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

Percentage Accurate: 97.4% → 97.4%

Time: 8.4s

Alternatives: 10

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: 97.4% 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: 97.4% 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]

Derivation

1. Initial program 96.6%

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

   1. associate-*l/ 85.1%

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

   2. associate-/l* 85.1%

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

3. Simplified 85.1%

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

   1. associate-*r/ 85.1%

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

   2. associate-*l/ 96.6%

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

   3. *-commutative 96.6%

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

   4. clear-num 96.4%

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

   5. un-div-inv 96.9%

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

6. Applied egg-rr 96.9%

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

Alternative 2: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.16e+166)
     t_1
     (if (<= y -3.8e-89)
       (* t (/ y (- y z)))
       (if (<= y 4.2e+25) (* x (/ t (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.16e+166) {
		tmp = t_1;
	} else if (y <= -3.8e-89) {
		tmp = t * (y / (y - z));
	} else if (y <= 4.2e+25) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.16d+166)) then
        tmp = t_1
    else if (y <= (-3.8d-89)) then
        tmp = t * (y / (y - z))
    else if (y <= 4.2d+25) then
        tmp = x * (t / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.16e+166) {
		tmp = t_1;
	} else if (y <= -3.8e-89) {
		tmp = t * (y / (y - z));
	} else if (y <= 4.2e+25) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.16e+166:
		tmp = t_1
	elif y <= -3.8e-89:
		tmp = t * (y / (y - z))
	elif y <= 4.2e+25:
		tmp = x * (t / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.16e+166)
		tmp = t_1;
	elseif (y <= -3.8e-89)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 4.2e+25)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.16e+166)
		tmp = t_1;
	elseif (y <= -3.8e-89)
		tmp = t * (y / (y - z));
	elseif (y <= 4.2e+25)
		tmp = x * (t / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.16e+166], t$95$1, If[LessEqual[y, -3.8e-89], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+25], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.16000000000000002e166 or 4.1999999999999998e25 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 69.5%

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

      2. associate-/l* 72.0%

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

   3. Simplified 72.0%

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

      1. associate-*r/ 69.5%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 62.3%

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

      1. associate-*r/ 62.3%

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

      2. neg-mul-1 62.3%

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

      3. distribute-rgt-neg-in 62.3%

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

      4. sub-neg 62.3%

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

      5. distribute-neg-out 62.3%

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

      6. remove-double-neg 62.3%

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

      7. +-commutative 62.3%

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

      8. sub-neg 62.3%

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

      9. associate-/l* 88.6%

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

      10. div-sub 88.6%

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

      11. *-inverses 88.6%

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

   9. Simplified 88.6%

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

   if -1.16000000000000002e166 < y < -3.8000000000000001e-89

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 69.1%

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

      1. neg-mul-1 69.1%

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

      2. distribute-neg-frac2 69.1%

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

      3. neg-sub0 69.1%

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

      4. sub-neg 69.1%

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

      5. +-commutative 69.1%

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

      6. associate--r+ 69.1%

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

      7. neg-sub0 69.1%

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

      8. remove-double-neg 69.1%

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

   5. Simplified 69.1%

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

   if -3.8000000000000001e-89 < y < 4.1999999999999998e25

   1. Initial program 92.8%

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

      1. associate-*l/ 93.2%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf 80.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+166}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.14 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-96}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.14e+15)
     t_1
     (if (<= y -1.6e-96)
       (* y (/ t (- y z)))
       (if (<= y 5.6e+26) (* x (/ t (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.14e+15) {
		tmp = t_1;
	} else if (y <= -1.6e-96) {
		tmp = y * (t / (y - z));
	} else if (y <= 5.6e+26) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.14d+15)) then
        tmp = t_1
    else if (y <= (-1.6d-96)) then
        tmp = y * (t / (y - z))
    else if (y <= 5.6d+26) then
        tmp = x * (t / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.14e+15) {
		tmp = t_1;
	} else if (y <= -1.6e-96) {
		tmp = y * (t / (y - z));
	} else if (y <= 5.6e+26) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.14e+15:
		tmp = t_1
	elif y <= -1.6e-96:
		tmp = y * (t / (y - z))
	elif y <= 5.6e+26:
		tmp = x * (t / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.14e+15)
		tmp = t_1;
	elseif (y <= -1.6e-96)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= 5.6e+26)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.14e+15)
		tmp = t_1;
	elseif (y <= -1.6e-96)
		tmp = y * (t / (y - z));
	elseif (y <= 5.6e+26)
		tmp = x * (t / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.14e+15], t$95$1, If[LessEqual[y, -1.6e-96], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+26], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.14e15 or 5.59999999999999999e26 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.4%

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

      2. associate-/l* 71.9%

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

   3. Simplified 71.9%

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

      1. associate-*r/ 74.4%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 60.6%

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

      1. associate-*r/ 60.6%

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

      2. neg-mul-1 60.6%

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

      3. distribute-rgt-neg-in 60.6%

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

      4. sub-neg 60.6%

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

      5. distribute-neg-out 60.6%

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

      6. remove-double-neg 60.6%

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

      7. +-commutative 60.6%

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

      8. sub-neg 60.6%

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

      9. associate-/l* 82.0%

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

      10. div-sub 82.0%

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

      11. *-inverses 82.0%

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

   9. Simplified 82.0%

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

   if -1.14e15 < y < -1.60000000000000006e-96

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. mul-1-neg 78.2%

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

      3. distribute-rgt-neg-out 78.2%

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

      4. associate-*l/ 78.2%

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

      5. *-commutative 78.2%

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

      6. distribute-lft-neg-out 78.2%

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

      7. distribute-rgt-neg-in 78.2%

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

      8. distribute-frac-neg2 78.2%

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

      9. neg-sub0 78.2%

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

      10. sub-neg 78.2%

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

      11. +-commutative 78.2%

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

      12. associate--r+ 78.2%

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

      13. neg-sub0 78.2%

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

      14. remove-double-neg 78.2%

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

   7. Simplified 78.2%

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

   if -1.60000000000000006e-96 < y < 5.59999999999999999e26

   1. Initial program 92.8%

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

      1. associate-*l/ 93.2%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf 80.7%

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

Alternative 4: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.65e+154)
   (* t (- 1.0 (/ x y)))
   (if (<= y 3.8e+194) (* (- x y) (/ t (- z y))) (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.65e+154) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.8e+194) {
		tmp = (x - y) * (t / (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 <= (-2.65d+154)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 3.8d+194) then
        tmp = (x - y) * (t / (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 <= -2.65e+154) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.8e+194) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.65e+154:
		tmp = t * (1.0 - (x / y))
	elif y <= 3.8e+194:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.65e+154)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 3.8e+194)
		tmp = Float64(Float64(x - y) * Float64(t / 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 <= -2.65e+154)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 3.8e+194)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.65e+154], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+194], N[(N[(x - y), $MachinePrecision] * N[(t / 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 < -2.65000000000000012e154

   1. Initial program 100.0%

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

      1. associate-*l/ 64.8%

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

      2. associate-/l* 69.2%

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

   3. Simplified 69.2%

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

      1. associate-*r/ 64.8%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 62.1%

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

      1. associate-*r/ 62.1%

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

      2. neg-mul-1 62.1%

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

      3. distribute-rgt-neg-in 62.1%

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

      4. sub-neg 62.1%

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

      5. distribute-neg-out 62.1%

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

      6. remove-double-neg 62.1%

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

      7. +-commutative 62.1%

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

      8. sub-neg 62.1%

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

      9. associate-/l* 97.2%

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

      10. div-sub 97.2%

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

      11. *-inverses 97.2%

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

   9. Simplified 97.2%

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

   if -2.65000000000000012e154 < y < 3.7999999999999999e194

   1. Initial program 95.6%

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

      1. associate-*l/ 90.2%

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

      2. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   if 3.7999999999999999e194 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.9%

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

      1. neg-mul-1 86.9%

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

      2. distribute-neg-frac2 86.9%

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

      3. neg-sub0 86.9%

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

      4. sub-neg 86.9%

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

      5. +-commutative 86.9%

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

      6. associate--r+ 86.9%

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

      7. neg-sub0 86.9%

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

      8. remove-double-neg 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+154}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-77} \lor \neg \left(z \leq 1.8 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.4e-77) (not (<= z 1.8e-17)))
   (/ t (/ z (- x y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.4e-77) || !(z <= 1.8e-17)) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t * (1.0 - (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 ((z <= (-6.4d-77)) .or. (.not. (z <= 1.8d-17))) then
        tmp = t / (z / (x - y))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.4e-77) || !(z <= 1.8e-17)) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.4e-77) or not (z <= 1.8e-17):
		tmp = t / (z / (x - y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.4e-77) || !(z <= 1.8e-17))
		tmp = Float64(t / Float64(z / Float64(x - y)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.4e-77) || ~((z <= 1.8e-17)))
		tmp = t / (z / (x - y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.4e-77], N[Not[LessEqual[z, 1.8e-17]], $MachinePrecision]], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.39999999999999999e-77 or 1.79999999999999997e-17 < z

   1. Initial program 97.3%

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

      1. associate-*l/ 86.4%

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

      2. associate-/l* 82.2%

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

   3. Simplified 82.2%

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

      1. associate-*r/ 86.4%

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

      2. associate-*l/ 97.3%

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

      3. *-commutative 97.3%

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

      4. clear-num 97.0%

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

      5. un-div-inv 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in z around inf 75.1%

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

   if -6.39999999999999999e-77 < z < 1.79999999999999997e-17

   1. Initial program 95.9%

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

      1. associate-*l/ 83.5%

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

      2. associate-/l* 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. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 83.5%

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

      2. associate-*l/ 95.9%

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

      3. *-commutative 95.9%

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

      4. clear-num 95.7%

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

      5. un-div-inv 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around 0 73.7%

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

      1. associate-*r/ 73.7%

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

      2. neg-mul-1 73.7%

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

      3. distribute-rgt-neg-in 73.7%

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

      4. sub-neg 73.7%

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

      5. distribute-neg-out 73.7%

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

      6. remove-double-neg 73.7%

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

      7. +-commutative 73.7%

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

      8. sub-neg 73.7%

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

      9. associate-/l* 86.9%

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

      10. div-sub 86.9%

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

      11. *-inverses 86.9%

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

   9. Simplified 86.9%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-77} \lor \neg \left(z \leq 1.8 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-92} \lor \neg \left(y \leq 9 \cdot 10^{+24}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.85e-92) (not (<= y 9e+24)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.85e-92) || !(y <= 9e+24)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.85d-92)) .or. (.not. (y <= 9d+24))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.85e-92) || !(y <= 9e+24)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.85e-92) or not (y <= 9e+24):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.85e-92) || !(y <= 9e+24))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.85e-92) || ~((y <= 9e+24)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.85e-92], N[Not[LessEqual[y, 9e+24]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.85000000000000004e-92 or 9.00000000000000039e24 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 78.4%

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

      2. associate-/l* 76.3%

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

   3. Simplified 76.3%

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

      1. associate-*r/ 78.4%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 60.4%

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

      1. associate-*r/ 60.4%

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

      2. neg-mul-1 60.4%

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

      3. distribute-rgt-neg-in 60.4%

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

      4. sub-neg 60.4%

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

      5. distribute-neg-out 60.4%

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

      6. remove-double-neg 60.4%

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

      7. +-commutative 60.4%

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

      8. sub-neg 60.4%

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

      9. associate-/l* 77.7%

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

      10. div-sub 77.8%

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

      11. *-inverses 77.8%

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

   9. Simplified 77.8%

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

   if -2.85000000000000004e-92 < y < 9.00000000000000039e24

   1. Initial program 92.8%

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

      1. associate-*l/ 93.2%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf 80.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-92} \lor \neg \left(y \leq 9 \cdot 10^{+24}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-90} \lor \neg \left(y \leq 5.4 \cdot 10^{-70}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.3e-90) (not (<= y 5.4e-70)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.3e-90) || !(y <= 5.4e-70)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (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 <= (-2.3d-90)) .or. (.not. (y <= 5.4d-70))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (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 <= -2.3e-90) || !(y <= 5.4e-70)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.3e-90) or not (y <= 5.4e-70):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.3e-90) || !(y <= 5.4e-70))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.3e-90) || ~((y <= 5.4e-70)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.3e-90], N[Not[LessEqual[y, 5.4e-70]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999998e-90 or 5.4000000000000003e-70 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 80.0%

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

      2. associate-/l* 78.8%

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

   3. Simplified 78.8%

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

      1. associate-*r/ 80.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 58.4%

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

      1. associate-*r/ 58.4%

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

      2. neg-mul-1 58.4%

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

      3. distribute-rgt-neg-in 58.4%

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

      4. sub-neg 58.4%

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

      5. distribute-neg-out 58.4%

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

      6. remove-double-neg 58.4%

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

      7. +-commutative 58.4%

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

      8. sub-neg 58.4%

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

      9. associate-/l* 74.1%

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

      10. div-sub 74.1%

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

      11. *-inverses 74.1%

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

   9. Simplified 74.1%

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

   if -2.2999999999999998e-90 < y < 5.4000000000000003e-70

   1. Initial program 91.2%

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

      1. associate-*l/ 93.7%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around inf 86.4%

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

   6. Taylor expanded in z around inf 78.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-90} \lor \neg \left(y \leq 5.4 \cdot 10^{-70}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-89}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e-89) t (if (<= y 1.12e+27) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-89) {
		tmp = t;
	} else if (y <= 1.12e+27) {
		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 <= (-4.1d-89)) then
        tmp = t
    else if (y <= 1.12d+27) 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 <= -4.1e-89) {
		tmp = t;
	} else if (y <= 1.12e+27) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e-89:
		tmp = t
	elif y <= 1.12e+27:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e-89)
		tmp = t;
	elseif (y <= 1.12e+27)
		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 <= -4.1e-89)
		tmp = t;
	elseif (y <= 1.12e+27)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e-89], t, If[LessEqual[y, 1.12e+27], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999998e-89 or 1.12e27 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 78.4%

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

      2. associate-/l* 76.3%

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

   3. Simplified 76.3%

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

   5. Taylor expanded in y around inf 58.3%

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

   if -4.0999999999999998e-89 < y < 1.12e27

   1. Initial program 92.8%

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

      1. associate-*l/ 93.2%

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

      2. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf 80.7%

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

   6. Taylor expanded in z around inf 71.5%

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

Alternative 9: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

3. Final simplification 96.6%

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

Alternative 10: 35.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. associate-*l/ 85.1%

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

   2. associate-/l* 85.1%

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

3. Simplified 85.1%

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

5. Taylor expanded in y around inf 36.9%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 97.4% 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 2024180 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

  (* (/ (- x y) (- z y)) t))