Average Error: 0.1 → 0.1
Time: 7.1s
Precision: binary64
Cost: 32512
\[0 \leq e \land e \leq 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]
↓
\[\frac{e \cdot \sin v}{1 + \log \left({\left(e^{e}\right)}^{\cos v}\right)} \]
(FPCore (e v) :precision binary64 (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))
↓
(FPCore (e v)
 :precision binary64
 (/ (* e (sin v)) (+ 1.0 (log (pow (exp e) (cos v))))))
double code(double e, double v) {
	return (e * sin(v)) / (1.0 + (e * cos(v)));
}
↓
double code(double e, double v) {
	return (e * sin(v)) / (1.0 + log(pow(exp(e), cos(v))));
}

real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = (e * sin(v)) / (1.0d0 + (e * cos(v)))
end function
↓
real(8) function code(e, v)
    real(8), intent (in) :: e
    real(8), intent (in) :: v
    code = (e * sin(v)) / (1.0d0 + log((exp(e) ** cos(v))))
end function

public static double code(double e, double v) {
	return (e * Math.sin(v)) / (1.0 + (e * Math.cos(v)));
}
↓
public static double code(double e, double v) {
	return (e * Math.sin(v)) / (1.0 + Math.log(Math.pow(Math.exp(e), Math.cos(v))));
}

def code(e, v):
	return (e * math.sin(v)) / (1.0 + (e * math.cos(v)))
↓
def code(e, v):
	return (e * math.sin(v)) / (1.0 + math.log(math.pow(math.exp(e), math.cos(v))))

function code(e, v)
	return Float64(Float64(e * sin(v)) / Float64(1.0 + Float64(e * cos(v))))
end
↓
function code(e, v)
	return Float64(Float64(e * sin(v)) / Float64(1.0 + log((exp(e) ^ cos(v)))))
end

function tmp = code(e, v)
	tmp = (e * sin(v)) / (1.0 + (e * cos(v)));
end
↓
function tmp = code(e, v)
	tmp = (e * sin(v)) / (1.0 + log((exp(e) ^ cos(v))));
end

code[e_, v_] := N[(N[(e * N[Sin[v], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(e * N[Cos[v], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[e_, v_] := N[(N[(e * N[Sin[v], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[Log[N[Power[N[Exp[e], $MachinePrecision], N[Cos[v], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + \log \left({\left(e^{e}\right)}^{\cos v}\right)}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]

  2. Applied egg-rr0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + \color{blue}{\log \left({\left(e^{e}\right)}^{\cos v}\right)}} \]

  3. Final simplification0.1

    \[\leadsto \frac{e \cdot \sin v}{1 + \log \left({\left(e^{e}\right)}^{\cos v}\right)} \]

Alternatives

Alternative 1
Error0.3
Cost13376
\[\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}} \]
Alternative 2
Error0.1
Cost13376
\[\sin v \cdot \frac{e}{1 + e \cdot \cos v} \]
Alternative 3
Error0.1
Cost13376
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v} \]
Alternative 4
Error0.9
Cost6848
\[\frac{\sin v}{\frac{e + 1}{e}} \]
Alternative 5
Error0.8
Cost6848
\[\sin v \cdot \frac{e}{e + 1} \]
Alternative 6
Error1.5
Cost6592
\[e \cdot \sin v \]
Alternative 7
Error30.3
Cost1472
\[e \cdot \frac{1}{v \cdot \left(e \cdot -0.5 + -0.16666666666666666 \cdot \left(-1 - e\right)\right) + \left(\frac{e}{v} + \frac{1}{v}\right)} \]
Alternative 8
Error30.4
Cost1344
\[\frac{e}{v \cdot \left(e \cdot -0.5 + -0.16666666666666666 \cdot \left(-1 - e\right)\right) + \left(\frac{e}{v} + \frac{1}{v}\right)} \]
Alternative 9
Error31.0
Cost704
\[e \cdot \frac{1}{\frac{1}{v} + v \cdot 0.16666666666666666} \]
Alternative 10
Error31.0
Cost576
\[\frac{e}{\frac{1}{v} + v \cdot 0.16666666666666666} \]
Alternative 11
Error31.1
Cost448
\[\frac{e}{\frac{e + 1}{v}} \]
Alternative 12
Error31.1
Cost448
\[e \cdot \frac{v}{e + 1} \]
Alternative 13
Error31.7
Cost192
\[e \cdot v \]
Alternative 14
Error61.1
Cost64
\[v \]

Error

Reproduce

herbie shell --seed 2022284 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (and (<= 0.0 e) (<= e 1.0))
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))