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

Percentage Accurate: 96.8% → 96.8%

Time: 8.8s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% 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]

Derivation

1. Initial program 96.4%

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

2. Final simplification 96.4%

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

Alternative 2: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3200000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -8.2e+29)
     t_2
     (if (<= y -4e-63)
       t_1
       (if (<= y -1.8e-67)
         t
         (if (<= y 2.6e-166)
           (* x (/ t (- z y)))
           (if (<= y 4.9e-60)
             t_1
             (if (<= y 3200000000000.0) (* t (/ x (- z y))) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -8.2e+29) {
		tmp = t_2;
	} else if (y <= -4e-63) {
		tmp = t_1;
	} else if (y <= -1.8e-67) {
		tmp = t;
	} else if (y <= 2.6e-166) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.9e-60) {
		tmp = t_1;
	} else if (y <= 3200000000000.0) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-8.2d+29)) then
        tmp = t_2
    else if (y <= (-4d-63)) then
        tmp = t_1
    else if (y <= (-1.8d-67)) then
        tmp = t
    else if (y <= 2.6d-166) then
        tmp = x * (t / (z - y))
    else if (y <= 4.9d-60) then
        tmp = t_1
    else if (y <= 3200000000000.0d0) then
        tmp = t * (x / (z - y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -8.2e+29) {
		tmp = t_2;
	} else if (y <= -4e-63) {
		tmp = t_1;
	} else if (y <= -1.8e-67) {
		tmp = t;
	} else if (y <= 2.6e-166) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.9e-60) {
		tmp = t_1;
	} else if (y <= 3200000000000.0) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -8.2e+29:
		tmp = t_2
	elif y <= -4e-63:
		tmp = t_1
	elif y <= -1.8e-67:
		tmp = t
	elif y <= 2.6e-166:
		tmp = x * (t / (z - y))
	elif y <= 4.9e-60:
		tmp = t_1
	elif y <= 3200000000000.0:
		tmp = t * (x / (z - y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -8.2e+29)
		tmp = t_2;
	elseif (y <= -4e-63)
		tmp = t_1;
	elseif (y <= -1.8e-67)
		tmp = t;
	elseif (y <= 2.6e-166)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 4.9e-60)
		tmp = t_1;
	elseif (y <= 3200000000000.0)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -8.2e+29)
		tmp = t_2;
	elseif (y <= -4e-63)
		tmp = t_1;
	elseif (y <= -1.8e-67)
		tmp = t;
	elseif (y <= 2.6e-166)
		tmp = x * (t / (z - y));
	elseif (y <= 4.9e-60)
		tmp = t_1;
	elseif (y <= 3200000000000.0)
		tmp = t * (x / (z - y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+29], t$95$2, If[LessEqual[y, -4e-63], t$95$1, If[LessEqual[y, -1.8e-67], t, If[LessEqual[y, 2.6e-166], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e-60], t$95$1, If[LessEqual[y, 3200000000000.0], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.2000000000000007e29 or 3.2e12 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. neg-mul-1 80.4%

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

      3. neg-sub0 80.4%

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

      4. associate--r- 80.4%

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

      5. neg-sub0 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in x around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

   7. Simplified 80.4%

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

   if -8.2000000000000007e29 < y < -4.00000000000000027e-63 or 2.59999999999999989e-166 < y < 4.89999999999999988e-60

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 76.1%

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

   if -4.00000000000000027e-63 < y < -1.8e-67

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

   if -1.8e-67 < y < 2.59999999999999989e-166

   1. Initial program 87.9%

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

      1. associate-*l/ 95.2%

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

      2. associate-*r/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in x around inf 84.7%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   if 4.89999999999999988e-60 < y < 3.2e12

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 68.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-67}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 3200000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 0.0046:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -3.8e+33)
     t_2
     (if (<= y -2.1e-147)
       t_1
       (if (<= y 1.25e-166)
         (/ (* x t) (- z y))
         (if (<= y 0.0046)
           t_1
           (if (<= y 9.5e+17) (* t (/ x (- z y))) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -3.8e+33) {
		tmp = t_2;
	} else if (y <= -2.1e-147) {
		tmp = t_1;
	} else if (y <= 1.25e-166) {
		tmp = (x * t) / (z - y);
	} else if (y <= 0.0046) {
		tmp = t_1;
	} else if (y <= 9.5e+17) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-3.8d+33)) then
        tmp = t_2
    else if (y <= (-2.1d-147)) then
        tmp = t_1
    else if (y <= 1.25d-166) then
        tmp = (x * t) / (z - y)
    else if (y <= 0.0046d0) then
        tmp = t_1
    else if (y <= 9.5d+17) then
        tmp = t * (x / (z - y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -3.8e+33) {
		tmp = t_2;
	} else if (y <= -2.1e-147) {
		tmp = t_1;
	} else if (y <= 1.25e-166) {
		tmp = (x * t) / (z - y);
	} else if (y <= 0.0046) {
		tmp = t_1;
	} else if (y <= 9.5e+17) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -3.8e+33:
		tmp = t_2
	elif y <= -2.1e-147:
		tmp = t_1
	elif y <= 1.25e-166:
		tmp = (x * t) / (z - y)
	elif y <= 0.0046:
		tmp = t_1
	elif y <= 9.5e+17:
		tmp = t * (x / (z - y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -3.8e+33)
		tmp = t_2;
	elseif (y <= -2.1e-147)
		tmp = t_1;
	elseif (y <= 1.25e-166)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 0.0046)
		tmp = t_1;
	elseif (y <= 9.5e+17)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -3.8e+33)
		tmp = t_2;
	elseif (y <= -2.1e-147)
		tmp = t_1;
	elseif (y <= 1.25e-166)
		tmp = (x * t) / (z - y);
	elseif (y <= 0.0046)
		tmp = t_1;
	elseif (y <= 9.5e+17)
		tmp = t * (x / (z - y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+33], t$95$2, If[LessEqual[y, -2.1e-147], t$95$1, If[LessEqual[y, 1.25e-166], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0046], t$95$1, If[LessEqual[y, 9.5e+17], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.80000000000000002e33 or 9.5e17 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. neg-mul-1 80.4%

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

      3. neg-sub0 80.4%

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

      4. associate--r- 80.4%

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

      5. neg-sub0 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in x around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

   7. Simplified 80.4%

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

   if -3.80000000000000002e33 < y < -2.1e-147 or 1.25e-166 < y < 0.0045999999999999999

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 72.0%

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

   if -2.1e-147 < y < 1.25e-166

   1. Initial program 85.1%

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

      1. associate-*l/ 97.3%

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

      2. associate-*r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 89.1%

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

   if 0.0045999999999999999 < y < 9.5e17

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 0.0046:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{-y}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -9.5e+30)
     t_1
     (if (<= y -2.1e-147)
       (* t (/ (- x y) z))
       (if (<= y 2.9e-37)
         (/ (* x t) (- z y))
         (if (<= y 1.2e+61) (/ (- y) (/ (- z y) t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -9.5e+30) {
		tmp = t_1;
	} else if (y <= -2.1e-147) {
		tmp = t * ((x - y) / z);
	} else if (y <= 2.9e-37) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.2e+61) {
		tmp = -y / ((z - y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-9.5d+30)) then
        tmp = t_1
    else if (y <= (-2.1d-147)) then
        tmp = t * ((x - y) / z)
    else if (y <= 2.9d-37) then
        tmp = (x * t) / (z - y)
    else if (y <= 1.2d+61) then
        tmp = -y / ((z - y) / t)
    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 tmp;
	if (y <= -9.5e+30) {
		tmp = t_1;
	} else if (y <= -2.1e-147) {
		tmp = t * ((x - y) / z);
	} else if (y <= 2.9e-37) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.2e+61) {
		tmp = -y / ((z - y) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -9.5e+30:
		tmp = t_1
	elif y <= -2.1e-147:
		tmp = t * ((x - y) / z)
	elif y <= 2.9e-37:
		tmp = (x * t) / (z - y)
	elif y <= 1.2e+61:
		tmp = -y / ((z - y) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -9.5e+30)
		tmp = t_1;
	elseif (y <= -2.1e-147)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 2.9e-37)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 1.2e+61)
		tmp = Float64(Float64(-y) / Float64(Float64(z - y) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -9.5e+30)
		tmp = t_1;
	elseif (y <= -2.1e-147)
		tmp = t * ((x - y) / z);
	elseif (y <= 2.9e-37)
		tmp = (x * t) / (z - y);
	elseif (y <= 1.2e+61)
		tmp = -y / ((z - y) / t);
	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]}, If[LessEqual[y, -9.5e+30], t$95$1, If[LessEqual[y, -2.1e-147], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-37], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+61], N[((-y) / N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.5000000000000003e30 or 1.1999999999999999e61 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

      3. neg-sub0 83.9%

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

      4. associate--r- 83.9%

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

      5. neg-sub0 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in x around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

   7. Simplified 83.9%

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

   if -9.5000000000000003e30 < y < -2.1e-147

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 72.7%

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

   if -2.1e-147 < y < 2.90000000000000005e-37

   1. Initial program 90.0%

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

      1. associate-*l/ 95.0%

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

      2. associate-*r/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around inf 81.6%

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

   if 2.90000000000000005e-37 < y < 1.1999999999999999e61

   1. Initial program 99.9%

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

      1. associate-*l/ 96.2%

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

      2. associate-*r/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. associate-/l* 73.3%

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

   6. Simplified 73.3%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-147}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{-y}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+56}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e-36)
   t
   (if (<= y 1.45e+22)
     (* x (/ t (- z y)))
     (if (<= y 4.4e+56) t (if (<= y 2.3e+124) (* t (/ (- y) z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e-36) {
		tmp = t;
	} else if (y <= 1.45e+22) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.4e+56) {
		tmp = t;
	} else if (y <= 2.3e+124) {
		tmp = t * (-y / 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-36)) then
        tmp = t
    else if (y <= 1.45d+22) then
        tmp = x * (t / (z - y))
    else if (y <= 4.4d+56) then
        tmp = t
    else if (y <= 2.3d+124) then
        tmp = t * (-y / 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-36) {
		tmp = t;
	} else if (y <= 1.45e+22) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.4e+56) {
		tmp = t;
	} else if (y <= 2.3e+124) {
		tmp = t * (-y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e-36:
		tmp = t
	elif y <= 1.45e+22:
		tmp = x * (t / (z - y))
	elif y <= 4.4e+56:
		tmp = t
	elif y <= 2.3e+124:
		tmp = t * (-y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e-36)
		tmp = t;
	elseif (y <= 1.45e+22)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 4.4e+56)
		tmp = t;
	elseif (y <= 2.3e+124)
		tmp = Float64(t * Float64(Float64(-y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e-36)
		tmp = t;
	elseif (y <= 1.45e+22)
		tmp = x * (t / (z - y));
	elseif (y <= 4.4e+56)
		tmp = t;
	elseif (y <= 2.3e+124)
		tmp = t * (-y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e-36], t, If[LessEqual[y, 1.45e+22], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+56], t, If[LessEqual[y, 2.3e+124], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999995e-36 or 1.45e22 < y < 4.40000000000000032e56 or 2.29999999999999985e124 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.2%

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

      2. associate-*r/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in y around inf 67.9%

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

   if -7.9999999999999995e-36 < y < 1.45e22

   1. Initial program 92.5%

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

      1. associate-*l/ 94.6%

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

      2. associate-*r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 76.6%

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

      1. associate-*l/ 76.2%

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

      2. *-commutative 76.2%

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

   6. Simplified 76.2%

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

   if 4.40000000000000032e56 < y < 2.29999999999999985e124

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 63.7%

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

      1. neg-mul-1 63.7%

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

      2. distribute-neg-frac 63.7%

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

   4. Simplified 63.7%

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

   5. Taylor expanded in y around 0 43.7%

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

      1. neg-mul-1 43.7%

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

      2. distribute-neg-frac 43.7%

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

   7. Simplified 43.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+56}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+83} \lor \neg \left(y \leq 2.3 \cdot 10^{+124}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.9e+83) (not (<= y 2.3e+124)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e+83) || !(y <= 2.3e+124)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (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 ((y <= (-2.9d+83)) .or. (.not. (y <= 2.3d+124))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (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 ((y <= -2.9e+83) || !(y <= 2.3e+124)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.9e+83) or not (y <= 2.3e+124):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.9e+83) || !(y <= 2.3e+124))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.9e+83) || ~((y <= 2.3e+124)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.9e+83], N[Not[LessEqual[y, 2.3e+124]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999999e83 or 2.29999999999999985e124 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 89.9%

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

      1. associate-*r/ 89.9%

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

      2. neg-mul-1 89.9%

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

      3. neg-sub0 89.9%

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

      4. associate--r- 89.9%

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

      5. neg-sub0 89.9%

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

   4. Simplified 89.9%

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

   5. Taylor expanded in x around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. unsub-neg 89.9%

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

   7. Simplified 89.9%

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

   if -2.89999999999999999e83 < y < 2.29999999999999985e124

   1. Initial program 94.7%

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

      1. associate-*l/ 94.1%

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

      2. associate-*r/ 91.5%

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

   3. Simplified 91.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+83} \lor \neg \left(y \leq 2.3 \cdot 10^{+124}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 7: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e+68)
   (* x (/ t (- z y)))
   (if (<= x 3.2e-30) (* t (/ (- y) (- z y))) (* t (/ x (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e+68) {
		tmp = x * (t / (z - y));
	} else if (x <= 3.2e-30) {
		tmp = t * (-y / (z - y));
	} else {
		tmp = t * (x / (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 <= (-9.5d+68)) then
        tmp = x * (t / (z - y))
    else if (x <= 3.2d-30) then
        tmp = t * (-y / (z - y))
    else
        tmp = t * (x / (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 <= -9.5e+68) {
		tmp = x * (t / (z - y));
	} else if (x <= 3.2e-30) {
		tmp = t * (-y / (z - y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e+68:
		tmp = x * (t / (z - y))
	elif x <= 3.2e-30:
		tmp = t * (-y / (z - y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e+68)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (x <= 3.2e-30)
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - y)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e+68)
		tmp = x * (t / (z - y));
	elseif (x <= 3.2e-30)
		tmp = t * (-y / (z - y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e+68], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e-30], N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000069e68

   1. Initial program 91.7%

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

      1. associate-*l/ 84.1%

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

      2. associate-*r/ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in x around inf 69.5%

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

      1. associate-*l/ 75.1%

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

      2. *-commutative 75.1%

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

   6. Simplified 75.1%

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

   if -9.50000000000000069e68 < x < 3.2e-30

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 83.4%

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

      1. neg-mul-1 83.4%

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

      2. distribute-neg-frac 83.4%

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

   4. Simplified 83.4%

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

   if 3.2e-30 < x

   1. Initial program 98.6%

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

   2. Taylor expanded in x around inf 76.4%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-30}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 8: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-38} \lor \neg \left(y \leq 1.75 \cdot 10^{-37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.9e-38) (not (<= y 1.75e-37)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.9e-38) || !(y <= 1.75e-37)) {
		tmp = t * (1.0 - (x / y));
	} 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 ((y <= (-2.9d-38)) .or. (.not. (y <= 1.75d-37))) then
        tmp = t * (1.0d0 - (x / y))
    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 ((y <= -2.9e-38) || !(y <= 1.75e-37)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.9e-38) or not (y <= 1.75e-37):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.9e-38) || !(y <= 1.75e-37))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	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 ((y <= -2.9e-38) || ~((y <= 1.75e-37)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.9e-38], N[Not[LessEqual[y, 1.75e-37]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999994e-38 or 1.7500000000000001e-37 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

      3. neg-sub0 75.0%

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

      4. associate--r- 75.0%

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

      5. neg-sub0 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in x around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   7. Simplified 75.0%

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

   if -2.89999999999999994e-38 < y < 1.7500000000000001e-37

   1. Initial program 91.8%

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

      1. associate-*l/ 94.1%

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

      2. associate-*r/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in x around inf 78.7%

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

      1. associate-*l/ 79.0%

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

      2. *-commutative 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-38} \lor \neg \left(y \leq 1.75 \cdot 10^{-37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 9: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+29} \lor \neg \left(y \leq 5.4 \cdot 10^{+20}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e+29) (not (<= y 5.4e+20)))
   (* t (- 1.0 (/ x y)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+29) || !(y <= 5.4e+20)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.5d+29)) .or. (.not. (y <= 5.4d+20))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+29) || !(y <= 5.4e+20)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e+29) or not (y <= 5.4e+20):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e+29) || !(y <= 5.4e+20))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.5e+29) || ~((y <= 5.4e+20)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e+29], N[Not[LessEqual[y, 5.4e+20]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000003e29 or 5.4e20 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. neg-mul-1 80.4%

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

      3. neg-sub0 80.4%

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

      4. associate--r- 80.4%

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

      5. neg-sub0 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in x around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

   7. Simplified 80.4%

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

   if -9.5000000000000003e29 < y < 5.4e20

   1. Initial program 93.2%

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

   2. Taylor expanded in x around inf 73.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+29} \lor \neg \left(y \leq 5.4 \cdot 10^{+20}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 10: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2100000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e-36) t (if (<= y 2100000000.0) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e-36) {
		tmp = t;
	} else if (y <= 2100000000.0) {
		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-36)) then
        tmp = t
    else if (y <= 2100000000.0d0) 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-36) {
		tmp = t;
	} else if (y <= 2100000000.0) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e-36:
		tmp = t
	elif y <= 2100000000.0:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e-36)
		tmp = t;
	elseif (y <= 2100000000.0)
		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-36)
		tmp = t;
	elseif (y <= 2100000000.0)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e-36], t, If[LessEqual[y, 2100000000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999995e-36 or 2.1e9 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.3%

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

      2. associate-*r/ 75.4%

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

   3. Simplified 75.4%

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

   4. Taylor expanded in y around inf 61.3%

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

   if -7.9999999999999995e-36 < y < 2.1e9

   1. Initial program 92.5%

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

      1. associate-*l/ 94.6%

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

      2. associate-*r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around inf 76.6%

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

      1. associate-*l/ 76.2%

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

      2. *-commutative 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in z around inf 64.0%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2100000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.45:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.45) t (if (<= y 2.05e+15) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.45) {
		tmp = t;
	} else if (y <= 2.05e+15) {
		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 <= (-0.45d0)) then
        tmp = t
    else if (y <= 2.05d+15) 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 <= -0.45) {
		tmp = t;
	} else if (y <= 2.05e+15) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.45:
		tmp = t
	elif y <= 2.05e+15:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.45)
		tmp = t;
	elseif (y <= 2.05e+15)
		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 <= -0.45)
		tmp = t;
	elseif (y <= 2.05e+15)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.45], t, If[LessEqual[y, 2.05e+15], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -0.450000000000000011 or 2.05e15 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.5%

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

      2. associate-*r/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around inf 62.0%

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

   if -0.450000000000000011 < y < 2.05e15

   1. Initial program 92.8%

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

   2. Taylor expanded in y around 0 64.6%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.45:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e-8) t (if (<= y 3.8e+14) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-8) {
		tmp = t;
	} else if (y <= 3.8e+14) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d-8)) then
        tmp = t
    else if (y <= 3.8d+14) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-8) {
		tmp = t;
	} else if (y <= 3.8e+14) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-8:
		tmp = t
	elif y <= 3.8e+14:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-8)
		tmp = t;
	elseif (y <= 3.8e+14)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e-8)
		tmp = t;
	elseif (y <= 3.8e+14)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e-8], t, If[LessEqual[y, 3.8e+14], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999998e-8 or 3.8e14 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.5%

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

      2. associate-*r/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around inf 62.0%

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

   if -2.39999999999999998e-8 < y < 3.8e14

   1. Initial program 92.8%

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

      1. associate-*l/ 94.9%

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

      2. associate-*r/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 62.9%

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

      1. associate-/l* 64.8%

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

   6. Simplified 64.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 34.3% 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 96.4%

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

   1. associate-*l/ 85.4%

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

   2. associate-*r/ 83.1%

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

3. Simplified 83.1%

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

4. Taylor expanded in y around inf 38.2%

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

5. Final simplification 38.2%

   \[\leadsto t \]

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 2023242 
(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))