Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 12

Speedup: 1.0×

• 34.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(y - z\right) \cdot \left(t - x\right) \end{array} \]

FPCore

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

C

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

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) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - z\right) \cdot \left(t - x\right) \end{array} \]

FPCore

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

C

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

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) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(t - x\right) \cdot \left(y - z\right) \end{array} \]

FPCore

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

C

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

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 + ((t - x) * (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \left(t - x\right) \cdot \left(y - z\right) \]
4. Add Preprocessing

Alternative 2: 38.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-15}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+184}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e-15)
   (* y t)
   (if (<= y 5.4e-185)
     (* t (- z))
     (if (<= y 1.15e+22) (* x z) (if (<= y 1.3e+184) (* y t) (* x (- y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-15) {
		tmp = y * t;
	} else if (y <= 5.4e-185) {
		tmp = t * -z;
	} else if (y <= 1.15e+22) {
		tmp = x * z;
	} else if (y <= 1.3e+184) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d-15)) then
        tmp = y * t
    else if (y <= 5.4d-185) then
        tmp = t * -z
    else if (y <= 1.15d+22) then
        tmp = x * z
    else if (y <= 1.3d+184) then
        tmp = y * t
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-15) {
		tmp = y * t;
	} else if (y <= 5.4e-185) {
		tmp = t * -z;
	} else if (y <= 1.15e+22) {
		tmp = x * z;
	} else if (y <= 1.3e+184) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e-15:
		tmp = y * t
	elif y <= 5.4e-185:
		tmp = t * -z
	elif y <= 1.15e+22:
		tmp = x * z
	elif y <= 1.3e+184:
		tmp = y * t
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e-15)
		tmp = Float64(y * t);
	elseif (y <= 5.4e-185)
		tmp = Float64(t * Float64(-z));
	elseif (y <= 1.15e+22)
		tmp = Float64(x * z);
	elseif (y <= 1.3e+184)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e-15)
		tmp = y * t;
	elseif (y <= 5.4e-185)
		tmp = t * -z;
	elseif (y <= 1.15e+22)
		tmp = x * z;
	elseif (y <= 1.3e+184)
		tmp = y * t;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e-15], N[(y * t), $MachinePrecision], If[LessEqual[y, 5.4e-185], N[(t * (-z)), $MachinePrecision], If[LessEqual[y, 1.15e+22], N[(x * z), $MachinePrecision], If[LessEqual[y, 1.3e+184], N[(y * t), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65e-15 or 1.1500000000000001e22 < y < 1.29999999999999997e184

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in x around 0 81.7%

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

   7. Taylor expanded in y around inf 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

   9. Simplified 84.4%

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

   10. Taylor expanded in t around inf 53.4%

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

   if -1.65e-15 < y < 5.39999999999999976e-185

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.6%

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

      1. mul-1-neg 92.6%

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

      2. unsub-neg 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in t around inf 77.9%

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

   7. Taylor expanded in x around 0 45.8%

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

      1. mul-1-neg 45.8%

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

      2. *-commutative 45.8%

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

      3. distribute-rgt-neg-in 45.8%

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

   9. Simplified 45.8%

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

   if 5.39999999999999976e-185 < y < 1.1500000000000001e22

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. distribute-rgt-neg-in 63.5%

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

      3. sub-neg 63.5%

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

      4. +-commutative 63.5%

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

      5. distribute-neg-in 63.5%

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

      6. remove-double-neg 63.5%

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

      7. sub-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in z around inf 63.5%

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Taylor expanded in z around inf 42.5%

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

   if 1.29999999999999997e184 < y

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 93.0%

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

      1. *-commutative 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around 0 85.7%

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

   7. Taylor expanded in y around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   9. Simplified 93.0%

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

   10. Taylor expanded in t around 0 53.1%

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

       1. neg-mul-1 53.1%

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

   12. Simplified 53.1%

       \[\leadsto y \cdot \color{blue}{\left(-x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-15}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+22}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+184}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-49}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+179}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.52e-49)
   (* y t)
   (if (<= y 9e-61)
     x
     (if (<= y 8.4e+21) (* x z) (if (<= y 1.12e+179) (* y t) (* x (- y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e-49) {
		tmp = y * t;
	} else if (y <= 9e-61) {
		tmp = x;
	} else if (y <= 8.4e+21) {
		tmp = x * z;
	} else if (y <= 1.12e+179) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.52d-49)) then
        tmp = y * t
    else if (y <= 9d-61) then
        tmp = x
    else if (y <= 8.4d+21) then
        tmp = x * z
    else if (y <= 1.12d+179) then
        tmp = y * t
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e-49) {
		tmp = y * t;
	} else if (y <= 9e-61) {
		tmp = x;
	} else if (y <= 8.4e+21) {
		tmp = x * z;
	} else if (y <= 1.12e+179) {
		tmp = y * t;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.52e-49:
		tmp = y * t
	elif y <= 9e-61:
		tmp = x
	elif y <= 8.4e+21:
		tmp = x * z
	elif y <= 1.12e+179:
		tmp = y * t
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.52e-49)
		tmp = Float64(y * t);
	elseif (y <= 9e-61)
		tmp = x;
	elseif (y <= 8.4e+21)
		tmp = Float64(x * z);
	elseif (y <= 1.12e+179)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.52e-49)
		tmp = y * t;
	elseif (y <= 9e-61)
		tmp = x;
	elseif (y <= 8.4e+21)
		tmp = x * z;
	elseif (y <= 1.12e+179)
		tmp = y * t;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.52e-49], N[(y * t), $MachinePrecision], If[LessEqual[y, 9e-61], x, If[LessEqual[y, 8.4e+21], N[(x * z), $MachinePrecision], If[LessEqual[y, 1.12e+179], N[(y * t), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.52e-49 or 8.4e21 < y < 1.11999999999999997e179

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

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

      1. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in x around 0 77.8%

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

   7. Taylor expanded in y around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

   9. Simplified 79.5%

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

   10. Taylor expanded in t around inf 51.0%

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

   if -1.52e-49 < y < 9e-61

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.9%

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

      1. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in y around 0 37.3%

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

   if 9e-61 < y < 8.4e21

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-rgt-neg-in 58.8%

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

      3. sub-neg 58.8%

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

      4. +-commutative 58.8%

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

      5. distribute-neg-in 58.8%

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

      6. remove-double-neg 58.8%

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

      7. sub-neg 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 58.8%

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Taylor expanded in z around inf 55.0%

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

   if 1.11999999999999997e179 < y

   1. Initial program 99.8%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 93.0%

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

      1. *-commutative 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around 0 85.7%

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

   7. Taylor expanded in y around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   9. Simplified 93.0%

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

   10. Taylor expanded in t around 0 53.1%

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

       1. neg-mul-1 53.1%

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

   12. Simplified 53.1%

       \[\leadsto y \cdot \color{blue}{\left(-x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-49}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+179}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-186}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+21}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -4e-11)
     t_1
     (if (<= y 4e-186) (- x (* z t)) (if (<= y 8.4e+21) (+ x (* x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -4e-11) {
		tmp = t_1;
	} else if (y <= 4e-186) {
		tmp = x - (z * t);
	} else if (y <= 8.4e+21) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-4d-11)) then
        tmp = t_1
    else if (y <= 4d-186) then
        tmp = x - (z * t)
    else if (y <= 8.4d+21) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -4e-11) {
		tmp = t_1;
	} else if (y <= 4e-186) {
		tmp = x - (z * t);
	} else if (y <= 8.4e+21) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -4e-11:
		tmp = t_1
	elif y <= 4e-186:
		tmp = x - (z * t)
	elif y <= 8.4e+21:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -4e-11)
		tmp = t_1;
	elseif (y <= 4e-186)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 8.4e+21)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -4e-11)
		tmp = t_1;
	elseif (y <= 4e-186)
		tmp = x - (z * t);
	elseif (y <= 8.4e+21)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e-11], t$95$1, If[LessEqual[y, 4e-186], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+21], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.99999999999999976e-11 or 8.4e21 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.1%

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

      1. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in x around 0 82.5%

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

   7. Taylor expanded in y around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

   9. Simplified 86.1%

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

   if -3.99999999999999976e-11 < y < 3.9999999999999996e-186

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. unsub-neg 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in t around inf 77.6%

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

   if 3.9999999999999996e-186 < y < 8.4e21

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. distribute-rgt-neg-in 64.3%

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

      3. sub-neg 64.3%

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

      4. +-commutative 64.3%

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

      5. distribute-neg-in 64.3%

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

      6. remove-double-neg 64.3%

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

      7. sub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in z around inf 64.3%

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

Alternative 5: 55.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -2.55e-18)
     t_1
     (if (<= y 5.5e-185) (* t (- z)) (if (<= y 8.4e+21) (* x z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2.55e-18) {
		tmp = t_1;
	} else if (y <= 5.5e-185) {
		tmp = t * -z;
	} else if (y <= 8.4e+21) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-2.55d-18)) then
        tmp = t_1
    else if (y <= 5.5d-185) then
        tmp = t * -z
    else if (y <= 8.4d+21) then
        tmp = x * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2.55e-18) {
		tmp = t_1;
	} else if (y <= 5.5e-185) {
		tmp = t * -z;
	} else if (y <= 8.4e+21) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -2.55e-18:
		tmp = t_1
	elif y <= 5.5e-185:
		tmp = t * -z
	elif y <= 8.4e+21:
		tmp = x * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -2.55e-18)
		tmp = t_1;
	elseif (y <= 5.5e-185)
		tmp = Float64(t * Float64(-z));
	elseif (y <= 8.4e+21)
		tmp = Float64(x * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -2.55e-18)
		tmp = t_1;
	elseif (y <= 5.5e-185)
		tmp = t * -z;
	elseif (y <= 8.4e+21)
		tmp = x * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e-18], t$95$1, If[LessEqual[y, 5.5e-185], N[(t * (-z)), $MachinePrecision], If[LessEqual[y, 8.4e+21], N[(x * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.54999999999999991e-18 or 8.4e21 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.5%

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

      1. *-commutative 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in x around 0 81.9%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. unsub-neg 85.5%

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

   9. Simplified 85.5%

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

   if -2.54999999999999991e-18 < y < 5.4999999999999998e-185

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. unsub-neg 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in t around inf 79.0%

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

   7. Taylor expanded in x around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. *-commutative 46.4%

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

      3. distribute-rgt-neg-in 46.4%

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

   9. Simplified 46.4%

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

   if 5.4999999999999998e-185 < y < 8.4e21

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. distribute-rgt-neg-in 63.5%

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

      3. sub-neg 63.5%

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

      4. +-commutative 63.5%

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

      5. distribute-neg-in 63.5%

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

      6. remove-double-neg 63.5%

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

      7. sub-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in z around inf 63.5%

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Taylor expanded in z around inf 42.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-185}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+21}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-53}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+22}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-53)
   (* y t)
   (if (<= y 5.8e-60) x (if (<= y 2.2e+22) (* x z) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-53) {
		tmp = y * t;
	} else if (y <= 5.8e-60) {
		tmp = x;
	} else if (y <= 2.2e+22) {
		tmp = x * z;
	} else {
		tmp = y * 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 <= (-1.45d-53)) then
        tmp = y * t
    else if (y <= 5.8d-60) then
        tmp = x
    else if (y <= 2.2d+22) then
        tmp = x * z
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-53) {
		tmp = y * t;
	} else if (y <= 5.8e-60) {
		tmp = x;
	} else if (y <= 2.2e+22) {
		tmp = x * z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-53:
		tmp = y * t
	elif y <= 5.8e-60:
		tmp = x
	elif y <= 2.2e+22:
		tmp = x * z
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-53)
		tmp = Float64(y * t);
	elseif (y <= 5.8e-60)
		tmp = x;
	elseif (y <= 2.2e+22)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e-53)
		tmp = y * t;
	elseif (y <= 5.8e-60)
		tmp = x;
	elseif (y <= 2.2e+22)
		tmp = x * z;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-53], N[(y * t), $MachinePrecision], If[LessEqual[y, 5.8e-60], x, If[LessEqual[y, 2.2e+22], N[(x * z), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e-53 or 2.2e22 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 82.7%

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

      1. *-commutative 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in x around 0 79.3%

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

   7. Taylor expanded in y around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   9. Simplified 82.0%

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

   10. Taylor expanded in t around inf 48.2%

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

   if -1.4499999999999999e-53 < y < 5.7999999999999999e-60

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.9%

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

      1. *-commutative 42.9%

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

   5. Simplified 42.9%

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

   6. Taylor expanded in y around 0 37.3%

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

   if 5.7999999999999999e-60 < y < 2.2e22

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-rgt-neg-in 58.8%

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

      3. sub-neg 58.8%

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

      4. +-commutative 58.8%

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

      5. distribute-neg-in 58.8%

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

      6. remove-double-neg 58.8%

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

      7. sub-neg 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in z around inf 58.8%

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Taylor expanded in z around inf 55.0%

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

Alternative 7: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-7} \lor \neg \left(y \leq 3 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.15e-7) (not (<= y 3e+22)))
   (* y (- t x))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.15e-7) || !(y <= 3e+22)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * (x - 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 <= (-3.15d-7)) .or. (.not. (y <= 3d+22))) then
        tmp = y * (t - x)
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.15e-7) || !(y <= 3e+22)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.15e-7) or not (y <= 3e+22):
		tmp = y * (t - x)
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.15e-7) || !(y <= 3e+22))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.15e-7) || ~((y <= 3e+22)))
		tmp = y * (t - x);
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.15e-7], N[Not[LessEqual[y, 3e+22]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.15000000000000002e-7 or 3e22 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.7%

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

      1. *-commutative 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in x around 0 83.1%

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

   7. Taylor expanded in y around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. unsub-neg 86.7%

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

   9. Simplified 86.7%

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

   if -3.15000000000000002e-7 < y < 3e22

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-7} \lor \neg \left(y \leq 3 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-40} \lor \neg \left(x \leq 3.4 \cdot 10^{+21}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.75e-40) (not (<= x 3.4e+21)))
   (+ x (* x (- z y)))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e-40) || !(x <= 3.4e+21)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (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 ((x <= (-1.75d-40)) .or. (.not. (x <= 3.4d+21))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e-40) || !(x <= 3.4e+21)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.75e-40) or not (x <= 3.4e+21):
		tmp = x + (x * (z - y))
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.75e-40) || !(x <= 3.4e+21))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.75e-40) || ~((x <= 3.4e+21)))
		tmp = x + (x * (z - y));
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.75e-40], N[Not[LessEqual[x, 3.4e+21]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7500000000000001e-40 or 3.4e21 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. distribute-rgt-neg-in 83.6%

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

      3. sub-neg 83.6%

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

      4. +-commutative 83.6%

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

      5. distribute-neg-in 83.6%

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

      6. remove-double-neg 83.6%

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

      7. sub-neg 83.6%

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

   5. Simplified 83.6%

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

   if -1.7500000000000001e-40 < x < 3.4e21

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-40} \lor \neg \left(x \leq 3.4 \cdot 10^{+21}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-7} \lor \neg \left(y \leq 8.4 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-7) (not (<= y 8.4e+21))) (* y (- t x)) (+ x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-7) || !(y <= 8.4e+21)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (x * 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 <= (-2d-7)) .or. (.not. (y <= 8.4d+21))) then
        tmp = y * (t - x)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-7) || !(y <= 8.4e+21)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-7) or not (y <= 8.4e+21):
		tmp = y * (t - x)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-7) || !(y <= 8.4e+21))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-7) || ~((y <= 8.4e+21)))
		tmp = y * (t - x);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-7], N[Not[LessEqual[y, 8.4e+21]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999999e-7 or 8.4e21 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 86.1%

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

      1. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in x around 0 82.5%

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

   7. Taylor expanded in y around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

   9. Simplified 86.1%

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

   if -1.9999999999999999e-7 < y < 8.4e21

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 55.3%

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

      1. mul-1-neg 55.3%

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

      2. distribute-rgt-neg-in 55.3%

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

      3. sub-neg 55.3%

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

      4. +-commutative 55.3%

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

      5. distribute-neg-in 55.3%

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

      6. remove-double-neg 55.3%

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

      7. sub-neg 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in z around inf 55.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-7} \lor \neg \left(y \leq 8.4 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-40} \lor \neg \left(x \leq 3.6 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.5e-40) (not (<= x 3.6e-100))) (* x (- 1.0 y)) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e-40) || !(x <= 3.6e-100)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * 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 ((x <= (-5.5d-40)) .or. (.not. (x <= 3.6d-100))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e-40) || !(x <= 3.6e-100)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.5e-40) or not (x <= 3.6e-100):
		tmp = x * (1.0 - y)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.5e-40) || !(x <= 3.6e-100))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.5e-40) || ~((x <= 3.6e-100)))
		tmp = x * (1.0 - y);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.5e-40], N[Not[LessEqual[x, 3.6e-100]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000002e-40 or 3.5999999999999999e-100 < x

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-rgt-neg-in 78.1%

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

      3. sub-neg 78.1%

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

      4. +-commutative 78.1%

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

      5. distribute-neg-in 78.1%

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

      6. remove-double-neg 78.1%

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

      7. sub-neg 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. *-rgt-identity 53.6%

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

      3. distribute-rgt-neg-out 53.6%

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

      4. distribute-lft-in 53.6%

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

      5. unsub-neg 53.6%

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

   8. Simplified 53.6%

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

   if -5.50000000000000002e-40 < x < 3.5999999999999999e-100

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 63.0%

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

      1. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in x around 0 63.0%

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

   7. Taylor expanded in y around inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unsub-neg 57.2%

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

   9. Simplified 57.2%

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

   10. Taylor expanded in t around inf 51.2%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-40} \lor \neg \left(x \leq 3.6 \cdot 10^{-100}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15) (not (<= z 1.0))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15) || !(z <= 1.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	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 <= (-1.15d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15) || !(z <= 1.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15) or not (z <= 1.0):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15) || !(z <= 1.0))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15) || ~((z <= 1.0)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999 or 1 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. distribute-rgt-neg-in 49.9%

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

      3. sub-neg 49.9%

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

      4. +-commutative 49.9%

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

      5. distribute-neg-in 49.9%

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

      6. remove-double-neg 49.9%

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

      7. sub-neg 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in z around inf 38.8%

      \[\leadsto x + x \cdot \color{blue}{z} \]

   7. Taylor expanded in z around inf 38.2%

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

   if -1.1499999999999999 < z < 1

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.8%

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

      1. *-commutative 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in y around 0 26.0%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 18.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Taylor expanded in y around inf 64.5%

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

   1. *-commutative 64.5%

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

5. Simplified 64.5%

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

6. Taylor expanded in y around 0 15.3%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer Target 1: 96.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right) \end{array} \]

FPCore

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

C

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

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 + ((t * (y - z)) + (-x * (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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