?

Average Error: 0.0 → 0.0
Time: 10.4s
Precision: binary64
Cost: 14016

?

\[\left(0.8 \leq x \land x \leq 1\right) \land \left(0 \leq t \land t \leq 0.01\right)\]
\[\frac{\frac{\left(1 - x\right) \cdot e^{\left(-0.5\right) \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}{\sqrt{t}}}{t} \]
↓
\[\frac{\frac{\left(1 - x\right) \cdot e^{-0.5 \cdot \frac{\left(1 - x\right) \cdot \left(1 - x\right)}{t}}}{\sqrt{t}}}{t} \]
(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) (exp (* -0.5 (/ (* (- 1.0 x) (- 1.0 x)) t)))) (sqrt t)) 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) * exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / sqrt(t)) / t;
}

real(8) function code(x, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: t
    code = (((1.0d0 - x) * exp((-0.5d0 * (((1.0d0 - x) * (1.0d0 - x)) / t)))) / sqrt(t)) / t
end function
↓
real(8) function code(x, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: t
    code = (((1.0d0 - x) * exp(((-0.5d0) * (((1.0d0 - x) * (1.0d0 - x)) / t)))) / sqrt(t)) / t
end function

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.exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / Math.sqrt(t)) / 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.exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / math.sqrt(t)) / 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(Float64(1.0 - x) * exp(Float64(-0.5 * Float64(Float64(Float64(1.0 - x) * Float64(1.0 - x)) / t)))) / sqrt(t)) / 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) * exp((-0.5 * (((1.0 - x) * (1.0 - x)) / t)))) / sqrt(t)) / 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[(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]

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

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

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
Error0.6
Cost13376
\[\frac{\sqrt{\frac{1}{t}} \cdot e^{\frac{-0.5}{t}}}{t} \]
Alternative 3
Error63.0
Cost6784
\[\frac{1 - x}{{t}^{1.5}} \]
Alternative 4
Error63.0
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 0.01)))
  (/ (/ (* (- 1.0 x) (exp (* (- 0.5) (/ (* (- 1.0 x) (- 1.0 x)) t)))) (sqrt t)) t))