?

Average Error: 23.17% → 0.5%
Time: 32.3s
Precision: binary64

?

\[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
↓
\[\frac{r}{-1} \cdot \frac{\sin b}{\mathsf{fma}\left(\sin a, \sin b, -\cos b \cdot \cos a\right)} \]
(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))
↓
(FPCore (r a b)
 :precision binary64
 (* (/ r -1.0) (/ (sin b) (fma (sin a) (sin b) (- (* (cos b) (cos a)))))))
double code(double r, double a, double b) {
	return (r * sin(b)) / cos((a + b));
}
↓
double code(double r, double a, double b) {
	return (r / -1.0) * (sin(b) / fma(sin(a), sin(b), -(cos(b) * cos(a))));
}

function code(r, a, b)
	return Float64(Float64(r * sin(b)) / cos(Float64(a + b)))
end
↓
function code(r, a, b)
	return Float64(Float64(r / -1.0) * Float64(sin(b) / fma(sin(a), sin(b), Float64(-Float64(cos(b) * cos(a))))))
end

code[r_, a_, b_] := N[(N[(r * N[Sin[b], $MachinePrecision]), $MachinePrecision] / N[Cos[N[(a + b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[r_, a_, b_] := N[(N[(r / -1.0), $MachinePrecision] * N[(N[Sin[b], $MachinePrecision] / N[(N[Sin[a], $MachinePrecision] * N[Sin[b], $MachinePrecision] + (-N[(N[Cos[b], $MachinePrecision] * N[Cos[a], $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{-1} \cdot \frac{\sin b}{\mathsf{fma}\left(\sin a, \sin b, -\cos b \cdot \cos a\right)}

Error?

Derivation?

  1. Initial program 23.17

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]

  2. Applied egg-rr0.53

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{-\left(\sin a \cdot \sin b - \cos a \cdot \cos b\right)}} \]

  3. Simplified0.5

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{-\mathsf{fma}\left(\sin a, \sin b, -\cos a \cdot \cos b\right)}} \]
    Proof

  4. Applied egg-rr0.5

    \[\leadsto \color{blue}{\frac{r}{-1} \cdot \frac{\sin b}{\mathsf{fma}\left(\sin a, \sin b, -\cos b \cdot \cos a\right)}} \]

Reproduce?

herbie shell --seed 2023136 
(FPCore (r a b)
  :name "rsin A (should all be same)"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))