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

Percentage Accurate: 97.1% → 97.1%

Time: 9.8s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Final simplification 97.0%

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

Alternative 2: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ t_2 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+26}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))) (t_2 (* t (/ y (- y z)))))
   (if (<= y -1.75e+84)
     t_2
     (if (<= y -2e+29)
       t_1
       (if (<= y -1.85e+26)
         (* (- x y) (/ t z))
         (if (<= y -2.8e-44)
           (* x (/ t (- z y)))
           (if (<= y -3.65e-87)
             t_2
             (if (<= y -8.5e-109)
               (/ t (/ z (- x y)))
               (if (<= y -4.7e-194)
                 (* t (/ x (- z y)))
                 (if (<= y 1.1e+38) (/ (* (- x y) t) z) t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double t_2 = t * (y / (y - z));
	double tmp;
	if (y <= -1.75e+84) {
		tmp = t_2;
	} else if (y <= -2e+29) {
		tmp = t_1;
	} else if (y <= -1.85e+26) {
		tmp = (x - y) * (t / z);
	} else if (y <= -2.8e-44) {
		tmp = x * (t / (z - y));
	} else if (y <= -3.65e-87) {
		tmp = t_2;
	} else if (y <= -8.5e-109) {
		tmp = t / (z / (x - y));
	} else if (y <= -4.7e-194) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.1e+38) {
		tmp = ((x - y) * t) / z;
	} 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 * ((y - x) / y)
    t_2 = t * (y / (y - z))
    if (y <= (-1.75d+84)) then
        tmp = t_2
    else if (y <= (-2d+29)) then
        tmp = t_1
    else if (y <= (-1.85d+26)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-2.8d-44)) then
        tmp = x * (t / (z - y))
    else if (y <= (-3.65d-87)) then
        tmp = t_2
    else if (y <= (-8.5d-109)) then
        tmp = t / (z / (x - y))
    else if (y <= (-4.7d-194)) then
        tmp = t * (x / (z - y))
    else if (y <= 1.1d+38) then
        tmp = ((x - y) * t) / z
    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 * ((y - x) / y);
	double t_2 = t * (y / (y - z));
	double tmp;
	if (y <= -1.75e+84) {
		tmp = t_2;
	} else if (y <= -2e+29) {
		tmp = t_1;
	} else if (y <= -1.85e+26) {
		tmp = (x - y) * (t / z);
	} else if (y <= -2.8e-44) {
		tmp = x * (t / (z - y));
	} else if (y <= -3.65e-87) {
		tmp = t_2;
	} else if (y <= -8.5e-109) {
		tmp = t / (z / (x - y));
	} else if (y <= -4.7e-194) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.1e+38) {
		tmp = ((x - y) * t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	t_2 = t * (y / (y - z))
	tmp = 0
	if y <= -1.75e+84:
		tmp = t_2
	elif y <= -2e+29:
		tmp = t_1
	elif y <= -1.85e+26:
		tmp = (x - y) * (t / z)
	elif y <= -2.8e-44:
		tmp = x * (t / (z - y))
	elif y <= -3.65e-87:
		tmp = t_2
	elif y <= -8.5e-109:
		tmp = t / (z / (x - y))
	elif y <= -4.7e-194:
		tmp = t * (x / (z - y))
	elif y <= 1.1e+38:
		tmp = ((x - y) * t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	t_2 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.75e+84)
		tmp = t_2;
	elseif (y <= -2e+29)
		tmp = t_1;
	elseif (y <= -1.85e+26)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -2.8e-44)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= -3.65e-87)
		tmp = t_2;
	elseif (y <= -8.5e-109)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= -4.7e-194)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 1.1e+38)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	t_2 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.75e+84)
		tmp = t_2;
	elseif (y <= -2e+29)
		tmp = t_1;
	elseif (y <= -1.85e+26)
		tmp = (x - y) * (t / z);
	elseif (y <= -2.8e-44)
		tmp = x * (t / (z - y));
	elseif (y <= -3.65e-87)
		tmp = t_2;
	elseif (y <= -8.5e-109)
		tmp = t / (z / (x - y));
	elseif (y <= -4.7e-194)
		tmp = t * (x / (z - y));
	elseif (y <= 1.1e+38)
		tmp = ((x - y) * t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+84], t$95$2, If[LessEqual[y, -2e+29], t$95$1, If[LessEqual[y, -1.85e+26], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-44], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.65e-87], t$95$2, If[LessEqual[y, -8.5e-109], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.7e-194], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+38], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -1.7499999999999999e84 or -2.8e-44 < y < -3.64999999999999984e-87

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.1%

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

      1. neg-mul-1 86.1%

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

      2. distribute-neg-frac 86.1%

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

   4. Simplified 86.1%

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

      1. frac-2neg 86.1%

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

      2. div-inv 85.9%

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

      3. remove-double-neg 85.9%

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

      4. sub-neg 85.9%

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

      5. distribute-neg-in 85.9%

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

      6. remove-double-neg 85.9%

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

      7. +-commutative 85.9%

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

      8. sub-neg 85.9%

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

   6. Applied egg-rr 85.9%

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

      1. associate-*r/ 86.1%

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

      2. *-rgt-identity 86.1%

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

   8. Simplified 86.1%

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

   if -1.7499999999999999e84 < y < -1.99999999999999983e29 or 1.10000000000000003e38 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.2%

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

      1. associate-*r/ 87.2%

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

      2. neg-mul-1 87.2%

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

      3. neg-sub0 87.2%

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

      4. associate--r- 87.2%

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

      5. neg-sub0 87.2%

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

   4. Simplified 87.2%

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

   if -1.99999999999999983e29 < y < -1.84999999999999994e26

   1. Initial program 99.6%

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

      1. associate-*l/ 52.9%

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

      2. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around inf 99.2%

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

   if -1.84999999999999994e26 < y < -2.8e-44

   1. Initial program 89.8%

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

      1. associate-*l/ 90.3%

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

      2. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 71.5%

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

      1. associate-*l/ 80.9%

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

      2. *-commutative 80.9%

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

   6. Simplified 80.9%

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

   if -3.64999999999999984e-87 < y < -8.50000000000000005e-109

   1. Initial program 99.1%

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

      1. associate-*l/ 81.0%

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

      2. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 81.0%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -8.50000000000000005e-109 < y < -4.7000000000000003e-194

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 91.9%

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

   if -4.7000000000000003e-194 < y < 1.10000000000000003e38

   1. Initial program 92.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around inf 86.5%

      \[\leadsto \color{blue}{\frac{t \cdot \left(x - y\right)}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+26}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-87}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ t_2 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-304}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))) (t_2 (* t (/ y (- y z)))))
   (if (<= y -7.5e+78)
     t_2
     (if (<= y -9.8e-230)
       t_1
       (if (<= y 8.8e-304)
         (* (- x y) (/ t z))
         (if (<= y 2.7e-205)
           (/ (* x t) (- z y))
           (if (<= y 2.6e-110)
             (/ t (/ z (- x y)))
             (if (<= y 7.5e+73) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double t_2 = t * (y / (y - z));
	double tmp;
	if (y <= -7.5e+78) {
		tmp = t_2;
	} else if (y <= -9.8e-230) {
		tmp = t_1;
	} else if (y <= 8.8e-304) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.7e-205) {
		tmp = (x * t) / (z - y);
	} else if (y <= 2.6e-110) {
		tmp = t / (z / (x - y));
	} else if (y <= 7.5e+73) {
		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 = t * (x / (z - y))
    t_2 = t * (y / (y - z))
    if (y <= (-7.5d+78)) then
        tmp = t_2
    else if (y <= (-9.8d-230)) then
        tmp = t_1
    else if (y <= 8.8d-304) then
        tmp = (x - y) * (t / z)
    else if (y <= 2.7d-205) then
        tmp = (x * t) / (z - y)
    else if (y <= 2.6d-110) then
        tmp = t / (z / (x - y))
    else if (y <= 7.5d+73) 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 = t * (x / (z - y));
	double t_2 = t * (y / (y - z));
	double tmp;
	if (y <= -7.5e+78) {
		tmp = t_2;
	} else if (y <= -9.8e-230) {
		tmp = t_1;
	} else if (y <= 8.8e-304) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.7e-205) {
		tmp = (x * t) / (z - y);
	} else if (y <= 2.6e-110) {
		tmp = t / (z / (x - y));
	} else if (y <= 7.5e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	t_2 = t * (y / (y - z))
	tmp = 0
	if y <= -7.5e+78:
		tmp = t_2
	elif y <= -9.8e-230:
		tmp = t_1
	elif y <= 8.8e-304:
		tmp = (x - y) * (t / z)
	elif y <= 2.7e-205:
		tmp = (x * t) / (z - y)
	elif y <= 2.6e-110:
		tmp = t / (z / (x - y))
	elif y <= 7.5e+73:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	t_2 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -7.5e+78)
		tmp = t_2;
	elseif (y <= -9.8e-230)
		tmp = t_1;
	elseif (y <= 8.8e-304)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 2.7e-205)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 2.6e-110)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= 7.5e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	t_2 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -7.5e+78)
		tmp = t_2;
	elseif (y <= -9.8e-230)
		tmp = t_1;
	elseif (y <= 8.8e-304)
		tmp = (x - y) * (t / z);
	elseif (y <= 2.7e-205)
		tmp = (x * t) / (z - y);
	elseif (y <= 2.6e-110)
		tmp = t / (z / (x - y));
	elseif (y <= 7.5e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e+78], t$95$2, If[LessEqual[y, -9.8e-230], t$95$1, If[LessEqual[y, 8.8e-304], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-205], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-110], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+73], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.49999999999999934e78 or 7.5e73 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 84.1%

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

      1. neg-mul-1 84.1%

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

      2. distribute-neg-frac 84.1%

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

   4. Simplified 84.1%

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

      1. frac-2neg 84.1%

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

      2. div-inv 83.9%

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

      3. remove-double-neg 83.9%

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

      4. sub-neg 83.9%

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

      5. distribute-neg-in 83.9%

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

      6. remove-double-neg 83.9%

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

      7. +-commutative 83.9%

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

      8. sub-neg 83.9%

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

   6. Applied egg-rr 83.9%

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

      1. associate-*r/ 84.1%

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

      2. *-rgt-identity 84.1%

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

   8. Simplified 84.1%

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

   if -7.49999999999999934e78 < y < -9.79999999999999984e-230 or 2.5999999999999999e-110 < y < 7.5e73

   1. Initial program 96.9%

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

   2. Taylor expanded in x around inf 69.7%

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

   if -9.79999999999999984e-230 < y < 8.799999999999999e-304

   1. Initial program 85.0%

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

      1. associate-*l/ 99.4%

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

      2. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   if 8.799999999999999e-304 < y < 2.7000000000000001e-205

   1. Initial program 85.2%

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

      1. associate-*l/ 99.4%

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

      2. associate-*r/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 99.4%

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

   if 2.7000000000000001e-205 < y < 2.5999999999999999e-110

   1. Initial program 99.9%

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

      1. associate-*l/ 95.4%

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

      2. associate-*r/ 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in z around inf 91.2%

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

      1. associate-/l* 94.6%

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

   6. Simplified 94.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-230}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-304}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-205}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 4: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-110}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -4.5e+92)
     t
     (if (<= y -8.5e-229)
       t_1
       (if (<= y 8e-110) (* (- x y) (/ t z)) (if (<= y 2.2e+75) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -4.5e+92) {
		tmp = t;
	} else if (y <= -8.5e-229) {
		tmp = t_1;
	} else if (y <= 8e-110) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.2e+75) {
		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 = t * (x / (z - y))
    if (y <= (-4.5d+92)) then
        tmp = t
    else if (y <= (-8.5d-229)) then
        tmp = t_1
    else if (y <= 8d-110) then
        tmp = (x - y) * (t / z)
    else if (y <= 2.2d+75) 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 = t * (x / (z - y));
	double tmp;
	if (y <= -4.5e+92) {
		tmp = t;
	} else if (y <= -8.5e-229) {
		tmp = t_1;
	} else if (y <= 8e-110) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.2e+75) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -4.5e+92:
		tmp = t
	elif y <= -8.5e-229:
		tmp = t_1
	elif y <= 8e-110:
		tmp = (x - y) * (t / z)
	elif y <= 2.2e+75:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -4.5e+92)
		tmp = t;
	elseif (y <= -8.5e-229)
		tmp = t_1;
	elseif (y <= 8e-110)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 2.2e+75)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -4.5e+92)
		tmp = t;
	elseif (y <= -8.5e-229)
		tmp = t_1;
	elseif (y <= 8e-110)
		tmp = (x - y) * (t / z);
	elseif (y <= 2.2e+75)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+92], t, If[LessEqual[y, -8.5e-229], t$95$1, If[LessEqual[y, 8e-110], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+75], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999999e92 or 2.20000000000000012e75 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.1%

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

      2. associate-*r/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 71.9%

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

   if -4.4999999999999999e92 < y < -8.49999999999999977e-229 or 8.0000000000000004e-110 < y < 2.20000000000000012e75

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 69.3%

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

   if -8.49999999999999977e-229 < y < 8.0000000000000004e-110

   1. Initial program 91.1%

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

      1. associate-*l/ 97.8%

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

      2. associate-*r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around inf 90.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-110}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ t_2 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-108}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))) (t_2 (* t (/ y (- y z)))))
   (if (<= y -1e+79)
     t_2
     (if (<= y -2.4e-228)
       t_1
       (if (<= y 9e-108) (* (- x y) (/ t z)) (if (<= y 5.4e+73) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double t_2 = t * (y / (y - z));
	double tmp;
	if (y <= -1e+79) {
		tmp = t_2;
	} else if (y <= -2.4e-228) {
		tmp = t_1;
	} else if (y <= 9e-108) {
		tmp = (x - y) * (t / z);
	} else if (y <= 5.4e+73) {
		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 = t * (x / (z - y))
    t_2 = t * (y / (y - z))
    if (y <= (-1d+79)) then
        tmp = t_2
    else if (y <= (-2.4d-228)) then
        tmp = t_1
    else if (y <= 9d-108) then
        tmp = (x - y) * (t / z)
    else if (y <= 5.4d+73) 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 = t * (x / (z - y));
	double t_2 = t * (y / (y - z));
	double tmp;
	if (y <= -1e+79) {
		tmp = t_2;
	} else if (y <= -2.4e-228) {
		tmp = t_1;
	} else if (y <= 9e-108) {
		tmp = (x - y) * (t / z);
	} else if (y <= 5.4e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	t_2 = t * (y / (y - z))
	tmp = 0
	if y <= -1e+79:
		tmp = t_2
	elif y <= -2.4e-228:
		tmp = t_1
	elif y <= 9e-108:
		tmp = (x - y) * (t / z)
	elif y <= 5.4e+73:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	t_2 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1e+79)
		tmp = t_2;
	elseif (y <= -2.4e-228)
		tmp = t_1;
	elseif (y <= 9e-108)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 5.4e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	t_2 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1e+79)
		tmp = t_2;
	elseif (y <= -2.4e-228)
		tmp = t_1;
	elseif (y <= 9e-108)
		tmp = (x - y) * (t / z);
	elseif (y <= 5.4e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+79], t$95$2, If[LessEqual[y, -2.4e-228], t$95$1, If[LessEqual[y, 9e-108], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+73], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999967e78 or 5.3999999999999998e73 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 84.1%

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

      1. neg-mul-1 84.1%

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

      2. distribute-neg-frac 84.1%

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

   4. Simplified 84.1%

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

      1. frac-2neg 84.1%

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

      2. div-inv 83.9%

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

      3. remove-double-neg 83.9%

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

      4. sub-neg 83.9%

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

      5. distribute-neg-in 83.9%

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

      6. remove-double-neg 83.9%

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

      7. +-commutative 83.9%

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

      8. sub-neg 83.9%

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

   6. Applied egg-rr 83.9%

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

      1. associate-*r/ 84.1%

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

      2. *-rgt-identity 84.1%

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

   8. Simplified 84.1%

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

   if -9.99999999999999967e78 < y < -2.40000000000000002e-228 or 8.99999999999999941e-108 < y < 5.3999999999999998e73

   1. Initial program 96.9%

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

   2. Taylor expanded in x around inf 69.7%

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

   if -2.40000000000000002e-228 < y < 8.99999999999999941e-108

   1. Initial program 91.1%

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

      1. associate-*l/ 97.8%

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

      2. associate-*r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around inf 90.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-228}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-108}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 6: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e+30)
   t
   (if (<= y -1.7e-217)
     (/ t (/ z x))
     (if (<= y 7e-206) (/ (* x t) z) (if (<= y 1.45e+38) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+30) {
		tmp = t;
	} else if (y <= -1.7e-217) {
		tmp = t / (z / x);
	} else if (y <= 7e-206) {
		tmp = (x * t) / z;
	} else if (y <= 1.45e+38) {
		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 <= (-3.2d+30)) then
        tmp = t
    else if (y <= (-1.7d-217)) then
        tmp = t / (z / x)
    else if (y <= 7d-206) then
        tmp = (x * t) / z
    else if (y <= 1.45d+38) 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 <= -3.2e+30) {
		tmp = t;
	} else if (y <= -1.7e-217) {
		tmp = t / (z / x);
	} else if (y <= 7e-206) {
		tmp = (x * t) / z;
	} else if (y <= 1.45e+38) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e+30:
		tmp = t
	elif y <= -1.7e-217:
		tmp = t / (z / x)
	elif y <= 7e-206:
		tmp = (x * t) / z
	elif y <= 1.45e+38:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e+30)
		tmp = t;
	elseif (y <= -1.7e-217)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 7e-206)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 1.45e+38)
		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 <= -3.2e+30)
		tmp = t;
	elseif (y <= -1.7e-217)
		tmp = t / (z / x);
	elseif (y <= 7e-206)
		tmp = (x * t) / z;
	elseif (y <= 1.45e+38)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e+30], t, If[LessEqual[y, -1.7e-217], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-206], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.45e+38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.19999999999999973e30 or 1.45000000000000003e38 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.3%

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

      2. associate-*r/ 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -3.19999999999999973e30 < y < -1.70000000000000008e-217

   1. Initial program 94.1%

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

      1. associate-*l/ 87.1%

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

      2. associate-*r/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around 0 44.2%

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

      1. associate-/l* 54.9%

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

   6. Simplified 54.9%

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

   if -1.70000000000000008e-217 < y < 6.99999999999999979e-206

   1. Initial program 85.9%

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

      1. associate-*l/ 99.4%

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

      2. associate-*r/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around 0 87.4%

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

   if 6.99999999999999979e-206 < y < 1.45000000000000003e38

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 69.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-206}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e+30)
   t
   (if (<= y -3.8e-30)
     (/ x (/ z t))
     (if (<= y -5.5e-57)
       (* x (/ (- t) y))
       (if (<= y 1.4e+38) (/ (* x t) z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+30) {
		tmp = t;
	} else if (y <= -3.8e-30) {
		tmp = x / (z / t);
	} else if (y <= -5.5e-57) {
		tmp = x * (-t / y);
	} else if (y <= 1.4e+38) {
		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 <= (-3.2d+30)) then
        tmp = t
    else if (y <= (-3.8d-30)) then
        tmp = x / (z / t)
    else if (y <= (-5.5d-57)) then
        tmp = x * (-t / y)
    else if (y <= 1.4d+38) 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 <= -3.2e+30) {
		tmp = t;
	} else if (y <= -3.8e-30) {
		tmp = x / (z / t);
	} else if (y <= -5.5e-57) {
		tmp = x * (-t / y);
	} else if (y <= 1.4e+38) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e+30:
		tmp = t
	elif y <= -3.8e-30:
		tmp = x / (z / t)
	elif y <= -5.5e-57:
		tmp = x * (-t / y)
	elif y <= 1.4e+38:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e+30)
		tmp = t;
	elseif (y <= -3.8e-30)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= -5.5e-57)
		tmp = Float64(x * Float64(Float64(-t) / y));
	elseif (y <= 1.4e+38)
		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 <= -3.2e+30)
		tmp = t;
	elseif (y <= -3.8e-30)
		tmp = x / (z / t);
	elseif (y <= -5.5e-57)
		tmp = x * (-t / y);
	elseif (y <= 1.4e+38)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e+30], t, If[LessEqual[y, -3.8e-30], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e-57], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+38], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.19999999999999973e30 or 1.4e38 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.3%

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

      2. associate-*r/ 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -3.19999999999999973e30 < y < -3.8000000000000003e-30

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 65.1%

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

      1. associate-*l/ 39.6%

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

      2. associate-/l* 65.3%

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

   4. Applied egg-rr 65.3%

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

   if -3.8000000000000003e-30 < y < -5.50000000000000011e-57

   1. Initial program 83.5%

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

      1. associate-*l/ 84.8%

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

      2. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 52.8%

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

      1. associate-*l/ 52.5%

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

      2. *-commutative 52.5%

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

   6. Simplified 52.5%

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

   7. Taylor expanded in z around 0 52.6%

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

      1. associate-*r/ 52.6%

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

      2. neg-mul-1 52.6%

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

   9. Simplified 52.6%

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

   if -5.50000000000000011e-57 < y < 1.4e38

   1. Initial program 93.9%

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

      1. associate-*l/ 96.1%

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

      2. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 70.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e+31)
   t
   (if (<= y -4.8e-30)
     (/ x (/ z t))
     (if (<= y -3.9e-53)
       (/ (* x (- t)) y)
       (if (<= y 1.45e+38) (/ (* x t) z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e+31) {
		tmp = t;
	} else if (y <= -4.8e-30) {
		tmp = x / (z / t);
	} else if (y <= -3.9e-53) {
		tmp = (x * -t) / y;
	} else if (y <= 1.45e+38) {
		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 <= (-2.2d+31)) then
        tmp = t
    else if (y <= (-4.8d-30)) then
        tmp = x / (z / t)
    else if (y <= (-3.9d-53)) then
        tmp = (x * -t) / y
    else if (y <= 1.45d+38) 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 <= -2.2e+31) {
		tmp = t;
	} else if (y <= -4.8e-30) {
		tmp = x / (z / t);
	} else if (y <= -3.9e-53) {
		tmp = (x * -t) / y;
	} else if (y <= 1.45e+38) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e+31:
		tmp = t
	elif y <= -4.8e-30:
		tmp = x / (z / t)
	elif y <= -3.9e-53:
		tmp = (x * -t) / y
	elif y <= 1.45e+38:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e+31)
		tmp = t;
	elseif (y <= -4.8e-30)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= -3.9e-53)
		tmp = Float64(Float64(x * Float64(-t)) / y);
	elseif (y <= 1.45e+38)
		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 <= -2.2e+31)
		tmp = t;
	elseif (y <= -4.8e-30)
		tmp = x / (z / t);
	elseif (y <= -3.9e-53)
		tmp = (x * -t) / y;
	elseif (y <= 1.45e+38)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e+31], t, If[LessEqual[y, -4.8e-30], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e-53], N[(N[(x * (-t)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.45e+38], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2000000000000001e31 or 1.45000000000000003e38 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.3%

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

      2. associate-*r/ 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -2.2000000000000001e31 < y < -4.7999999999999997e-30

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 65.1%

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

      1. associate-*l/ 39.6%

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

      2. associate-/l* 65.3%

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

   4. Applied egg-rr 65.3%

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

   if -4.7999999999999997e-30 < y < -3.9000000000000002e-53

   1. Initial program 83.5%

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

      1. associate-*l/ 84.8%

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

      2. associate-*r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 52.8%

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

      1. associate-*l/ 52.5%

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

      2. *-commutative 52.5%

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

   6. Simplified 52.5%

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

   7. Taylor expanded in z around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. distribute-neg-frac 52.9%

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

      3. distribute-rgt-neg-out 52.9%

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

   9. Simplified 52.9%

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

   if -3.9000000000000002e-53 < y < 1.45000000000000003e38

   1. Initial program 93.9%

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

      1. associate-*l/ 96.1%

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

      2. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 70.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+38}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -8e+78)
     t_1
     (if (<= y -1.4e-195)
       (* t (/ x (- z y)))
       (if (<= y 1.4e+38) (/ (* (- x y) t) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -8e+78) {
		tmp = t_1;
	} else if (y <= -1.4e-195) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.4e+38) {
		tmp = ((x - y) * t) / z;
	} 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 * (y / (y - z))
    if (y <= (-8d+78)) then
        tmp = t_1
    else if (y <= (-1.4d-195)) then
        tmp = t * (x / (z - y))
    else if (y <= 1.4d+38) then
        tmp = ((x - y) * t) / z
    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 * (y / (y - z));
	double tmp;
	if (y <= -8e+78) {
		tmp = t_1;
	} else if (y <= -1.4e-195) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.4e+38) {
		tmp = ((x - y) * t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -8e+78:
		tmp = t_1
	elif y <= -1.4e-195:
		tmp = t * (x / (z - y))
	elif y <= 1.4e+38:
		tmp = ((x - y) * t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -8e+78)
		tmp = t_1;
	elseif (y <= -1.4e-195)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 1.4e+38)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -8e+78)
		tmp = t_1;
	elseif (y <= -1.4e-195)
		tmp = t * (x / (z - y));
	elseif (y <= 1.4e+38)
		tmp = ((x - y) * t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+78], t$95$1, If[LessEqual[y, -1.4e-195], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+38], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000007e78 or 1.4e38 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

      2. distribute-neg-frac 80.9%

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

   4. Simplified 80.9%

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

      1. frac-2neg 80.9%

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

      2. div-inv 80.7%

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

      3. remove-double-neg 80.7%

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

      4. sub-neg 80.7%

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

      5. distribute-neg-in 80.7%

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

      6. remove-double-neg 80.7%

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

      7. +-commutative 80.7%

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

      8. sub-neg 80.7%

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

   6. Applied egg-rr 80.7%

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

      1. associate-*r/ 80.9%

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

      2. *-rgt-identity 80.9%

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

   8. Simplified 80.9%

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

   if -8.00000000000000007e78 < y < -1.40000000000000002e-195

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 67.9%

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

   if -1.40000000000000002e-195 < y < 1.4e38

   1. Initial program 93.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around inf 85.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 10: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+152}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e+102)
   (* t (/ y (- y z)))
   (if (<= y 2.8e+152) (* (- x y) (/ t (- z y))) (* t (/ (- y x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+102) {
		tmp = t * (y / (y - z));
	} else if (y <= 2.8e+152) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * ((y - x) / 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 <= (-3d+102)) then
        tmp = t * (y / (y - z))
    else if (y <= 2.8d+152) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+102) {
		tmp = t * (y / (y - z));
	} else if (y <= 2.8e+152) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e+102:
		tmp = t * (y / (y - z))
	elif y <= 2.8e+152:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e+102)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 2.8e+152)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e+102)
		tmp = t * (y / (y - z));
	elseif (y <= 2.8e+152)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e+102], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+152], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9999999999999998e102

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. distribute-neg-frac 86.9%

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

   4. Simplified 86.9%

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

      1. frac-2neg 86.9%

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

      2. div-inv 86.7%

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

      3. remove-double-neg 86.7%

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

      4. sub-neg 86.7%

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

      5. distribute-neg-in 86.7%

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

      6. remove-double-neg 86.7%

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

      7. +-commutative 86.7%

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

      8. sub-neg 86.7%

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

   6. Applied egg-rr 86.7%

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

      1. associate-*r/ 86.9%

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

      2. *-rgt-identity 86.9%

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

   8. Simplified 86.9%

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

   if -2.9999999999999998e102 < y < 2.8000000000000002e152

   1. Initial program 95.3%

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

      1. associate-*l/ 91.7%

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

      2. associate-*r/ 92.2%

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

   3. Simplified 92.2%

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

   if 2.8000000000000002e152 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 92.7%

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

      1. associate-*r/ 92.7%

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

      2. neg-mul-1 92.7%

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

      3. neg-sub0 92.7%

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

      4. associate--r- 92.7%

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

      5. neg-sub0 92.7%

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

   4. Simplified 92.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+152}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 11: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.55e+92) t (if (<= y 1.45e+74) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.55e+92) {
		tmp = t;
	} else if (y <= 1.45e+74) {
		tmp = x * (t / (z - 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 <= (-3.55d+92)) then
        tmp = t
    else if (y <= 1.45d+74) then
        tmp = x * (t / (z - 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 <= -3.55e+92) {
		tmp = t;
	} else if (y <= 1.45e+74) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.55e+92:
		tmp = t
	elif y <= 1.45e+74:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.55e+92)
		tmp = t;
	elseif (y <= 1.45e+74)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.55e+92)
		tmp = t;
	elseif (y <= 1.45e+74)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.55e+92], t, If[LessEqual[y, 1.45e+74], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.55e92 or 1.4500000000000001e74 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.1%

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

      2. associate-*r/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 71.9%

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

   if -3.55e92 < y < 1.4500000000000001e74

   1. Initial program 94.8%

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

      1. associate-*l/ 91.4%

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

      2. associate-*r/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around inf 71.6%

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

      1. associate-*l/ 69.8%

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

      2. *-commutative 69.8%

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

   6. Simplified 69.8%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+92}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e+31) t (if (<= y 1.4e+38) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+31) {
		tmp = t;
	} else if (y <= 1.4e+38) {
		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 <= (-3d+31)) then
        tmp = t
    else if (y <= 1.4d+38) 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 <= -3e+31) {
		tmp = t;
	} else if (y <= 1.4e+38) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e+31:
		tmp = t
	elif y <= 1.4e+38:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e+31)
		tmp = t;
	elseif (y <= 1.4e+38)
		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 <= -3e+31)
		tmp = t;
	elseif (y <= 1.4e+38)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e+31], t, If[LessEqual[y, 1.4e+38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999989e31 or 1.4e38 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.3%

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

      2. associate-*r/ 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -2.99999999999999989e31 < y < 1.4e38

   1. Initial program 93.9%

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

   2. Taylor expanded in y around 0 65.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+31}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.9e+30) t (if (<= y 1.6e+38) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e+30) {
		tmp = t;
	} else if (y <= 1.6e+38) {
		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 <= (-2.9d+30)) then
        tmp = t
    else if (y <= 1.6d+38) 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 <= -2.9e+30) {
		tmp = t;
	} else if (y <= 1.6e+38) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.9e+30:
		tmp = t
	elif y <= 1.6e+38:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.9e+30)
		tmp = t;
	elseif (y <= 1.6e+38)
		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 <= -2.9e+30)
		tmp = t;
	elseif (y <= 1.6e+38)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.9e+30], t, If[LessEqual[y, 1.6e+38], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999998e30 or 1.59999999999999993e38 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.3%

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

      2. associate-*r/ 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in y around inf 66.0%

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

   if -2.8999999999999998e30 < y < 1.59999999999999993e38

   1. Initial program 93.9%

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

      1. associate-*l/ 93.5%

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

      2. associate-*r/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around 0 64.6%

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

      1. associate-/l* 65.3%

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

   6. Simplified 65.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 34.7% 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 97.0%

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

   1. associate-*l/ 83.0%

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

   2. associate-*r/ 83.4%

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

3. Simplified 83.4%

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

4. Taylor expanded in y around inf 39.4%

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

5. Final simplification 39.4%

   \[\leadsto t \]

Developer target: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023238 
(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))