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

Percentage Accurate: 96.8% → 97.3%

Time: 11.9s

Alternatives: 12

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x - y) / (z - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x - y) / (z - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+136}:\\ \;\;\;\;t\_1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e+136) (* t_1 t) (* x (/ t (- z y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e+136) {
		tmp = t_1 * t;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d+136) then
        tmp = t_1 * t
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e+136) {
		tmp = t_1 * t;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e+136:
		tmp = t_1 * t
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e+136)
		tmp = Float64(t_1 * t);
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e+136)
		tmp = t_1 * t;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+136], N[(t$95$1 * t), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000002e136

   1. Initial program 97.7%

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

   if 5.0000000000000002e136 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 78.2%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*r/ 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+136}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.085:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- z y)))))
   (if (<= y -1.4e+55)
     t
     (if (<= y -0.085)
       t_1
       (if (<= y -7.8e-29)
         t
         (if (<= y -1.45e-196)
           t_1
           (if (<= y 2.7e-261) (/ (* x t) z) (if (<= y 3.15e+66) t_1 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double tmp;
	if (y <= -1.4e+55) {
		tmp = t;
	} else if (y <= -0.085) {
		tmp = t_1;
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= -1.45e-196) {
		tmp = t_1;
	} else if (y <= 2.7e-261) {
		tmp = (x * t) / z;
	} else if (y <= 3.15e+66) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z - y))
    if (y <= (-1.4d+55)) then
        tmp = t
    else if (y <= (-0.085d0)) then
        tmp = t_1
    else if (y <= (-7.8d-29)) then
        tmp = t
    else if (y <= (-1.45d-196)) then
        tmp = t_1
    else if (y <= 2.7d-261) then
        tmp = (x * t) / z
    else if (y <= 3.15d+66) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double tmp;
	if (y <= -1.4e+55) {
		tmp = t;
	} else if (y <= -0.085) {
		tmp = t_1;
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= -1.45e-196) {
		tmp = t_1;
	} else if (y <= 2.7e-261) {
		tmp = (x * t) / z;
	} else if (y <= 3.15e+66) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z - y))
	tmp = 0
	if y <= -1.4e+55:
		tmp = t
	elif y <= -0.085:
		tmp = t_1
	elif y <= -7.8e-29:
		tmp = t
	elif y <= -1.45e-196:
		tmp = t_1
	elif y <= 2.7e-261:
		tmp = (x * t) / z
	elif y <= 3.15e+66:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.4e+55)
		tmp = t;
	elseif (y <= -0.085)
		tmp = t_1;
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= -1.45e-196)
		tmp = t_1;
	elseif (y <= 2.7e-261)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 3.15e+66)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z - y));
	tmp = 0.0;
	if (y <= -1.4e+55)
		tmp = t;
	elseif (y <= -0.085)
		tmp = t_1;
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= -1.45e-196)
		tmp = t_1;
	elseif (y <= 2.7e-261)
		tmp = (x * t) / z;
	elseif (y <= 3.15e+66)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+55], t, If[LessEqual[y, -0.085], t$95$1, If[LessEqual[y, -7.8e-29], t, If[LessEqual[y, -1.45e-196], t$95$1, If[LessEqual[y, 2.7e-261], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3.15e+66], t$95$1, t]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e55 or -0.0850000000000000061 < y < -7.7999999999999995e-29 or 3.1499999999999999e66 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.5%

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

   if -1.4e55 < y < -0.0850000000000000061 or -7.7999999999999995e-29 < y < -1.44999999999999994e-196 or 2.6999999999999999e-261 < y < 3.1499999999999999e66

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*r/ 77.3%

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

   5. Simplified 77.3%

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

   if -1.44999999999999994e-196 < y < 2.6999999999999999e-261

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0 91.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.085:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z - y}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -0.7:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- z y)))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -5.5e+51)
     t_2
     (if (<= y -0.7)
       t_1
       (if (<= y -7.8e-29)
         t
         (if (<= y -1.45e-196)
           t_1
           (if (<= y 6.4e-261) (/ (* x t) z) (if (<= y 6.4e-67) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5.5e+51) {
		tmp = t_2;
	} else if (y <= -0.7) {
		tmp = t_1;
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= -1.45e-196) {
		tmp = t_1;
	} else if (y <= 6.4e-261) {
		tmp = (x * t) / z;
	} else if (y <= 6.4e-67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t / (z - y))
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-5.5d+51)) then
        tmp = t_2
    else if (y <= (-0.7d0)) then
        tmp = t_1
    else if (y <= (-7.8d-29)) then
        tmp = t
    else if (y <= (-1.45d-196)) then
        tmp = t_1
    else if (y <= 6.4d-261) then
        tmp = (x * t) / z
    else if (y <= 6.4d-67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5.5e+51) {
		tmp = t_2;
	} else if (y <= -0.7) {
		tmp = t_1;
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= -1.45e-196) {
		tmp = t_1;
	} else if (y <= 6.4e-261) {
		tmp = (x * t) / z;
	} else if (y <= 6.4e-67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z - y))
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -5.5e+51:
		tmp = t_2
	elif y <= -0.7:
		tmp = t_1
	elif y <= -7.8e-29:
		tmp = t
	elif y <= -1.45e-196:
		tmp = t_1
	elif y <= 6.4e-261:
		tmp = (x * t) / z
	elif y <= 6.4e-67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z - y)))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -5.5e+51)
		tmp = t_2;
	elseif (y <= -0.7)
		tmp = t_1;
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= -1.45e-196)
		tmp = t_1;
	elseif (y <= 6.4e-261)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 6.4e-67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z - y));
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -5.5e+51)
		tmp = t_2;
	elseif (y <= -0.7)
		tmp = t_1;
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= -1.45e-196)
		tmp = t_1;
	elseif (y <= 6.4e-261)
		tmp = (x * t) / z;
	elseif (y <= 6.4e-67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+51], t$95$2, If[LessEqual[y, -0.7], t$95$1, If[LessEqual[y, -7.8e-29], t, If[LessEqual[y, -1.45e-196], t$95$1, If[LessEqual[y, 6.4e-261], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.4e-67], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5e51 or 6.40000000000000043e-67 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 74.6%

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

      1. associate-*r/ 74.6%

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

      2. neg-mul-1 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in x around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. unsub-neg 74.6%

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

   8. Simplified 74.6%

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

   if -5.5e51 < y < -0.69999999999999996 or -7.7999999999999995e-29 < y < -1.44999999999999994e-196 or 6.40000000000000008e-261 < y < 6.40000000000000043e-67

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r/ 81.4%

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

   5. Simplified 81.4%

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

   if -0.69999999999999996 < y < -7.7999999999999995e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.6%

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

   if -1.44999999999999994e-196 < y < 6.40000000000000008e-261

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0 91.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -0.7:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-196}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.105:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e+51)
   t
   (if (<= y -0.105)
     (/ t (/ z x))
     (if (<= y -7.8e-29)
       t
       (if (<= y 5.8e-260)
         (/ (* x t) z)
         (if (<= y 7.1e-7)
           (* x (/ t z))
           (if (<= y 2e+86) (/ (- (* y t)) z) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e+51) {
		tmp = t;
	} else if (y <= -0.105) {
		tmp = t / (z / x);
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= 5.8e-260) {
		tmp = (x * t) / z;
	} else if (y <= 7.1e-7) {
		tmp = x * (t / z);
	} else if (y <= 2e+86) {
		tmp = -(y * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.2d+51)) then
        tmp = t
    else if (y <= (-0.105d0)) then
        tmp = t / (z / x)
    else if (y <= (-7.8d-29)) then
        tmp = t
    else if (y <= 5.8d-260) then
        tmp = (x * t) / z
    else if (y <= 7.1d-7) then
        tmp = x * (t / z)
    else if (y <= 2d+86) then
        tmp = -(y * t) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e+51) {
		tmp = t;
	} else if (y <= -0.105) {
		tmp = t / (z / x);
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= 5.8e-260) {
		tmp = (x * t) / z;
	} else if (y <= 7.1e-7) {
		tmp = x * (t / z);
	} else if (y <= 2e+86) {
		tmp = -(y * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e+51:
		tmp = t
	elif y <= -0.105:
		tmp = t / (z / x)
	elif y <= -7.8e-29:
		tmp = t
	elif y <= 5.8e-260:
		tmp = (x * t) / z
	elif y <= 7.1e-7:
		tmp = x * (t / z)
	elif y <= 2e+86:
		tmp = -(y * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e+51)
		tmp = t;
	elseif (y <= -0.105)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= 5.8e-260)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 7.1e-7)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 2e+86)
		tmp = Float64(Float64(-Float64(y * t)) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.2e+51)
		tmp = t;
	elseif (y <= -0.105)
		tmp = t / (z / x);
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= 5.8e-260)
		tmp = (x * t) / z;
	elseif (y <= 7.1e-7)
		tmp = x * (t / z);
	elseif (y <= 2e+86)
		tmp = -(y * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e+51], t, If[LessEqual[y, -0.105], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.8e-29], t, If[LessEqual[y, 5.8e-260], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7.1e-7], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+86], N[((-N[(y * t), $MachinePrecision]) / z), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.20000000000000022e51 or -0.104999999999999996 < y < -7.7999999999999995e-29 or 2e86 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.7%

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

   if -7.20000000000000022e51 < y < -0.104999999999999996

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 44.1%

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

      1. associate-/l* 59.7%

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

   5. Simplified 59.7%

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

   if -7.7999999999999995e-29 < y < 5.7999999999999999e-260

   1. Initial program 89.3%

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

   3. Taylor expanded in y around 0 69.9%

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

   if 5.7999999999999999e-260 < y < 7.0999999999999998e-7

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 54.9%

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

      1. associate-/l* 59.5%

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

      2. associate-/r/ 62.9%

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

   5. Simplified 62.9%

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

   if 7.0999999999999998e-7 < y < 2e86

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 55.4%

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

      1. associate-/l* 55.4%

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

   5. Simplified 55.4%

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

   6. Taylor expanded in x around 0 43.1%

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

      1. mul-1-neg 43.1%

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

   8. Simplified 43.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.105:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-67}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))) (t_2 (* x (/ t (- z y)))))
   (if (<= y -1.8e+56)
     t_1
     (if (<= y -6e-32)
       (* y (/ t (- y z)))
       (if (<= y -1.6e-195)
         t_2
         (if (<= y 3.7e-261) (/ (* x t) z) (if (<= y 7.5e-67) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -1.8e+56) {
		tmp = t_1;
	} else if (y <= -6e-32) {
		tmp = y * (t / (y - z));
	} else if (y <= -1.6e-195) {
		tmp = t_2;
	} else if (y <= 3.7e-261) {
		tmp = (x * t) / z;
	} else if (y <= 7.5e-67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    t_2 = x * (t / (z - y))
    if (y <= (-1.8d+56)) then
        tmp = t_1
    else if (y <= (-6d-32)) then
        tmp = y * (t / (y - z))
    else if (y <= (-1.6d-195)) then
        tmp = t_2
    else if (y <= 3.7d-261) then
        tmp = (x * t) / z
    else if (y <= 7.5d-67) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -1.8e+56) {
		tmp = t_1;
	} else if (y <= -6e-32) {
		tmp = y * (t / (y - z));
	} else if (y <= -1.6e-195) {
		tmp = t_2;
	} else if (y <= 3.7e-261) {
		tmp = (x * t) / z;
	} else if (y <= 7.5e-67) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	t_2 = x * (t / (z - y))
	tmp = 0
	if y <= -1.8e+56:
		tmp = t_1
	elif y <= -6e-32:
		tmp = y * (t / (y - z))
	elif y <= -1.6e-195:
		tmp = t_2
	elif y <= 3.7e-261:
		tmp = (x * t) / z
	elif y <= 7.5e-67:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.8e+56)
		tmp = t_1;
	elseif (y <= -6e-32)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= -1.6e-195)
		tmp = t_2;
	elseif (y <= 3.7e-261)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 7.5e-67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (y <= -1.8e+56)
		tmp = t_1;
	elseif (y <= -6e-32)
		tmp = y * (t / (y - z));
	elseif (y <= -1.6e-195)
		tmp = t_2;
	elseif (y <= 3.7e-261)
		tmp = (x * t) / z;
	elseif (y <= 7.5e-67)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+56], t$95$1, If[LessEqual[y, -6e-32], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-195], t$95$2, If[LessEqual[y, 3.7e-261], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7.5e-67], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.79999999999999999e56 or 7.5000000000000005e-67 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. neg-mul-1 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. unsub-neg 75.1%

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

   8. Simplified 75.1%

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

   if -1.79999999999999999e56 < y < -6.0000000000000001e-32

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 70.2%

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

      1. neg-mul-1 70.2%

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

      2. distribute-neg-frac 70.2%

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

   5. Simplified 70.2%

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

      1. frac-2neg 70.2%

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

      2. remove-double-neg 70.2%

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

      3. associate-*l/ 70.2%

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

      4. sub-neg 70.2%

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

      5. distribute-neg-in 70.2%

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

      6. remove-double-neg 70.2%

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

   7. Applied egg-rr 70.2%

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

      1. associate-/l* 70.2%

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

      2. associate-/r/ 70.2%

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

      3. +-commutative 70.2%

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

      4. unsub-neg 70.2%

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

   9. Simplified 70.2%

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

   10. Taylor expanded in t around 0 70.2%

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

       1. associate-/l* 70.3%

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

       2. associate-/r/ 70.2%

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

   12. Simplified 70.2%

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

   if -6.0000000000000001e-32 < y < -1.6000000000000001e-195 or 3.7000000000000002e-261 < y < 7.5000000000000005e-67

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-*r/ 85.1%

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

   5. Simplified 85.1%

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

   if -1.6000000000000001e-195 < y < 3.7000000000000002e-261

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0 91.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-195}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+53}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.31 \lor \neg \left(y \leq -5.2 \cdot 10^{-29}\right) \land y \leq 2.4 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e+53)
   t
   (if (or (<= y -0.31) (and (not (<= y -5.2e-29)) (<= y 2.4e-70)))
     (* x (/ t z))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+53) {
		tmp = t;
	} else if ((y <= -0.31) || (!(y <= -5.2e-29) && (y <= 2.4e-70))) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8d+53)) then
        tmp = t
    else if ((y <= (-0.31d0)) .or. (.not. (y <= (-5.2d-29))) .and. (y <= 2.4d-70)) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+53) {
		tmp = t;
	} else if ((y <= -0.31) || (!(y <= -5.2e-29) && (y <= 2.4e-70))) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e+53:
		tmp = t
	elif (y <= -0.31) or (not (y <= -5.2e-29) and (y <= 2.4e-70)):
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e+53)
		tmp = t;
	elseif ((y <= -0.31) || (!(y <= -5.2e-29) && (y <= 2.4e-70)))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e+53)
		tmp = t;
	elseif ((y <= -0.31) || (~((y <= -5.2e-29)) && (y <= 2.4e-70)))
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e+53], t, If[Or[LessEqual[y, -0.31], And[N[Not[LessEqual[y, -5.2e-29]], $MachinePrecision], LessEqual[y, 2.4e-70]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999999e53 or -0.309999999999999998 < y < -5.2000000000000004e-29 or 2.4000000000000001e-70 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 61.0%

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

   if -7.9999999999999999e53 < y < -0.309999999999999998 or -5.2000000000000004e-29 < y < 2.4000000000000001e-70

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0 64.6%

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

      1. associate-/l* 65.5%

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

      2. associate-/r/ 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+53}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.31 \lor \neg \left(y \leq -5.2 \cdot 10^{-29}\right) \land y \leq 2.4 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.44 \lor \neg \left(y \leq -7.8 \cdot 10^{-29}\right) \land y \leq 4 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e+52)
   t
   (if (or (<= y -0.44) (and (not (<= y -7.8e-29)) (<= y 4e+66)))
     (* t (/ x z))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+52) {
		tmp = t;
	} else if ((y <= -0.44) || (!(y <= -7.8e-29) && (y <= 4e+66))) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d+52)) then
        tmp = t
    else if ((y <= (-0.44d0)) .or. (.not. (y <= (-7.8d-29))) .and. (y <= 4d+66)) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+52) {
		tmp = t;
	} else if ((y <= -0.44) || (!(y <= -7.8e-29) && (y <= 4e+66))) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e+52:
		tmp = t
	elif (y <= -0.44) or (not (y <= -7.8e-29) and (y <= 4e+66)):
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e+52)
		tmp = t;
	elseif ((y <= -0.44) || (!(y <= -7.8e-29) && (y <= 4e+66)))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e+52)
		tmp = t;
	elseif ((y <= -0.44) || (~((y <= -7.8e-29)) && (y <= 4e+66)))
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e+52], t, If[Or[LessEqual[y, -0.44], And[N[Not[LessEqual[y, -7.8e-29]], $MachinePrecision], LessEqual[y, 4e+66]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e52 or -0.440000000000000002 < y < -7.7999999999999995e-29 or 3.99999999999999978e66 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.5%

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

   if -1.65e52 < y < -0.440000000000000002 or -7.7999999999999995e-29 < y < 3.99999999999999978e66

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 61.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.44 \lor \neg \left(y \leq -7.8 \cdot 10^{-29}\right) \land y \leq 4 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.11:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e+52)
   t
   (if (<= y -0.11)
     (/ t (/ z x))
     (if (<= y -7.8e-29) t (if (<= y 3.1e+66) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+52) {
		tmp = t;
	} else if (y <= -0.11) {
		tmp = t / (z / x);
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= 3.1e+66) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d+52)) then
        tmp = t
    else if (y <= (-0.11d0)) then
        tmp = t / (z / x)
    else if (y <= (-7.8d-29)) then
        tmp = t
    else if (y <= 3.1d+66) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+52) {
		tmp = t;
	} else if (y <= -0.11) {
		tmp = t / (z / x);
	} else if (y <= -7.8e-29) {
		tmp = t;
	} else if (y <= 3.1e+66) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e+52:
		tmp = t
	elif y <= -0.11:
		tmp = t / (z / x)
	elif y <= -7.8e-29:
		tmp = t
	elif y <= 3.1e+66:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e+52)
		tmp = t;
	elseif (y <= -0.11)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= 3.1e+66)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e+52)
		tmp = t;
	elseif (y <= -0.11)
		tmp = t / (z / x);
	elseif (y <= -7.8e-29)
		tmp = t;
	elseif (y <= 3.1e+66)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e+52], t, If[LessEqual[y, -0.11], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.8e-29], t, If[LessEqual[y, 3.1e+66], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e52 or -0.110000000000000001 < y < -7.7999999999999995e-29 or 3.10000000000000019e66 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 66.5%

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

   if -1.4e52 < y < -0.110000000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 44.1%

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

      1. associate-/l* 59.7%

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

   5. Simplified 59.7%

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

   if -7.7999999999999995e-29 < y < 3.10000000000000019e66

   1. Initial program 92.6%

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

   3. Taylor expanded in y around 0 61.4%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.11:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.195:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e+51)
   t
   (if (<= y -0.195)
     (/ t (/ z x))
     (if (<= y -6.6e-29) t (if (<= y 1.35e-76) (/ (* x t) z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e+51) {
		tmp = t;
	} else if (y <= -0.195) {
		tmp = t / (z / x);
	} else if (y <= -6.6e-29) {
		tmp = t;
	} else if (y <= 1.35e-76) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.5d+51)) then
        tmp = t
    else if (y <= (-0.195d0)) then
        tmp = t / (z / x)
    else if (y <= (-6.6d-29)) then
        tmp = t
    else if (y <= 1.35d-76) then
        tmp = (x * t) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e+51) {
		tmp = t;
	} else if (y <= -0.195) {
		tmp = t / (z / x);
	} else if (y <= -6.6e-29) {
		tmp = t;
	} else if (y <= 1.35e-76) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e+51:
		tmp = t
	elif y <= -0.195:
		tmp = t / (z / x)
	elif y <= -6.6e-29:
		tmp = t
	elif y <= 1.35e-76:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e+51)
		tmp = t;
	elseif (y <= -0.195)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -6.6e-29)
		tmp = t;
	elseif (y <= 1.35e-76)
		tmp = Float64(Float64(x * t) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.5e+51)
		tmp = t;
	elseif (y <= -0.195)
		tmp = t / (z / x);
	elseif (y <= -6.6e-29)
		tmp = t;
	elseif (y <= 1.35e-76)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e+51], t, If[LessEqual[y, -0.195], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e-29], t, If[LessEqual[y, 1.35e-76], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999999e51 or -0.19500000000000001 < y < -6.60000000000000055e-29 or 1.35e-76 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 60.5%

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

   if -8.4999999999999999e51 < y < -0.19500000000000001

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 44.1%

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

      1. associate-/l* 59.7%

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

   5. Simplified 59.7%

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

   if -6.60000000000000055e-29 < y < 1.35e-76

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 67.8%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+51}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.195:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-76}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e+21)
   (* t (/ x (- z y)))
   (if (<= x 2.55e+95) (* t (/ y (- y z))) (* x (/ t (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e+21) {
		tmp = t * (x / (z - y));
	} else if (x <= 2.55e+95) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.15d+21)) then
        tmp = t * (x / (z - y))
    else if (x <= 2.55d+95) then
        tmp = t * (y / (y - z))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e+21) {
		tmp = t * (x / (z - y));
	} else if (x <= 2.55e+95) {
		tmp = t * (y / (y - z));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.15e+21:
		tmp = t * (x / (z - y))
	elif x <= 2.55e+95:
		tmp = t * (y / (y - z))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.15e+21)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= 2.55e+95)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.15e+21)
		tmp = t * (x / (z - y));
	elseif (x <= 2.55e+95)
		tmp = t * (y / (y - z));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.15e+21], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e+95], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e21

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 76.5%

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

   if -1.15e21 < x < 2.55000000000000001e95

   1. Initial program 97.2%

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

   3. Taylor expanded in x around 0 79.8%

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

      1. neg-mul-1 79.8%

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

      2. distribute-neg-frac 79.8%

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

   5. Simplified 79.8%

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

      1. frac-2neg 79.8%

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

      2. remove-double-neg 79.8%

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

      3. associate-*l/ 67.6%

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

      4. sub-neg 67.6%

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

      5. distribute-neg-in 67.6%

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

      6. remove-double-neg 67.6%

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

   7. Applied egg-rr 67.6%

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

      1. associate-/l* 66.0%

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

      2. associate-/r/ 79.8%

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

      3. +-commutative 79.8%

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

      4. unsub-neg 79.8%

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

   9. Simplified 79.8%

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

   if 2.55000000000000001e95 < x

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf 79.5%

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

      1. *-commutative 79.5%

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

      2. associate-*r/ 79.3%

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

   5. Simplified 79.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-98}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e-98) t (if (<= y 2.25e-80) (* x (/ t y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-98) {
		tmp = t;
	} else if (y <= 2.25e-80) {
		tmp = x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.8d-98)) then
        tmp = t
    else if (y <= 2.25d-80) then
        tmp = x * (t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e-98) {
		tmp = t;
	} else if (y <= 2.25e-80) {
		tmp = x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e-98:
		tmp = t
	elif y <= 2.25e-80:
		tmp = x * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e-98)
		tmp = t;
	elseif (y <= 2.25e-80)
		tmp = Float64(x * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e-98)
		tmp = t;
	elseif (y <= 2.25e-80)
		tmp = x * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e-98], t, If[LessEqual[y, 2.25e-80], N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e-98 or 2.2500000000000001e-80 < y

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 51.8%

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

   if -2.7999999999999999e-98 < y < 2.2500000000000001e-80

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 21.8%

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

      1. associate-*r/ 21.8%

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

      2. neg-mul-1 21.8%

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

   5. Simplified 21.8%

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

   6. Taylor expanded in x around inf 27.0%

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

      1. associate-*r/ 27.0%

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

      2. neg-mul-1 27.0%

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

   8. Simplified 27.0%

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

      1. frac-2neg 27.0%

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

      2. remove-double-neg 27.0%

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

      3. associate-*l/ 30.1%

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

      4. *-commutative 30.1%

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

      5. add-sqr-sqrt 5.7%

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

      6. sqrt-unprod 10.9%

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

      7. sqr-neg 10.9%

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

      8. sqrt-unprod 9.7%

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

      9. add-sqr-sqrt 17.0%

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

   10. Applied egg-rr 17.0%

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

       1. associate-/l* 13.7%

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

       2. associate-/r/ 13.8%

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

   12. Applied egg-rr 13.8%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-98}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Taylor expanded in y around inf 34.8%

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

4. Final simplification 34.8%

   \[\leadsto t \]
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 2024029 
(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))