?

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}

Error?

Try it out?

Your Program's Arguments

Results

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

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

    associate-/l* [=>]0.0

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

    metadata-eval [=>]0.0

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

    associate-*l/ [<=]0.0

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

  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

    \[ \frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\left(\frac{{\left(1 - x\right)}^{2}}{t} \cdot -0.5\right)}}}}{t} \]

    associate-*l/ [=>]0.0

    \[ \frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\color{blue}{\left(\frac{{\left(1 - x\right)}^{2} \cdot -0.5}{t}\right)}}}}}{t} \]

    associate-/l* [=>]0.0

    \[ \frac{\frac{1 - x}{\frac{\sqrt{t}}{{e}^{\color{blue}{\left(\frac{{\left(1 - x\right)}^{2}}{\frac{t}{-0.5}}\right)}}}}}{t} \]

  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
\[\frac{\sqrt{\frac{1}{t}}}{t} \]

Error

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))