Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A

Percentage Accurate: 99.4% → 99.8%

Time: 13.4s

Alternatives: 5

Speedup: 1.0×

• 45.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}

Fortran

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

Java

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));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * exp(((t * t) / 2.0));
}

Fortran

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

Java

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));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (- (* x 0.5) y) (sqrt (* (* z 2.0) (exp (* t t))))))

C

double code(double x, double y, double z, double t) {
	return ((x * 0.5) - y) * sqrt(((z * 2.0) * exp((t * t))));
}

Fortran

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))))
end function

Java

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))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(N[(z * 2.0), $MachinePrecision] * N[Exp[N[(t * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

   1. associate-*l* 99.8%

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

   2. remove-double-neg 99.8%

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

   3. remove-double-neg 99.8%

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

   4. exp-sqrt 99.5%

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

   5. exp-prod 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \sqrt{{\left(e^{t}\right)}^{t}}\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. pow1 99.5%

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

   2. sqrt-unprod 99.5%

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

   3. associate-*l* 99.5%

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

   4. pow-exp 99.5%

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

   5. pow2 99.5%

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

6. Applied egg-rr 99.5%

   \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{{\left(\sqrt{z \cdot \left(2 \cdot e^{{t}^{2}}\right)}\right)}^{1}} \]
7. Step-by-step derivation

   1. unpow1 99.5%

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

   2. associate-*r* 99.5%

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

8. Simplified 99.5%

   \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\sqrt{\left(z \cdot 2\right) \cdot e^{{t}^{2}}}} \]
9. Step-by-step derivation

   1. pow2 99.5%

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

10. Applied egg-rr 99.5%

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

Alternative 2: 59.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot 0.5 - y\\ \mathbf{if}\;t \leq 600:\\ \;\;\;\;t\_1 \cdot \sqrt{z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot \left(2 \cdot {t\_1}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x 0.5) y)))
   (if (<= t 600.0)
     (* t_1 (sqrt (* z 2.0)))
     (sqrt (* z (* 2.0 (pow t_1 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 0.5) - y;
	double tmp;
	if (t <= 600.0) {
		tmp = t_1 * sqrt((z * 2.0));
	} else {
		tmp = sqrt((z * (2.0 * pow(t_1, 2.0))));
	}
	return tmp;
}

Fortran

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
    real(8) :: tmp
    t_1 = (x * 0.5d0) - y
    if (t <= 600.0d0) then
        tmp = t_1 * sqrt((z * 2.0d0))
    else
        tmp = sqrt((z * (2.0d0 * (t_1 ** 2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * 0.5) - y;
	double tmp;
	if (t <= 600.0) {
		tmp = t_1 * Math.sqrt((z * 2.0));
	} else {
		tmp = Math.sqrt((z * (2.0 * Math.pow(t_1, 2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 0.5) - y
	tmp = 0
	if t <= 600.0:
		tmp = t_1 * math.sqrt((z * 2.0))
	else:
		tmp = math.sqrt((z * (2.0 * math.pow(t_1, 2.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (t <= 600.0)
		tmp = Float64(t_1 * sqrt(Float64(z * 2.0)));
	else
		tmp = sqrt(Float64(z * Float64(2.0 * (t_1 ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 0.5) - y;
	tmp = 0.0;
	if (t <= 600.0)
		tmp = t_1 * sqrt((z * 2.0));
	else
		tmp = sqrt((z * (2.0 * (t_1 ^ 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t, 600.0], N[(t$95$1 * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(z * N[(2.0 * N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 600

   1. Initial program 98.7%

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

      1. associate-*l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. exp-sqrt 99.3%

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

      5. exp-prod 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \sqrt{{\left(e^{t}\right)}^{t}}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 99.3%

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

      2. sqrt-unprod 99.3%

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

      3. associate-*l* 99.3%

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

      4. pow-exp 99.3%

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

      5. pow2 99.3%

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

   6. Applied egg-rr 99.3%

      \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{{\left(\sqrt{z \cdot \left(2 \cdot e^{{t}^{2}}\right)}\right)}^{1}} \]
   7. Step-by-step derivation

      1. unpow1 99.3%

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

      2. associate-*r* 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in t around 0 69.2%

      \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]
   10. Step-by-step derivation

       1. *-commutative 69.2%

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

   11. Simplified 69.2%

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

   if 600 < t

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. exp-sqrt 100.0%

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

      5. exp-prod 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \sqrt{{\left(e^{t}\right)}^{t}}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 100.0%

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

      2. sqrt-unprod 100.0%

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

      3. associate-*l* 100.0%

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

      4. pow-exp 100.0%

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

      5. pow2 100.0%

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

   6. Applied egg-rr 100.0%

      \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{{\left(\sqrt{z \cdot \left(2 \cdot e^{{t}^{2}}\right)}\right)}^{1}} \]
   7. Step-by-step derivation

      1. unpow1 100.0%

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

      2. associate-*r* 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in t around 0 8.9%

      \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]
   10. Step-by-step derivation

       1. *-commutative 8.9%

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

   11. Simplified 8.9%

       \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \sqrt{\color{blue}{z \cdot 2}} \]
   12. Step-by-step derivation

       1. add-sqr-sqrt 7.2%

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

       2. sqrt-unprod 22.7%

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

       3. *-commutative 22.7%

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

       4. *-commutative 22.7%

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

       5. swap-sqr 29.0%

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

       6. add-sqr-sqrt 29.0%

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

       7. pow2 29.0%

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

       8. fmm-def 29.0%

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

   13. Applied egg-rr 29.0%

       \[\leadsto \color{blue}{\sqrt{\left(z \cdot 2\right) \cdot {\left(\mathsf{fma}\left(x, 0.5, -y\right)\right)}^{2}}} \]
   14. Step-by-step derivation

       1. associate-*l* 29.0%

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

       2. fmm-undef 29.0%

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

       3. *-commutative 29.0%

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

   15. Simplified 29.0%

       \[\leadsto \color{blue}{\sqrt{z \cdot \left(2 \cdot {\left(0.5 \cdot x - y\right)}^{2}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 600:\\ \;\;\;\;\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot \left(2 \cdot {\left(x \cdot 0.5 - y\right)}^{2}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 920000:\\ \;\;\;\;\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \sqrt{\left(z \cdot 2\right) \cdot {x}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 920000.0)
   (* (- (* x 0.5) y) (sqrt (* z 2.0)))
   (* 0.5 (sqrt (* (* z 2.0) (pow x 2.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 920000.0) {
		tmp = ((x * 0.5) - y) * sqrt((z * 2.0));
	} else {
		tmp = 0.5 * sqrt(((z * 2.0) * pow(x, 2.0)));
	}
	return tmp;
}

Fortran

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) :: tmp
    if (t <= 920000.0d0) then
        tmp = ((x * 0.5d0) - y) * sqrt((z * 2.0d0))
    else
        tmp = 0.5d0 * sqrt(((z * 2.0d0) * (x ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 920000.0) {
		tmp = ((x * 0.5) - y) * Math.sqrt((z * 2.0));
	} else {
		tmp = 0.5 * Math.sqrt(((z * 2.0) * Math.pow(x, 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 920000.0:
		tmp = ((x * 0.5) - y) * math.sqrt((z * 2.0))
	else:
		tmp = 0.5 * math.sqrt(((z * 2.0) * math.pow(x, 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 920000.0)
		tmp = Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0)));
	else
		tmp = Float64(0.5 * sqrt(Float64(Float64(z * 2.0) * (x ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 920000.0)
		tmp = ((x * 0.5) - y) * sqrt((z * 2.0));
	else
		tmp = 0.5 * sqrt(((z * 2.0) * (x ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 920000.0], N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[Sqrt[N[(N[(z * 2.0), $MachinePrecision] * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.2e5

   1. Initial program 98.7%

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

      1. associate-*l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. exp-sqrt 99.3%

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

      5. exp-prod 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \sqrt{{\left(e^{t}\right)}^{t}}\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. pow1 99.3%

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

      2. sqrt-unprod 99.3%

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

      3. associate-*l* 99.3%

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

      4. pow-exp 99.3%

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

      5. pow2 99.3%

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

   6. Applied egg-rr 99.3%

      \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{{\left(\sqrt{z \cdot \left(2 \cdot e^{{t}^{2}}\right)}\right)}^{1}} \]
   7. Step-by-step derivation

      1. unpow1 99.3%

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

      2. associate-*r* 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in t around 0 69.2%

      \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]
   10. Step-by-step derivation

       1. *-commutative 69.2%

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

   11. Simplified 69.2%

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

   if 9.2e5 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 8.9%

      \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

   4. Taylor expanded in x around inf 4.6%

      \[\leadsto \color{blue}{0.5 \cdot \left(\left(x \cdot \sqrt{2}\right) \cdot \sqrt{z}\right)} \]
   5. Step-by-step derivation

      1. associate-*l* 4.6%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right)} \]

   6. Simplified 4.6%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right)} \]
   7. Step-by-step derivation

      1. add-sqr-sqrt 3.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\sqrt{x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)} \cdot \sqrt{x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)}\right)} \]

      2. sqrt-unprod 11.6%

         \[\leadsto 0.5 \cdot \color{blue}{\sqrt{\left(x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right) \cdot \left(x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right)}} \]

      3. *-commutative 11.6%

         \[\leadsto 0.5 \cdot \sqrt{\color{blue}{\left(\left(\sqrt{2} \cdot \sqrt{z}\right) \cdot x\right)} \cdot \left(x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right)} \]

      4. *-commutative 11.6%

         \[\leadsto 0.5 \cdot \sqrt{\left(\left(\sqrt{2} \cdot \sqrt{z}\right) \cdot x\right) \cdot \color{blue}{\left(\left(\sqrt{2} \cdot \sqrt{z}\right) \cdot x\right)}} \]

      5. swap-sqr 16.3%

         \[\leadsto 0.5 \cdot \sqrt{\color{blue}{\left(\left(\sqrt{2} \cdot \sqrt{z}\right) \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right) \cdot \left(x \cdot x\right)}} \]

      6. sqrt-unprod 16.3%

         \[\leadsto 0.5 \cdot \sqrt{\left(\color{blue}{\sqrt{2 \cdot z}} \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right) \cdot \left(x \cdot x\right)} \]

      7. sqrt-unprod 16.3%

         \[\leadsto 0.5 \cdot \sqrt{\left(\sqrt{2 \cdot z} \cdot \color{blue}{\sqrt{2 \cdot z}}\right) \cdot \left(x \cdot x\right)} \]

      8. add-sqr-sqrt 16.3%

         \[\leadsto 0.5 \cdot \sqrt{\color{blue}{\left(2 \cdot z\right)} \cdot \left(x \cdot x\right)} \]

      9. *-commutative 16.3%

         \[\leadsto 0.5 \cdot \sqrt{\color{blue}{\left(z \cdot 2\right)} \cdot \left(x \cdot x\right)} \]

      10. pow2 16.3%

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

   8. Applied egg-rr 16.3%

      \[\leadsto 0.5 \cdot \color{blue}{\sqrt{\left(z \cdot 2\right) \cdot {x}^{2}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 56.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (- (* x 0.5) y) (sqrt (* z 2.0))))

C

double code(double x, double y, double z, double t) {
	return ((x * 0.5) - y) * sqrt((z * 2.0));
}

Fortran

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))
end function

Java

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

Python

def code(x, y, z, t):
	return ((x * 0.5) - y) * math.sqrt((z * 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0)))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

   1. associate-*l* 99.8%

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

   2. remove-double-neg 99.8%

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

   3. remove-double-neg 99.8%

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

   4. exp-sqrt 99.5%

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

   5. exp-prod 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \sqrt{{\left(e^{t}\right)}^{t}}\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. pow1 99.5%

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

   2. sqrt-unprod 99.5%

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

   3. associate-*l* 99.5%

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

   4. pow-exp 99.5%

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

   5. pow2 99.5%

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

6. Applied egg-rr 99.5%

   \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{{\left(\sqrt{z \cdot \left(2 \cdot e^{{t}^{2}}\right)}\right)}^{1}} \]
7. Step-by-step derivation

   1. unpow1 99.5%

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

   2. associate-*r* 99.5%

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

8. Simplified 99.5%

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

9. Taylor expanded in t around 0 54.9%

   \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \sqrt{\color{blue}{2 \cdot z}} \]
10. Step-by-step derivation

    1. *-commutative 54.9%

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

11. Simplified 54.9%

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \sqrt{\color{blue}{z \cdot 2}} \]
12. Add Preprocessing

Alternative 5: 29.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(x \cdot \sqrt{z \cdot 2}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 0.5 (* x (sqrt (* z 2.0)))))

C

double code(double x, double y, double z, double t) {
	return 0.5 * (x * sqrt((z * 2.0)));
}

Fortran

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 = 0.5d0 * (x * sqrt((z * 2.0d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.5 * (x * Math.sqrt((z * 2.0)));
}

Python

def code(x, y, z, t):
	return 0.5 * (x * math.sqrt((z * 2.0)))

Julia

function code(x, y, z, t)
	return Float64(0.5 * Float64(x * sqrt(Float64(z * 2.0))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.5 * (x * sqrt((z * 2.0)));
end

Wolfram

code[x_, y_, z_, t_] := N[(0.5 * N[(x * N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

3. Taylor expanded in t around 0 54.9%

   \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{1} \]

4. Taylor expanded in x around inf 26.7%

   \[\leadsto \color{blue}{0.5 \cdot \left(\left(x \cdot \sqrt{2}\right) \cdot \sqrt{z}\right)} \]
5. Step-by-step derivation

   1. associate-*l* 26.6%

      \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right)} \]

6. Simplified 26.6%

   \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \left(\sqrt{2} \cdot \sqrt{z}\right)\right)} \]
7. Step-by-step derivation

   1. sqrt-unprod 26.7%

      \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\sqrt{2 \cdot z}}\right) \]

   2. *-commutative 26.7%

      \[\leadsto 0.5 \cdot \left(x \cdot \sqrt{\color{blue}{z \cdot 2}}\right) \]

8. Applied egg-rr 26.7%

   \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\sqrt{z \cdot 2}}\right) \]
9. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0))))

C

double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * sqrt((z * 2.0))) * pow(exp(1.0), ((t * t) / 2.0));
}

Fortran

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(1.0d0) ** ((t * t) / 2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x * 0.5) - y) * Math.sqrt((z * 2.0))) * Math.pow(Math.exp(1.0), ((t * t) / 2.0));
}

Python

def code(x, y, z, t):
	return (((x * 0.5) - y) * math.sqrt((z * 2.0))) * math.pow(math.exp(1.0), ((t * t) / 2.0))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x * 0.5) - y) * sqrt(Float64(z * 2.0))) * (exp(1.0) ^ Float64(Float64(t * t) / 2.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x * 0.5) - y) * sqrt((z * 2.0))) * (exp(1.0) ^ ((t * t) / 2.0));
end

Wolfram

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[Power[N[Exp[1.0], $MachinePrecision], N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* (* (- (* x 1/2) y) (sqrt (* z 2))) (pow (exp 1) (/ (* t t) 2))))

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