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

Percentage Accurate: 96.7% → 96.9%

Time: 9.7s

Alternatives: 15

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: 96.7% 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, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 5.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{t\_m \cdot \left(x - y\right)}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x - y}{z - y}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= t_m 5.6e-49)
    (/ (* t_m (- x y)) (- z y))
    (* t_m (/ (- x y) (- z y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (t_m <= 5.6e-49) {
		tmp = (t_m * (x - y)) / (z - y);
	} else {
		tmp = t_m * ((x - y) / (z - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (t_m <= 5.6d-49) then
        tmp = (t_m * (x - y)) / (z - y)
    else
        tmp = t_m * ((x - y) / (z - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (t_m <= 5.6e-49) {
		tmp = (t_m * (x - y)) / (z - y);
	} else {
		tmp = t_m * ((x - y) / (z - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if t_m <= 5.6e-49:
		tmp = (t_m * (x - y)) / (z - y)
	else:
		tmp = t_m * ((x - y) / (z - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (t_m <= 5.6e-49)
		tmp = Float64(Float64(t_m * Float64(x - y)) / Float64(z - y));
	else
		tmp = Float64(t_m * Float64(Float64(x - y) / Float64(z - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (t_m <= 5.6e-49)
		tmp = (t_m * (x - y)) / (z - y);
	else
		tmp = t_m * ((x - y) / (z - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[t$95$m, 5.6e-49], N[(N[(t$95$m * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 5.59999999999999995e-49

   1. Initial program 95.5%

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

      1. associate-*l/ 92.6%

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

      2. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

      1. associate-*r/ 92.6%

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

   6. Applied egg-rr 92.6%

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

   if 5.59999999999999995e-49 < t

   1. Initial program 96.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := t\_m \cdot \frac{y}{y - z}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-253}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-189}:\\ \;\;\;\;\frac{t\_m \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (/ y (- y z)))))
   (*
    t_s
    (if (<= y -1.2e-52)
      t_2
      (if (<= y -5.1e-253)
        (* t_m (/ x (- z y)))
        (if (<= y 1.35e-189)
          (/ (* t_m (- x y)) z)
          (if (<= y 8.5e+59) (/ (* t_m x) (- z y)) t_2)))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -1.2e-52) {
		tmp = t_2;
	} else if (y <= -5.1e-253) {
		tmp = t_m * (x / (z - y));
	} else if (y <= 1.35e-189) {
		tmp = (t_m * (x - y)) / z;
	} else if (y <= 8.5e+59) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m * (y / (y - z))
    if (y <= (-1.2d-52)) then
        tmp = t_2
    else if (y <= (-5.1d-253)) then
        tmp = t_m * (x / (z - y))
    else if (y <= 1.35d-189) then
        tmp = (t_m * (x - y)) / z
    else if (y <= 8.5d+59) then
        tmp = (t_m * x) / (z - y)
    else
        tmp = t_2
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -1.2e-52) {
		tmp = t_2;
	} else if (y <= -5.1e-253) {
		tmp = t_m * (x / (z - y));
	} else if (y <= 1.35e-189) {
		tmp = (t_m * (x - y)) / z;
	} else if (y <= 8.5e+59) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = t_m * (y / (y - z))
	tmp = 0
	if y <= -1.2e-52:
		tmp = t_2
	elif y <= -5.1e-253:
		tmp = t_m * (x / (z - y))
	elif y <= 1.35e-189:
		tmp = (t_m * (x - y)) / z
	elif y <= 8.5e+59:
		tmp = (t_m * x) / (z - y)
	else:
		tmp = t_2
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(t_m * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.2e-52)
		tmp = t_2;
	elseif (y <= -5.1e-253)
		tmp = Float64(t_m * Float64(x / Float64(z - y)));
	elseif (y <= 1.35e-189)
		tmp = Float64(Float64(t_m * Float64(x - y)) / z);
	elseif (y <= 8.5e+59)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	else
		tmp = t_2;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = t_m * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.2e-52)
		tmp = t_2;
	elseif (y <= -5.1e-253)
		tmp = t_m * (x / (z - y));
	elseif (y <= 1.35e-189)
		tmp = (t_m * (x - y)) / z;
	elseif (y <= 8.5e+59)
		tmp = (t_m * x) / (z - y);
	else
		tmp = t_2;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -1.2e-52], t$95$2, If[LessEqual[y, -5.1e-253], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-189], N[(N[(t$95$m * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 8.5e+59], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2000000000000001e-52 or 8.4999999999999999e59 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.1%

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

      1. neg-mul-1 83.1%

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

      2. distribute-neg-frac2 83.1%

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

      3. neg-sub0 83.1%

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

      4. sub-neg 83.1%

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

      5. +-commutative 83.1%

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

      6. associate--r+ 83.1%

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

      7. neg-sub0 83.1%

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

      8. remove-double-neg 83.1%

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

   5. Simplified 83.1%

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

   if -1.2000000000000001e-52 < y < -5.10000000000000008e-253

   1. Initial program 95.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.1%

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

   if -5.10000000000000008e-253 < y < 1.35e-189

   1. Initial program 88.5%

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

      1. associate-*l/ 96.2%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 92.9%

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

   if 1.35e-189 < y < 8.4999999999999999e59

   1. Initial program 94.1%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 76.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-189}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := t\_m \cdot \frac{y}{y - z}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-47}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-125}:\\ \;\;\;\;t\_m \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (/ y (- y z)))))
   (*
    t_s
    (if (<= y -8.5e-47)
      t_2
      (if (<= y -3.7e-125)
        (* t_m (/ (- x y) z))
        (if (<= y 3.8e+57) (/ (* t_m x) (- z y)) t_2))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -8.5e-47) {
		tmp = t_2;
	} else if (y <= -3.7e-125) {
		tmp = t_m * ((x - y) / z);
	} else if (y <= 3.8e+57) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m * (y / (y - z))
    if (y <= (-8.5d-47)) then
        tmp = t_2
    else if (y <= (-3.7d-125)) then
        tmp = t_m * ((x - y) / z)
    else if (y <= 3.8d+57) then
        tmp = (t_m * x) / (z - y)
    else
        tmp = t_2
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -8.5e-47) {
		tmp = t_2;
	} else if (y <= -3.7e-125) {
		tmp = t_m * ((x - y) / z);
	} else if (y <= 3.8e+57) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = t_m * (y / (y - z))
	tmp = 0
	if y <= -8.5e-47:
		tmp = t_2
	elif y <= -3.7e-125:
		tmp = t_m * ((x - y) / z)
	elif y <= 3.8e+57:
		tmp = (t_m * x) / (z - y)
	else:
		tmp = t_2
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(t_m * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -8.5e-47)
		tmp = t_2;
	elseif (y <= -3.7e-125)
		tmp = Float64(t_m * Float64(Float64(x - y) / z));
	elseif (y <= 3.8e+57)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	else
		tmp = t_2;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = t_m * (y / (y - z));
	tmp = 0.0;
	if (y <= -8.5e-47)
		tmp = t_2;
	elseif (y <= -3.7e-125)
		tmp = t_m * ((x - y) / z);
	elseif (y <= 3.8e+57)
		tmp = (t_m * x) / (z - y);
	else
		tmp = t_2;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -8.5e-47], t$95$2, If[LessEqual[y, -3.7e-125], N[(t$95$m * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+57], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999999e-47 or 3.7999999999999999e57 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.5%

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

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac2 83.5%

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

      3. neg-sub0 83.5%

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

      4. sub-neg 83.5%

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

      5. +-commutative 83.5%

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

      6. associate--r+ 83.5%

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

      7. neg-sub0 83.5%

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

      8. remove-double-neg 83.5%

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

   5. Simplified 83.5%

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

   if -8.4999999999999999e-47 < y < -3.6999999999999999e-125

   1. Initial program 95.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 74.7%

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

   if -3.6999999999999999e-125 < y < 3.7999999999999999e57

   1. Initial program 93.0%

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

      1. associate-*l/ 97.9%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 80.2%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-125}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+154} \lor \neg \left(y \leq 10^{+83}\right):\\ \;\;\;\;t\_m \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z - y}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= y -4.8e+154) (not (<= y 1e+83)))
    (* t_m (/ y (- y z)))
    (* (- x y) (/ t_m (- z y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -4.8e+154) || !(y <= 1e+83)) {
		tmp = t_m * (y / (y - z));
	} else {
		tmp = (x - y) * (t_m / (z - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((y <= (-4.8d+154)) .or. (.not. (y <= 1d+83))) then
        tmp = t_m * (y / (y - z))
    else
        tmp = (x - y) * (t_m / (z - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -4.8e+154) || !(y <= 1e+83)) {
		tmp = t_m * (y / (y - z));
	} else {
		tmp = (x - y) * (t_m / (z - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if (y <= -4.8e+154) or not (y <= 1e+83):
		tmp = t_m * (y / (y - z))
	else:
		tmp = (x - y) * (t_m / (z - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if ((y <= -4.8e+154) || !(y <= 1e+83))
		tmp = Float64(t_m * Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(x - y) * Float64(t_m / Float64(z - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if ((y <= -4.8e+154) || ~((y <= 1e+83)))
		tmp = t_m * (y / (y - z));
	else
		tmp = (x - y) * (t_m / (z - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[Or[LessEqual[y, -4.8e+154], N[Not[LessEqual[y, 1e+83]], $MachinePrecision]], N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000003e154 or 1.00000000000000003e83 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.7%

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

      1. neg-mul-1 93.7%

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

      2. distribute-neg-frac2 93.7%

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

      3. neg-sub0 93.7%

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

      4. sub-neg 93.7%

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

      5. +-commutative 93.7%

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

      6. associate--r+ 93.7%

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

      7. neg-sub0 93.7%

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

      8. remove-double-neg 93.7%

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

   5. Simplified 93.7%

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

   if -4.8000000000000003e154 < y < 1.00000000000000003e83

   1. Initial program 94.6%

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

      1. associate-*l/ 93.6%

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

      2. associate-/l* 92.1%

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

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+154} \lor \neg \left(y \leq 10^{+83}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-55} \lor \neg \left(y \leq 1.95 \cdot 10^{+57}\right):\\ \;\;\;\;t\_m \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= y -6.5e-55) (not (<= y 1.95e+57)))
    (* t_m (/ y (- y z)))
    (* t_m (/ x (- z y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -6.5e-55) || !(y <= 1.95e+57)) {
		tmp = t_m * (y / (y - z));
	} else {
		tmp = t_m * (x / (z - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((y <= (-6.5d-55)) .or. (.not. (y <= 1.95d+57))) then
        tmp = t_m * (y / (y - z))
    else
        tmp = t_m * (x / (z - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -6.5e-55) || !(y <= 1.95e+57)) {
		tmp = t_m * (y / (y - z));
	} else {
		tmp = t_m * (x / (z - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if (y <= -6.5e-55) or not (y <= 1.95e+57):
		tmp = t_m * (y / (y - z))
	else:
		tmp = t_m * (x / (z - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if ((y <= -6.5e-55) || !(y <= 1.95e+57))
		tmp = Float64(t_m * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t_m * Float64(x / Float64(z - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if ((y <= -6.5e-55) || ~((y <= 1.95e+57)))
		tmp = t_m * (y / (y - z));
	else
		tmp = t_m * (x / (z - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[Or[LessEqual[y, -6.5e-55], N[Not[LessEqual[y, 1.95e+57]], $MachinePrecision]], N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000006e-55 or 1.94999999999999984e57 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.1%

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

      1. neg-mul-1 83.1%

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

      2. distribute-neg-frac2 83.1%

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

      3. neg-sub0 83.1%

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

      4. sub-neg 83.1%

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

      5. +-commutative 83.1%

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

      6. associate--r+ 83.1%

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

      7. neg-sub0 83.1%

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

      8. remove-double-neg 83.1%

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

   5. Simplified 83.1%

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

   if -6.50000000000000006e-55 < y < 1.94999999999999984e57

   1. Initial program 93.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-55} \lor \neg \left(y \leq 1.95 \cdot 10^{+57}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+61} \lor \neg \left(y \leq 2.75 \cdot 10^{+41}\right):\\ \;\;\;\;t\_m \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= y -3.7e+61) (not (<= y 2.75e+41)))
    (* t_m (- 1.0 (/ x y)))
    (* t_m (/ x (- z y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -3.7e+61) || !(y <= 2.75e+41)) {
		tmp = t_m * (1.0 - (x / y));
	} else {
		tmp = t_m * (x / (z - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((y <= (-3.7d+61)) .or. (.not. (y <= 2.75d+41))) then
        tmp = t_m * (1.0d0 - (x / y))
    else
        tmp = t_m * (x / (z - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -3.7e+61) || !(y <= 2.75e+41)) {
		tmp = t_m * (1.0 - (x / y));
	} else {
		tmp = t_m * (x / (z - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if (y <= -3.7e+61) or not (y <= 2.75e+41):
		tmp = t_m * (1.0 - (x / y))
	else:
		tmp = t_m * (x / (z - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if ((y <= -3.7e+61) || !(y <= 2.75e+41))
		tmp = Float64(t_m * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t_m * Float64(x / Float64(z - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if ((y <= -3.7e+61) || ~((y <= 2.75e+41)))
		tmp = t_m * (1.0 - (x / y));
	else
		tmp = t_m * (x / (z - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[Or[LessEqual[y, -3.7e+61], N[Not[LessEqual[y, 2.75e+41]], $MachinePrecision]], N[(t$95$m * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000003e61 or 2.7500000000000002e41 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

      3. neg-sub0 78.6%

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

      4. sub-neg 78.6%

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

      5. +-commutative 78.6%

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

      6. associate--r+ 78.6%

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

      7. neg-sub0 78.6%

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

      8. remove-double-neg 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in y around 0 78.6%

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

      1. neg-mul-1 78.6%

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

      2. sub-neg 78.6%

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

      3. div-sub 78.6%

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

      4. *-inverses 78.6%

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

   8. Simplified 78.6%

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

   if -3.70000000000000003e61 < y < 2.7500000000000002e41

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+61} \lor \neg \left(y \leq 2.75 \cdot 10^{+41}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-48} \lor \neg \left(z \leq 10^{-20}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= z -8e-48) (not (<= z 1e-20)))
    (* (- x y) (/ t_m z))
    (* t_m (- 1.0 (/ x y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((z <= -8e-48) || !(z <= 1e-20)) {
		tmp = (x - y) * (t_m / z);
	} else {
		tmp = t_m * (1.0 - (x / y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((z <= (-8d-48)) .or. (.not. (z <= 1d-20))) then
        tmp = (x - y) * (t_m / z)
    else
        tmp = t_m * (1.0d0 - (x / y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((z <= -8e-48) || !(z <= 1e-20)) {
		tmp = (x - y) * (t_m / z);
	} else {
		tmp = t_m * (1.0 - (x / y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if (z <= -8e-48) or not (z <= 1e-20):
		tmp = (x - y) * (t_m / z)
	else:
		tmp = t_m * (1.0 - (x / y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if ((z <= -8e-48) || !(z <= 1e-20))
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	else
		tmp = Float64(t_m * Float64(1.0 - Float64(x / y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if ((z <= -8e-48) || ~((z <= 1e-20)))
		tmp = (x - y) * (t_m / z);
	else
		tmp = t_m * (1.0 - (x / y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[Or[LessEqual[z, -8e-48], N[Not[LessEqual[z, 1e-20]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999998e-48 or 9.99999999999999945e-21 < z

   1. Initial program 95.6%

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

      1. associate-*l/ 88.8%

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

      2. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around inf 72.5%

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

   if -7.9999999999999998e-48 < z < 9.99999999999999945e-21

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 76.9%

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

      1. associate-*r/ 76.9%

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

      2. neg-mul-1 76.9%

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

      3. neg-sub0 76.9%

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

      4. sub-neg 76.9%

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

      5. +-commutative 76.9%

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

      6. associate--r+ 76.9%

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

      7. neg-sub0 76.9%

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

      8. remove-double-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in y around 0 76.9%

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

      1. neg-mul-1 76.9%

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

      2. sub-neg 76.9%

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

      3. div-sub 76.9%

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

      4. *-inverses 76.9%

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

   8. Simplified 76.9%

      \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right)} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-48} \lor \neg \left(z \leq 10^{-20}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+63} \lor \neg \left(y \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;t\_m \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= y -2.2e+63) (not (<= y 2.4e+41)))
    (* t_m (- 1.0 (/ x y)))
    (* x (/ t_m (- z y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -2.2e+63) || !(y <= 2.4e+41)) {
		tmp = t_m * (1.0 - (x / y));
	} else {
		tmp = x * (t_m / (z - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if ((y <= (-2.2d+63)) .or. (.not. (y <= 2.4d+41))) then
        tmp = t_m * (1.0d0 - (x / y))
    else
        tmp = x * (t_m / (z - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if ((y <= -2.2e+63) || !(y <= 2.4e+41)) {
		tmp = t_m * (1.0 - (x / y));
	} else {
		tmp = x * (t_m / (z - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if (y <= -2.2e+63) or not (y <= 2.4e+41):
		tmp = t_m * (1.0 - (x / y))
	else:
		tmp = x * (t_m / (z - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if ((y <= -2.2e+63) || !(y <= 2.4e+41))
		tmp = Float64(t_m * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if ((y <= -2.2e+63) || ~((y <= 2.4e+41)))
		tmp = t_m * (1.0 - (x / y));
	else
		tmp = x * (t_m / (z - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[Or[LessEqual[y, -2.2e+63], N[Not[LessEqual[y, 2.4e+41]], $MachinePrecision]], N[(t$95$m * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999999e63 or 2.4000000000000002e41 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

      3. neg-sub0 78.6%

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

      4. sub-neg 78.6%

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

      5. +-commutative 78.6%

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

      6. associate--r+ 78.6%

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

      7. neg-sub0 78.6%

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

      8. remove-double-neg 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in y around 0 78.6%

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

      1. neg-mul-1 78.6%

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

      2. sub-neg 78.6%

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

      3. div-sub 78.6%

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

      4. *-inverses 78.6%

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

   8. Simplified 78.6%

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

   if -2.1999999999999999e63 < y < 2.4000000000000002e41

   1. Initial program 93.7%

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

      1. associate-*l/ 95.4%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in x around inf 71.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+63} \lor \neg \left(y \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+62}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -6.4e+62) t_m (if (<= y 3.1e+82) (* x (/ t_m (- z y))) t_m))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -6.4e+62) {
		tmp = t_m;
	} else if (y <= 3.1e+82) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-6.4d+62)) then
        tmp = t_m
    else if (y <= 3.1d+82) then
        tmp = x * (t_m / (z - y))
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -6.4e+62) {
		tmp = t_m;
	} else if (y <= 3.1e+82) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -6.4e+62:
		tmp = t_m
	elif y <= 3.1e+82:
		tmp = x * (t_m / (z - y))
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -6.4e+62)
		tmp = t_m;
	elseif (y <= 3.1e+82)
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -6.4e+62)
		tmp = t_m;
	elseif (y <= 3.1e+82)
		tmp = x * (t_m / (z - y));
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -6.4e+62], t$95$m, If[LessEqual[y, 3.1e+82], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.39999999999999968e62 or 3.10000000000000032e82 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 75.8%

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

      2. associate-/l* 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in y around inf 73.2%

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

   if -6.39999999999999968e62 < y < 3.10000000000000032e82

   1. Initial program 94.1%

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

      1. associate-*l/ 95.7%

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

      2. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in x around inf 69.4%

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

Alternative 10: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+61}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{t\_m}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (if (<= y -2.15e+61) t_m (if (<= y 1.4e+40) (/ t_m (/ z x)) t_m))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.15e+61) {
		tmp = t_m;
	} else if (y <= 1.4e+40) {
		tmp = t_m / (z / x);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-2.15d+61)) then
        tmp = t_m
    else if (y <= 1.4d+40) then
        tmp = t_m / (z / x)
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.15e+61) {
		tmp = t_m;
	} else if (y <= 1.4e+40) {
		tmp = t_m / (z / x);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -2.15e+61:
		tmp = t_m
	elif y <= 1.4e+40:
		tmp = t_m / (z / x)
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -2.15e+61)
		tmp = t_m;
	elseif (y <= 1.4e+40)
		tmp = Float64(t_m / Float64(z / x));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -2.15e+61)
		tmp = t_m;
	elseif (y <= 1.4e+40)
		tmp = t_m / (z / x);
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -2.15e+61], t$95$m, If[LessEqual[y, 1.4e+40], N[(t$95$m / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.1500000000000001e61 or 1.4000000000000001e40 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 78.7%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around inf 69.0%

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

   if -2.1500000000000001e61 < y < 1.4000000000000001e40

   1. Initial program 93.7%

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

      1. associate-*l/ 95.4%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. associate-*r/ 95.4%

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

      2. associate-*l/ 93.7%

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

      3. *-commutative 93.7%

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

      4. clear-num 93.4%

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

      5. un-div-inv 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in y around 0 57.7%

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

Alternative 11: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+61}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;t\_m \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (if (<= y -2.15e+61) t_m (if (<= y 6.2e+41) (* t_m (/ x z)) t_m))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.15e+61) {
		tmp = t_m;
	} else if (y <= 6.2e+41) {
		tmp = t_m * (x / z);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-2.15d+61)) then
        tmp = t_m
    else if (y <= 6.2d+41) then
        tmp = t_m * (x / z)
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.15e+61) {
		tmp = t_m;
	} else if (y <= 6.2e+41) {
		tmp = t_m * (x / z);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -2.15e+61:
		tmp = t_m
	elif y <= 6.2e+41:
		tmp = t_m * (x / z)
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -2.15e+61)
		tmp = t_m;
	elseif (y <= 6.2e+41)
		tmp = Float64(t_m * Float64(x / z));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -2.15e+61)
		tmp = t_m;
	elseif (y <= 6.2e+41)
		tmp = t_m * (x / z);
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -2.15e+61], t$95$m, If[LessEqual[y, 6.2e+41], N[(t$95$m * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.1500000000000001e61 or 6.2e41 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 78.7%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around inf 69.0%

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

   if -2.1500000000000001e61 < y < 6.2e41

   1. Initial program 93.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 57.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+61}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{t\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (if (<= y -2.7e+61) t_m (if (<= y 4.3e+41) (* x (/ t_m z)) t_m))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.7e+61) {
		tmp = t_m;
	} else if (y <= 4.3e+41) {
		tmp = x * (t_m / z);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-2.7d+61)) then
        tmp = t_m
    else if (y <= 4.3d+41) then
        tmp = x * (t_m / z)
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.7e+61) {
		tmp = t_m;
	} else if (y <= 4.3e+41) {
		tmp = x * (t_m / z);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -2.7e+61:
		tmp = t_m
	elif y <= 4.3e+41:
		tmp = x * (t_m / z)
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -2.7e+61)
		tmp = t_m;
	elseif (y <= 4.3e+41)
		tmp = Float64(x * Float64(t_m / z));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -2.7e+61)
		tmp = t_m;
	elseif (y <= 4.3e+41)
		tmp = x * (t_m / z);
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -2.7e+61], t$95$m, If[LessEqual[y, 4.3e+41], N[(x * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000002e61 or 4.30000000000000024e41 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 78.7%

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

      2. associate-/l* 72.8%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in y around inf 69.0%

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

   if -2.7000000000000002e61 < y < 4.30000000000000024e41

   1. Initial program 93.7%

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

      1. associate-*l/ 95.4%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around inf 68.2%

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

   6. Taylor expanded in x around inf 54.5%

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

Alternative 13: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \frac{t\_m}{\frac{z - y}{x - y}} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (/ t_m (/ (- z y) (- x y)))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * (t_m / ((z - y) / (x - y)));
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * (t_m / ((z - y) / (x - y)))
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * (t_m / ((z - y) / (x - y)));
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	return t_s * (t_m / ((z - y) / (x - y)))

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	return Float64(t_s * Float64(t_m / Float64(Float64(z - y) / Float64(x - y))))
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, x, y, z, t_m)
	tmp = t_s * (t_m / ((z - y) / (x - y)));
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * N[(t$95$m / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.9%

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

   1. associate-*l/ 89.5%

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

   2. associate-/l* 84.8%

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

3. Simplified 84.8%

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

   1. associate-*r/ 89.5%

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

   2. associate-*l/ 95.9%

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

   3. *-commutative 95.9%

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

   4. clear-num 95.6%

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

   5. un-div-inv 95.9%

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

6. Applied egg-rr 95.9%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
7. Add Preprocessing

Alternative 14: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \left(t\_m \cdot \frac{x - y}{z - y}\right) \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (* t_m (/ (- x y) (- z y)))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * (t_m * ((x - y) / (z - y)));
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * (t_m * ((x - y) / (z - y)))
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * (t_m * ((x - y) / (z - y)));
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	return t_s * (t_m * ((x - y) / (z - y)))

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	return Float64(t_s * Float64(t_m * Float64(Float64(x - y) / Float64(z - y))))
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, x, y, z, t_m)
	tmp = t_s * (t_m * ((x - y) / (z - y)));
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * N[(t$95$m * N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.9%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Final simplification 95.9%

   \[\leadsto t \cdot \frac{x - y}{z - y} \]
4. Add Preprocessing

Alternative 15: 34.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot t\_m \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m) :precision binary64 (* t_s t_m))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * t_m;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * t_m
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * t_m;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	return t_s * t_m

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	return Float64(t_s * t_m)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, x, y, z, t_m)
	tmp = t_s * t_m;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * t$95$m), $MachinePrecision]

Derivation

1. Initial program 95.9%

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

   1. associate-*l/ 89.5%

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

   2. associate-/l* 84.8%

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

3. Simplified 84.8%

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

5. Taylor expanded in y around inf 30.5%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 96.7% 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 2024185 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

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