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

Percentage Accurate: 99.3% → 99.8%

Time: 15.8s

Alternatives: 12

Speedup: 1.0×

• 44.8% 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: 99.3% 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, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return sqrt((z * 2.0)) * (((x * 0.5) - y) * pow(exp(t), (0.5 * 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 = sqrt((z * 2.0d0)) * (((x * 0.5d0) - y) * (exp(t) ** (0.5d0 * t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Power[N[Exp[t], $MachinePrecision], N[(0.5 * t), $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. *-commutative 99.0%

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

   2. associate-*l* 99.8%

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

   3. exp-sqrt 99.8%

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

3. Simplified 99.8%

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

   1. pow-exp 99.8%

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

   2. pow1/2 99.8%

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

   3. pow-pow 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return sqrt((z * 2.0)) * (((x * 0.5) - y) * sqrt(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 = sqrt((z * 2.0d0)) * (((x * 0.5d0) - y) * sqrt(exp((t * t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Sqrt[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. *-commutative 99.0%

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

   2. associate-*l* 99.8%

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

   3. exp-sqrt 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 91.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ t_2 := x \cdot 0.5 - y\\ \mathbf{if}\;t \cdot t \leq 10^{-9}:\\ \;\;\;\;t\_1 \cdot t\_2\\ \mathbf{elif}\;t \cdot t \leq 5 \cdot 10^{+111}:\\ \;\;\;\;e^{\frac{t \cdot t}{2}} \cdot \left(t\_1 \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(0.5 \cdot \left(t\_2 \cdot {t}^{2}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))) (t_2 (- (* x 0.5) y)))
   (if (<= (* t t) 1e-9)
     (* t_1 t_2)
     (if (<= (* t t) 5e+111)
       (* (exp (/ (* t t) 2.0)) (* t_1 (- y)))
       (* t_1 (* 0.5 (* t_2 (pow t 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if ((t * t) <= 1e-9) {
		tmp = t_1 * t_2;
	} else if ((t * t) <= 5e+111) {
		tmp = exp(((t * t) / 2.0)) * (t_1 * -y);
	} else {
		tmp = t_1 * (0.5 * (t_2 * pow(t, 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) :: t_2
    real(8) :: tmp
    t_1 = sqrt((z * 2.0d0))
    t_2 = (x * 0.5d0) - y
    if ((t * t) <= 1d-9) then
        tmp = t_1 * t_2
    else if ((t * t) <= 5d+111) then
        tmp = exp(((t * t) / 2.0d0)) * (t_1 * -y)
    else
        tmp = t_1 * (0.5d0 * (t_2 * (t ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double t_2 = (x * 0.5) - y;
	double tmp;
	if ((t * t) <= 1e-9) {
		tmp = t_1 * t_2;
	} else if ((t * t) <= 5e+111) {
		tmp = Math.exp(((t * t) / 2.0)) * (t_1 * -y);
	} else {
		tmp = t_1 * (0.5 * (t_2 * Math.pow(t, 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	t_2 = (x * 0.5) - y
	tmp = 0
	if (t * t) <= 1e-9:
		tmp = t_1 * t_2
	elif (t * t) <= 5e+111:
		tmp = math.exp(((t * t) / 2.0)) * (t_1 * -y)
	else:
		tmp = t_1 * (0.5 * (t_2 * math.pow(t, 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	t_2 = Float64(Float64(x * 0.5) - y)
	tmp = 0.0
	if (Float64(t * t) <= 1e-9)
		tmp = Float64(t_1 * t_2);
	elseif (Float64(t * t) <= 5e+111)
		tmp = Float64(exp(Float64(Float64(t * t) / 2.0)) * Float64(t_1 * Float64(-y)));
	else
		tmp = Float64(t_1 * Float64(0.5 * Float64(t_2 * (t ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	t_2 = (x * 0.5) - y;
	tmp = 0.0;
	if ((t * t) <= 1e-9)
		tmp = t_1 * t_2;
	elseif ((t * t) <= 5e+111)
		tmp = exp(((t * t) / 2.0)) * (t_1 * -y);
	else
		tmp = t_1 * (0.5 * (t_2 * (t ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[N[(t * t), $MachinePrecision], 1e-9], N[(t$95$1 * t$95$2), $MachinePrecision], If[LessEqual[N[(t * t), $MachinePrecision], 5e+111], N[(N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * (-y)), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(0.5 * N[(t$95$2 * N[Power[t, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 t t) < 1.00000000000000006e-9

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. exp-sqrt 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.2%

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

   if 1.00000000000000006e-9 < (*.f64 t t) < 4.9999999999999997e111

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. associate-*l* 76.7%

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

      3. *-commutative 76.7%

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

      4. distribute-rgt-neg-in 76.7%

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

      5. *-commutative 76.7%

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

   5. Simplified 76.7%

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

      1. *-commutative 76.7%

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

      2. sqrt-prod 76.7%

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

   7. Applied egg-rr 76.7%

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

   if 4.9999999999999997e111 < (*.f64 t t)

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*l* 100.0%

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

      3. exp-sqrt 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in t around inf 88.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot t \leq 10^{-9}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(x \cdot 0.5 - y\right)\\ \mathbf{elif}\;t \cdot t \leq 5 \cdot 10^{+111}:\\ \;\;\;\;e^{\frac{t \cdot t}{2}} \cdot \left(\sqrt{z \cdot 2} \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(0.5 \cdot \left(\left(x \cdot 0.5 - y\right) \cdot {t}^{2}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;t \cdot t \leq 10^{-9}:\\ \;\;\;\;t\_1 \cdot \left(0.5 \cdot \left(x - y \cdot {t}^{2}\right) - y\right)\\ \mathbf{elif}\;t \cdot t \leq 5 \cdot 10^{+111}:\\ \;\;\;\;e^{\frac{t \cdot t}{2}} \cdot \left(t\_1 \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(0.5 \cdot \left(\left(x \cdot 0.5 - y\right) \cdot {t}^{2}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (<= (* t t) 1e-9)
     (* t_1 (- (* 0.5 (- x (* y (pow t 2.0)))) y))
     (if (<= (* t t) 5e+111)
       (* (exp (/ (* t t) 2.0)) (* t_1 (- y)))
       (* t_1 (* 0.5 (* (- (* x 0.5) y) (pow t 2.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1e-9) {
		tmp = t_1 * ((0.5 * (x - (y * pow(t, 2.0)))) - y);
	} else if ((t * t) <= 5e+111) {
		tmp = exp(((t * t) / 2.0)) * (t_1 * -y);
	} else {
		tmp = t_1 * (0.5 * (((x * 0.5) - y) * pow(t, 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 = sqrt((z * 2.0d0))
    if ((t * t) <= 1d-9) then
        tmp = t_1 * ((0.5d0 * (x - (y * (t ** 2.0d0)))) - y)
    else if ((t * t) <= 5d+111) then
        tmp = exp(((t * t) / 2.0d0)) * (t_1 * -y)
    else
        tmp = t_1 * (0.5d0 * (((x * 0.5d0) - y) * (t ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1e-9) {
		tmp = t_1 * ((0.5 * (x - (y * Math.pow(t, 2.0)))) - y);
	} else if ((t * t) <= 5e+111) {
		tmp = Math.exp(((t * t) / 2.0)) * (t_1 * -y);
	} else {
		tmp = t_1 * (0.5 * (((x * 0.5) - y) * Math.pow(t, 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if (t * t) <= 1e-9:
		tmp = t_1 * ((0.5 * (x - (y * math.pow(t, 2.0)))) - y)
	elif (t * t) <= 5e+111:
		tmp = math.exp(((t * t) / 2.0)) * (t_1 * -y)
	else:
		tmp = t_1 * (0.5 * (((x * 0.5) - y) * math.pow(t, 2.0)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if (Float64(t * t) <= 1e-9)
		tmp = Float64(t_1 * Float64(Float64(0.5 * Float64(x - Float64(y * (t ^ 2.0)))) - y));
	elseif (Float64(t * t) <= 5e+111)
		tmp = Float64(exp(Float64(Float64(t * t) / 2.0)) * Float64(t_1 * Float64(-y)));
	else
		tmp = Float64(t_1 * Float64(0.5 * Float64(Float64(Float64(x * 0.5) - y) * (t ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if ((t * t) <= 1e-9)
		tmp = t_1 * ((0.5 * (x - (y * (t ^ 2.0)))) - y);
	elseif ((t * t) <= 5e+111)
		tmp = exp(((t * t) / 2.0)) * (t_1 * -y);
	else
		tmp = t_1 * (0.5 * (((x * 0.5) - y) * (t ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t * t), $MachinePrecision], 1e-9], N[(t$95$1 * N[(N[(0.5 * N[(x - N[(y * N[Power[t, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t * t), $MachinePrecision], 5e+111], N[(N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * (-y)), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(0.5 * N[(N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision] * N[Power[t, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 t t) < 1.00000000000000006e-9

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. exp-sqrt 99.7%

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

   3. Simplified 99.7%

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

      1. pow-exp 99.7%

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

      2. pow1/2 99.7%

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

      3. pow-pow 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around 0 99.7%

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

      1. distribute-lft-out 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 99.5%

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

       1. associate-*r* 99.5%

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

       2. neg-mul-1 99.5%

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

   12. Simplified 99.5%

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

   if 1.00000000000000006e-9 < (*.f64 t t) < 4.9999999999999997e111

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. associate-*l* 76.7%

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

      3. *-commutative 76.7%

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

      4. distribute-rgt-neg-in 76.7%

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

      5. *-commutative 76.7%

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

   5. Simplified 76.7%

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

      1. *-commutative 76.7%

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

      2. sqrt-prod 76.7%

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

   7. Applied egg-rr 76.7%

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

   if 4.9999999999999997e111 < (*.f64 t t)

   1. Initial program 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*l* 100.0%

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

      3. exp-sqrt 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 88.1%

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

      1. *-commutative 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in t around inf 88.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot t \leq 10^{-9}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(0.5 \cdot \left(x - y \cdot {t}^{2}\right) - y\right)\\ \mathbf{elif}\;t \cdot t \leq 5 \cdot 10^{+111}:\\ \;\;\;\;e^{\frac{t \cdot t}{2}} \cdot \left(\sqrt{z \cdot 2} \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(0.5 \cdot \left(\left(x \cdot 0.5 - y\right) \cdot {t}^{2}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;t \cdot t \leq 10^{-9}:\\ \;\;\;\;t\_1 \cdot \left(x \cdot 0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\frac{t \cdot t}{2}} \cdot \left(t\_1 \cdot \left(-y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (<= (* t t) 1e-9)
     (* t_1 (- (* x 0.5) y))
     (* (exp (/ (* t t) 2.0)) (* t_1 (- y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1e-9) {
		tmp = t_1 * ((x * 0.5) - y);
	} else {
		tmp = exp(((t * t) / 2.0)) * (t_1 * -y);
	}
	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 = sqrt((z * 2.0d0))
    if ((t * t) <= 1d-9) then
        tmp = t_1 * ((x * 0.5d0) - y)
    else
        tmp = exp(((t * t) / 2.0d0)) * (t_1 * -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1e-9) {
		tmp = t_1 * ((x * 0.5) - y);
	} else {
		tmp = Math.exp(((t * t) / 2.0)) * (t_1 * -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if (t * t) <= 1e-9:
		tmp = t_1 * ((x * 0.5) - y)
	else:
		tmp = math.exp(((t * t) / 2.0)) * (t_1 * -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if (Float64(t * t) <= 1e-9)
		tmp = Float64(t_1 * Float64(Float64(x * 0.5) - y));
	else
		tmp = Float64(exp(Float64(Float64(t * t) / 2.0)) * Float64(t_1 * Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if ((t * t) <= 1e-9)
		tmp = t_1 * ((x * 0.5) - y);
	else
		tmp = exp(((t * t) / 2.0)) * (t_1 * -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t * t), $MachinePrecision], 1e-9], N[(t$95$1 * N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 t t) < 1.00000000000000006e-9

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. exp-sqrt 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 99.2%

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

   if 1.00000000000000006e-9 < (*.f64 t t)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-*l* 72.3%

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

      3. *-commutative 72.3%

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

      4. distribute-rgt-neg-in 72.3%

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

      5. *-commutative 72.3%

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

   5. Simplified 72.3%

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

      1. *-commutative 72.3%

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

      2. sqrt-prod 72.3%

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

   7. Applied egg-rr 72.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot t \leq 10^{-9}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(x \cdot 0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\frac{t \cdot t}{2}} \cdot \left(\sqrt{z \cdot 2} \cdot \left(-y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;t \cdot t \leq 10^{+64}:\\ \;\;\;\;t\_1 \cdot \left(x \cdot 0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left({t}^{2} \cdot \left(x \cdot 0.25\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (<= (* t t) 1e+64)
     (* t_1 (- (* x 0.5) y))
     (* t_1 (* (pow t 2.0) (* x 0.25))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1e+64) {
		tmp = t_1 * ((x * 0.5) - y);
	} else {
		tmp = t_1 * (pow(t, 2.0) * (x * 0.25));
	}
	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 = sqrt((z * 2.0d0))
    if ((t * t) <= 1d+64) then
        tmp = t_1 * ((x * 0.5d0) - y)
    else
        tmp = t_1 * ((t ** 2.0d0) * (x * 0.25d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if ((t * t) <= 1e+64) {
		tmp = t_1 * ((x * 0.5) - y);
	} else {
		tmp = t_1 * (Math.pow(t, 2.0) * (x * 0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if (t * t) <= 1e+64:
		tmp = t_1 * ((x * 0.5) - y)
	else:
		tmp = t_1 * (math.pow(t, 2.0) * (x * 0.25))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if (Float64(t * t) <= 1e+64)
		tmp = Float64(t_1 * Float64(Float64(x * 0.5) - y));
	else
		tmp = Float64(t_1 * Float64((t ^ 2.0) * Float64(x * 0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if ((t * t) <= 1e+64)
		tmp = t_1 * ((x * 0.5) - y);
	else
		tmp = t_1 * ((t ^ 2.0) * (x * 0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t * t), $MachinePrecision], 1e+64], N[(t$95$1 * N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(N[Power[t, 2.0], $MachinePrecision] * N[(x * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 t t) < 1.00000000000000002e64

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. exp-sqrt 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 94.4%

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

   if 1.00000000000000002e64 < (*.f64 t t)

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-*l* 100.0%

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

      3. exp-sqrt 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 83.3%

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

      1. *-commutative 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in x around inf 49.2%

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

   9. Taylor expanded in t around inf 49.2%

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

       1. associate-*r* 49.2%

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

       2. *-commutative 49.2%

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

   11. Simplified 49.2%

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

   12. Taylor expanded in x around 0 49.2%

       \[\leadsto \sqrt{z \cdot 2} \cdot \color{blue}{\left(0.25 \cdot \left({t}^{2} \cdot x\right)\right)} \]
   13. Step-by-step derivation

       1. *-commutative 49.2%

          \[\leadsto \sqrt{z \cdot 2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot 0.25\right)} \]

       2. associate-*l* 49.2%

          \[\leadsto \sqrt{z \cdot 2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot 0.25\right)\right)} \]

   14. Simplified 49.2%

       \[\leadsto \sqrt{z \cdot 2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot 0.25\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot t \leq 10^{+64}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(x \cdot 0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left({t}^{2} \cdot \left(x \cdot 0.25\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = exp(((t * t) / 2.0d0)) * (sqrt((z * 2.0d0)) * ((x * 0.5d0) - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Exp[N[(N[(t * t), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[(x * 0.5), $MachinePrecision] - y), $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. Final simplification 99.0%

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

Alternative 8: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;t \leq 2.3 \cdot 10^{+32}:\\ \;\;\;\;t\_1 \cdot \left(x \cdot 0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(0.5 \cdot \left(x \cdot \frac{t}{\frac{2}{t}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (<= t 2.3e+32)
     (* t_1 (- (* x 0.5) y))
     (* t_1 (* 0.5 (* x (/ t (/ 2.0 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if (t <= 2.3e+32) {
		tmp = t_1 * ((x * 0.5) - y);
	} else {
		tmp = t_1 * (0.5 * (x * (t / (2.0 / t))));
	}
	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 = sqrt((z * 2.0d0))
    if (t <= 2.3d+32) then
        tmp = t_1 * ((x * 0.5d0) - y)
    else
        tmp = t_1 * (0.5d0 * (x * (t / (2.0d0 / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if (t <= 2.3e+32) {
		tmp = t_1 * ((x * 0.5) - y);
	} else {
		tmp = t_1 * (0.5 * (x * (t / (2.0 / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if t <= 2.3e+32:
		tmp = t_1 * ((x * 0.5) - y)
	else:
		tmp = t_1 * (0.5 * (x * (t / (2.0 / t))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if (t <= 2.3e+32)
		tmp = Float64(t_1 * Float64(Float64(x * 0.5) - y));
	else
		tmp = Float64(t_1 * Float64(0.5 * Float64(x * Float64(t / Float64(2.0 / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if (t <= 2.3e+32)
		tmp = t_1 * ((x * 0.5) - y);
	else
		tmp = t_1 * (0.5 * (x * (t / (2.0 / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, 2.3e+32], N[(t$95$1 * N[(N[(x * 0.5), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(0.5 * N[(x * N[(t / N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 2.3e32

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.8%

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

      3. exp-sqrt 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 68.9%

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

   if 2.3e32 < t

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-*l* 100.0%

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

      3. exp-sqrt 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 82.2%

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

      1. *-commutative 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in x around inf 39.9%

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

   9. Taylor expanded in t around inf 39.9%

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

       1. associate-*r* 39.9%

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

       2. *-commutative 39.9%

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

   11. Simplified 39.9%

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

       1. *-commutative 39.9%

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

       2. metadata-eval 39.9%

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

       3. div-inv 39.9%

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

       4. pow2 39.9%

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

       5. associate-/l* 39.9%

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

   13. Applied egg-rr 39.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.3 \cdot 10^{+32}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(x \cdot 0.5 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(0.5 \cdot \left(x \cdot \frac{t}{\frac{2}{t}}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{z \cdot 2}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-110} \lor \neg \left(y \leq 4.7 \cdot 10^{+157}\right):\\ \;\;\;\;t\_1 \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (* z 2.0))))
   (if (or (<= y -6.6e-110) (not (<= y 4.7e+157)))
     (* t_1 (- y))
     (* t_1 (* x 0.5)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = sqrt((z * 2.0));
	double tmp;
	if ((y <= -6.6e-110) || !(y <= 4.7e+157)) {
		tmp = t_1 * -y;
	} else {
		tmp = t_1 * (x * 0.5);
	}
	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 = sqrt((z * 2.0d0))
    if ((y <= (-6.6d-110)) .or. (.not. (y <= 4.7d+157))) then
        tmp = t_1 * -y
    else
        tmp = t_1 * (x * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((z * 2.0));
	double tmp;
	if ((y <= -6.6e-110) || !(y <= 4.7e+157)) {
		tmp = t_1 * -y;
	} else {
		tmp = t_1 * (x * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.sqrt((z * 2.0))
	tmp = 0
	if (y <= -6.6e-110) or not (y <= 4.7e+157):
		tmp = t_1 * -y
	else:
		tmp = t_1 * (x * 0.5)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = sqrt(Float64(z * 2.0))
	tmp = 0.0
	if ((y <= -6.6e-110) || !(y <= 4.7e+157))
		tmp = Float64(t_1 * Float64(-y));
	else
		tmp = Float64(t_1 * Float64(x * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((z * 2.0));
	tmp = 0.0;
	if ((y <= -6.6e-110) || ~((y <= 4.7e+157)))
		tmp = t_1 * -y;
	else
		tmp = t_1 * (x * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[y, -6.6e-110], N[Not[LessEqual[y, 4.7e+157]], $MachinePrecision]], N[(t$95$1 * (-y)), $MachinePrecision], N[(t$95$1 * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999998e-110 or 4.7000000000000003e157 < y

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. exp-sqrt 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 60.1%

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

   6. Taylor expanded in x around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. *-commutative 46.5%

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

      3. distribute-rgt-neg-in 46.5%

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

   8. Simplified 46.5%

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

      1. distribute-rgt-neg-out 46.5%

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

      2. neg-sub0 46.5%

         \[\leadsto \color{blue}{0 - \sqrt{z} \cdot \left(y \cdot \sqrt{2}\right)} \]

      3. *-commutative 46.5%

         \[\leadsto 0 - \sqrt{z} \cdot \color{blue}{\left(\sqrt{2} \cdot y\right)} \]

      4. associate-*r* 46.5%

         \[\leadsto 0 - \color{blue}{\left(\sqrt{z} \cdot \sqrt{2}\right) \cdot y} \]

      5. sqrt-prod 46.6%

         \[\leadsto 0 - \color{blue}{\sqrt{z \cdot 2}} \cdot y \]

   10. Applied egg-rr 46.6%

       \[\leadsto \color{blue}{0 - \sqrt{z \cdot 2} \cdot y} \]
   11. Step-by-step derivation

       1. neg-sub0 46.6%

          \[\leadsto \color{blue}{-\sqrt{z \cdot 2} \cdot y} \]

       2. distribute-rgt-neg-in 46.6%

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

       3. *-commutative 46.6%

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

       4. *-commutative 46.6%

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

   12. Simplified 46.6%

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

   if -6.5999999999999998e-110 < y < 4.7000000000000003e157

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. associate-*l* 99.8%

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

      3. exp-sqrt 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.8%

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

      1. *-commutative 86.8%

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

   7. Simplified 86.8%

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

   8. Taylor expanded in x around inf 65.4%

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

   9. Taylor expanded in t around 0 41.2%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-110} \lor \neg \left(y \leq 4.7 \cdot 10^{+157}\right):\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot 2} \cdot \left(x \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision] * N[(N[(x * 0.5), $MachinePrecision] - y), $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. *-commutative 99.0%

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

   2. associate-*l* 99.8%

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

   3. exp-sqrt 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in t around 0 56.7%

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

6. Final simplification 56.7%

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

Alternative 11: 30.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

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 = sqrt((z * 2.0d0)) * -y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision] * (-y)), $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. *-commutative 99.0%

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

   2. associate-*l* 99.8%

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

   3. exp-sqrt 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in t around 0 56.7%

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

6. Taylor expanded in x around 0 30.1%

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

   1. mul-1-neg 30.1%

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

   2. *-commutative 30.1%

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

   3. distribute-rgt-neg-in 30.1%

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

8. Simplified 30.1%

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

   1. distribute-rgt-neg-out 30.1%

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

   2. neg-sub0 30.1%

      \[\leadsto \color{blue}{0 - \sqrt{z} \cdot \left(y \cdot \sqrt{2}\right)} \]

   3. *-commutative 30.1%

      \[\leadsto 0 - \sqrt{z} \cdot \color{blue}{\left(\sqrt{2} \cdot y\right)} \]

   4. associate-*r* 30.1%

      \[\leadsto 0 - \color{blue}{\left(\sqrt{z} \cdot \sqrt{2}\right) \cdot y} \]

   5. sqrt-prod 30.2%

      \[\leadsto 0 - \color{blue}{\sqrt{z \cdot 2}} \cdot y \]

10. Applied egg-rr 30.2%

    \[\leadsto \color{blue}{0 - \sqrt{z \cdot 2} \cdot y} \]
11. Step-by-step derivation

    1. neg-sub0 30.2%

       \[\leadsto \color{blue}{-\sqrt{z \cdot 2} \cdot y} \]

    2. distribute-rgt-neg-in 30.2%

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

    3. *-commutative 30.2%

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

    4. *-commutative 30.2%

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

12. Simplified 30.2%

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

13. Final simplification 30.2%

    \[\leadsto \sqrt{z \cdot 2} \cdot \left(-y\right) \]
14. Add Preprocessing

Alternative 12: 2.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{z \cdot 2} \cdot y \end{array} \]

FPCore

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

C

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

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 = sqrt((z * 2.0d0)) * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Sqrt[N[(z * 2.0), $MachinePrecision]], $MachinePrecision] * y), $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. *-commutative 99.0%

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

   2. associate-*l* 99.8%

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

   3. exp-sqrt 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in t around 0 56.7%

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

6. Taylor expanded in x around 0 30.1%

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

   1. mul-1-neg 30.1%

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

   2. *-commutative 30.1%

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

   3. distribute-rgt-neg-in 30.1%

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

8. Simplified 30.1%

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

   1. expm1-log1p-u 18.1%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{z} \cdot \left(-y \cdot \sqrt{2}\right)\right)\right)} \]

   2. expm1-udef 10.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{z} \cdot \left(-y \cdot \sqrt{2}\right)\right)} - 1} \]

   3. add-sqr-sqrt 9.0%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{z} \cdot \color{blue}{\left(\sqrt{-y \cdot \sqrt{2}} \cdot \sqrt{-y \cdot \sqrt{2}}\right)}\right)} - 1 \]

   4. sqrt-unprod 13.7%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{z} \cdot \color{blue}{\sqrt{\left(-y \cdot \sqrt{2}\right) \cdot \left(-y \cdot \sqrt{2}\right)}}\right)} - 1 \]

   5. sqr-neg 13.7%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{z} \cdot \sqrt{\color{blue}{\left(y \cdot \sqrt{2}\right) \cdot \left(y \cdot \sqrt{2}\right)}}\right)} - 1 \]

   6. sqrt-unprod 1.1%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{z} \cdot \color{blue}{\left(\sqrt{y \cdot \sqrt{2}} \cdot \sqrt{y \cdot \sqrt{2}}\right)}\right)} - 1 \]

   7. add-sqr-sqrt 2.2%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{z} \cdot \color{blue}{\left(y \cdot \sqrt{2}\right)}\right)} - 1 \]

   8. *-commutative 2.2%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{z} \cdot \color{blue}{\left(\sqrt{2} \cdot y\right)}\right)} - 1 \]

   9. associate-*r* 2.2%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{z} \cdot \sqrt{2}\right) \cdot y}\right)} - 1 \]

   10. sqrt-prod 2.2%

       \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{z \cdot 2}} \cdot y\right)} - 1 \]

10. Applied egg-rr 2.2%

    \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{z \cdot 2} \cdot y\right)} - 1} \]
11. Step-by-step derivation

    1. expm1-def 2.2%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{z \cdot 2} \cdot y\right)\right)} \]

    2. expm1-log1p 2.4%

       \[\leadsto \color{blue}{\sqrt{z \cdot 2} \cdot y} \]

    3. *-commutative 2.4%

       \[\leadsto \color{blue}{y \cdot \sqrt{z \cdot 2}} \]

    4. *-commutative 2.4%

       \[\leadsto y \cdot \sqrt{\color{blue}{2 \cdot z}} \]

12. Simplified 2.4%

    \[\leadsto \color{blue}{y \cdot \sqrt{2 \cdot z}} \]

13. Final simplification 2.4%

    \[\leadsto \sqrt{z \cdot 2} \cdot y \]
14. Add Preprocessing

Developer target: 99.3% 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 2024027 
(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))))