Average Error: 3.3 → 1.0
Time: 9.1s
Precision: 64
$x \cdot \left(\frac{y}{z} - a\right)$
$\left(-a\right) \cdot x + \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}$
x \cdot \left(\frac{y}{z} - a\right)
\left(-a\right) \cdot x + \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}
double f(double x, double y, double z, double a) {
double r523446 = x;
double r523447 = y;
double r523448 = z;
double r523449 = r523447 / r523448;
double r523450 = a;
double r523451 = r523449 - r523450;
double r523452 = r523446 * r523451;
return r523452;
}


double f(double x, double y, double z, double a) {
double r523453 = a;
double r523454 = -r523453;
double r523455 = x;
double r523456 = r523454 * r523455;
double r523457 = z;
double r523458 = cbrt(r523457);
double r523459 = y;
double r523460 = cbrt(r523459);
double r523461 = r523458 / r523460;
double r523462 = r523461 * r523461;
double r523463 = r523455 / r523462;
double r523464 = r523460 / r523458;
double r523465 = r523463 * r523464;
double r523466 = r523456 + r523465;
return r523466;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 3.3

$x \cdot \left(\frac{y}{z} - a\right)$
2. Using strategy rm
3. Applied sub-neg3.3

$\leadsto x \cdot \color{blue}{\left(\frac{y}{z} + \left(-a\right)\right)}$
4. Applied distribute-lft-in3.3

$\leadsto \color{blue}{x \cdot \frac{y}{z} + x \cdot \left(-a\right)}$
5. Using strategy rm

$\leadsto x \cdot \frac{y}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}} + x \cdot \left(-a\right)$

$\leadsto x \cdot \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}} + x \cdot \left(-a\right)$
8. Applied times-frac3.9

$\leadsto x \cdot \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}\right)} + x \cdot \left(-a\right)$
9. Applied associate-*r*1.1

$\leadsto \color{blue}{\left(x \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}} + x \cdot \left(-a\right)$
10. Simplified1.0

$\leadsto \color{blue}{\frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}} + x \cdot \left(-a\right)$
11. Final simplification1.0

$\leadsto \left(-a\right) \cdot x + \frac{x}{\frac{\sqrt[3]{z}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{z}}{\sqrt[3]{y}}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z}}$

# Reproduce

herbie shell --seed 1
(FPCore (x y z a)
:name "x*(y/z-a)"
(* x (- (/ y z) a)))