Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.8% → 96.9%

Time: 9.5s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * 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 - y) / (z - y)) * t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Python

def code(x, y, z, t):
	return ((x - y) / (z - y)) * t

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * 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 - y) / (z - y)) * t
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

Python

def code(x, y, z, t):
	return ((x - y) / (z - y)) * t

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ t (/ (- z y) (- x y))))

C

double code(double x, double y, double z, double t) {
	return t / ((z - y) / (x - 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 = t / ((z - y) / (x - y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t / ((z - y) / (x - y));
}

Python

def code(x, y, z, t):
	return t / ((z - y) / (x - y))

Julia

function code(x, y, z, t)
	return Float64(t / Float64(Float64(z - y) / Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t / ((z - y) / (x - y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 85.2%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

   2. associate-*r/ 86.6%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

3. Simplified 86.6%

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

   1. associate-*r/ 85.2%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

   2. associate-*l/ 96.3%

      \[\leadsto \color{blue}{\frac{x - y}{z - y} \cdot t} \]

   3. *-commutative 96.3%

      \[\leadsto \color{blue}{t \cdot \frac{x - y}{z - y}} \]

   4. clear-num 96.1%

      \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \]

   5. un-div-inv 96.4%

      \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

5. Applied egg-rr 96.4%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

6. Final simplification 96.4%

   \[\leadsto \frac{t}{\frac{z - y}{x - y}} \]

Alternative 2: 67.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))) (t_2 (* x (/ t (- z y)))))
   (if (<= y -7e+66)
     t
     (if (<= y -4.3e-38)
       t_2
       (if (<= y -1.95e-252)
         t_1
         (if (<= y 8e-31)
           t_2
           (if (<= y 4.5e+21)
             t_1
             (if (<= y 3.5e+47) t (if (<= y 5e+85) t_2 t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -7e+66) {
		tmp = t;
	} else if (y <= -4.3e-38) {
		tmp = t_2;
	} else if (y <= -1.95e-252) {
		tmp = t_1;
	} else if (y <= 8e-31) {
		tmp = t_2;
	} else if (y <= 4.5e+21) {
		tmp = t_1;
	} else if (y <= 3.5e+47) {
		tmp = t;
	} else if (y <= 5e+85) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    t_2 = x * (t / (z - y))
    if (y <= (-7d+66)) then
        tmp = t
    else if (y <= (-4.3d-38)) then
        tmp = t_2
    else if (y <= (-1.95d-252)) then
        tmp = t_1
    else if (y <= 8d-31) then
        tmp = t_2
    else if (y <= 4.5d+21) then
        tmp = t_1
    else if (y <= 3.5d+47) then
        tmp = t
    else if (y <= 5d+85) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -7e+66) {
		tmp = t;
	} else if (y <= -4.3e-38) {
		tmp = t_2;
	} else if (y <= -1.95e-252) {
		tmp = t_1;
	} else if (y <= 8e-31) {
		tmp = t_2;
	} else if (y <= 4.5e+21) {
		tmp = t_1;
	} else if (y <= 3.5e+47) {
		tmp = t;
	} else if (y <= 5e+85) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	t_2 = x * (t / (z - y))
	tmp = 0
	if y <= -7e+66:
		tmp = t
	elif y <= -4.3e-38:
		tmp = t_2
	elif y <= -1.95e-252:
		tmp = t_1
	elif y <= 8e-31:
		tmp = t_2
	elif y <= 4.5e+21:
		tmp = t_1
	elif y <= 3.5e+47:
		tmp = t
	elif y <= 5e+85:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -7e+66)
		tmp = t;
	elseif (y <= -4.3e-38)
		tmp = t_2;
	elseif (y <= -1.95e-252)
		tmp = t_1;
	elseif (y <= 8e-31)
		tmp = t_2;
	elseif (y <= 4.5e+21)
		tmp = t_1;
	elseif (y <= 3.5e+47)
		tmp = t;
	elseif (y <= 5e+85)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (y <= -7e+66)
		tmp = t;
	elseif (y <= -4.3e-38)
		tmp = t_2;
	elseif (y <= -1.95e-252)
		tmp = t_1;
	elseif (y <= 8e-31)
		tmp = t_2;
	elseif (y <= 4.5e+21)
		tmp = t_1;
	elseif (y <= 3.5e+47)
		tmp = t;
	elseif (y <= 5e+85)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+66], t, If[LessEqual[y, -4.3e-38], t$95$2, If[LessEqual[y, -1.95e-252], t$95$1, If[LessEqual[y, 8e-31], t$95$2, If[LessEqual[y, 4.5e+21], t$95$1, If[LessEqual[y, 3.5e+47], t, If[LessEqual[y, 5e+85], t$95$2, t]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999994e66 or 4.5e21 < y < 3.50000000000000015e47 or 5.0000000000000001e85 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 77.4%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around inf 71.1%

      \[\leadsto \color{blue}{t} \]

   if -6.9999999999999994e66 < y < -4.3000000000000002e-38 or -1.9499999999999999e-252 < y < 8.000000000000001e-31 or 3.50000000000000015e47 < y < 5.0000000000000001e85

   1. Initial program 94.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 95.7%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 95.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in x around inf 72.2%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   5. Step-by-step derivation

      1. associate-*l/ 75.1%

         \[\leadsto \color{blue}{\frac{t}{z - y} \cdot x} \]

      2. *-commutative 75.1%

         \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]

   6. Simplified 75.1%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]

   if -4.3000000000000002e-38 < y < -1.9499999999999999e-252 or 8.000000000000001e-31 < y < 4.5e21

   1. Initial program 93.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.1%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 90.1%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 90.1%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in z around inf 76.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-252}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))) (t_2 (* x (/ t (- z y)))))
   (if (<= y -1.65e+66)
     t
     (if (<= y -1.32e-42)
       (* t (/ x (- z y)))
       (if (<= y -9.5e-251)
         t_1
         (if (<= y 2.6e-31)
           t_2
           (if (<= y 7.8e+31)
             t_1
             (if (<= y 3.3e+47) t (if (<= y 5.5e+84) t_2 t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -1.65e+66) {
		tmp = t;
	} else if (y <= -1.32e-42) {
		tmp = t * (x / (z - y));
	} else if (y <= -9.5e-251) {
		tmp = t_1;
	} else if (y <= 2.6e-31) {
		tmp = t_2;
	} else if (y <= 7.8e+31) {
		tmp = t_1;
	} else if (y <= 3.3e+47) {
		tmp = t;
	} else if (y <= 5.5e+84) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    t_2 = x * (t / (z - y))
    if (y <= (-1.65d+66)) then
        tmp = t
    else if (y <= (-1.32d-42)) then
        tmp = t * (x / (z - y))
    else if (y <= (-9.5d-251)) then
        tmp = t_1
    else if (y <= 2.6d-31) then
        tmp = t_2
    else if (y <= 7.8d+31) then
        tmp = t_1
    else if (y <= 3.3d+47) then
        tmp = t
    else if (y <= 5.5d+84) then
        tmp = t_2
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -1.65e+66) {
		tmp = t;
	} else if (y <= -1.32e-42) {
		tmp = t * (x / (z - y));
	} else if (y <= -9.5e-251) {
		tmp = t_1;
	} else if (y <= 2.6e-31) {
		tmp = t_2;
	} else if (y <= 7.8e+31) {
		tmp = t_1;
	} else if (y <= 3.3e+47) {
		tmp = t;
	} else if (y <= 5.5e+84) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	t_2 = x * (t / (z - y))
	tmp = 0
	if y <= -1.65e+66:
		tmp = t
	elif y <= -1.32e-42:
		tmp = t * (x / (z - y))
	elif y <= -9.5e-251:
		tmp = t_1
	elif y <= 2.6e-31:
		tmp = t_2
	elif y <= 7.8e+31:
		tmp = t_1
	elif y <= 3.3e+47:
		tmp = t
	elif y <= 5.5e+84:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.65e+66)
		tmp = t;
	elseif (y <= -1.32e-42)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= -9.5e-251)
		tmp = t_1;
	elseif (y <= 2.6e-31)
		tmp = t_2;
	elseif (y <= 7.8e+31)
		tmp = t_1;
	elseif (y <= 3.3e+47)
		tmp = t;
	elseif (y <= 5.5e+84)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (y <= -1.65e+66)
		tmp = t;
	elseif (y <= -1.32e-42)
		tmp = t * (x / (z - y));
	elseif (y <= -9.5e-251)
		tmp = t_1;
	elseif (y <= 2.6e-31)
		tmp = t_2;
	elseif (y <= 7.8e+31)
		tmp = t_1;
	elseif (y <= 3.3e+47)
		tmp = t;
	elseif (y <= 5.5e+84)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+66], t, If[LessEqual[y, -1.32e-42], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-251], t$95$1, If[LessEqual[y, 2.6e-31], t$95$2, If[LessEqual[y, 7.8e+31], t$95$1, If[LessEqual[y, 3.3e+47], t, If[LessEqual[y, 5.5e+84], t$95$2, t]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6500000000000001e66 or 7.79999999999999999e31 < y < 3.2999999999999999e47 or 5.5000000000000004e84 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 77.4%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around inf 71.1%

      \[\leadsto \color{blue}{t} \]

   if -1.6500000000000001e66 < y < -1.32000000000000006e-42

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf 67.5%

      \[\leadsto \color{blue}{\frac{x}{z - y}} \cdot t \]

   if -1.32000000000000006e-42 < y < -9.49999999999999927e-251 or 2.59999999999999995e-31 < y < 7.79999999999999999e31

   1. Initial program 93.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 91.0%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in z around inf 77.3%

      \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{t}{z}} \]

   if -9.49999999999999927e-251 < y < 2.59999999999999995e-31 or 3.2999999999999999e47 < y < 5.5000000000000004e84

   1. Initial program 92.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.2%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 94.2%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 94.2%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in x around inf 78.1%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   5. Step-by-step derivation

      1. associate-*l/ 78.9%

         \[\leadsto \color{blue}{\frac{t}{z - y} \cdot x} \]

      2. *-commutative 78.9%

         \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]

   6. Simplified 78.9%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-42}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-251}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+31}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))))
   (if (<= y -3.4e+72)
     t
     (if (<= y -3e-36)
       (* t (/ x (- z y)))
       (if (<= y 1.02e-271)
         t_1
         (if (<= y 2.8e-147)
           (* x (/ t (- z y)))
           (if (<= y 3.6e+33) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (y <= -3.4e+72) {
		tmp = t;
	} else if (y <= -3e-36) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.02e-271) {
		tmp = t_1;
	} else if (y <= 2.8e-147) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.6e+33) {
		tmp = t_1;
	} else {
		tmp = 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 = t * ((x - y) / z)
    if (y <= (-3.4d+72)) then
        tmp = t
    else if (y <= (-3d-36)) then
        tmp = t * (x / (z - y))
    else if (y <= 1.02d-271) then
        tmp = t_1
    else if (y <= 2.8d-147) then
        tmp = x * (t / (z - y))
    else if (y <= 3.6d+33) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (y <= -3.4e+72) {
		tmp = t;
	} else if (y <= -3e-36) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.02e-271) {
		tmp = t_1;
	} else if (y <= 2.8e-147) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.6e+33) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	tmp = 0
	if y <= -3.4e+72:
		tmp = t
	elif y <= -3e-36:
		tmp = t * (x / (z - y))
	elif y <= 1.02e-271:
		tmp = t_1
	elif y <= 2.8e-147:
		tmp = x * (t / (z - y))
	elif y <= 3.6e+33:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (y <= -3.4e+72)
		tmp = t;
	elseif (y <= -3e-36)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 1.02e-271)
		tmp = t_1;
	elseif (y <= 2.8e-147)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 3.6e+33)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	tmp = 0.0;
	if (y <= -3.4e+72)
		tmp = t;
	elseif (y <= -3e-36)
		tmp = t * (x / (z - y));
	elseif (y <= 1.02e-271)
		tmp = t_1;
	elseif (y <= 2.8e-147)
		tmp = x * (t / (z - y));
	elseif (y <= 3.6e+33)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+72], t, If[LessEqual[y, -3e-36], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-271], t$95$1, If[LessEqual[y, 2.8e-147], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+33], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.3999999999999998e72 or 3.6000000000000003e33 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.4%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 78.6%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around inf 68.4%

      \[\leadsto \color{blue}{t} \]

   if -3.3999999999999998e72 < y < -3.0000000000000002e-36

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in x around inf 64.6%

      \[\leadsto \color{blue}{\frac{x}{z - y}} \cdot t \]

   if -3.0000000000000002e-36 < y < 1.02e-271 or 2.8e-147 < y < 3.6000000000000003e33

   1. Initial program 94.4%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{\frac{x - y}{z}} \cdot t \]

   if 1.02e-271 < y < 2.8e-147

   1. Initial program 84.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 97.3%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in x around inf 91.9%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   5. Step-by-step derivation

      1. associate-*l/ 93.4%

         \[\leadsto \color{blue}{\frac{t}{z - y} \cdot x} \]

      2. *-commutative 93.4%

         \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]

   6. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t - t \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (- t (* t (/ x y)))))
   (if (<= y -1.3e-35)
     t_2
     (if (<= y 1e-272)
       t_1
       (if (<= y 1.85e-147)
         (* x (/ t (- z y)))
         (if (<= y 9.2e+25) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t - (t * (x / y));
	double tmp;
	if (y <= -1.3e-35) {
		tmp = t_2;
	} else if (y <= 1e-272) {
		tmp = t_1;
	} else if (y <= 1.85e-147) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.2e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = t * ((x - y) / z)
    t_2 = t - (t * (x / y))
    if (y <= (-1.3d-35)) then
        tmp = t_2
    else if (y <= 1d-272) then
        tmp = t_1
    else if (y <= 1.85d-147) then
        tmp = x * (t / (z - y))
    else if (y <= 9.2d+25) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t - (t * (x / y));
	double tmp;
	if (y <= -1.3e-35) {
		tmp = t_2;
	} else if (y <= 1e-272) {
		tmp = t_1;
	} else if (y <= 1.85e-147) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.2e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t - (t * (x / y))
	tmp = 0
	if y <= -1.3e-35:
		tmp = t_2
	elif y <= 1e-272:
		tmp = t_1
	elif y <= 1.85e-147:
		tmp = x * (t / (z - y))
	elif y <= 9.2e+25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t - Float64(t * Float64(x / y)))
	tmp = 0.0
	if (y <= -1.3e-35)
		tmp = t_2;
	elseif (y <= 1e-272)
		tmp = t_1;
	elseif (y <= 1.85e-147)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 9.2e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t - (t * (x / y));
	tmp = 0.0;
	if (y <= -1.3e-35)
		tmp = t_2;
	elseif (y <= 1e-272)
		tmp = t_1;
	elseif (y <= 1.85e-147)
		tmp = x * (t / (z - y));
	elseif (y <= 9.2e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e-35], t$95$2, If[LessEqual[y, 1e-272], t$95$1, If[LessEqual[y, 1.85e-147], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+25], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000002e-35 or 9.1999999999999992e25 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 78.2%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 82.0%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in z around 0 61.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(x - y\right)}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 61.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(x - y\right)\right)}{y}} \]

      2. *-commutative 61.0%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(\left(x - y\right) \cdot t\right)}}{y} \]

      3. neg-mul-1 61.0%

         \[\leadsto \frac{\color{blue}{-\left(x - y\right) \cdot t}}{y} \]

      4. distribute-rgt-neg-in 61.0%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot \left(-t\right)}}{y} \]

   6. Simplified 61.0%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot \left(-t\right)}{y}} \]

   7. Taylor expanded in x around 0 72.0%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   8. Step-by-step derivation

      1. mul-1-neg 72.0%

         \[\leadsto t + \color{blue}{\left(-\frac{t \cdot x}{y}\right)} \]

      2. unsub-neg 72.0%

         \[\leadsto \color{blue}{t - \frac{t \cdot x}{y}} \]

      3. *-commutative 72.0%

         \[\leadsto t - \frac{\color{blue}{x \cdot t}}{y} \]

      4. associate-*l/ 78.7%

         \[\leadsto t - \color{blue}{\frac{x}{y} \cdot t} \]

   9. Simplified 78.7%

      \[\leadsto \color{blue}{t - \frac{x}{y} \cdot t} \]

   if -1.30000000000000002e-35 < y < 9.9999999999999993e-273 or 1.8500000000000001e-147 < y < 9.1999999999999992e25

   1. Initial program 94.4%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{\frac{x - y}{z}} \cdot t \]

   if 9.9999999999999993e-273 < y < 1.8500000000000001e-147

   1. Initial program 84.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 97.3%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in x around inf 91.9%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   5. Step-by-step derivation

      1. associate-*l/ 93.4%

         \[\leadsto \color{blue}{\frac{t}{z - y} \cdot x} \]

      2. *-commutative 93.4%

         \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]

   6. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-35}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 10^{-272}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-147}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-33}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -3.4e+75)
     t_1
     (if (<= y -2.8e-33)
       (- t (* t (/ x y)))
       (if (<= y 1.1e-272)
         (* t (/ (- x y) z))
         (if (<= y 5.8e-29) (* x (/ t (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -3.4e+75) {
		tmp = t_1;
	} else if (y <= -2.8e-33) {
		tmp = t - (t * (x / y));
	} else if (y <= 1.1e-272) {
		tmp = t * ((x - y) / z);
	} else if (y <= 5.8e-29) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	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 = t / (1.0d0 - (z / y))
    if (y <= (-3.4d+75)) then
        tmp = t_1
    else if (y <= (-2.8d-33)) then
        tmp = t - (t * (x / y))
    else if (y <= 1.1d-272) then
        tmp = t * ((x - y) / z)
    else if (y <= 5.8d-29) then
        tmp = x * (t / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -3.4e+75) {
		tmp = t_1;
	} else if (y <= -2.8e-33) {
		tmp = t - (t * (x / y));
	} else if (y <= 1.1e-272) {
		tmp = t * ((x - y) / z);
	} else if (y <= 5.8e-29) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -3.4e+75:
		tmp = t_1
	elif y <= -2.8e-33:
		tmp = t - (t * (x / y))
	elif y <= 1.1e-272:
		tmp = t * ((x - y) / z)
	elif y <= 5.8e-29:
		tmp = x * (t / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -3.4e+75)
		tmp = t_1;
	elseif (y <= -2.8e-33)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= 1.1e-272)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 5.8e-29)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -3.4e+75)
		tmp = t_1;
	elseif (y <= -2.8e-33)
		tmp = t - (t * (x / y));
	elseif (y <= 1.1e-272)
		tmp = t * ((x - y) / z);
	elseif (y <= 5.8e-29)
		tmp = x * (t / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+75], t$95$1, If[LessEqual[y, -2.8e-33], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-272], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-29], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.40000000000000011e75 or 5.80000000000000048e-29 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.6%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 79.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 79.8%

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

      1. associate-*r/ 76.6%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{z - y} \cdot t} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{t \cdot \frac{x - y}{z - y}} \]

      4. clear-num 99.8%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \]

      5. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

   6. Taylor expanded in x around 0 83.8%

      \[\leadsto \frac{t}{\color{blue}{-1 \cdot \frac{z - y}{y}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 83.8%

         \[\leadsto \frac{t}{\color{blue}{\frac{-1 \cdot \left(z - y\right)}{y}}} \]

      2. neg-mul-1 83.8%

         \[\leadsto \frac{t}{\frac{\color{blue}{-\left(z - y\right)}}{y}} \]

      3. neg-sub0 83.8%

         \[\leadsto \frac{t}{\frac{\color{blue}{0 - \left(z - y\right)}}{y}} \]

      4. associate--r- 83.8%

         \[\leadsto \frac{t}{\frac{\color{blue}{\left(0 - z\right) + y}}{y}} \]

      5. neg-sub0 83.8%

         \[\leadsto \frac{t}{\frac{\color{blue}{\left(-z\right)} + y}{y}} \]

   8. Simplified 83.8%

      \[\leadsto \frac{t}{\color{blue}{\frac{\left(-z\right) + y}{y}}} \]

   9. Taylor expanded in z around 0 83.8%

      \[\leadsto \frac{t}{\color{blue}{1 + -1 \cdot \frac{z}{y}}} \]
   10. Step-by-step derivation

       1. mul-1-neg 83.8%

          \[\leadsto \frac{t}{1 + \color{blue}{\left(-\frac{z}{y}\right)}} \]

       2. unsub-neg 83.8%

          \[\leadsto \frac{t}{\color{blue}{1 - \frac{z}{y}}} \]

   11. Simplified 83.8%

       \[\leadsto \frac{t}{\color{blue}{1 - \frac{z}{y}}} \]

   if -3.40000000000000011e75 < y < -2.8e-33

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 88.3%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in z around 0 64.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(x - y\right)}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(x - y\right)\right)}{y}} \]

      2. *-commutative 64.6%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(\left(x - y\right) \cdot t\right)}}{y} \]

      3. neg-mul-1 64.6%

         \[\leadsto \frac{\color{blue}{-\left(x - y\right) \cdot t}}{y} \]

      4. distribute-rgt-neg-in 64.6%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot \left(-t\right)}}{y} \]

   6. Simplified 64.6%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot \left(-t\right)}{y}} \]

   7. Taylor expanded in x around 0 68.2%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   8. Step-by-step derivation

      1. mul-1-neg 68.2%

         \[\leadsto t + \color{blue}{\left(-\frac{t \cdot x}{y}\right)} \]

      2. unsub-neg 68.2%

         \[\leadsto \color{blue}{t - \frac{t \cdot x}{y}} \]

      3. *-commutative 68.2%

         \[\leadsto t - \frac{\color{blue}{x \cdot t}}{y} \]

      4. associate-*l/ 71.1%

         \[\leadsto t - \color{blue}{\frac{x}{y} \cdot t} \]

   9. Simplified 71.1%

      \[\leadsto \color{blue}{t - \frac{x}{y} \cdot t} \]

   if -2.8e-33 < y < 1.09999999999999994e-272

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in z around inf 85.4%

      \[\leadsto \color{blue}{\frac{x - y}{z}} \cdot t \]

   if 1.09999999999999994e-272 < y < 5.80000000000000048e-29

   1. Initial program 88.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.8%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 93.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in x around inf 75.0%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   5. Step-by-step derivation

      1. associate-*l/ 76.3%

         \[\leadsto \color{blue}{\frac{t}{z - y} \cdot x} \]

      2. *-commutative 76.3%

         \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]

   6. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+75}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-33}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 7: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+239}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+85}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+239)
   (- t (* t (/ x y)))
   (if (<= y 5.9e+85) (* (- x y) (/ t (- z y))) (/ t (- 1.0 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+239) {
		tmp = t - (t * (x / y));
	} else if (y <= 5.9e+85) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (1.0 - (z / 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) :: tmp
    if (y <= (-7.6d+239)) then
        tmp = t - (t * (x / y))
    else if (y <= 5.9d+85) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+239) {
		tmp = t - (t * (x / y));
	} else if (y <= 5.9e+85) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e+239:
		tmp = t - (t * (x / y))
	elif y <= 5.9e+85:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.6e+239)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= 5.9e+85)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+239)
		tmp = t - (t * (x / y));
	elseif (y <= 5.9e+85)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.6e+239], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.9e+85], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.6000000000000003e239

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 66.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 63.7%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in z around 0 66.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot \left(x - y\right)}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 66.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot \left(x - y\right)\right)}{y}} \]

      2. *-commutative 66.0%

         \[\leadsto \frac{-1 \cdot \color{blue}{\left(\left(x - y\right) \cdot t\right)}}{y} \]

      3. neg-mul-1 66.0%

         \[\leadsto \frac{\color{blue}{-\left(x - y\right) \cdot t}}{y} \]

      4. distribute-rgt-neg-in 66.0%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot \left(-t\right)}}{y} \]

   6. Simplified 66.0%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot \left(-t\right)}{y}} \]

   7. Taylor expanded in x around 0 86.6%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   8. Step-by-step derivation

      1. mul-1-neg 86.6%

         \[\leadsto t + \color{blue}{\left(-\frac{t \cdot x}{y}\right)} \]

      2. unsub-neg 86.6%

         \[\leadsto \color{blue}{t - \frac{t \cdot x}{y}} \]

      3. *-commutative 86.6%

         \[\leadsto t - \frac{\color{blue}{x \cdot t}}{y} \]

      4. associate-*l/ 100.0%

         \[\leadsto t - \color{blue}{\frac{x}{y} \cdot t} \]

   9. Simplified 100.0%

      \[\leadsto \color{blue}{t - \frac{x}{y} \cdot t} \]

   if -7.6000000000000003e239 < y < 5.9e85

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 88.6%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 91.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   if 5.9e85 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 78.1%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 73.3%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 73.3%

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

      1. associate-*r/ 78.1%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{x - y}{z - y} \cdot t} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{t \cdot \frac{x - y}{z - y}} \]

      4. clear-num 99.8%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \]

      5. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

   6. Taylor expanded in x around 0 90.6%

      \[\leadsto \frac{t}{\color{blue}{-1 \cdot \frac{z - y}{y}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 90.6%

         \[\leadsto \frac{t}{\color{blue}{\frac{-1 \cdot \left(z - y\right)}{y}}} \]

      2. neg-mul-1 90.6%

         \[\leadsto \frac{t}{\frac{\color{blue}{-\left(z - y\right)}}{y}} \]

      3. neg-sub0 90.6%

         \[\leadsto \frac{t}{\frac{\color{blue}{0 - \left(z - y\right)}}{y}} \]

      4. associate--r- 90.6%

         \[\leadsto \frac{t}{\frac{\color{blue}{\left(0 - z\right) + y}}{y}} \]

      5. neg-sub0 90.6%

         \[\leadsto \frac{t}{\frac{\color{blue}{\left(-z\right)} + y}{y}} \]

   8. Simplified 90.6%

      \[\leadsto \frac{t}{\color{blue}{\frac{\left(-z\right) + y}{y}}} \]

   9. Taylor expanded in z around 0 90.6%

      \[\leadsto \frac{t}{\color{blue}{1 + -1 \cdot \frac{z}{y}}} \]
   10. Step-by-step derivation

       1. mul-1-neg 90.6%

          \[\leadsto \frac{t}{1 + \color{blue}{\left(-\frac{z}{y}\right)}} \]

       2. unsub-neg 90.6%

          \[\leadsto \frac{t}{\color{blue}{1 - \frac{z}{y}}} \]

   11. Simplified 90.6%

       \[\leadsto \frac{t}{\color{blue}{1 - \frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+239}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+85}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 8: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.35e+69) t (if (<= y 2.3e+85) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.35e+69) {
		tmp = t;
	} else if (y <= 2.3e+85) {
		tmp = x * (t / (z - y));
	} else {
		tmp = 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) :: tmp
    if (y <= (-3.35d+69)) then
        tmp = t
    else if (y <= 2.3d+85) then
        tmp = x * (t / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.35e+69) {
		tmp = t;
	} else if (y <= 2.3e+85) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.35e+69:
		tmp = t
	elif y <= 2.3e+85:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.35e+69)
		tmp = t;
	elseif (y <= 2.3e+85)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.35e+69)
		tmp = t;
	elseif (y <= 2.3e+85)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.35e+69], t, If[LessEqual[y, 2.3e+85], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.35000000000000005e69 or 2.2999999999999999e85 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 75.3%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 76.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around inf 71.2%

      \[\leadsto \color{blue}{t} \]

   if -3.35000000000000005e69 < y < 2.2999999999999999e85

   1. Initial program 93.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 93.3%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in x around inf 68.5%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   5. Step-by-step derivation

      1. associate-*l/ 69.0%

         \[\leadsto \color{blue}{\frac{t}{z - y} \cdot x} \]

      2. *-commutative 69.0%

         \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e-18) t (if (<= y 1.15e-26) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-18) {
		tmp = t;
	} else if (y <= 1.15e-26) {
		tmp = x * (t / z);
	} else {
		tmp = 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) :: tmp
    if (y <= (-3.3d-18)) then
        tmp = t
    else if (y <= 1.15d-26) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-18) {
		tmp = t;
	} else if (y <= 1.15e-26) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e-18:
		tmp = t
	elif y <= 1.15e-26:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e-18)
		tmp = t;
	elseif (y <= 1.15e-26)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e-18)
		tmp = t;
	elseif (y <= 1.15e-26)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e-18], t, If[LessEqual[y, 1.15e-26], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3000000000000002e-18 or 1.15000000000000004e-26 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.8%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 82.5%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around inf 63.2%

      \[\leadsto \color{blue}{t} \]

   if -3.3000000000000002e-18 < y < 1.15000000000000004e-26

   1. Initial program 92.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 91.4%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 91.4%

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

      1. associate-*r/ 94.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*l/ 92.2%

         \[\leadsto \color{blue}{\frac{x - y}{z - y} \cdot t} \]

      3. *-commutative 92.2%

         \[\leadsto \color{blue}{t \cdot \frac{x - y}{z - y}} \]

      4. clear-num 91.6%

         \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \]

      5. un-div-inv 92.2%

         \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

   5. Applied egg-rr 92.2%

      \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

   6. Taylor expanded in y around 0 61.6%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   7. Step-by-step derivation

      1. associate-*l/ 60.3%

         \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]

      2. *-commutative 60.3%

         \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]

   8. Simplified 60.3%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e-18) t (if (<= y 9.2e-27) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-18) {
		tmp = t;
	} else if (y <= 9.2e-27) {
		tmp = t * (x / z);
	} else {
		tmp = 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) :: tmp
    if (y <= (-2.6d-18)) then
        tmp = t
    else if (y <= 9.2d-27) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e-18) {
		tmp = t;
	} else if (y <= 9.2e-27) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e-18:
		tmp = t
	elif y <= 9.2e-27:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e-18)
		tmp = t;
	elseif (y <= 9.2e-27)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e-18)
		tmp = t;
	elseif (y <= 9.2e-27)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e-18], t, If[LessEqual[y, 9.2e-27], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-18 or 9.1999999999999998e-27 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.8%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 82.5%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around inf 63.2%

      \[\leadsto \color{blue}{t} \]

   if -2.6e-18 < y < 9.1999999999999998e-27

   1. Initial program 92.2%

      \[\frac{x - y}{z - y} \cdot t \]

   2. Taylor expanded in y around 0 63.8%

      \[\leadsto \color{blue}{\frac{x}{z}} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e-18) t (if (<= y 1.2e-26) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-18) {
		tmp = t;
	} else if (y <= 1.2e-26) {
		tmp = t / (z / x);
	} else {
		tmp = 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) :: tmp
    if (y <= (-3.3d-18)) then
        tmp = t
    else if (y <= 1.2d-26) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e-18) {
		tmp = t;
	} else if (y <= 1.2e-26) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e-18:
		tmp = t
	elif y <= 1.2e-26:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e-18)
		tmp = t;
	elseif (y <= 1.2e-26)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e-18)
		tmp = t;
	elseif (y <= 1.2e-26)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e-18], t, If[LessEqual[y, 1.2e-26], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3000000000000002e-18 or 1.2e-26 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.8%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 82.5%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around inf 63.2%

      \[\leadsto \color{blue}{t} \]

   if -3.3000000000000002e-18 < y < 1.2e-26

   1. Initial program 92.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

      2. associate-*r/ 91.4%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   4. Taylor expanded in y around 0 61.6%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z}} \]
   5. Step-by-step derivation

      1. associate-/l* 63.8%

         \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]

   6. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{z}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t \cdot \frac{x - y}{z - y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t * ((x - y) / (z - 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 = t * ((x - y) / (z - y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * ((x - y) / (z - y));
}

Python

def code(x, y, z, t):
	return t * ((x - y) / (z - y))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

   \[\frac{x - y}{z - y} \cdot t \]

2. Final simplification 96.3%

   \[\leadsto t \cdot \frac{x - y}{z - y} \]

Alternative 13: 35.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

double code(double x, double y, double z, double t) {
	return 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 = t
end function

Java

public static double code(double x, double y, double z, double t) {
	return t;
}

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 85.2%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]

   2. associate-*r/ 86.6%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

3. Simplified 86.6%

   \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

4. Taylor expanded in y around inf 37.7%

   \[\leadsto \color{blue}{t} \]

5. Final simplification 37.7%

   \[\leadsto t \]

Developer target: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ t (/ (- z y) (- x y))))

C

double code(double x, double y, double z, double t) {
	return t / ((z - y) / (x - 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 = t / ((z - y) / (x - y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t / ((z - y) / (x - y));
}

Python

def code(x, y, z, t):
	return t / ((z - y) / (x - y))

Julia

function code(x, y, z, t)
	return Float64(t / Float64(Float64(z - y) / Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t / ((z - y) / (x - y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023174 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))