;
        double r348211 = sin(r348210);
        double r348212 = r348211 / r348210;
        double r348213 = r348209 / r348212;
        double r348214 = r348208 / r348213;
        return r348214;
}

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

Original2.8
Target0.2
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -3.088891312397517e-278 or 8.1864372841967e-209 < (* x (/ (sin y) y))

    1. Initial program 0.2

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

    3. Applied clear-num0.2

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

    if -3.088891312397517e-278 < (* x (/ (sin y) y)) < 8.1864372841967e-209

    1. Initial program 10.2

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

    3. Applied associate-/l*0.2

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\frac{\sin y}{y}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.21737202034271466e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.44670236911381103e64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

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