Average Error: 0.1 → 0
Time: 19.5s
Precision: 64
$-\left(\left(az - dz\right) - \frac{vz}{vx} \cdot \left(ax - dx\right)\right)$
$-\left(\left(az - dz\right) - \frac{1}{\sqrt[3]{vx} \cdot \sqrt[3]{vx}} \cdot \left(\frac{vz}{\sqrt[3]{vx}} \cdot \left(ax - dx\right)\right)\right)$
-\left(\left(az - dz\right) - \frac{vz}{vx} \cdot \left(ax - dx\right)\right)
-\left(\left(az - dz\right) - \frac{1}{\sqrt[3]{vx} \cdot \sqrt[3]{vx}} \cdot \left(\frac{vz}{\sqrt[3]{vx}} \cdot \left(ax - dx\right)\right)\right)
double f(double az, double dz, double vz, double vx, double ax, double dx) {
double r2408908 = az;
double r2408909 = dz;
double r2408910 = r2408908 - r2408909;
double r2408911 = vz;
double r2408912 = vx;
double r2408913 = r2408911 / r2408912;
double r2408914 = ax;
double r2408915 = dx;
double r2408916 = r2408914 - r2408915;
double r2408917 = r2408913 * r2408916;
double r2408918 = r2408910 - r2408917;
double r2408919 = -r2408918;
return r2408919;
}


double f(double az, double dz, double vz, double vx, double ax, double dx) {
double r2408920 = az;
double r2408921 = dz;
double r2408922 = r2408920 - r2408921;
double r2408923 = 1.0;
double r2408924 = vx;
double r2408925 = cbrt(r2408924);
double r2408926 = r2408925 * r2408925;
double r2408927 = r2408923 / r2408926;
double r2408928 = vz;
double r2408929 = r2408928 / r2408925;
double r2408930 = ax;
double r2408931 = dx;
double r2408932 = r2408930 - r2408931;
double r2408933 = r2408929 * r2408932;
double r2408934 = r2408927 * r2408933;
double r2408935 = r2408922 - r2408934;
double r2408936 = -r2408935;
return r2408936;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.1

$-\left(\left(az - dz\right) - \frac{vz}{vx} \cdot \left(ax - dx\right)\right)$
2. Using strategy rm

$\leadsto -\left(\left(az - dz\right) - \frac{vz}{\color{blue}{\left(\sqrt[3]{vx} \cdot \sqrt[3]{vx}\right) \cdot \sqrt[3]{vx}}} \cdot \left(ax - dx\right)\right)$
4. Applied *-un-lft-identity0.1

$\leadsto -\left(\left(az - dz\right) - \frac{\color{blue}{1 \cdot vz}}{\left(\sqrt[3]{vx} \cdot \sqrt[3]{vx}\right) \cdot \sqrt[3]{vx}} \cdot \left(ax - dx\right)\right)$
5. Applied times-frac0.1

$\leadsto -\left(\left(az - dz\right) - \color{blue}{\left(\frac{1}{\sqrt[3]{vx} \cdot \sqrt[3]{vx}} \cdot \frac{vz}{\sqrt[3]{vx}}\right)} \cdot \left(ax - dx\right)\right)$
6. Applied associate-*l*0

$\leadsto -\left(\left(az - dz\right) - \color{blue}{\frac{1}{\sqrt[3]{vx} \cdot \sqrt[3]{vx}} \cdot \left(\frac{vz}{\sqrt[3]{vx}} \cdot \left(ax - dx\right)\right)}\right)$
7. Final simplification0

$\leadsto -\left(\left(az - dz\right) - \frac{1}{\sqrt[3]{vx} \cdot \sqrt[3]{vx}} \cdot \left(\frac{vz}{\sqrt[3]{vx}} \cdot \left(ax - dx\right)\right)\right)$

# Reproduce

herbie shell --seed 1
(FPCore (az dz vz vx ax dx)
:name "-((az - dz) - (vz/vx) * (ax - dx))"
:precision binary32
(- (- (- az dz) (* (/ vz vx) (- ax dx)))))