Average Error: 0.3 → 0.3
Time: 8.8s
Precision: binary64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}} \]
↓
\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(z \cdot e^{t \cdot t}\right)}\\ t_1 \cdot \left(x \cdot 0.5\right) - t_1 \cdot y \end{array} \]
(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))
↓
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* 2.0 (* z (exp (* t t)))))))
   (- (* t_1 (* x 0.5)) (* t_1 y))))
double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}
↓
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((2.0 * (z * exp((t * t)))));
	return (t_1 * (x * 0.5)) - (t_1 * y);
}

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * 0.5d0) - y) * sqrt((z * 2.0d0))) * exp(((t * t) / 2.0d0))
end function
↓
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = sqrt((2.0d0 * (z * exp((t * t)))))
    code = (t_1 * (x * 0.5d0)) - (t_1 * y)
end function

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.exp(((t * t) / 2.0));
}
↓
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((2.0 * (z * Math.exp((t * t)))));
	return (t_1 * (x * 0.5)) - (t_1 * y);
}

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.exp(((t * t) / 2.0))
↓
def code(x, y, z, t):
	t_1 = math.sqrt((2.0 * (z * math.exp((t * t)))))
	return (t_1 * (x * 0.5)) - (t_1 * y)

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * exp(Float64(Float64(t * t) / 2.0)))
end
↓
function code(x, y, z, t)
	t_1 = sqrt(Float64(2.0 * Float64(z * exp(Float64(t * t)))))
	return Float64(Float64(t_1 * Float64(x * 0.5)) - Float64(t_1 * y))
end

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
end
↓
function tmp = code(x, y, z, t)
	t_1 = sqrt((2.0 * (z * exp((t * t)))));
	tmp = (t_1 * (x * 0.5)) - (t_1 * y);
end

code[x_, y_, z_, t_] := N[(N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(2.0 * N[(z * N[Exp[N[(t * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(N[(t$95$1 * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * y), $MachinePrecision]), $MachinePrecision]]

\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\begin{array}{l}
t_1 := \sqrt{2 \cdot \left(z \cdot e^{t \cdot t}\right)}\\
t_1 \cdot \left(x \cdot 0.5\right) - t_1 \cdot y
\end{array}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)} \]

Derivation

  1. Initial program 0.3

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

  2. Simplified0.3

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

  3. Applied egg-rr0.7

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

  4. Applied egg-rr0.3

    \[\leadsto \color{blue}{\sqrt{2 \cdot \left(z \cdot e^{t \cdot t}\right)} \cdot \left(x \cdot 0.5\right) + \sqrt{2 \cdot \left(z \cdot e^{t \cdot t}\right)} \cdot \left(-y\right)} \]

  5. Final simplification0.3

    \[\leadsto \sqrt{2 \cdot \left(z \cdot e^{t \cdot t}\right)} \cdot \left(x \cdot 0.5\right) - \sqrt{2 \cdot \left(z \cdot e^{t \cdot t}\right)} \cdot y \]

Reproduce

herbie shell --seed 2022148 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))