Average Error: 0.4 → 0.5
Time: 12.4s
Precision: 64
$\frac{1}{1 - \sin x}$
$\frac{1}{{e}^{\left(\log \left(1 - \sin x\right)\right)}}$
\frac{1}{1 - \sin x}
\frac{1}{{e}^{\left(\log \left(1 - \sin x\right)\right)}}
double f(double x) {
double r24170730 = 1.0;
double r24170731 = x;
double r24170732 = sin(r24170731);
double r24170733 = r24170730 - r24170732;
double r24170734 = r24170730 / r24170733;
return r24170734;
}


double f(double x) {
double r24170735 = 1.0;
double r24170736 = exp(1.0);
double r24170737 = x;
double r24170738 = sin(r24170737);
double r24170739 = r24170735 - r24170738;
double r24170740 = log(r24170739);
double r24170741 = pow(r24170736, r24170740);
double r24170742 = r24170735 / r24170741;
return r24170742;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.4

$\frac{1}{1 - \sin x}$
2. Using strategy rm

$\leadsto \frac{1}{\color{blue}{e^{\log \left(1 - \sin x\right)}}}$
4. Using strategy rm
5. Applied pow10.4

$\leadsto \frac{1}{e^{\log \color{blue}{\left({\left(1 - \sin x\right)}^{1}\right)}}}$
6. Applied log-pow0.4

$\leadsto \frac{1}{e^{\color{blue}{1 \cdot \log \left(1 - \sin x\right)}}}$
7. Applied exp-prod0.5

$\leadsto \frac{1}{\color{blue}{{\left(e^{1}\right)}^{\left(\log \left(1 - \sin x\right)\right)}}}$
8. Simplified0.5

$\leadsto \frac{1}{{\color{blue}{e}}^{\left(\log \left(1 - \sin x\right)\right)}}$
9. Final simplification0.5

$\leadsto \frac{1}{{e}^{\left(\log \left(1 - \sin x\right)\right)}}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "1/(1-sin(x))"
(/ 1.0 (- 1.0 (sin x))))