# ?

Average Error: 0.0 → 0.0
Time: 14.0s
Precision: binary64
Cost: 20416

# ?

$\left(0.8 \leq x \land x \leq 1\right) \land \left(0 \leq t \land t \leq 30\right)$
$\frac{\frac{\left(1 - x\right) \cdot e^{\left(-0.5\right) \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}{\sqrt{t}}}{t}$
$\frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\left(\frac{\left(1 - x\right) \cdot \left(1 - x\right)}{\frac{t}{-0.5}}\right)}}}}{t}$
(FPCore (x t)
:precision binary64
(/
(/ (* (- 1.0 x) (exp (* (- 0.5) (/ (* (- 1.0 x) (- 1.0 x)) t)))) (sqrt t))
t))
(FPCore (x t)
:precision binary64
(/
(/ (- 1.0 x) (/ (sqrt t) (pow E (/ (* (- 1.0 x) (- 1.0 x)) (/ t -0.5)))))
t))
double code(double x, double t) {
return (((1.0 - x) * exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / sqrt(t)) / t;
}

double code(double x, double t) {
return ((1.0 - x) / (sqrt(t) / pow(((double) M_E), (((1.0 - x) * (1.0 - x)) / (t / -0.5))))) / t;
}

public static double code(double x, double t) {
return (((1.0 - x) * Math.exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / Math.sqrt(t)) / t;
}

public static double code(double x, double t) {
return ((1.0 - x) / (Math.sqrt(t) / Math.pow(Math.E, (((1.0 - x) * (1.0 - x)) / (t / -0.5))))) / t;
}

def code(x, t):
return (((1.0 - x) * math.exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / math.sqrt(t)) / t

def code(x, t):
return ((1.0 - x) / (math.sqrt(t) / math.pow(math.e, (((1.0 - x) * (1.0 - x)) / (t / -0.5))))) / t

function code(x, t)
return Float64(Float64(Float64(Float64(1.0 - x) * exp(Float64(Float64(-0.5) * Float64(Float64(Float64(1.0 - x) * Float64(1.0 - x)) / t)))) / sqrt(t)) / t)
end

function code(x, t)
return Float64(Float64(Float64(1.0 - x) / Float64(sqrt(t) / (exp(1) ^ Float64(Float64(Float64(1.0 - x) * Float64(1.0 - x)) / Float64(t / -0.5))))) / t)
end

function tmp = code(x, t)
tmp = (((1.0 - x) * exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / sqrt(t)) / t;
end

function tmp = code(x, t)
tmp = ((1.0 - x) / (sqrt(t) / (2.71828182845904523536 ^ (((1.0 - x) * (1.0 - x)) / (t / -0.5))))) / t;
end

code[x_, t_] := N[(N[(N[(N[(1.0 - x), $MachinePrecision] * N[Exp[N[((-0.5) * N[(N[(N[(1.0 - x),$MachinePrecision] * N[(1.0 - x), $MachinePrecision]),$MachinePrecision] / t), $MachinePrecision]),$MachinePrecision]], $MachinePrecision]),$MachinePrecision] / N[Sqrt[t], $MachinePrecision]),$MachinePrecision] / t), $MachinePrecision]  code[x_, t_] := N[(N[(N[(1.0 - x),$MachinePrecision] / N[(N[Sqrt[t], $MachinePrecision] / N[Power[E, N[(N[(N[(1.0 - x),$MachinePrecision] * N[(1.0 - x), $MachinePrecision]),$MachinePrecision] / N[(t / -0.5), $MachinePrecision]),$MachinePrecision]], $MachinePrecision]),$MachinePrecision]), $MachinePrecision] / t),$MachinePrecision]

\frac{\frac{\left(1 - x\right) \cdot e^{\left(-0.5\right) \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}{\sqrt{t}}}{t}

\frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\left(\frac{\left(1 - x\right) \cdot \left(1 - x\right)}{\frac{t}{-0.5}}\right)}}}}{t}


# Try it out?

Results

 In Out
Enter valid numbers for all inputs

# Derivation?

1. Initial program 0.0

$\frac{\frac{\left(1 - x\right) \cdot e^{\left(-0.5\right) \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}{\sqrt{t}}}{t}$
2. Simplified0.0

$\leadsto \color{blue}{\frac{\frac{1 - x}{\frac{\sqrt{t}}{e^{-0.5 \cdot \left(\frac{1 - x}{t} \cdot \left(1 - x\right)\right)}}}}{t}}$
Proof
[Start]0.0 $\frac{\frac{\left(1 - x\right) \cdot e^{\left(-0.5\right) \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}{\sqrt{t}}}{t}$ $\frac{\color{blue}{\frac{1 - x}{\frac{\sqrt{t}}{e^{\left(-0.5\right) \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}}}}{t}$ $\frac{\frac{1 - x}{\frac{\sqrt{t}}{e^{\color{blue}{-0.5} \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}}}{t}$ $\frac{\frac{1 - x}{\frac{\sqrt{t}}{e^{-0.5 \cdot \color{blue}{\left(\frac{1 - x}{t} \cdot \left(1 - x\right)\right)}}}}}{t}$
3. Applied egg-rr0.0

$\leadsto \frac{\frac{1 - x}{\frac{\sqrt{t}}{\color{blue}{{e}^{\left(\frac{{\left(1 - x\right)}^{2}}{t} \cdot -0.5\right)}}}}}{t}$
4. Simplified0.0

$\leadsto \frac{\frac{1 - x}{\frac{\sqrt{t}}{\color{blue}{{e}^{\left(\frac{{\left(1 - x\right)}^{2}}{\frac{t}{-0.5}}\right)}}}}}{t}$
Proof
[Start]0.0 $\frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\left(\frac{{\left(1 - x\right)}^{2}}{t} \cdot -0.5\right)}}}}{t}$ $\frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\color{blue}{\left(\frac{{\left(1 - x\right)}^{2} \cdot -0.5}{t}\right)}}}}}{t}$ $\frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\color{blue}{\left(\frac{{\left(1 - x\right)}^{2}}{\frac{t}{-0.5}}\right)}}}}}{t}$
5. Applied egg-rr0.0

$\leadsto \frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\left(\frac{\color{blue}{\left(1 - x\right) \cdot \left(1 - x\right)}}{\frac{t}{-0.5}}\right)}}}}{t}$
6. Final simplification0.0

$\leadsto \frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\left(\frac{\left(1 - x\right) \cdot \left(1 - x\right)}{\frac{t}{-0.5}}\right)}}}}{t}$

# Alternatives

Alternative 1
Error0.0
Cost14016
$\frac{\frac{1 - x}{\frac{\sqrt{t}}{e^{-0.5 \cdot \left(\left(1 - x\right) \cdot \frac{1 - x}{t}\right)}}}}{t}$
Alternative 2
Error0.0
Cost14016
$\frac{\frac{\left(1 - x\right) \cdot e^{-0.5 \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}{\sqrt{t}}}{t}$
Alternative 3
Error1.3
Cost13312
$\frac{{t}^{-0.5} \cdot e^{\frac{-0.5}{t}}}{t}$
Alternative 4
Error62.8
Cost6784
$\frac{1 - x}{{t}^{1.5}}$
Alternative 5
Error62.9
Cost6720
$\frac{\sqrt{\frac{1}{t}}}{t}$

# Reproduce?

herbie shell --seed 1
(FPCore (x t)
:name "((1 - x) * exp((-0.5 * (((1 - x) * (1 - x)) / t)))) / sqrt(t) / t"
:precision binary64
:pre (and (and (<= 0.8 x) (<= x 1.0)) (and (<= 0.0 t) (<= t 30.0)))
(/ (/ (* (- 1.0 x) (exp (* (- 0.5) (/ (* (- 1.0 x) (- 1.0 x)) t)))) (sqrt t)) t))