Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.1s

Alternatives: 14

Speedup: 1.0×

• 35.7% 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: 36.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+195}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-244}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+195)
   (* x z)
   (if (<= z -2.3e-101)
     (* t (- z))
     (if (<= z -2.2e-246)
       (* y (- x))
       (if (<= z 3.9e-244)
         (* y t)
         (if (<= z 1.25e-21) x (if (<= z 9.5e+62) (* y t) (* x z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+195) {
		tmp = x * z;
	} else if (z <= -2.3e-101) {
		tmp = t * -z;
	} else if (z <= -2.2e-246) {
		tmp = y * -x;
	} else if (z <= 3.9e-244) {
		tmp = y * t;
	} else if (z <= 1.25e-21) {
		tmp = x;
	} else if (z <= 9.5e+62) {
		tmp = y * t;
	} else {
		tmp = 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 (z <= (-5.2d+195)) then
        tmp = x * z
    else if (z <= (-2.3d-101)) then
        tmp = t * -z
    else if (z <= (-2.2d-246)) then
        tmp = y * -x
    else if (z <= 3.9d-244) then
        tmp = y * t
    else if (z <= 1.25d-21) then
        tmp = x
    else if (z <= 9.5d+62) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+195) {
		tmp = x * z;
	} else if (z <= -2.3e-101) {
		tmp = t * -z;
	} else if (z <= -2.2e-246) {
		tmp = y * -x;
	} else if (z <= 3.9e-244) {
		tmp = y * t;
	} else if (z <= 1.25e-21) {
		tmp = x;
	} else if (z <= 9.5e+62) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+195:
		tmp = x * z
	elif z <= -2.3e-101:
		tmp = t * -z
	elif z <= -2.2e-246:
		tmp = y * -x
	elif z <= 3.9e-244:
		tmp = y * t
	elif z <= 1.25e-21:
		tmp = x
	elif z <= 9.5e+62:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+195)
		tmp = Float64(x * z);
	elseif (z <= -2.3e-101)
		tmp = Float64(t * Float64(-z));
	elseif (z <= -2.2e-246)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 3.9e-244)
		tmp = Float64(y * t);
	elseif (z <= 1.25e-21)
		tmp = x;
	elseif (z <= 9.5e+62)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+195)
		tmp = x * z;
	elseif (z <= -2.3e-101)
		tmp = t * -z;
	elseif (z <= -2.2e-246)
		tmp = y * -x;
	elseif (z <= 3.9e-244)
		tmp = y * t;
	elseif (z <= 1.25e-21)
		tmp = x;
	elseif (z <= 9.5e+62)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+195], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.3e-101], N[(t * (-z)), $MachinePrecision], If[LessEqual[z, -2.2e-246], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 3.9e-244], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.25e-21], x, If[LessEqual[z, 9.5e+62], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.20000000000000004e195 or 9.5000000000000003e62 < z

   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 56.9%

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

      1. mul-1-neg 56.9%

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

      2. distribute-rgt-neg-in 56.9%

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

      3. sub-neg 56.9%

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

      4. +-commutative 56.9%

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

      5. distribute-neg-in 56.9%

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

      6. remove-double-neg 56.9%

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

      7. sub-neg 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in z around inf 52.1%

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

   7. Taylor expanded in z around inf 52.1%

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

   if -5.20000000000000004e195 < z < -2.2999999999999999e-101

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 72.7%

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

   4. Taylor expanded in y around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. *-commutative 53.7%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in x around 0 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

   9. Simplified 50.2%

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

   if -2.2999999999999999e-101 < z < -2.19999999999999998e-246

   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 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-rgt-neg-in 77.3%

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

      3. sub-neg 77.3%

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

      4. +-commutative 77.3%

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

      5. distribute-neg-in 77.3%

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

      6. remove-double-neg 77.3%

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

      7. sub-neg 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. *-rgt-identity 77.3%

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

      3. distribute-rgt-neg-out 77.3%

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

      4. distribute-lft-in 77.3%

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

      5. unsub-neg 77.3%

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

   8. Simplified 77.3%

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

   9. Taylor expanded in y around inf 51.4%

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

       1. mul-1-neg 51.4%

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

       2. distribute-rgt-neg-in 51.4%

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

   11. Simplified 51.4%

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

   if -2.19999999999999998e-246 < z < 3.8999999999999999e-244 or 1.24999999999999993e-21 < z < 9.5000000000000003e62

   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 88.8%

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

      1. *-commutative 88.8%

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

   5. Simplified 88.8%

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

      1. *-commutative 88.8%

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

      2. sub-neg 88.8%

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

      3. distribute-lft-in 84.5%

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

   7. Applied egg-rr 84.5%

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

      1. associate-+r+ 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

      3. unsub-neg 84.5%

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

      4. +-commutative 84.5%

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

   9. Applied egg-rr 84.5%

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

   10. Taylor expanded in t around inf 53.1%

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

       1. *-commutative 53.1%

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

   12. Simplified 53.1%

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

   if 3.8999999999999999e-244 < z < 1.24999999999999993e-21

   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 89.5%

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

      1. *-commutative 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 55.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+195}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-244}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+62}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -145000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-240}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+62}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -145000000.0)
   (* x z)
   (if (<= z -3.1e-243)
     (* y (- x))
     (if (<= z 4.8e-240)
       (* y t)
       (if (<= z 5.5e-37) x (if (<= z 3.2e+62) (* y t) (* x z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -145000000.0) {
		tmp = x * z;
	} else if (z <= -3.1e-243) {
		tmp = y * -x;
	} else if (z <= 4.8e-240) {
		tmp = y * t;
	} else if (z <= 5.5e-37) {
		tmp = x;
	} else if (z <= 3.2e+62) {
		tmp = y * t;
	} else {
		tmp = 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 (z <= (-145000000.0d0)) then
        tmp = x * z
    else if (z <= (-3.1d-243)) then
        tmp = y * -x
    else if (z <= 4.8d-240) then
        tmp = y * t
    else if (z <= 5.5d-37) then
        tmp = x
    else if (z <= 3.2d+62) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -145000000.0) {
		tmp = x * z;
	} else if (z <= -3.1e-243) {
		tmp = y * -x;
	} else if (z <= 4.8e-240) {
		tmp = y * t;
	} else if (z <= 5.5e-37) {
		tmp = x;
	} else if (z <= 3.2e+62) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -145000000.0:
		tmp = x * z
	elif z <= -3.1e-243:
		tmp = y * -x
	elif z <= 4.8e-240:
		tmp = y * t
	elif z <= 5.5e-37:
		tmp = x
	elif z <= 3.2e+62:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -145000000.0)
		tmp = Float64(x * z);
	elseif (z <= -3.1e-243)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 4.8e-240)
		tmp = Float64(y * t);
	elseif (z <= 5.5e-37)
		tmp = x;
	elseif (z <= 3.2e+62)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -145000000.0)
		tmp = x * z;
	elseif (z <= -3.1e-243)
		tmp = y * -x;
	elseif (z <= 4.8e-240)
		tmp = y * t;
	elseif (z <= 5.5e-37)
		tmp = x;
	elseif (z <= 3.2e+62)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -145000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -3.1e-243], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 4.8e-240], N[(y * t), $MachinePrecision], If[LessEqual[z, 5.5e-37], x, If[LessEqual[z, 3.2e+62], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45e8 or 3.19999999999999984e62 < z

   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 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-rgt-neg-in 51.0%

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

      3. sub-neg 51.0%

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

      4. +-commutative 51.0%

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

      5. distribute-neg-in 51.0%

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

      6. remove-double-neg 51.0%

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

      7. sub-neg 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in z around inf 45.9%

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

   7. Taylor expanded in z around inf 45.9%

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

   if -1.45e8 < z < -3.0999999999999999e-243

   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 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-rgt-neg-in 60.4%

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

      3. sub-neg 60.4%

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

      4. +-commutative 60.4%

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

      5. distribute-neg-in 60.4%

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

      6. remove-double-neg 60.4%

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

      7. sub-neg 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in z around 0 60.5%

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

      1. mul-1-neg 60.5%

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

      2. *-rgt-identity 60.5%

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

      3. distribute-rgt-neg-out 60.5%

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

      4. distribute-lft-in 60.5%

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

      5. unsub-neg 60.5%

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

   8. Simplified 60.5%

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

   9. Taylor expanded in y around inf 40.7%

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

       1. mul-1-neg 40.7%

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

       2. distribute-rgt-neg-in 40.7%

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

   11. Simplified 40.7%

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

   if -3.0999999999999999e-243 < z < 4.7999999999999999e-240 or 5.4999999999999998e-37 < z < 3.19999999999999984e62

   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 88.8%

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

      1. *-commutative 88.8%

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

   5. Simplified 88.8%

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

      1. *-commutative 88.8%

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

      2. sub-neg 88.8%

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

      3. distribute-lft-in 84.5%

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

   7. Applied egg-rr 84.5%

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

      1. associate-+r+ 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

      3. unsub-neg 84.5%

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

      4. +-commutative 84.5%

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

   9. Applied egg-rr 84.5%

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

   10. Taylor expanded in t around inf 53.1%

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

       1. *-commutative 53.1%

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

   12. Simplified 53.1%

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

   if 4.7999999999999999e-240 < z < 5.4999999999999998e-37

   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 89.5%

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

      1. *-commutative 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 55.7%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -145000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-243}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-240}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+62}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-255}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-184}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 980000000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -5.8e-9)
     t_1
     (if (<= y 4.1e-255)
       (* t (- z))
       (if (<= y 1.14e-184)
         (* x z)
         (if (<= y 980000000000.0) (* x (- 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5.8e-9) {
		tmp = t_1;
	} else if (y <= 4.1e-255) {
		tmp = t * -z;
	} else if (y <= 1.14e-184) {
		tmp = x * z;
	} else if (y <= 980000000000.0) {
		tmp = x * (1.0 - 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 = y * (t - x)
    if (y <= (-5.8d-9)) then
        tmp = t_1
    else if (y <= 4.1d-255) then
        tmp = t * -z
    else if (y <= 1.14d-184) then
        tmp = x * z
    else if (y <= 980000000000.0d0) then
        tmp = x * (1.0d0 - 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 = y * (t - x);
	double tmp;
	if (y <= -5.8e-9) {
		tmp = t_1;
	} else if (y <= 4.1e-255) {
		tmp = t * -z;
	} else if (y <= 1.14e-184) {
		tmp = x * z;
	} else if (y <= 980000000000.0) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -5.8e-9:
		tmp = t_1
	elif y <= 4.1e-255:
		tmp = t * -z
	elif y <= 1.14e-184:
		tmp = x * z
	elif y <= 980000000000.0:
		tmp = x * (1.0 - y)
	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 <= -5.8e-9)
		tmp = t_1;
	elseif (y <= 4.1e-255)
		tmp = Float64(t * Float64(-z));
	elseif (y <= 1.14e-184)
		tmp = Float64(x * z);
	elseif (y <= 980000000000.0)
		tmp = Float64(x * Float64(1.0 - y));
	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 <= -5.8e-9)
		tmp = t_1;
	elseif (y <= 4.1e-255)
		tmp = t * -z;
	elseif (y <= 1.14e-184)
		tmp = x * z;
	elseif (y <= 980000000000.0)
		tmp = x * (1.0 - y);
	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, -5.8e-9], t$95$1, If[LessEqual[y, 4.1e-255], N[(t * (-z)), $MachinePrecision], If[LessEqual[y, 1.14e-184], N[(x * z), $MachinePrecision], If[LessEqual[y, 980000000000.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999982e-9 or 9.8e11 < y

   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 77.0%

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

      1. *-commutative 77.0%

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

   5. Simplified 77.0%

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

      1. *-commutative 77.0%

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

      2. sub-neg 77.0%

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

      3. distribute-lft-in 75.5%

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

   7. Applied egg-rr 75.5%

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

      1. associate-+r+ 75.5%

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

      2. distribute-rgt-neg-out 75.5%

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

      3. unsub-neg 75.5%

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

      4. +-commutative 75.5%

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

   9. Applied egg-rr 75.5%

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

   10. Taylor expanded in y around inf 76.1%

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

   if -5.79999999999999982e-9 < y < 4.1e-255

   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 77.2%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

      3. *-commutative 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in x around 0 49.3%

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

      1. associate-*r* 49.3%

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

      2. neg-mul-1 49.3%

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

   9. Simplified 49.3%

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

   if 4.1e-255 < y < 1.13999999999999997e-184

   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 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-rgt-neg-in 64.8%

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

      3. sub-neg 64.8%

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

      4. +-commutative 64.8%

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

      5. distribute-neg-in 64.8%

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

      6. remove-double-neg 64.8%

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

      7. sub-neg 64.8%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in z around inf 64.8%

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

   7. Taylor expanded in z around inf 52.9%

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

   if 1.13999999999999997e-184 < y < 9.8e11

   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 73.2%

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

      1. mul-1-neg 73.2%

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

      2. distribute-rgt-neg-in 73.2%

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

      3. sub-neg 73.2%

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

      4. +-commutative 73.2%

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

      5. distribute-neg-in 73.2%

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

      6. remove-double-neg 73.2%

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

      7. sub-neg 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in z around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. *-rgt-identity 49.0%

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

      3. distribute-rgt-neg-out 49.0%

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

      4. distribute-lft-in 49.0%

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

      5. unsub-neg 49.0%

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

   8. Simplified 49.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-255}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-184}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 980000000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -150000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-237}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+62}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -150000000.0)
   (* x z)
   (if (<= z 1.8e-237)
     (* y t)
     (if (<= z 5.4e-27) x (if (<= z 3.9e+62) (* y t) (* x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -150000000.0) {
		tmp = x * z;
	} else if (z <= 1.8e-237) {
		tmp = y * t;
	} else if (z <= 5.4e-27) {
		tmp = x;
	} else if (z <= 3.9e+62) {
		tmp = y * t;
	} else {
		tmp = 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 (z <= (-150000000.0d0)) then
        tmp = x * z
    else if (z <= 1.8d-237) then
        tmp = y * t
    else if (z <= 5.4d-27) then
        tmp = x
    else if (z <= 3.9d+62) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -150000000.0) {
		tmp = x * z;
	} else if (z <= 1.8e-237) {
		tmp = y * t;
	} else if (z <= 5.4e-27) {
		tmp = x;
	} else if (z <= 3.9e+62) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -150000000.0:
		tmp = x * z
	elif z <= 1.8e-237:
		tmp = y * t
	elif z <= 5.4e-27:
		tmp = x
	elif z <= 3.9e+62:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -150000000.0)
		tmp = Float64(x * z);
	elseif (z <= 1.8e-237)
		tmp = Float64(y * t);
	elseif (z <= 5.4e-27)
		tmp = x;
	elseif (z <= 3.9e+62)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -150000000.0)
		tmp = x * z;
	elseif (z <= 1.8e-237)
		tmp = y * t;
	elseif (z <= 5.4e-27)
		tmp = x;
	elseif (z <= 3.9e+62)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -150000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 1.8e-237], N[(y * t), $MachinePrecision], If[LessEqual[z, 5.4e-27], x, If[LessEqual[z, 3.9e+62], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e8 or 3.9e62 < z

   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 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-rgt-neg-in 51.0%

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

      3. sub-neg 51.0%

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

      4. +-commutative 51.0%

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

      5. distribute-neg-in 51.0%

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

      6. remove-double-neg 51.0%

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

      7. sub-neg 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in z around inf 45.9%

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

   7. Taylor expanded in z around inf 45.9%

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

   if -1.5e8 < z < 1.79999999999999998e-237 or 5.39999999999999978e-27 < z < 3.9e62

   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 84.5%

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

      1. *-commutative 84.5%

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

   5. Simplified 84.5%

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

      1. *-commutative 84.5%

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

      2. sub-neg 84.5%

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

      3. distribute-lft-in 82.6%

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

   7. Applied egg-rr 82.6%

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

      1. associate-+r+ 82.6%

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

      2. distribute-rgt-neg-out 82.6%

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

      3. unsub-neg 82.6%

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

      4. +-commutative 82.6%

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

   9. Applied egg-rr 82.6%

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

   10. Taylor expanded in t around inf 39.1%

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

       1. *-commutative 39.1%

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

   12. Simplified 39.1%

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

   if 1.79999999999999998e-237 < z < 5.39999999999999978e-27

   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 89.5%

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

      1. *-commutative 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 55.7%

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

Alternative 6: 71.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{-8}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-254}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -2.45e-8)
     (+ x t_1)
     (if (<= y 4.3e-254)
       (- x (* z t))
       (if (<= y 7.5e+19) (+ x (* x (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2.45e-8) {
		tmp = x + t_1;
	} else if (y <= 4.3e-254) {
		tmp = x - (z * t);
	} else if (y <= 7.5e+19) {
		tmp = x + (x * (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 = y * (t - x)
    if (y <= (-2.45d-8)) then
        tmp = x + t_1
    else if (y <= 4.3d-254) then
        tmp = x - (z * t)
    else if (y <= 7.5d+19) then
        tmp = x + (x * (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 = y * (t - x);
	double tmp;
	if (y <= -2.45e-8) {
		tmp = x + t_1;
	} else if (y <= 4.3e-254) {
		tmp = x - (z * t);
	} else if (y <= 7.5e+19) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -2.45e-8:
		tmp = x + t_1
	elif y <= 4.3e-254:
		tmp = x - (z * t)
	elif y <= 7.5e+19:
		tmp = x + (x * (z - y))
	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 <= -2.45e-8)
		tmp = Float64(x + t_1);
	elseif (y <= 4.3e-254)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 7.5e+19)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	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 <= -2.45e-8)
		tmp = x + t_1;
	elseif (y <= 4.3e-254)
		tmp = x - (z * t);
	elseif (y <= 7.5e+19)
		tmp = x + (x * (z - y));
	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, -2.45e-8], N[(x + t$95$1), $MachinePrecision], If[LessEqual[y, 4.3e-254], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+19], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4500000000000001e-8

   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 81.6%

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

      1. *-commutative 81.6%

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

   5. Simplified 81.6%

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

   if -2.4500000000000001e-8 < y < 4.2999999999999997e-254

   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 77.2%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

      3. *-commutative 71.8%

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

   6. Simplified 71.8%

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

   if 4.2999999999999997e-254 < y < 7.5e19

   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 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-in 70.7%

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

      3. sub-neg 70.7%

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

      4. +-commutative 70.7%

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

      5. distribute-neg-in 70.7%

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

      6. remove-double-neg 70.7%

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

      7. sub-neg 70.7%

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

   5. Simplified 70.7%

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

   if 7.5e19 < y

   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 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

      1. *-commutative 72.7%

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

      2. sub-neg 72.7%

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

      3. distribute-lft-in 70.9%

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

   7. Applied egg-rr 70.9%

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

      1. associate-+r+ 70.9%

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

      2. distribute-rgt-neg-out 70.9%

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

      3. unsub-neg 70.9%

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

      4. +-commutative 70.9%

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

   9. Applied egg-rr 70.9%

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

   10. Taylor expanded in y around inf 72.7%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-254}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-254}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+20}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -4.5e-7)
     t_1
     (if (<= y 3.3e-254)
       (- x (* z t))
       (if (<= y 2.75e+20) (+ x (* x (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -4.5e-7) {
		tmp = t_1;
	} else if (y <= 3.3e-254) {
		tmp = x - (z * t);
	} else if (y <= 2.75e+20) {
		tmp = x + (x * (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 = y * (t - x)
    if (y <= (-4.5d-7)) then
        tmp = t_1
    else if (y <= 3.3d-254) then
        tmp = x - (z * t)
    else if (y <= 2.75d+20) then
        tmp = x + (x * (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 = y * (t - x);
	double tmp;
	if (y <= -4.5e-7) {
		tmp = t_1;
	} else if (y <= 3.3e-254) {
		tmp = x - (z * t);
	} else if (y <= 2.75e+20) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -4.5e-7:
		tmp = t_1
	elif y <= 3.3e-254:
		tmp = x - (z * t)
	elif y <= 2.75e+20:
		tmp = x + (x * (z - y))
	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 <= -4.5e-7)
		tmp = t_1;
	elseif (y <= 3.3e-254)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 2.75e+20)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	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 <= -4.5e-7)
		tmp = t_1;
	elseif (y <= 3.3e-254)
		tmp = x - (z * t);
	elseif (y <= 2.75e+20)
		tmp = x + (x * (z - y));
	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, -4.5e-7], t$95$1, If[LessEqual[y, 3.3e-254], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+20], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999998e-7 or 2.75e20 < y

   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 77.7%

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

      1. *-commutative 77.7%

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

   5. Simplified 77.7%

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

      1. *-commutative 77.7%

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

      2. sub-neg 77.7%

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

      3. distribute-lft-in 76.2%

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

   7. Applied egg-rr 76.2%

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

      1. associate-+r+ 76.2%

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

      2. distribute-rgt-neg-out 76.2%

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

      3. unsub-neg 76.2%

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

      4. +-commutative 76.2%

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

   9. Applied egg-rr 76.2%

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

   10. Taylor expanded in y around inf 77.4%

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

   if -4.4999999999999998e-7 < y < 3.30000000000000016e-254

   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 76.8%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if 3.30000000000000016e-254 < y < 2.75e20

   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 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-rgt-neg-in 70.7%

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

      3. sub-neg 70.7%

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

      4. +-commutative 70.7%

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

      5. distribute-neg-in 70.7%

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

      6. remove-double-neg 70.7%

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

      7. sub-neg 70.7%

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

   5. Simplified 70.7%

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

Alternative 8: 49.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+193}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+193)
   (* x z)
   (if (<= z -1e-33) (* t (- z)) (if (<= z 3.8e+39) (* x (- 1.0 y)) (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+193) {
		tmp = x * z;
	} else if (z <= -1e-33) {
		tmp = t * -z;
	} else if (z <= 3.8e+39) {
		tmp = x * (1.0 - y);
	} else {
		tmp = 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 (z <= (-5d+193)) then
        tmp = x * z
    else if (z <= (-1d-33)) then
        tmp = t * -z
    else if (z <= 3.8d+39) then
        tmp = x * (1.0d0 - y)
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+193) {
		tmp = x * z;
	} else if (z <= -1e-33) {
		tmp = t * -z;
	} else if (z <= 3.8e+39) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e+193:
		tmp = x * z
	elif z <= -1e-33:
		tmp = t * -z
	elif z <= 3.8e+39:
		tmp = x * (1.0 - y)
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+193)
		tmp = Float64(x * z);
	elseif (z <= -1e-33)
		tmp = Float64(t * Float64(-z));
	elseif (z <= 3.8e+39)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e+193)
		tmp = x * z;
	elseif (z <= -1e-33)
		tmp = t * -z;
	elseif (z <= 3.8e+39)
		tmp = x * (1.0 - y);
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+193], N[(x * z), $MachinePrecision], If[LessEqual[z, -1e-33], N[(t * (-z)), $MachinePrecision], If[LessEqual[z, 3.8e+39], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999972e193 or 3.7999999999999998e39 < z

   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 56.5%

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

      1. mul-1-neg 56.5%

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

      2. distribute-rgt-neg-in 56.5%

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

      3. sub-neg 56.5%

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

      4. +-commutative 56.5%

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

      5. distribute-neg-in 56.5%

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

      6. remove-double-neg 56.5%

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

      7. sub-neg 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in z around inf 50.9%

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

   7. Taylor expanded in z around inf 50.9%

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

   if -4.99999999999999972e193 < z < -1.0000000000000001e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 73.0%

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

   4. Taylor expanded in y around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

      3. *-commutative 52.1%

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

   6. Simplified 52.1%

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

   7. Taylor expanded in x around 0 52.0%

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

      1. associate-*r* 52.0%

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

      2. neg-mul-1 52.0%

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

   9. Simplified 52.0%

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

   if -1.0000000000000001e-33 < z < 3.7999999999999998e39

   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 59.1%

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

      1. mul-1-neg 59.1%

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

      2. distribute-rgt-neg-in 59.1%

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

      3. sub-neg 59.1%

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

      4. +-commutative 59.1%

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

      5. distribute-neg-in 59.1%

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

      6. remove-double-neg 59.1%

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

      7. sub-neg 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around 0 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-rgt-identity 59.1%

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

      3. distribute-rgt-neg-out 59.1%

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

      4. distribute-lft-in 59.1%

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

      5. unsub-neg 59.1%

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

   8. Simplified 59.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+193}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-10} \lor \neg \left(z \leq 2.2 \cdot 10^{+64}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.6e-10) (not (<= z 2.2e+64)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-10) || !(z <= 2.2e+64)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - 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 <= (-4.6d-10)) .or. (.not. (z <= 2.2d+64))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-10) || !(z <= 2.2e+64)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.6e-10) or not (z <= 2.2e+64):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.6e-10) || !(z <= 2.2e+64))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.6e-10) || ~((z <= 2.2e+64)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.6e-10], N[Not[LessEqual[z, 2.2e+64]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000014e-10 or 2.20000000000000002e64 < z

   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 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

   5. Simplified 85.9%

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

   if -4.60000000000000014e-10 < z < 2.20000000000000002e64

   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 87.5%

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

      1. *-commutative 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-10} \lor \neg \left(z \leq 2.2 \cdot 10^{+64}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+29} \lor \neg \left(t \leq 2.1 \cdot 10^{-81}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.05e+29) (not (<= t 2.1e-81)))
   (+ x (* t (- y z)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+29) || !(t <= 2.1e-81)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.05d+29)) .or. (.not. (t <= 2.1d-81))) then
        tmp = x + (t * (y - z))
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+29) || !(t <= 2.1e-81)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.05e+29) or not (t <= 2.1e-81):
		tmp = x + (t * (y - z))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.05e+29) || !(t <= 2.1e-81))
		tmp = Float64(x + Float64(t * Float64(y - z)));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.05e+29) || ~((t <= 2.1e-81)))
		tmp = x + (t * (y - z));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.05e+29], N[Not[LessEqual[t, 2.1e-81]], $MachinePrecision]], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0500000000000001e29 or 2.0999999999999999e-81 < t

   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 86.5%

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

   if -1.0500000000000001e29 < t < 2.0999999999999999e-81

   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 84.4%

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

      1. mul-1-neg 84.4%

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

      2. distribute-rgt-neg-in 84.4%

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

      3. sub-neg 84.4%

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

      4. +-commutative 84.4%

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

      5. distribute-neg-in 84.4%

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

      6. remove-double-neg 84.4%

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

      7. sub-neg 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+29} \lor \neg \left(t \leq 2.1 \cdot 10^{-81}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-7} \lor \neg \left(y \leq 490000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-7) (not (<= y 490000000.0))) (* y (- t x)) (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-7) || !(y <= 490000000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * 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 <= (-5.2d-7)) .or. (.not. (y <= 490000000.0d0))) then
        tmp = y * (t - x)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-7) || !(y <= 490000000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-7) or not (y <= 490000000.0):
		tmp = y * (t - x)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e-7) || !(y <= 490000000.0))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.2e-7) || ~((y <= 490000000.0)))
		tmp = y * (t - x);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e-7], N[Not[LessEqual[y, 490000000.0]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999998e-7 or 4.9e8 < y

   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 77.0%

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

      1. *-commutative 77.0%

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

   5. Simplified 77.0%

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

      1. *-commutative 77.0%

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

      2. sub-neg 77.0%

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

      3. distribute-lft-in 75.5%

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

   7. Applied egg-rr 75.5%

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

      1. associate-+r+ 75.5%

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

      2. distribute-rgt-neg-out 75.5%

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

      3. unsub-neg 75.5%

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

      4. +-commutative 75.5%

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

   9. Applied egg-rr 75.5%

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

   10. Taylor expanded in y around inf 76.6%

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

   if -5.19999999999999998e-7 < y < 4.9e8

   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 72.4%

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

   4. Taylor expanded in y around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. unsub-neg 67.3%

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

      3. *-commutative 67.3%

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

   6. Simplified 67.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-7} \lor \neg \left(y \leq 490000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-7} \lor \neg \left(y \leq 29500\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.4e-7) (not (<= y 29500.0))) (* y (- t x)) (+ x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e-7) || !(y <= 29500.0)) {
		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 <= (-6.4d-7)) .or. (.not. (y <= 29500.0d0))) 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 <= -6.4e-7) || !(y <= 29500.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.4e-7) or not (y <= 29500.0):
		tmp = y * (t - x)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.4e-7) || !(y <= 29500.0))
		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 <= -6.4e-7) || ~((y <= 29500.0)))
		tmp = y * (t - x);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.4e-7], N[Not[LessEqual[y, 29500.0]], $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 < -6.4000000000000001e-7 or 29500 < y

   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 77.0%

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

      1. *-commutative 77.0%

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

   5. Simplified 77.0%

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

      1. *-commutative 77.0%

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

      2. sub-neg 77.0%

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

      3. distribute-lft-in 75.5%

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

   7. Applied egg-rr 75.5%

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

      1. associate-+r+ 75.5%

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

      2. distribute-rgt-neg-out 75.5%

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

      3. unsub-neg 75.5%

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

      4. +-commutative 75.5%

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

   9. Applied egg-rr 75.5%

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

   10. Taylor expanded in y around inf 76.6%

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

   if -6.4000000000000001e-7 < y < 29500

   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 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-rgt-neg-in 59.9%

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

      3. sub-neg 59.9%

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

      4. +-commutative 59.9%

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

      5. distribute-neg-in 59.9%

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

      6. remove-double-neg 59.9%

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

      7. sub-neg 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in z around inf 58.8%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-7} \lor \neg \left(y \leq 29500\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -135000000 \lor \neg \left(z \leq 3.9 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -135000000.0) (not (<= z 3.9e-7))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -135000000.0) || !(z <= 3.9e-7)) {
		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 <= (-135000000.0d0)) .or. (.not. (z <= 3.9d-7))) 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 <= -135000000.0) || !(z <= 3.9e-7)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -135000000.0) or not (z <= 3.9e-7):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -135000000.0) || !(z <= 3.9e-7))
		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 <= -135000000.0) || ~((z <= 3.9e-7)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -135000000.0], N[Not[LessEqual[z, 3.9e-7]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e8 or 3.90000000000000025e-7 < z

   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 49.2%

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

      1. mul-1-neg 49.2%

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

      2. distribute-rgt-neg-in 49.2%

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

      3. sub-neg 49.2%

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

      4. +-commutative 49.2%

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

      5. distribute-neg-in 49.2%

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

      6. remove-double-neg 49.2%

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

      7. sub-neg 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in z around inf 42.4%

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

   7. Taylor expanded in z around inf 42.4%

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

   if -1.35e8 < z < 3.90000000000000025e-7

   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 87.9%

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

      1. *-commutative 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in y around 0 31.3%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -135000000 \lor \neg \left(z \leq 3.9 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 17.4% 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 58.7%

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

   1. *-commutative 58.7%

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

5. Simplified 58.7%

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

6. Taylor expanded in y around 0 16.7%

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

Developer Target 1: 96.4% 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 2024133 
(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))))