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

Percentage Accurate: 96.8% → 96.8%

Time: 10.6s

Alternatives: 12

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 97.5%

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

2. Final simplification 97.5%

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

Alternative 2: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ t_2 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))) (t_2 (* t (/ (- y x) y))))
   (if (<= y -3.6e+78)
     t_2
     (if (<= y -3.8e-51)
       t_1
       (if (<= y 1.8e-66)
         (/ x (/ (- z y) t))
         (if (<= y 1.65e-23)
           (* y (/ t (- y z)))
           (if (<= y 4e+55) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (y <= -3.6e+78) {
		tmp = t_2;
	} else if (y <= -3.8e-51) {
		tmp = t_1;
	} else if (y <= 1.8e-66) {
		tmp = x / ((z - y) / t);
	} else if (y <= 1.65e-23) {
		tmp = y * (t / (y - z));
	} else if (y <= 4e+55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    t_2 = t * ((y - x) / y)
    if (y <= (-3.6d+78)) then
        tmp = t_2
    else if (y <= (-3.8d-51)) then
        tmp = t_1
    else if (y <= 1.8d-66) then
        tmp = x / ((z - y) / t)
    else if (y <= 1.65d-23) then
        tmp = y * (t / (y - z))
    else if (y <= 4d+55) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (y <= -3.6e+78) {
		tmp = t_2;
	} else if (y <= -3.8e-51) {
		tmp = t_1;
	} else if (y <= 1.8e-66) {
		tmp = x / ((z - y) / t);
	} else if (y <= 1.65e-23) {
		tmp = y * (t / (y - z));
	} else if (y <= 4e+55) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	t_2 = t * ((y - x) / y)
	tmp = 0
	if y <= -3.6e+78:
		tmp = t_2
	elif y <= -3.8e-51:
		tmp = t_1
	elif y <= 1.8e-66:
		tmp = x / ((z - y) / t)
	elif y <= 1.65e-23:
		tmp = y * (t / (y - z))
	elif y <= 4e+55:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	t_2 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -3.6e+78)
		tmp = t_2;
	elseif (y <= -3.8e-51)
		tmp = t_1;
	elseif (y <= 1.8e-66)
		tmp = Float64(x / Float64(Float64(z - y) / t));
	elseif (y <= 1.65e-23)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= 4e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	t_2 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -3.6e+78)
		tmp = t_2;
	elseif (y <= -3.8e-51)
		tmp = t_1;
	elseif (y <= 1.8e-66)
		tmp = x / ((z - y) / t);
	elseif (y <= 1.65e-23)
		tmp = y * (t / (y - z));
	elseif (y <= 4e+55)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+78], t$95$2, If[LessEqual[y, -3.8e-51], t$95$1, If[LessEqual[y, 1.8e-66], N[(x / N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-23], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+55], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6000000000000002e78 or 1.6500000000000001e-23 < y < 4.00000000000000004e55

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 86.3%

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

      1. associate-*r/ 86.3%

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

      2. neg-mul-1 86.3%

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

      3. neg-sub0 86.3%

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

      4. associate--r- 86.3%

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

      5. neg-sub0 86.3%

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

   4. Simplified 86.3%

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

   if -3.6000000000000002e78 < y < -3.80000000000000003e-51 or 4.00000000000000004e55 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 82.0%

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

      1. neg-mul-1 82.0%

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

      2. distribute-neg-frac 82.0%

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

   4. Simplified 82.0%

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

      1. frac-2neg 82.0%

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

      2. div-inv 81.9%

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

      3. remove-double-neg 81.9%

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

      4. sub-neg 81.9%

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

      5. distribute-neg-in 81.9%

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

      6. remove-double-neg 81.9%

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

   6. Applied egg-rr 81.9%

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

      1. associate-*r/ 82.0%

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

      2. *-rgt-identity 82.0%

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

      3. +-commutative 82.0%

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

      4. unsub-neg 82.0%

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

   8. Simplified 82.0%

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

   9. Taylor expanded in t around 0 62.6%

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

       1. *-commutative 62.6%

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

       2. associate-/l* 82.0%

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

       3. div-sub 82.1%

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

       4. *-inverses 82.1%

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

   11. Simplified 82.1%

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

   if -3.80000000000000003e-51 < y < 1.80000000000000006e-66

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 85.9%

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

      1. associate-/r/ 89.5%

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

   4. Applied egg-rr 89.5%

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

   if 1.80000000000000006e-66 < y < 1.6500000000000001e-23

   1. Initial program 92.7%

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

   2. Taylor expanded in x around 0 66.9%

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

      1. neg-mul-1 66.9%

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

      2. distribute-neg-frac 66.9%

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

   4. Simplified 66.9%

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

      1. frac-2neg 66.9%

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

      2. remove-double-neg 66.9%

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

      3. associate-*l/ 70.2%

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

      4. sub-neg 70.2%

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

      5. distribute-neg-in 70.2%

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

      6. remove-double-neg 70.2%

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

   6. Applied egg-rr 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-/l* 65.9%

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

      3. associate-/r/ 82.5%

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

      4. +-commutative 82.5%

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

      5. unsub-neg 82.5%

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

   8. Simplified 82.5%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 3: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+214}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.03 \lor \neg \left(y \leq 9.8 \cdot 10^{-67}\right):\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e+214)
   t
   (if (or (<= y -0.03) (not (<= y 9.8e-67)))
     (* y (/ t (- y z)))
     (* (- x y) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+214) {
		tmp = t;
	} else if ((y <= -0.03) || !(y <= 9.8e-67)) {
		tmp = y * (t / (y - z));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.1d+214)) then
        tmp = t
    else if ((y <= (-0.03d0)) .or. (.not. (y <= 9.8d-67))) then
        tmp = y * (t / (y - z))
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+214) {
		tmp = t;
	} else if ((y <= -0.03) || !(y <= 9.8e-67)) {
		tmp = y * (t / (y - z));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e+214:
		tmp = t
	elif (y <= -0.03) or not (y <= 9.8e-67):
		tmp = y * (t / (y - z))
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e+214)
		tmp = t;
	elseif ((y <= -0.03) || !(y <= 9.8e-67))
		tmp = Float64(y * Float64(t / Float64(y - z)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e+214)
		tmp = t;
	elseif ((y <= -0.03) || ~((y <= 9.8e-67)))
		tmp = y * (t / (y - z));
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e+214], t, If[Or[LessEqual[y, -0.03], N[Not[LessEqual[y, 9.8e-67]], $MachinePrecision]], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.10000000000000012e214

   1. Initial program 100.0%

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

      1. associate-*l/ 61.5%

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

      2. associate-*r/ 65.3%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in y around inf 81.4%

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

   if -1.10000000000000012e214 < y < -0.029999999999999999 or 9.79999999999999987e-67 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 76.5%

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

      1. neg-mul-1 76.5%

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

      2. distribute-neg-frac 76.5%

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

   4. Simplified 76.5%

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

      1. frac-2neg 76.5%

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

      2. remove-double-neg 76.5%

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

      3. associate-*l/ 59.6%

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

      4. sub-neg 59.6%

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

      5. distribute-neg-in 59.6%

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

      6. remove-double-neg 59.6%

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

   6. Applied egg-rr 59.6%

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

      1. *-commutative 59.6%

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

      2. associate-/l* 76.5%

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

      3. associate-/r/ 67.0%

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

      4. +-commutative 67.0%

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

      5. unsub-neg 67.0%

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

   8. Simplified 67.0%

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

   if -0.029999999999999999 < y < 9.79999999999999987e-67

   1. Initial program 94.7%

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

      1. associate-*l/ 95.1%

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

      2. associate-*r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around inf 81.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+214}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.03 \lor \neg \left(y \leq 9.8 \cdot 10^{-67}\right):\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 4: 67.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+213}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -780000000000 \lor \neg \left(y \leq 1.9 \cdot 10^{-66}\right):\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e+213)
   t
   (if (or (<= y -780000000000.0) (not (<= y 1.9e-66)))
     (* y (/ t (- y z)))
     (* t (/ x (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e+213) {
		tmp = t;
	} else if ((y <= -780000000000.0) || !(y <= 1.9e-66)) {
		tmp = y * (t / (y - z));
	} 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 <= (-7.2d+213)) then
        tmp = t
    else if ((y <= (-780000000000.0d0)) .or. (.not. (y <= 1.9d-66))) then
        tmp = y * (t / (y - z))
    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 <= -7.2e+213) {
		tmp = t;
	} else if ((y <= -780000000000.0) || !(y <= 1.9e-66)) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e+213:
		tmp = t
	elif (y <= -780000000000.0) or not (y <= 1.9e-66):
		tmp = y * (t / (y - z))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e+213)
		tmp = t;
	elseif ((y <= -780000000000.0) || !(y <= 1.9e-66))
		tmp = Float64(y * Float64(t / Float64(y - z)));
	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 <= -7.2e+213)
		tmp = t;
	elseif ((y <= -780000000000.0) || ~((y <= 1.9e-66)))
		tmp = y * (t / (y - z));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e+213], t, If[Or[LessEqual[y, -780000000000.0], N[Not[LessEqual[y, 1.9e-66]], $MachinePrecision]], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2000000000000002e213

   1. Initial program 100.0%

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

      1. associate-*l/ 61.5%

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

      2. associate-*r/ 65.3%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in y around inf 81.4%

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

   if -7.2000000000000002e213 < y < -7.8e11 or 1.8999999999999999e-66 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 77.3%

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

      1. neg-mul-1 77.3%

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

      2. distribute-neg-frac 77.3%

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

   4. Simplified 77.3%

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

      1. frac-2neg 77.3%

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

      2. remove-double-neg 77.3%

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

      3. associate-*l/ 59.9%

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

      4. sub-neg 59.9%

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

      5. distribute-neg-in 59.9%

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

      6. remove-double-neg 59.9%

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

   6. Applied egg-rr 59.9%

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

      1. *-commutative 59.9%

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

      2. associate-/l* 77.2%

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

      3. associate-/r/ 67.4%

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

      4. +-commutative 67.4%

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

      5. unsub-neg 67.4%

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

   8. Simplified 67.4%

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

   if -7.8e11 < y < 1.8999999999999999e-66

   1. Initial program 94.9%

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

   2. Taylor expanded in x around inf 83.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+213}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -780000000000 \lor \neg \left(y \leq 1.9 \cdot 10^{-66}\right):\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 5: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+205}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+78)
   (* t (/ (- y x) y))
   (if (<= y 7.5e+205) (* (- x y) (/ t (- z y))) (/ t (- 1.0 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+78) {
		tmp = t * ((y - x) / y);
	} else if (y <= 7.5e+205) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (1.0 - (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 <= (-2.8d+78)) then
        tmp = t * ((y - x) / y)
    else if (y <= 7.5d+205) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t / (1.0d0 - (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 <= -2.8e+78) {
		tmp = t * ((y - x) / y);
	} else if (y <= 7.5e+205) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+78:
		tmp = t * ((y - x) / y)
	elif y <= 7.5e+205:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+78)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 7.5e+205)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+78)
		tmp = t * ((y - x) / y);
	elseif (y <= 7.5e+205)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+78], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+205], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8000000000000001e78

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 90.5%

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

      1. associate-*r/ 90.5%

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

      2. neg-mul-1 90.5%

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

      3. neg-sub0 90.5%

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

      4. associate--r- 90.5%

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

      5. neg-sub0 90.5%

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

   4. Simplified 90.5%

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

   if -2.8000000000000001e78 < y < 7.5000000000000003e205

   1. Initial program 96.7%

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

      1. associate-*l/ 90.7%

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

      2. associate-*r/ 94.1%

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

   3. Simplified 94.1%

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

   if 7.5000000000000003e205 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.3%

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

      1. neg-mul-1 95.3%

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

      2. distribute-neg-frac 95.3%

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

   4. Simplified 95.3%

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

      1. frac-2neg 95.3%

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

      2. div-inv 95.0%

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

      3. remove-double-neg 95.0%

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

      4. sub-neg 95.0%

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

      5. distribute-neg-in 95.0%

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

      6. remove-double-neg 95.0%

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

   6. Applied egg-rr 95.0%

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

      1. associate-*r/ 95.3%

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

      2. *-rgt-identity 95.3%

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

      3. +-commutative 95.3%

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

      4. unsub-neg 95.3%

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

   8. Simplified 95.3%

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

   9. Taylor expanded in t around 0 36.6%

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

       1. *-commutative 36.6%

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

       2. associate-/l* 95.3%

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

       3. div-sub 95.3%

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

       4. *-inverses 95.3%

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

   11. Simplified 95.3%

       \[\leadsto \color{blue}{\frac{t}{1 - \frac{z}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+205}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 6: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-52} \lor \neg \left(y \leq 1.95 \cdot 10^{-66}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.95e-52) (not (<= y 1.95e-66)))
   (* t (/ y (- y z)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95e-52) || !(y <= 1.95e-66)) {
		tmp = t * (y / (y - z));
	} 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 <= (-1.95d-52)) .or. (.not. (y <= 1.95d-66))) then
        tmp = t * (y / (y - z))
    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 <= -1.95e-52) || !(y <= 1.95e-66)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.95e-52) or not (y <= 1.95e-66):
		tmp = t * (y / (y - z))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.95e-52) || !(y <= 1.95e-66))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 <= -1.95e-52) || ~((y <= 1.95e-66)))
		tmp = t * (y / (y - z));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.95e-52], N[Not[LessEqual[y, 1.95e-66]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000009e-52 or 1.94999999999999991e-66 < y

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 77.6%

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

      1. neg-mul-1 77.6%

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

      2. distribute-neg-frac 77.6%

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

   4. Simplified 77.6%

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

      1. frac-2neg 77.6%

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

      2. div-inv 77.5%

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

      3. remove-double-neg 77.5%

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

      4. sub-neg 77.5%

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

      5. distribute-neg-in 77.5%

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

      6. remove-double-neg 77.5%

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

   6. Applied egg-rr 77.5%

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

      1. associate-*r/ 77.6%

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

      2. *-rgt-identity 77.6%

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

      3. +-commutative 77.6%

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

      4. unsub-neg 77.6%

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

   8. Simplified 77.6%

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

   if -1.95000000000000009e-52 < y < 1.94999999999999991e-66

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 85.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-52} \lor \neg \left(y \leq 1.95 \cdot 10^{-66}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 7: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-5}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e+66) t (if (<= y 1.55e-5) (* (- x y) (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e+66) {
		tmp = t;
	} else if (y <= 1.55e-5) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d+66)) then
        tmp = t
    else if (y <= 1.55d-5) then
        tmp = (x - y) * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e+66) {
		tmp = t;
	} else if (y <= 1.55e-5) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e+66:
		tmp = t
	elif y <= 1.55e-5:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e+66)
		tmp = t;
	elseif (y <= 1.55e-5)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e+66)
		tmp = t;
	elseif (y <= 1.55e-5)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e+66], t, If[LessEqual[y, 1.55e-5], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4000000000000003e66 or 1.55000000000000007e-5 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.5%

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

      2. associate-*r/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in y around inf 63.7%

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

   if -3.4000000000000003e66 < y < 1.55000000000000007e-5

   1. Initial program 95.5%

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

      1. associate-*l/ 95.3%

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

      2. associate-*r/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 74.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-5}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-50)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 1.05e-66) (* t (/ x (- z y))) (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-50) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.05e-66) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.3d-50)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 1.05d-66) then
        tmp = t * (x / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-50) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.05e-66) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-50:
		tmp = t / (1.0 - (z / y))
	elif y <= 1.05e-66:
		tmp = t * (x / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-50)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 1.05e-66)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-50)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 1.05e-66)
		tmp = t * (x / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-50], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-66], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3000000000000001e-50

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

      2. distribute-neg-frac 78.1%

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

   4. Simplified 78.1%

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

      1. frac-2neg 78.1%

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

      2. div-inv 78.0%

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

      3. remove-double-neg 78.0%

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

      4. sub-neg 78.0%

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

      5. distribute-neg-in 78.0%

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

      6. remove-double-neg 78.0%

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

   6. Applied egg-rr 78.0%

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

      1. associate-*r/ 78.1%

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

      2. *-rgt-identity 78.1%

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

      3. +-commutative 78.1%

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

      4. unsub-neg 78.1%

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

   8. Simplified 78.1%

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

   9. Taylor expanded in t around 0 65.3%

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

       1. *-commutative 65.3%

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

       2. associate-/l* 78.1%

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

       3. div-sub 78.1%

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

       4. *-inverses 78.1%

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

   11. Simplified 78.1%

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

   if -1.3000000000000001e-50 < y < 1.05e-66

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 85.9%

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

   if 1.05e-66 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 77.1%

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

      1. neg-mul-1 77.1%

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

      2. distribute-neg-frac 77.1%

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

   4. Simplified 77.1%

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

      1. frac-2neg 77.1%

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

      2. div-inv 77.0%

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

      3. remove-double-neg 77.0%

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

      4. sub-neg 77.0%

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

      5. distribute-neg-in 77.0%

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

      6. remove-double-neg 77.0%

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

   6. Applied egg-rr 77.0%

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

      1. associate-*r/ 77.1%

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

      2. *-rgt-identity 77.1%

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

      3. +-commutative 77.1%

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

      4. unsub-neg 77.1%

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

   8. Simplified 77.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 9: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.4e-51)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 1.95e-66) (/ x (/ (- z y) t)) (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.4e-51) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.95e-66) {
		tmp = x / ((z - y) / t);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.4d-51)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 1.95d-66) then
        tmp = x / ((z - y) / t)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.4e-51) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.95e-66) {
		tmp = x / ((z - y) / t);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.4e-51:
		tmp = t / (1.0 - (z / y))
	elif y <= 1.95e-66:
		tmp = x / ((z - y) / t)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.4e-51)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 1.95e-66)
		tmp = Float64(x / Float64(Float64(z - y) / t));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.4e-51)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 1.95e-66)
		tmp = x / ((z - y) / t);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.4e-51], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-66], N[(x / N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999946e-51

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

      2. distribute-neg-frac 78.1%

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

   4. Simplified 78.1%

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

      1. frac-2neg 78.1%

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

      2. div-inv 78.0%

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

      3. remove-double-neg 78.0%

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

      4. sub-neg 78.0%

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

      5. distribute-neg-in 78.0%

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

      6. remove-double-neg 78.0%

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

   6. Applied egg-rr 78.0%

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

      1. associate-*r/ 78.1%

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

      2. *-rgt-identity 78.1%

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

      3. +-commutative 78.1%

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

      4. unsub-neg 78.1%

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

   8. Simplified 78.1%

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

   9. Taylor expanded in t around 0 65.3%

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

       1. *-commutative 65.3%

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

       2. associate-/l* 78.1%

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

       3. div-sub 78.1%

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

       4. *-inverses 78.1%

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

   11. Simplified 78.1%

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

   if -7.39999999999999946e-51 < y < 1.94999999999999991e-66

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 85.9%

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

      1. associate-/r/ 89.5%

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

   4. Applied egg-rr 89.5%

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

   if 1.94999999999999991e-66 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 77.1%

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

      1. neg-mul-1 77.1%

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

      2. distribute-neg-frac 77.1%

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

   4. Simplified 77.1%

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

      1. frac-2neg 77.1%

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

      2. div-inv 77.0%

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

      3. remove-double-neg 77.0%

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

      4. sub-neg 77.0%

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

      5. distribute-neg-in 77.0%

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

      6. remove-double-neg 77.0%

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

   6. Applied egg-rr 77.0%

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

      1. associate-*r/ 77.1%

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

      2. *-rgt-identity 77.1%

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

      3. +-commutative 77.1%

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

      4. unsub-neg 77.1%

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

   8. Simplified 77.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 10: 35.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e-8) t (if (<= y 2.4e-120) (* x (/ t y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e-8) {
		tmp = t;
	} else if (y <= 2.4e-120) {
		tmp = x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.8d-8)) then
        tmp = t
    else if (y <= 2.4d-120) then
        tmp = x * (t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e-8) {
		tmp = t;
	} else if (y <= 2.4e-120) {
		tmp = x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e-8:
		tmp = t
	elif y <= 2.4e-120:
		tmp = x * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e-8)
		tmp = t;
	elseif (y <= 2.4e-120)
		tmp = Float64(x * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e-8)
		tmp = t;
	elseif (y <= 2.4e-120)
		tmp = x * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e-8], t, If[LessEqual[y, 2.4e-120], N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e-8 or 2.3999999999999999e-120 < y

   1. Initial program 99.3%

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

      1. associate-*l/ 76.7%

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

      2. associate-*r/ 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around inf 53.5%

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

   if -6.8e-8 < y < 2.3999999999999999e-120

   1. Initial program 94.1%

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

   2. Taylor expanded in x around inf 83.9%

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

   3. Taylor expanded in z around 0 32.7%

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

      1. associate-*r/ 32.7%

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

      2. mul-1-neg 32.7%

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

      3. distribute-rgt-neg-out 32.7%

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

   5. Simplified 32.7%

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

      1. associate-/l* 30.3%

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

      2. associate-/r/ 31.5%

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

      3. add-sqr-sqrt 14.1%

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

      4. sqrt-unprod 23.3%

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

      5. sqr-neg 23.3%

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

      6. sqrt-unprod 8.9%

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

      7. add-sqr-sqrt 18.9%

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

   7. Applied egg-rr 18.9%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e+14) t (if (<= y 3.6e+14) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+14) {
		tmp = t;
	} else if (y <= 3.6e+14) {
		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 <= (-1.4d+14)) then
        tmp = t
    else if (y <= 3.6d+14) 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 <= -1.4e+14) {
		tmp = t;
	} else if (y <= 3.6e+14) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e+14:
		tmp = t
	elif y <= 3.6e+14:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e+14)
		tmp = t;
	elseif (y <= 3.6e+14)
		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 <= -1.4e+14)
		tmp = t;
	elseif (y <= 3.6e+14)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e+14], t, If[LessEqual[y, 3.6e+14], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e14 or 3.6e14 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.2%

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

      2. associate-*r/ 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in y around inf 61.1%

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

   if -1.4e14 < y < 3.6e14

   1. Initial program 95.0%

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

      1. clear-num 93.7%

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

      2. inv-pow 93.7%

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

   3. Applied egg-rr 93.7%

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

      1. unpow-1 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in y around 0 62.0%

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

      1. associate-/l* 63.4%

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

      2. associate-/r/ 65.8%

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

   8. Simplified 65.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 35.5% 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 97.5%

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

   1. associate-*l/ 83.6%

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

   2. associate-*r/ 88.7%

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

3. Simplified 88.7%

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

4. Taylor expanded in y around inf 37.2%

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

5. Final simplification 37.2%

   \[\leadsto t \]

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 2023199 
(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))