?

Average Accuracy: 99.8% → 99.9%
Time: 15.5s
Precision: binary64
Cost: 20032

?

\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
↓
\[\left(x + \left(-1 + \left(e^{\mathsf{log1p}\left(y\right)} + \log y \cdot \left(-0.5 - y\right)\right)\right)\right) - z \]
(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))
↓
(FPCore (x y z)
 :precision binary64
 (- (+ x (+ -1.0 (+ (exp (log1p y)) (* (log y) (- -0.5 y))))) z))
double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}
↓
double code(double x, double y, double z) {
	return (x + (-1.0 + (exp(log1p(y)) + (log(y) * (-0.5 - y))))) - z;
}

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}
↓
public static double code(double x, double y, double z) {
	return (x + (-1.0 + (Math.exp(Math.log1p(y)) + (Math.log(y) * (-0.5 - y))))) - z;
}

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z
↓
def code(x, y, z):
	return (x + (-1.0 + (math.exp(math.log1p(y)) + (math.log(y) * (-0.5 - y))))) - z

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end
↓
function code(x, y, z)
	return Float64(Float64(x + Float64(-1.0 + Float64(exp(log1p(y)) + Float64(log(y) * Float64(-0.5 - y))))) - z)
end

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]
↓
code[x_, y_, z_] := N[(N[(x + N[(-1.0 + N[(N[Exp[N[Log[1 + y], $MachinePrecision]], $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(-0.5 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(x + \left(-1 + \left(e^{\mathsf{log1p}\left(y\right)} + \log y \cdot \left(-0.5 - y\right)\right)\right)\right) - z

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original99.8%
Target99.8%
Herbie99.9%
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y \]

Derivation?

  1. Initial program 99.8%

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

  2. Simplified99.8%

    \[\leadsto \color{blue}{\left(x - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right) - z} \]
    Proof

    [Start]99.8

    \[ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]

    associate-+l- [=>]99.8

    \[ \color{blue}{\left(x - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z \]

  3. Applied egg-rr99.9%

    \[\leadsto \left(x - \color{blue}{\left(\left(\left(y + 0.5\right) \cdot \log y - e^{\mathsf{log1p}\left(y\right)}\right) + 1\right)}\right) - z \]

  4. Final simplification99.9%

    \[\leadsto \left(x + \left(-1 + \left(e^{\mathsf{log1p}\left(y\right)} + \log y \cdot \left(-0.5 - y\right)\right)\right)\right) - z \]

Alternatives

Alternative 1
Accuracy99.9%
Cost13376
\[x + \mathsf{fma}\left(\log y, -0.5 - y, y - z\right) \]
Alternative 2
Accuracy73.1%
Cost7772
\[\begin{array}{l} t_0 := y + \left(x - y \cdot \log y\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+139}:\\ \;\;\;\;\log y \cdot \left(-y\right) - z\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-5}:\\ \;\;\;\;x - z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;y - \log y \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-204}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.92 \cdot 10^{-240}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+166}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
Alternative 3
Accuracy73.6%
Cost7376
\[\begin{array}{l} t_0 := y + \left(x - y \cdot \log y\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+139}:\\ \;\;\;\;\log y \cdot \left(-y\right) - z\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-204}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-240}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+166}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x - z\\ \end{array} \]
Alternative 4
Accuracy76.5%
Cost7376
\[\begin{array}{l} t_0 := y + \left(x - y \cdot \log y\right)\\ t_1 := y \cdot \left(1 - \log y\right) - z\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{-240}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+122}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Accuracy76.5%
Cost7376
\[\begin{array}{l} t_0 := y \cdot \log y\\ t_1 := y \cdot \left(1 - \log y\right) - z\\ \mathbf{if}\;z \leq -5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-204}:\\ \;\;\;\;y + \left(x - t_0\right)\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-239}:\\ \;\;\;\;x + \log y \cdot -0.5\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\left(x + y\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Accuracy89.4%
Cost7244
\[\begin{array}{l} t_0 := \left(x + \log y \cdot -0.5\right) - z\\ \mathbf{if}\;y \leq 1.9 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;y + \left(x - y \cdot \log y\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right) - z\\ \end{array} \]
Alternative 7
Accuracy98.3%
Cost7241
\[\begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+20} \lor \neg \left(x \leq 3.8 \cdot 10^{-30}\right):\\ \;\;\;\;\left(x + \left(y - y \cdot \log y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(y - \log y \cdot \left(y + 0.5\right)\right) - z\\ \end{array} \]
Alternative 8
Accuracy99.3%
Cost7108
\[\begin{array}{l} \mathbf{if}\;y \leq 3.2:\\ \;\;\;\;\left(x + \log y \cdot -0.5\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y - y \cdot \log y\right)\right) - z\\ \end{array} \]
Alternative 9
Accuracy99.8%
Cost7104
\[\left(y + \left(x + \log y \cdot \left(-0.5 - y\right)\right)\right) - z \]
Alternative 10
Accuracy71.8%
Cost6852
\[\begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;x - z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \log y\right)\\ \end{array} \]
Alternative 11
Accuracy48.5%
Cost392
\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+139}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
Alternative 12
Accuracy59.5%
Cost192
\[x - z \]
Alternative 13
Accuracy31.1%
Cost64
\[x \]

Error

Reproduce?

herbie shell --seed 2023125 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))