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;
}



# Try it out

Results

 In Out
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

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