Average Error: 0.1 → 0
Time: 21.7s
Precision: 64
$-\left(\left(az - dz\right) - \frac{vz}{vx} \cdot \left(ax - dx\right)\right)$
$\left(\sqrt[3]{vz} \cdot \sqrt[3]{vz}\right) \cdot \left(\frac{\sqrt[3]{vz}}{vx} \cdot \left(ax - dx\right)\right) - \left(az - dz\right)$
-\left(\left(az - dz\right) - \frac{vz}{vx} \cdot \left(ax - dx\right)\right)
\left(\sqrt[3]{vz} \cdot \sqrt[3]{vz}\right) \cdot \left(\frac{\sqrt[3]{vz}}{vx} \cdot \left(ax - dx\right)\right) - \left(az - dz\right)
double f(double az, double dz, double vz, double vx, double ax, double dx) {
double r2410527 = az;
double r2410528 = dz;
double r2410529 = r2410527 - r2410528;
double r2410530 = vz;
double r2410531 = vx;
double r2410532 = r2410530 / r2410531;
double r2410533 = ax;
double r2410534 = dx;
double r2410535 = r2410533 - r2410534;
double r2410536 = r2410532 * r2410535;
double r2410537 = r2410529 - r2410536;
double r2410538 = -r2410537;
return r2410538;
}


double f(double az, double dz, double vz, double vx, double ax, double dx) {
double r2410539 = vz;
double r2410540 = cbrt(r2410539);
double r2410541 = r2410540 * r2410540;
double r2410542 = vx;
double r2410543 = r2410540 / r2410542;
double r2410544 = ax;
double r2410545 = dx;
double r2410546 = r2410544 - r2410545;
double r2410547 = r2410543 * r2410546;
double r2410548 = r2410541 * r2410547;
double r2410549 = az;
double r2410550 = dz;
double r2410551 = r2410549 - r2410550;
double r2410552 = r2410548 - r2410551;
return r2410552;
}



# 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. Simplified0.1

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

$\leadsto \frac{vz}{\color{blue}{1 \cdot vx}} \cdot \left(ax - dx\right) - \left(az - dz\right)$

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

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

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

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

# 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)))))