?

Average Error: 0.0 → 0.0
Time: 31.2s
Precision: binary64
Cost: 13504

?

\[e^{\left(x + y \cdot \log y\right) - z} \]
↓
\[e^{\left(-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right) + x\right) - z} \]
(FPCore (x y z) :precision binary64 (exp (- (+ x (* y (log y))) z)))
↓
(FPCore (x y z)
 :precision binary64
 (exp (- (+ (* -1.0 (* y (log (/ 1.0 y)))) x) z)))
double code(double x, double y, double z) {
	return exp(((x + (y * log(y))) - z));
}
↓
double code(double x, double y, double z) {
	return exp((((-1.0 * (y * log((1.0 / y)))) + x) - z));
}

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((x + (y * log(y))) - z))
end function
↓
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = exp(((((-1.0d0) * (y * log((1.0d0 / y)))) + x) - z))
end function

public static double code(double x, double y, double z) {
	return Math.exp(((x + (y * Math.log(y))) - z));
}
↓
public static double code(double x, double y, double z) {
	return Math.exp((((-1.0 * (y * Math.log((1.0 / y)))) + x) - z));
}

def code(x, y, z):
	return math.exp(((x + (y * math.log(y))) - z))
↓
def code(x, y, z):
	return math.exp((((-1.0 * (y * math.log((1.0 / y)))) + x) - z))

function code(x, y, z)
	return exp(Float64(Float64(x + Float64(y * log(y))) - z))
end
↓
function code(x, y, z)
	return exp(Float64(Float64(Float64(-1.0 * Float64(y * log(Float64(1.0 / y)))) + x) - z))
end

function tmp = code(x, y, z)
	tmp = exp(((x + (y * log(y))) - z));
end
↓
function tmp = code(x, y, z)
	tmp = exp((((-1.0 * (y * log((1.0 / y)))) + x) - z));
end

code[x_, y_, z_] := N[Exp[N[(N[(x + N[(y * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision]
↓
code[x_, y_, z_] := N[Exp[N[(N[(N[(-1.0 * N[(y * N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - z), $MachinePrecision]], $MachinePrecision]

e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right) + x\right) - z}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y} \]

Derivation?

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z} \]

  2. Taylor expanded in y around inf 0.0

    \[\leadsto e^{\color{blue}{\left(-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right) + x\right) - z}} \]

Alternatives

Alternative 1
Error0.0
Cost13248
\[e^{\left(x + y \cdot \log y\right) - z} \]
Alternative 2
Error1.4
Cost6660
\[\begin{array}{l} \mathbf{if}\;z \leq 3.1 \cdot 10^{-15}:\\ \;\;\;\;e^{x}\\ \mathbf{else}:\\ \;\;\;\;e^{-z}\\ \end{array} \]
Alternative 3
Error0.7
Cost6592
\[e^{x - z} \]
Alternative 4
Error19.2
Cost6464
\[e^{x} \]

Error

Reproduce?

herbie shell --seed 2023033 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))