Average Error: 3.0 → 3.0
Time: 1.6s
Precision: binary64
\[\frac{e^{\frac{1}{3} \cdot \frac{r}{d}} + {\left(e^{\frac{1}{3} \cdot \frac{r}{d}}\right)}^{3}}{d \cdot r}\]
↓
\[\frac{e^{\frac{1}{3} \cdot \frac{r}{d}} + {\left(e^{\frac{1}{3} \cdot \frac{r}{d}}\right)}^{3}}{d \cdot r}\]
\frac{e^{\frac{1}{3} \cdot \frac{r}{d}} + {\left(e^{\frac{1}{3} \cdot \frac{r}{d}}\right)}^{3}}{d \cdot r}
↓
\frac{e^{\frac{1}{3} \cdot \frac{r}{d}} + {\left(e^{\frac{1}{3} \cdot \frac{r}{d}}\right)}^{3}}{d \cdot r}
double code(double r, double d) {
	return ((double) (((double) (((double) exp(((double) (((double) (1.0 / 3.0)) * ((double) (r / d)))))) + ((double) pow(((double) exp(((double) (((double) (1.0 / 3.0)) * ((double) (r / d)))))), 3.0)))) / ((double) (d * r))));
}
↓
double code(double r, double d) {
	return ((double) (((double) (((double) exp(((double) (((double) (1.0 / 3.0)) * ((double) (r / d)))))) + ((double) pow(((double) exp(((double) (((double) (1.0 / 3.0)) * ((double) (r / d)))))), 3.0)))) / ((double) (d * r))));
}

Error

Bits error versus r

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.0

    \[\frac{e^{\frac{1}{3} \cdot \frac{r}{d}} + {\left(e^{\frac{1}{3} \cdot \frac{r}{d}}\right)}^{3}}{d \cdot r}\]

  2. Final simplification3.0

    \[\leadsto \frac{e^{\frac{1}{3} \cdot \frac{r}{d}} + {\left(e^{\frac{1}{3} \cdot \frac{r}{d}}\right)}^{3}}{d \cdot r}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (r d)
  :name "(/ (+ (exp (* (/ 1 3) (/ r d))) (pow (exp (* (/ 1 3) (/ r d))) 3)) (* d r))"
  :precision binary64
  (/ (+ (exp (* (/ 1.0 3.0) (/ r d))) (pow (exp (* (/ 1.0 3.0) (/ r d))) 3.0)) (* d r)))