Average Error: 29.5 → 29.7
Time: 23.7s
Precision: 64
\[\frac{\left(1 - t\right) \cdot \frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}{\frac{\sin y}{y}}\]
\[\frac{\left(\left(1 - t\right) \cdot \left(\sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}} \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}\right)\right) \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}}{\frac{\sin y}{y}}\]
\frac{\left(1 - t\right) \cdot \frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}{\frac{\sin y}{y}}
\frac{\left(\left(1 - t\right) \cdot \left(\sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}} \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}\right)\right) \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}}{\frac{\sin y}{y}}
double f(double t, double y) {
        double r28143 = 1.0;
        double r28144 = t;
        double r28145 = r28143 - r28144;
        double r28146 = y;
        double r28147 = r28145 * r28146;
        double r28148 = sin(r28147);
        double r28149 = r28148 / r28147;
        double r28150 = r28145 * r28149;
        double r28151 = sin(r28146);
        double r28152 = r28151 / r28146;
        double r28153 = r28150 / r28152;
        return r28153;
}

double f(double t, double y) {
        double r28154 = 1.0;
        double r28155 = t;
        double r28156 = r28154 - r28155;
        double r28157 = y;
        double r28158 = r28156 * r28157;
        double r28159 = sin(r28158);
        double r28160 = r28159 / r28158;
        double r28161 = cbrt(r28160);
        double r28162 = r28161 * r28161;
        double r28163 = r28156 * r28162;
        double r28164 = r28163 * r28161;
        double r28165 = sin(r28157);
        double r28166 = r28165 / r28157;
        double r28167 = r28164 / r28166;
        return r28167;
}

Error

Bits error versus t

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.5

    \[\frac{\left(1 - t\right) \cdot \frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}{\frac{\sin y}{y}}\]
  2. Using strategy rm
  3. Applied add-cube-cbrt29.7

    \[\leadsto \frac{\left(1 - t\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}} \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}\right) \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}\right)}}{\frac{\sin y}{y}}\]
  4. Applied associate-*r*29.7

    \[\leadsto \frac{\color{blue}{\left(\left(1 - t\right) \cdot \left(\sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}} \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}\right)\right) \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}}}{\frac{\sin y}{y}}\]
  5. Final simplification29.7

    \[\leadsto \frac{\left(\left(1 - t\right) \cdot \left(\sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}} \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}\right)\right) \cdot \sqrt[3]{\frac{\sin \left(\left(1 - t\right) \cdot y\right)}{\left(1 - t\right) \cdot y}}}{\frac{\sin y}{y}}\]

Reproduce

herbie shell --seed 1 
(FPCore (t y)
  :name "(1-t) * (sin((1-t) * y) / ((1-t) * y)) / (sin(y) / y)"
  :precision binary64
  (/ (* (- 1 t) (/ (sin (* (- 1 t) y)) (* (- 1 t) y))) (/ (sin y) y)))