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

Percentage Accurate: 96.7% → 96.4%

Time: 13.8s

Alternatives: 16

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: 96.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 1.05 \cdot 10^{+149}:\\ \;\;\;\;t\_m \cdot \frac{x - y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t\_m}}\\ \end{array} \end{array} \]

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 1.05e+149)
    (* 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 <= 1.05e+149) {
		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 <= 1.05d+149) 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 <= 1.05e+149) {
		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 <= 1.05e+149:
		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 <= 1.05e+149)
		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 <= 1.05e+149)
		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, 1.05e+149], 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 < 1.0500000000000001e149

   1. Initial program 96.3%

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

   if 1.0500000000000001e149 < t

   1. Initial program 93.7%

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

      1. associate-/r/ 97.4%

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

   3. Simplified 97.4%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{+149}:\\ \;\;\;\;t \cdot \frac{x - y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := x \cdot \frac{t\_m}{z - y}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+179}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-189}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (* x (/ t_m (- z y)))))
   (*
    t_s
    (if (<= y -3.1e+179)
      t_m
      (if (<= y -7.4e+17)
        t_2
        (if (<= y -5e-189)
          (* (- x y) (/ t_m z))
          (if (<= y 3e+126) t_2 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 t_2 = x * (t_m / (z - y));
	double tmp;
	if (y <= -3.1e+179) {
		tmp = t_m;
	} else if (y <= -7.4e+17) {
		tmp = t_2;
	} else if (y <= -5e-189) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 3e+126) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_2 = x * (t_m / (z - y))
    if (y <= (-3.1d+179)) then
        tmp = t_m
    else if (y <= (-7.4d+17)) then
        tmp = t_2
    else if (y <= (-5d-189)) then
        tmp = (x - y) * (t_m / z)
    else if (y <= 3d+126) then
        tmp = t_2
    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 t_2 = x * (t_m / (z - y));
	double tmp;
	if (y <= -3.1e+179) {
		tmp = t_m;
	} else if (y <= -7.4e+17) {
		tmp = t_2;
	} else if (y <= -5e-189) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 3e+126) {
		tmp = t_2;
	} 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):
	t_2 = x * (t_m / (z - y))
	tmp = 0
	if y <= -3.1e+179:
		tmp = t_m
	elif y <= -7.4e+17:
		tmp = t_2
	elif y <= -5e-189:
		tmp = (x - y) * (t_m / z)
	elif y <= 3e+126:
		tmp = t_2
	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)
	t_2 = Float64(x * Float64(t_m / Float64(z - y)))
	tmp = 0.0
	if (y <= -3.1e+179)
		tmp = t_m;
	elseif (y <= -7.4e+17)
		tmp = t_2;
	elseif (y <= -5e-189)
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	elseif (y <= 3e+126)
		tmp = t_2;
	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)
	t_2 = x * (t_m / (z - y));
	tmp = 0.0;
	if (y <= -3.1e+179)
		tmp = t_m;
	elseif (y <= -7.4e+17)
		tmp = t_2;
	elseif (y <= -5e-189)
		tmp = (x - y) * (t_m / z);
	elseif (y <= 3e+126)
		tmp = t_2;
	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_] := Block[{t$95$2 = N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -3.1e+179], t$95$m, If[LessEqual[y, -7.4e+17], t$95$2, If[LessEqual[y, -5e-189], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+126], t$95$2, t$95$m]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e179 or 3.0000000000000002e126 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 75.4%

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

   if -3.1e179 < y < -7.4e17 or -4.9999999999999997e-189 < y < 3.0000000000000002e126

   1. Initial program 94.4%

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

   3. Taylor expanded in x around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-*r/ 66.7%

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

   5. Simplified 66.7%

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

   if -7.4e17 < y < -4.9999999999999997e-189

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf 76.9%

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

      1. associate-/l* 74.5%

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

      2. associate-/r/ 81.9%

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

   5. Simplified 81.9%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+179}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-189}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := t\_m \cdot \frac{x}{z - y}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+190}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-222}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (/ x (- z y)))))
   (*
    t_s
    (if (<= y -2.6e+190)
      t_m
      (if (<= y -1.76e+17)
        t_2
        (if (<= y 4.2e-222)
          (* (- x y) (/ t_m z))
          (if (<= y 3.6e+129) t_2 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 t_2 = t_m * (x / (z - y));
	double tmp;
	if (y <= -2.6e+190) {
		tmp = t_m;
	} else if (y <= -1.76e+17) {
		tmp = t_2;
	} else if (y <= 4.2e-222) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 3.6e+129) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_2 = t_m * (x / (z - y))
    if (y <= (-2.6d+190)) then
        tmp = t_m
    else if (y <= (-1.76d+17)) then
        tmp = t_2
    else if (y <= 4.2d-222) then
        tmp = (x - y) * (t_m / z)
    else if (y <= 3.6d+129) then
        tmp = t_2
    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 t_2 = t_m * (x / (z - y));
	double tmp;
	if (y <= -2.6e+190) {
		tmp = t_m;
	} else if (y <= -1.76e+17) {
		tmp = t_2;
	} else if (y <= 4.2e-222) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 3.6e+129) {
		tmp = t_2;
	} 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):
	t_2 = t_m * (x / (z - y))
	tmp = 0
	if y <= -2.6e+190:
		tmp = t_m
	elif y <= -1.76e+17:
		tmp = t_2
	elif y <= 4.2e-222:
		tmp = (x - y) * (t_m / z)
	elif y <= 3.6e+129:
		tmp = t_2
	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)
	t_2 = Float64(t_m * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -2.6e+190)
		tmp = t_m;
	elseif (y <= -1.76e+17)
		tmp = t_2;
	elseif (y <= 4.2e-222)
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	elseif (y <= 3.6e+129)
		tmp = t_2;
	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)
	t_2 = t_m * (x / (z - y));
	tmp = 0.0;
	if (y <= -2.6e+190)
		tmp = t_m;
	elseif (y <= -1.76e+17)
		tmp = t_2;
	elseif (y <= 4.2e-222)
		tmp = (x - y) * (t_m / z);
	elseif (y <= 3.6e+129)
		tmp = t_2;
	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_] := Block[{t$95$2 = N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -2.6e+190], t$95$m, If[LessEqual[y, -1.76e+17], t$95$2, If[LessEqual[y, 4.2e-222], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+129], t$95$2, t$95$m]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -2.60000000000000011e190 or 3.6000000000000001e129 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 76.9%

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

   if -2.60000000000000011e190 < y < -1.76e17 or 4.1999999999999998e-222 < y < 3.6000000000000001e129

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 59.3%

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

   if -1.76e17 < y < 4.1999999999999998e-222

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 79.0%

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

      2. associate-/r/ 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-222}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := t\_m \cdot \frac{x}{z - y}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+190}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-228}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_m + \frac{t\_m}{\frac{y}{z}}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (/ x (- z y)))))
   (*
    t_s
    (if (<= y -2.6e+190)
      t_m
      (if (<= y -3.05e+17)
        t_2
        (if (<= y 1.45e-228)
          (* (- x y) (/ t_m z))
          (if (<= y 6.8e+134) t_2 (+ t_m (/ t_m (/ y 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 t_2 = t_m * (x / (z - y));
	double tmp;
	if (y <= -2.6e+190) {
		tmp = t_m;
	} else if (y <= -3.05e+17) {
		tmp = t_2;
	} else if (y <= 1.45e-228) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 6.8e+134) {
		tmp = t_2;
	} else {
		tmp = t_m + (t_m / (y / 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) :: t_2
    real(8) :: tmp
    t_2 = t_m * (x / (z - y))
    if (y <= (-2.6d+190)) then
        tmp = t_m
    else if (y <= (-3.05d+17)) then
        tmp = t_2
    else if (y <= 1.45d-228) then
        tmp = (x - y) * (t_m / z)
    else if (y <= 6.8d+134) then
        tmp = t_2
    else
        tmp = t_m + (t_m / (y / 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 t_2 = t_m * (x / (z - y));
	double tmp;
	if (y <= -2.6e+190) {
		tmp = t_m;
	} else if (y <= -3.05e+17) {
		tmp = t_2;
	} else if (y <= 1.45e-228) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 6.8e+134) {
		tmp = t_2;
	} else {
		tmp = t_m + (t_m / (y / 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):
	t_2 = t_m * (x / (z - y))
	tmp = 0
	if y <= -2.6e+190:
		tmp = t_m
	elif y <= -3.05e+17:
		tmp = t_2
	elif y <= 1.45e-228:
		tmp = (x - y) * (t_m / z)
	elif y <= 6.8e+134:
		tmp = t_2
	else:
		tmp = t_m + (t_m / (y / 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)
	t_2 = Float64(t_m * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -2.6e+190)
		tmp = t_m;
	elseif (y <= -3.05e+17)
		tmp = t_2;
	elseif (y <= 1.45e-228)
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	elseif (y <= 6.8e+134)
		tmp = t_2;
	else
		tmp = Float64(t_m + Float64(t_m / Float64(y / 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)
	t_2 = t_m * (x / (z - y));
	tmp = 0.0;
	if (y <= -2.6e+190)
		tmp = t_m;
	elseif (y <= -3.05e+17)
		tmp = t_2;
	elseif (y <= 1.45e-228)
		tmp = (x - y) * (t_m / z);
	elseif (y <= 6.8e+134)
		tmp = t_2;
	else
		tmp = t_m + (t_m / (y / 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_] := Block[{t$95$2 = N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -2.6e+190], t$95$m, If[LessEqual[y, -3.05e+17], t$95$2, If[LessEqual[y, 1.45e-228], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+134], t$95$2, N[(t$95$m + N[(t$95$m / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -2.60000000000000011e190

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 79.0%

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

   if -2.60000000000000011e190 < y < -3.05e17 or 1.4500000000000001e-228 < y < 6.80000000000000035e134

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 58.7%

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

   if -3.05e17 < y < 1.4500000000000001e-228

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 79.0%

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

      2. associate-/r/ 87.4%

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

   5. Simplified 87.4%

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

   if 6.80000000000000035e134 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 89.3%

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

      1. neg-mul-1 89.3%

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

      2. distribute-neg-frac 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in y around inf 76.8%

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

      1. associate-/l* 78.8%

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

   8. Simplified 78.8%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.05 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-228}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\_m\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-228}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t\_m}}\\ \mathbf{elif}\;y \leq 620000:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+265}:\\ \;\;\;\;\frac{t\_m}{\frac{y - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_m - \frac{t\_m \cdot x}{y}\\ \end{array} \end{array} \]

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 (<= y -2.5e+19)
    (* (+ (/ x y) -1.0) (- t_m))
    (if (<= y -1.9e-228)
      (/ (- x y) (/ z t_m))
      (if (<= y 620000.0)
        (/ (* t_m x) (- z y))
        (if (<= y 3.8e+265) (/ t_m (/ (- y z) y)) (- t_m (/ (* t_m 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 (y <= -2.5e+19) {
		tmp = ((x / y) + -1.0) * -t_m;
	} else if (y <= -1.9e-228) {
		tmp = (x - y) / (z / t_m);
	} else if (y <= 620000.0) {
		tmp = (t_m * x) / (z - y);
	} else if (y <= 3.8e+265) {
		tmp = t_m / ((y - z) / y);
	} else {
		tmp = t_m - ((t_m * 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 (y <= (-2.5d+19)) then
        tmp = ((x / y) + (-1.0d0)) * -t_m
    else if (y <= (-1.9d-228)) then
        tmp = (x - y) / (z / t_m)
    else if (y <= 620000.0d0) then
        tmp = (t_m * x) / (z - y)
    else if (y <= 3.8d+265) then
        tmp = t_m / ((y - z) / y)
    else
        tmp = t_m - ((t_m * 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 (y <= -2.5e+19) {
		tmp = ((x / y) + -1.0) * -t_m;
	} else if (y <= -1.9e-228) {
		tmp = (x - y) / (z / t_m);
	} else if (y <= 620000.0) {
		tmp = (t_m * x) / (z - y);
	} else if (y <= 3.8e+265) {
		tmp = t_m / ((y - z) / y);
	} else {
		tmp = t_m - ((t_m * 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 y <= -2.5e+19:
		tmp = ((x / y) + -1.0) * -t_m
	elif y <= -1.9e-228:
		tmp = (x - y) / (z / t_m)
	elif y <= 620000.0:
		tmp = (t_m * x) / (z - y)
	elif y <= 3.8e+265:
		tmp = t_m / ((y - z) / y)
	else:
		tmp = t_m - ((t_m * 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 (y <= -2.5e+19)
		tmp = Float64(Float64(Float64(x / y) + -1.0) * Float64(-t_m));
	elseif (y <= -1.9e-228)
		tmp = Float64(Float64(x - y) / Float64(z / t_m));
	elseif (y <= 620000.0)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	elseif (y <= 3.8e+265)
		tmp = Float64(t_m / Float64(Float64(y - z) / y));
	else
		tmp = Float64(t_m - Float64(Float64(t_m * 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 (y <= -2.5e+19)
		tmp = ((x / y) + -1.0) * -t_m;
	elseif (y <= -1.9e-228)
		tmp = (x - y) / (z / t_m);
	elseif (y <= 620000.0)
		tmp = (t_m * x) / (z - y);
	elseif (y <= 3.8e+265)
		tmp = t_m / ((y - z) / y);
	else
		tmp = t_m - ((t_m * 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[LessEqual[y, -2.5e+19], N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * (-t$95$m)), $MachinePrecision], If[LessEqual[y, -1.9e-228], N[(N[(x - y), $MachinePrecision] / N[(z / t$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 620000.0], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+265], N[(t$95$m / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t$95$m - N[(N[(t$95$m * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -2.5e19

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. div-sub 82.4%

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

      3. sub-neg 82.4%

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

      4. *-inverses 82.4%

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

      5. metadata-eval 82.4%

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

   5. Simplified 82.4%

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

   if -2.5e19 < y < -1.8999999999999999e-228

   1. Initial program 94.5%

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

      1. associate-/r/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 84.1%

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

   if -1.8999999999999999e-228 < y < 6.2e5

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 85.4%

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

   if 6.2e5 < y < 3.80000000000000015e265

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 76.4%

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

      1. neg-mul-1 76.4%

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

      2. distribute-neg-frac 76.4%

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

   5. Simplified 76.4%

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

      1. distribute-frac-neg 76.4%

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

      2. frac-2neg 76.4%

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

      3. distribute-frac-neg 76.4%

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

      4. remove-double-neg 76.4%

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

      5. associate-*l/ 56.8%

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

      6. sub-neg 56.8%

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

      7. distribute-neg-in 56.8%

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

      8. remove-double-neg 56.8%

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

   7. Applied egg-rr 56.8%

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

      1. *-commutative 56.8%

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

      2. associate-/l* 76.4%

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

      3. +-commutative 76.4%

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

      4. unsub-neg 76.4%

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

   9. Simplified 76.4%

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

   if 3.80000000000000015e265 < y

   1. Initial program 99.8%

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

      1. associate-/r/ 40.7%

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

      2. div-inv 40.6%

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

      3. associate-/r* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. associate-/l* 99.8%

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

      3. distribute-neg-frac 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r/ 94.0%

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

      4. unsub-neg 94.0%

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

      5. associate-*r/ 99.8%

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

      6. *-commutative 99.8%

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

   10. Simplified 99.8%

       \[\leadsto \color{blue}{t - \frac{t \cdot x}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-228}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 620000:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+265}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+28}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_m}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+113}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+155}:\\ \;\;\;\;t\_m \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

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 -6.6e+28)
    t_m
    (if (<= y 7.8e+21)
      (/ x (/ z t_m))
      (if (<= y 1.45e+113)
        t_m
        (if (<= y 1.82e+155) (* t_m (/ (- y) 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 <= -6.6e+28) {
		tmp = t_m;
	} else if (y <= 7.8e+21) {
		tmp = x / (z / t_m);
	} else if (y <= 1.45e+113) {
		tmp = t_m;
	} else if (y <= 1.82e+155) {
		tmp = t_m * (-y / 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 <= (-6.6d+28)) then
        tmp = t_m
    else if (y <= 7.8d+21) then
        tmp = x / (z / t_m)
    else if (y <= 1.45d+113) then
        tmp = t_m
    else if (y <= 1.82d+155) then
        tmp = t_m * (-y / 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 <= -6.6e+28) {
		tmp = t_m;
	} else if (y <= 7.8e+21) {
		tmp = x / (z / t_m);
	} else if (y <= 1.45e+113) {
		tmp = t_m;
	} else if (y <= 1.82e+155) {
		tmp = t_m * (-y / 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 <= -6.6e+28:
		tmp = t_m
	elif y <= 7.8e+21:
		tmp = x / (z / t_m)
	elif y <= 1.45e+113:
		tmp = t_m
	elif y <= 1.82e+155:
		tmp = t_m * (-y / 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 <= -6.6e+28)
		tmp = t_m;
	elseif (y <= 7.8e+21)
		tmp = Float64(x / Float64(z / t_m));
	elseif (y <= 1.45e+113)
		tmp = t_m;
	elseif (y <= 1.82e+155)
		tmp = Float64(t_m * Float64(Float64(-y) / 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 <= -6.6e+28)
		tmp = t_m;
	elseif (y <= 7.8e+21)
		tmp = x / (z / t_m);
	elseif (y <= 1.45e+113)
		tmp = t_m;
	elseif (y <= 1.82e+155)
		tmp = t_m * (-y / 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, -6.6e+28], t$95$m, If[LessEqual[y, 7.8e+21], N[(x / N[(z / t$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+113], t$95$m, If[LessEqual[y, 1.82e+155], N[(t$95$m * N[((-y) / z), $MachinePrecision]), $MachinePrecision], t$95$m]]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -6.6e28 or 7.8e21 < y < 1.44999999999999992e113 or 1.81999999999999989e155 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 63.6%

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

   if -6.6e28 < y < 7.8e21

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 66.2%

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

      1. associate-/l* 64.6%

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

      2. associate-/r/ 67.7%

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

   5. Simplified 67.7%

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

      1. *-commutative 67.7%

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

      2. clear-num 67.7%

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

      3. un-div-inv 67.8%

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

   7. Applied egg-rr 67.8%

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

   if 1.44999999999999992e113 < y < 1.81999999999999989e155

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 67.1%

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

      1. neg-mul-1 67.1%

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

      2. distribute-neg-frac 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in y around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-neg-frac 49.9%

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

   8. Simplified 49.9%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{+28}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_m}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+110}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+155}:\\ \;\;\;\;\frac{t\_m}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

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 -7.9e+28)
    t_m
    (if (<= y 5.5e+21)
      (/ x (/ z t_m))
      (if (<= y 9.4e+110)
        t_m
        (if (<= y 1.75e+155) (/ 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 <= -7.9e+28) {
		tmp = t_m;
	} else if (y <= 5.5e+21) {
		tmp = x / (z / t_m);
	} else if (y <= 9.4e+110) {
		tmp = t_m;
	} else if (y <= 1.75e+155) {
		tmp = 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 <= (-7.9d+28)) then
        tmp = t_m
    else if (y <= 5.5d+21) then
        tmp = x / (z / t_m)
    else if (y <= 9.4d+110) then
        tmp = t_m
    else if (y <= 1.75d+155) then
        tmp = 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 <= -7.9e+28) {
		tmp = t_m;
	} else if (y <= 5.5e+21) {
		tmp = x / (z / t_m);
	} else if (y <= 9.4e+110) {
		tmp = t_m;
	} else if (y <= 1.75e+155) {
		tmp = 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 <= -7.9e+28:
		tmp = t_m
	elif y <= 5.5e+21:
		tmp = x / (z / t_m)
	elif y <= 9.4e+110:
		tmp = t_m
	elif y <= 1.75e+155:
		tmp = 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 <= -7.9e+28)
		tmp = t_m;
	elseif (y <= 5.5e+21)
		tmp = Float64(x / Float64(z / t_m));
	elseif (y <= 9.4e+110)
		tmp = t_m;
	elseif (y <= 1.75e+155)
		tmp = Float64(t_m / Float64(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 <= -7.9e+28)
		tmp = t_m;
	elseif (y <= 5.5e+21)
		tmp = x / (z / t_m);
	elseif (y <= 9.4e+110)
		tmp = t_m;
	elseif (y <= 1.75e+155)
		tmp = 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, -7.9e+28], t$95$m, If[LessEqual[y, 5.5e+21], N[(x / N[(z / t$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e+110], t$95$m, If[LessEqual[y, 1.75e+155], N[(t$95$m / N[((-z) / y), $MachinePrecision]), $MachinePrecision], t$95$m]]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -7.8999999999999997e28 or 5.5e21 < y < 9.3999999999999996e110 or 1.74999999999999992e155 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 63.6%

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

   if -7.8999999999999997e28 < y < 5.5e21

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 66.2%

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

      1. associate-/l* 64.6%

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

      2. associate-/r/ 67.7%

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

   5. Simplified 67.7%

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

      1. *-commutative 67.7%

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

      2. clear-num 67.7%

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

      3. un-div-inv 67.8%

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

   7. Applied egg-rr 67.8%

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

   if 9.3999999999999996e110 < y < 1.74999999999999992e155

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 42.4%

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

      1. associate-/l* 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in x around 0 50.0%

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

      1. associate-*r/ 50.0%

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

      2. neg-mul-1 50.0%

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

   8. Simplified 50.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+155}:\\ \;\;\;\;\frac{t}{\frac{-z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;t\_m - \frac{t\_m \cdot x}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-230}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

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 (<= y -3.1e+19)
    (- t_m (/ (* t_m x) y))
    (if (<= y 5.2e-230)
      (* (- x y) (/ t_m z))
      (if (<= y 160000.0) (* t_m (/ x (- z y))) (/ t_m (/ (- 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 (y <= -3.1e+19) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= 5.2e-230) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 160000.0) {
		tmp = t_m * (x / (z - y));
	} else {
		tmp = t_m / ((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 (y <= (-3.1d+19)) then
        tmp = t_m - ((t_m * x) / y)
    else if (y <= 5.2d-230) then
        tmp = (x - y) * (t_m / z)
    else if (y <= 160000.0d0) then
        tmp = t_m * (x / (z - y))
    else
        tmp = t_m / ((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 (y <= -3.1e+19) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= 5.2e-230) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 160000.0) {
		tmp = t_m * (x / (z - y));
	} else {
		tmp = t_m / ((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 y <= -3.1e+19:
		tmp = t_m - ((t_m * x) / y)
	elif y <= 5.2e-230:
		tmp = (x - y) * (t_m / z)
	elif y <= 160000.0:
		tmp = t_m * (x / (z - y))
	else:
		tmp = t_m / ((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 (y <= -3.1e+19)
		tmp = Float64(t_m - Float64(Float64(t_m * x) / y));
	elseif (y <= 5.2e-230)
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	elseif (y <= 160000.0)
		tmp = Float64(t_m * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t_m / Float64(Float64(y - 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 <= -3.1e+19)
		tmp = t_m - ((t_m * x) / y);
	elseif (y <= 5.2e-230)
		tmp = (x - y) * (t_m / z);
	elseif (y <= 160000.0)
		tmp = t_m * (x / (z - y));
	else
		tmp = t_m / ((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[y, -3.1e+19], N[(t$95$m - N[(N[(t$95$m * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-230], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 160000.0], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -3.1e19

   1. Initial program 99.8%

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

      1. associate-/r/ 79.8%

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

      2. div-inv 79.7%

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

      3. associate-/r* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-/l* 82.3%

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

      3. distribute-neg-frac 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r/ 79.1%

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

      4. unsub-neg 79.1%

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

      5. associate-*r/ 78.1%

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

      6. *-commutative 78.1%

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

   10. Simplified 78.1%

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

   if -3.1e19 < y < 5.2000000000000003e-230

   1. Initial program 87.4%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 79.0%

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

      2. associate-/r/ 87.4%

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

   5. Simplified 87.4%

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

   if 5.2000000000000003e-230 < y < 1.6e5

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 78.7%

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

   if 1.6e5 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. neg-mul-1 78.7%

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

      2. distribute-neg-frac 78.7%

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

   5. Simplified 78.7%

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

      1. distribute-frac-neg 78.7%

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

      2. frac-2neg 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. remove-double-neg 78.7%

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

      5. associate-*l/ 58.3%

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

      6. sub-neg 58.3%

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

      7. distribute-neg-in 58.3%

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

      8. remove-double-neg 58.3%

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

   7. Applied egg-rr 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-/l* 78.8%

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

      3. +-commutative 78.8%

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

      4. unsub-neg 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-230}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 160000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+16}:\\ \;\;\;\;t\_m - \frac{t\_m \cdot x}{y}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-228}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \mathbf{elif}\;y \leq 1500000:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

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 (<= y -9e+16)
    (- t_m (/ (* t_m x) y))
    (if (<= y -7.6e-228)
      (* (- x y) (/ t_m z))
      (if (<= y 1500000.0) (/ (* t_m x) (- z y)) (/ t_m (/ (- 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 (y <= -9e+16) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= -7.6e-228) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 1500000.0) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_m / ((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 (y <= (-9d+16)) then
        tmp = t_m - ((t_m * x) / y)
    else if (y <= (-7.6d-228)) then
        tmp = (x - y) * (t_m / z)
    else if (y <= 1500000.0d0) then
        tmp = (t_m * x) / (z - y)
    else
        tmp = t_m / ((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 (y <= -9e+16) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= -7.6e-228) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 1500000.0) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_m / ((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 y <= -9e+16:
		tmp = t_m - ((t_m * x) / y)
	elif y <= -7.6e-228:
		tmp = (x - y) * (t_m / z)
	elif y <= 1500000.0:
		tmp = (t_m * x) / (z - y)
	else:
		tmp = t_m / ((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 (y <= -9e+16)
		tmp = Float64(t_m - Float64(Float64(t_m * x) / y));
	elseif (y <= -7.6e-228)
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	elseif (y <= 1500000.0)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	else
		tmp = Float64(t_m / Float64(Float64(y - 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 <= -9e+16)
		tmp = t_m - ((t_m * x) / y);
	elseif (y <= -7.6e-228)
		tmp = (x - y) * (t_m / z);
	elseif (y <= 1500000.0)
		tmp = (t_m * x) / (z - y);
	else
		tmp = t_m / ((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[y, -9e+16], N[(t$95$m - N[(N[(t$95$m * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-228], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1500000.0], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -9e16

   1. Initial program 99.8%

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

      1. associate-/r/ 79.8%

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

      2. div-inv 79.7%

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

      3. associate-/r* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-/l* 82.3%

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

      3. distribute-neg-frac 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r/ 79.1%

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

      4. unsub-neg 79.1%

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

      5. associate-*r/ 78.1%

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

      6. *-commutative 78.1%

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

   10. Simplified 78.1%

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

   if -9e16 < y < -7.5999999999999997e-228

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. associate-/l* 77.4%

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

      2. associate-/r/ 84.0%

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

   5. Simplified 84.0%

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

   if -7.5999999999999997e-228 < y < 1.5e6

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 85.4%

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

   if 1.5e6 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. neg-mul-1 78.7%

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

      2. distribute-neg-frac 78.7%

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

   5. Simplified 78.7%

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

      1. distribute-frac-neg 78.7%

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

      2. frac-2neg 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. remove-double-neg 78.7%

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

      5. associate-*l/ 58.3%

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

      6. sub-neg 58.3%

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

      7. distribute-neg-in 58.3%

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

      8. remove-double-neg 58.3%

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

   7. Applied egg-rr 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-/l* 78.8%

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

      3. +-commutative 78.8%

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

      4. unsub-neg 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+16}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-228}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1500000:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+19}:\\ \;\;\;\;t\_m - \frac{t\_m \cdot x}{y}\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-227}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t\_m}}\\ \mathbf{elif}\;y \leq 155000:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

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 (<= y -1.38e+19)
    (- t_m (/ (* t_m x) y))
    (if (<= y -2.85e-227)
      (/ (- x y) (/ z t_m))
      (if (<= y 155000.0) (/ (* t_m x) (- z y)) (/ t_m (/ (- 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 (y <= -1.38e+19) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= -2.85e-227) {
		tmp = (x - y) / (z / t_m);
	} else if (y <= 155000.0) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_m / ((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 (y <= (-1.38d+19)) then
        tmp = t_m - ((t_m * x) / y)
    else if (y <= (-2.85d-227)) then
        tmp = (x - y) / (z / t_m)
    else if (y <= 155000.0d0) then
        tmp = (t_m * x) / (z - y)
    else
        tmp = t_m / ((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 (y <= -1.38e+19) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= -2.85e-227) {
		tmp = (x - y) / (z / t_m);
	} else if (y <= 155000.0) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_m / ((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 y <= -1.38e+19:
		tmp = t_m - ((t_m * x) / y)
	elif y <= -2.85e-227:
		tmp = (x - y) / (z / t_m)
	elif y <= 155000.0:
		tmp = (t_m * x) / (z - y)
	else:
		tmp = t_m / ((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 (y <= -1.38e+19)
		tmp = Float64(t_m - Float64(Float64(t_m * x) / y));
	elseif (y <= -2.85e-227)
		tmp = Float64(Float64(x - y) / Float64(z / t_m));
	elseif (y <= 155000.0)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	else
		tmp = Float64(t_m / Float64(Float64(y - 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 <= -1.38e+19)
		tmp = t_m - ((t_m * x) / y);
	elseif (y <= -2.85e-227)
		tmp = (x - y) / (z / t_m);
	elseif (y <= 155000.0)
		tmp = (t_m * x) / (z - y);
	else
		tmp = t_m / ((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[y, -1.38e+19], N[(t$95$m - N[(N[(t$95$m * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.85e-227], N[(N[(x - y), $MachinePrecision] / N[(z / t$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 155000.0], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -1.38e19

   1. Initial program 99.8%

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

      1. associate-/r/ 79.8%

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

      2. div-inv 79.7%

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

      3. associate-/r* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-/l* 82.3%

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

      3. distribute-neg-frac 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*r/ 79.1%

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

      4. unsub-neg 79.1%

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

      5. associate-*r/ 78.1%

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

      6. *-commutative 78.1%

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

   10. Simplified 78.1%

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

   if -1.38e19 < y < -2.84999999999999995e-227

   1. Initial program 94.5%

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

      1. associate-/r/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 84.1%

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

   if -2.84999999999999995e-227 < y < 155000

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 85.4%

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

   if 155000 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 78.7%

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

      1. neg-mul-1 78.7%

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

      2. distribute-neg-frac 78.7%

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

   5. Simplified 78.7%

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

      1. distribute-frac-neg 78.7%

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

      2. frac-2neg 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. remove-double-neg 78.7%

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

      5. associate-*l/ 58.3%

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

      6. sub-neg 58.3%

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

      7. distribute-neg-in 58.3%

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

      8. remove-double-neg 58.3%

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

   7. Applied egg-rr 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-/l* 78.8%

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

      3. +-commutative 78.8%

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

      4. unsub-neg 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+19}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-227}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 155000:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+18} \lor \neg \left(y \leq 3.15 \cdot 10^{-83}\right):\\ \;\;\;\;t\_m - \frac{t\_m \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \end{array} \end{array} \]

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 -5.6e+18) (not (<= y 3.15e-83)))
    (- t_m (/ (* t_m 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 <= -5.6e+18) || !(y <= 3.15e-83)) {
		tmp = t_m - ((t_m * 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 <= (-5.6d+18)) .or. (.not. (y <= 3.15d-83))) then
        tmp = t_m - ((t_m * 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 <= -5.6e+18) || !(y <= 3.15e-83)) {
		tmp = t_m - ((t_m * 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 <= -5.6e+18) or not (y <= 3.15e-83):
		tmp = t_m - ((t_m * 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 <= -5.6e+18) || !(y <= 3.15e-83))
		tmp = Float64(t_m - Float64(Float64(t_m * 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 <= -5.6e+18) || ~((y <= 3.15e-83)))
		tmp = t_m - ((t_m * 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, -5.6e+18], N[Not[LessEqual[y, 3.15e-83]], $MachinePrecision]], N[(t$95$m - N[(N[(t$95$m * x), $MachinePrecision] / y), $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 < -5.6e18 or 3.14999999999999983e-83 < y

   1. Initial program 99.7%

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

      1. associate-/r/ 75.4%

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

      2. div-inv 75.2%

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

      3. associate-/r* 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. associate-/l* 78.6%

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

      3. distribute-neg-frac 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in y around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*r/ 76.7%

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

      4. unsub-neg 76.7%

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

      5. associate-*r/ 75.7%

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

      6. *-commutative 75.7%

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

   10. Simplified 75.7%

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

   if -5.6e18 < y < 3.14999999999999983e-83

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 81.5%

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

      1. associate-/l* 78.5%

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

      2. associate-/r/ 84.2%

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

   5. Simplified 84.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+18} \lor \neg \left(y \leq 3.15 \cdot 10^{-83}\right):\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+179}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

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 -3.1e+179) t_m (if (<= y 3.4e+126) (* 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 <= -3.1e+179) {
		tmp = t_m;
	} else if (y <= 3.4e+126) {
		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 <= (-3.1d+179)) then
        tmp = t_m
    else if (y <= 3.4d+126) 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 <= -3.1e+179) {
		tmp = t_m;
	} else if (y <= 3.4e+126) {
		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 <= -3.1e+179:
		tmp = t_m
	elif y <= 3.4e+126:
		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 <= -3.1e+179)
		tmp = t_m;
	elseif (y <= 3.4e+126)
		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 <= -3.1e+179)
		tmp = t_m;
	elseif (y <= 3.4e+126)
		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, -3.1e+179], t$95$m, If[LessEqual[y, 3.4e+126], 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 < -3.1e179 or 3.39999999999999989e126 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 75.4%

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

   if -3.1e179 < y < 3.39999999999999989e126

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. associate-*r/ 66.4%

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

   5. Simplified 66.4%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+179}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{t\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

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 -1e+29) t_m (if (<= y 8.6e+21) (* 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 <= -1e+29) {
		tmp = t_m;
	} else if (y <= 8.6e+21) {
		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 <= (-1d+29)) then
        tmp = t_m
    else if (y <= 8.6d+21) 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 <= -1e+29) {
		tmp = t_m;
	} else if (y <= 8.6e+21) {
		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 <= -1e+29:
		tmp = t_m
	elif y <= 8.6e+21:
		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 <= -1e+29)
		tmp = t_m;
	elseif (y <= 8.6e+21)
		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 <= -1e+29)
		tmp = t_m;
	elseif (y <= 8.6e+21)
		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, -1e+29], t$95$m, If[LessEqual[y, 8.6e+21], N[(x * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999914e28 or 8.6e21 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 59.1%

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

   if -9.99999999999999914e28 < y < 8.6e21

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 66.2%

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

      1. associate-/l* 64.6%

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

      2. associate-/r/ 67.7%

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

   5. Simplified 67.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+28}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{\frac{z}{t\_m}}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

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 -6.7e+28) t_m (if (<= y 1.55e+22) (/ x (/ z t_m)) 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 <= -6.7e+28) {
		tmp = t_m;
	} else if (y <= 1.55e+22) {
		tmp = x / (z / t_m);
	} 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 <= (-6.7d+28)) then
        tmp = t_m
    else if (y <= 1.55d+22) then
        tmp = x / (z / t_m)
    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 <= -6.7e+28) {
		tmp = t_m;
	} else if (y <= 1.55e+22) {
		tmp = x / (z / t_m);
	} 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 <= -6.7e+28:
		tmp = t_m
	elif y <= 1.55e+22:
		tmp = x / (z / t_m)
	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 <= -6.7e+28)
		tmp = t_m;
	elseif (y <= 1.55e+22)
		tmp = Float64(x / Float64(z / t_m));
	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 <= -6.7e+28)
		tmp = t_m;
	elseif (y <= 1.55e+22)
		tmp = x / (z / t_m);
	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, -6.7e+28], t$95$m, If[LessEqual[y, 1.55e+22], N[(x / N[(z / t$95$m), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.7e28 or 1.5500000000000001e22 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 59.1%

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

   if -6.7e28 < y < 1.5500000000000001e22

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0 66.2%

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

      1. associate-/l* 64.6%

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

      2. associate-/r/ 67.7%

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

   5. Simplified 67.7%

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

      1. *-commutative 67.7%

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

      2. clear-num 67.7%

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

      3. un-div-inv 67.8%

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

   7. Applied egg-rr 67.8%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 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 96.0%

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

3. Final simplification 96.0%

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

Alternative 16: 35.1% 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 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 96.0%

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

3. Taylor expanded in y around inf 36.7%

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

4. Final simplification 36.7%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 96.8% 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 2024036 
(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))