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

Percentage Accurate: 97.1% → 96.6%

Time: 9.1s

Alternatives: 10

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: 97.1% 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: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 10^{-40}:\\ \;\;\;\;t_m \cdot \frac{x - y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t_m}}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= t_m 1e-40) (* t_m (/ (- x y) (- z y))) (/ (- x y) (/ (- 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 (t_m <= 1e-40) {
		tmp = t_m * ((x - y) / (z - y));
	} else {
		tmp = (x - y) / ((z - y) / 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 (t_m <= 1d-40) then
        tmp = t_m * ((x - y) / (z - y))
    else
        tmp = (x - y) / ((z - y) / 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 (t_m <= 1e-40) {
		tmp = t_m * ((x - y) / (z - y));
	} else {
		tmp = (x - y) / ((z - y) / 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 t_m <= 1e-40:
		tmp = t_m * ((x - y) / (z - y))
	else:
		tmp = (x - y) / ((z - y) / 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 (t_m <= 1e-40)
		tmp = Float64(t_m * Float64(Float64(x - y) / Float64(z - y)));
	else
		tmp = Float64(Float64(x - y) / Float64(Float64(z - y) / 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 (t_m <= 1e-40)
		tmp = t_m * ((x - y) / (z - y));
	else
		tmp = (x - y) / ((z - y) / 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[t$95$m, 1e-40], N[(t$95$m * N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 9.9999999999999993e-41

   1. Initial program 95.4%

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

   if 9.9999999999999993e-41 < t

   1. Initial program 95.7%

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

      1. associate-/r/ 96.7%

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

   3. Simplified 96.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-40}:\\ \;\;\;\;t \cdot \frac{x - y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;t_m\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;t_m \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -3600000000:\\ \;\;\;\;t_m\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{t_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_m\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -1.6e+119)
    t_m
    (if (<= y -3.6e+65)
      (* t_m (/ (- y) z))
      (if (<= y -3600000000.0)
        t_m
        (if (<= y 1.2e+62) (* 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 <= -1.6e+119) {
		tmp = t_m;
	} else if (y <= -3.6e+65) {
		tmp = t_m * (-y / z);
	} else if (y <= -3600000000.0) {
		tmp = t_m;
	} else if (y <= 1.2e+62) {
		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 <= (-1.6d+119)) then
        tmp = t_m
    else if (y <= (-3.6d+65)) then
        tmp = t_m * (-y / z)
    else if (y <= (-3600000000.0d0)) then
        tmp = t_m
    else if (y <= 1.2d+62) 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 <= -1.6e+119) {
		tmp = t_m;
	} else if (y <= -3.6e+65) {
		tmp = t_m * (-y / z);
	} else if (y <= -3600000000.0) {
		tmp = t_m;
	} else if (y <= 1.2e+62) {
		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 <= -1.6e+119:
		tmp = t_m
	elif y <= -3.6e+65:
		tmp = t_m * (-y / z)
	elif y <= -3600000000.0:
		tmp = t_m
	elif y <= 1.2e+62:
		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 <= -1.6e+119)
		tmp = t_m;
	elseif (y <= -3.6e+65)
		tmp = Float64(t_m * Float64(Float64(-y) / z));
	elseif (y <= -3600000000.0)
		tmp = t_m;
	elseif (y <= 1.2e+62)
		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 <= -1.6e+119)
		tmp = t_m;
	elseif (y <= -3.6e+65)
		tmp = t_m * (-y / z);
	elseif (y <= -3600000000.0)
		tmp = t_m;
	elseif (y <= 1.2e+62)
		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, -1.6e+119], t$95$m, If[LessEqual[y, -3.6e+65], N[(t$95$m * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3600000000.0], t$95$m, If[LessEqual[y, 1.2e+62], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$m]]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.59999999999999995e119 or -3.59999999999999978e65 < y < -3.6e9 or 1.2e62 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 69.0%

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

   if -1.59999999999999995e119 < y < -3.59999999999999978e65

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 74.8%

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

   4. Taylor expanded in x around 0 60.6%

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

      1. neg-mul-1 60.6%

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

      2. distribute-neg-frac 60.6%

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

   6. Simplified 60.6%

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

   if -3.6e9 < y < 1.2e62

   1. Initial program 92.9%

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

   3. Taylor expanded in x around inf 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*r/ 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -3600000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+118}:\\ \;\;\;\;t_m\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+66}:\\ \;\;\;\;t_m \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -370000000:\\ \;\;\;\;t_m\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{t_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t_m\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -7e+118)
    t_m
    (if (<= y -2.25e+66)
      (* t_m (/ (- y) z))
      (if (<= y -370000000.0) t_m (if (<= y 4e+62) (* 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 <= -7e+118) {
		tmp = t_m;
	} else if (y <= -2.25e+66) {
		tmp = t_m * (-y / z);
	} else if (y <= -370000000.0) {
		tmp = t_m;
	} else if (y <= 4e+62) {
		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 <= (-7d+118)) then
        tmp = t_m
    else if (y <= (-2.25d+66)) then
        tmp = t_m * (-y / z)
    else if (y <= (-370000000.0d0)) then
        tmp = t_m
    else if (y <= 4d+62) 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 <= -7e+118) {
		tmp = t_m;
	} else if (y <= -2.25e+66) {
		tmp = t_m * (-y / z);
	} else if (y <= -370000000.0) {
		tmp = t_m;
	} else if (y <= 4e+62) {
		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 <= -7e+118:
		tmp = t_m
	elif y <= -2.25e+66:
		tmp = t_m * (-y / z)
	elif y <= -370000000.0:
		tmp = t_m
	elif y <= 4e+62:
		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 <= -7e+118)
		tmp = t_m;
	elseif (y <= -2.25e+66)
		tmp = Float64(t_m * Float64(Float64(-y) / z));
	elseif (y <= -370000000.0)
		tmp = t_m;
	elseif (y <= 4e+62)
		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 <= -7e+118)
		tmp = t_m;
	elseif (y <= -2.25e+66)
		tmp = t_m * (-y / z);
	elseif (y <= -370000000.0)
		tmp = t_m;
	elseif (y <= 4e+62)
		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, -7e+118], t$95$m, If[LessEqual[y, -2.25e+66], N[(t$95$m * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -370000000.0], t$95$m, If[LessEqual[y, 4e+62], N[(x * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$m]]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000033e118 or -2.2499999999999999e66 < y < -3.7e8 or 4.00000000000000014e62 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 68.3%

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

   if -7.00000000000000033e118 < y < -2.2499999999999999e66

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 74.8%

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

   4. Taylor expanded in x around 0 60.6%

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

      1. neg-mul-1 60.6%

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

      2. distribute-neg-frac 60.6%

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

   6. Simplified 60.6%

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

   if -3.7e8 < y < 4.00000000000000014e62

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 61.4%

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

      1. associate-/l* 59.9%

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

      2. associate-/r/ 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -370000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-47} \lor \neg \left(y \leq 6.2 \cdot 10^{+62}\right):\\ \;\;\;\;t_m \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t_m}{z - y}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= y -3.8e-47) (not (<= y 6.2e+62)))
    (* 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 <= -3.8e-47) || !(y <= 6.2e+62)) {
		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 <= (-3.8d-47)) .or. (.not. (y <= 6.2d+62))) 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 <= -3.8e-47) || !(y <= 6.2e+62)) {
		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 <= -3.8e-47) or not (y <= 6.2e+62):
		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 <= -3.8e-47) || !(y <= 6.2e+62))
		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 <= -3.8e-47) || ~((y <= 6.2e+62)))
		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, -3.8e-47], N[Not[LessEqual[y, 6.2e+62]], $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 < -3.80000000000000015e-47 or 6.20000000000000029e62 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in x around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

   8. Simplified 77.0%

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

   if -3.80000000000000015e-47 < y < 6.20000000000000029e62

   1. Initial program 92.2%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-*r/ 73.9%

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

   5. Simplified 73.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-47} \lor \neg \left(y \leq 6.2 \cdot 10^{+62}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-61} \lor \neg \left(y \leq 5.7 \cdot 10^{+32}\right):\\ \;\;\;\;t_m \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t_m}{z}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= y -5.2e-61) (not (<= y 5.7e+32)))
    (* t_m (- 1.0 (/ x y)))
    (* (- x y) (/ t_m z)))))

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 <= -5.2e-61) || !(y <= 5.7e+32)) {
		tmp = t_m * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t_m / z);
	}
	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 <= (-5.2d-61)) .or. (.not. (y <= 5.7d+32))) then
        tmp = t_m * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (t_m / z)
    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 <= -5.2e-61) || !(y <= 5.7e+32)) {
		tmp = t_m * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t_m / z);
	}
	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 <= -5.2e-61) or not (y <= 5.7e+32):
		tmp = t_m * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t_m / z)
	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 <= -5.2e-61) || !(y <= 5.7e+32))
		tmp = Float64(t_m * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	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 <= -5.2e-61) || ~((y <= 5.7e+32)))
		tmp = t_m * (1.0 - (x / y));
	else
		tmp = (x - y) * (t_m / z);
	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, -5.2e-61], N[Not[LessEqual[y, 5.7e+32]], $MachinePrecision]], N[(t$95$m * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -5.20000000000000021e-61 or 5.7e32 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in x around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

   8. Simplified 75.7%

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

   if -5.20000000000000021e-61 < y < 5.7e32

   1. Initial program 91.7%

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

      1. associate-/r/ 95.4%

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

      2. div-inv 95.4%

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

      3. associate-/r* 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in z around inf 80.9%

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

      1. associate-*l/ 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-61} \lor \neg \left(y \leq 5.7 \cdot 10^{+32}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-21} \lor \neg \left(z \leq 4.5 \cdot 10^{+36}\right):\\ \;\;\;\;t_m \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_m \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= z -9.5e-21) (not (<= z 4.5e+36)))
    (* t_m (/ (- x y) 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 <= -9.5e-21) || !(z <= 4.5e+36)) {
		tmp = t_m * ((x - y) / 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 <= (-9.5d-21)) .or. (.not. (z <= 4.5d+36))) then
        tmp = t_m * ((x - y) / 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 <= -9.5e-21) || !(z <= 4.5e+36)) {
		tmp = t_m * ((x - y) / 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 <= -9.5e-21) or not (z <= 4.5e+36):
		tmp = t_m * ((x - y) / 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 <= -9.5e-21) || !(z <= 4.5e+36))
		tmp = Float64(t_m * Float64(Float64(x - y) / 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 <= -9.5e-21) || ~((z <= 4.5e+36)))
		tmp = t_m * ((x - y) / 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, -9.5e-21], N[Not[LessEqual[z, 4.5e+36]], $MachinePrecision]], N[(t$95$m * N[(N[(x - y), $MachinePrecision] / 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 < -9.4999999999999994e-21 or 4.49999999999999997e36 < z

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 81.3%

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

   if -9.4999999999999994e-21 < z < 4.49999999999999997e36

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 78.7%

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

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in x around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

   8. Simplified 78.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-21} \lor \neg \left(z \leq 4.5 \cdot 10^{+36}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-21} \lor \neg \left(z \leq 7.5 \cdot 10^{+37}\right):\\ \;\;\;\;t_m \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_m}{\frac{y}{y - x}}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (or (<= z -3.2e-21) (not (<= z 7.5e+37)))
    (* t_m (/ (- x y) z))
    (/ t_m (/ y (- y x))))))

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 <= -3.2e-21) || !(z <= 7.5e+37)) {
		tmp = t_m * ((x - y) / z);
	} else {
		tmp = t_m / (y / (y - x));
	}
	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 <= (-3.2d-21)) .or. (.not. (z <= 7.5d+37))) then
        tmp = t_m * ((x - y) / z)
    else
        tmp = t_m / (y / (y - x))
    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 <= -3.2e-21) || !(z <= 7.5e+37)) {
		tmp = t_m * ((x - y) / z);
	} else {
		tmp = t_m / (y / (y - x));
	}
	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 <= -3.2e-21) or not (z <= 7.5e+37):
		tmp = t_m * ((x - y) / z)
	else:
		tmp = t_m / (y / (y - x))
	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 <= -3.2e-21) || !(z <= 7.5e+37))
		tmp = Float64(t_m * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t_m / Float64(y / Float64(y - x)));
	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 <= -3.2e-21) || ~((z <= 7.5e+37)))
		tmp = t_m * ((x - y) / z);
	else
		tmp = t_m / (y / (y - x));
	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, -3.2e-21], N[Not[LessEqual[z, 7.5e+37]], $MachinePrecision]], N[(t$95$m * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002e-21 or 7.5000000000000003e37 < z

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf 81.3%

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

   if -3.2000000000000002e-21 < z < 7.5000000000000003e37

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 78.7%

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

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. associate-/l* 78.7%

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

   8. Simplified 78.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-21} \lor \neg \left(z \leq 7.5 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2050000000:\\ \;\;\;\;t_m\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{t_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t_m\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (if (<= y -2050000000.0) t_m (if (<= y 4.8e+62) (* 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 <= -2050000000.0) {
		tmp = t_m;
	} else if (y <= 4.8e+62) {
		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 <= (-2050000000.0d0)) then
        tmp = t_m
    else if (y <= 4.8d+62) 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 <= -2050000000.0) {
		tmp = t_m;
	} else if (y <= 4.8e+62) {
		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 <= -2050000000.0:
		tmp = t_m
	elif y <= 4.8e+62:
		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 <= -2050000000.0)
		tmp = t_m;
	elseif (y <= 4.8e+62)
		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 <= -2050000000.0)
		tmp = t_m;
	elseif (y <= 4.8e+62)
		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, -2050000000.0], t$95$m, If[LessEqual[y, 4.8e+62], N[(x * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e9 or 4.8e62 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 63.0%

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

   if -2.05e9 < y < 4.8e62

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 61.4%

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

      1. associate-/l* 59.9%

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

      2. associate-/r/ 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2050000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.1% 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 1 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 95.5%

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

3. Final simplification 95.5%

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

Alternative 10: 35.7% 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 1 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 95.5%

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

3. Taylor expanded in y around inf 31.7%

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

4. Final simplification 31.7%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.1% 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 2024020 
(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))