Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 16

Speedup: 1.0×

• 35.0% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, t - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 36.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+68}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+68)
   (* z x)
   (if (<= z -3.6e-154)
     (* y (- x))
     (if (<= z -3.5e-274)
       x
       (if (<= z 3e+89) (* y t) (if (<= z 1.85e+161) (* z (- t)) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+68) {
		tmp = z * x;
	} else if (z <= -3.6e-154) {
		tmp = y * -x;
	} else if (z <= -3.5e-274) {
		tmp = x;
	} else if (z <= 3e+89) {
		tmp = y * t;
	} else if (z <= 1.85e+161) {
		tmp = z * -t;
	} else {
		tmp = z * 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 <= (-2.9d+68)) then
        tmp = z * x
    else if (z <= (-3.6d-154)) then
        tmp = y * -x
    else if (z <= (-3.5d-274)) then
        tmp = x
    else if (z <= 3d+89) then
        tmp = y * t
    else if (z <= 1.85d+161) then
        tmp = z * -t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+68) {
		tmp = z * x;
	} else if (z <= -3.6e-154) {
		tmp = y * -x;
	} else if (z <= -3.5e-274) {
		tmp = x;
	} else if (z <= 3e+89) {
		tmp = y * t;
	} else if (z <= 1.85e+161) {
		tmp = z * -t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e+68:
		tmp = z * x
	elif z <= -3.6e-154:
		tmp = y * -x
	elif z <= -3.5e-274:
		tmp = x
	elif z <= 3e+89:
		tmp = y * t
	elif z <= 1.85e+161:
		tmp = z * -t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+68)
		tmp = Float64(z * x);
	elseif (z <= -3.6e-154)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -3.5e-274)
		tmp = x;
	elseif (z <= 3e+89)
		tmp = Float64(y * t);
	elseif (z <= 1.85e+161)
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e+68)
		tmp = z * x;
	elseif (z <= -3.6e-154)
		tmp = y * -x;
	elseif (z <= -3.5e-274)
		tmp = x;
	elseif (z <= 3e+89)
		tmp = y * t;
	elseif (z <= 1.85e+161)
		tmp = z * -t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e+68], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.6e-154], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -3.5e-274], x, If[LessEqual[z, 3e+89], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.85e+161], N[(z * (-t)), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.90000000000000011e68 or 1.8499999999999999e161 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.6%

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

      1. mul-1-neg 60.6%

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

      2. unsub-neg 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in z around inf 56.1%

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

   if -2.90000000000000011e68 < z < -3.6000000000000003e-154

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in y around inf 34.6%

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

      1. neg-mul-1 34.6%

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

   8. Simplified 34.6%

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

   if -3.6000000000000003e-154 < z < -3.49999999999999982e-274

   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 94.8%

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

      1. *-commutative 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in y around 0 53.0%

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

   if -3.49999999999999982e-274 < z < 3.00000000000000013e89

   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 92.1%

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

      1. associate--l+ 92.1%

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

      2. +-commutative 92.1%

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

      3. mul-1-neg 92.1%

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

      4. unsub-neg 92.1%

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

      5. div-sub 93.3%

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

      6. unsub-neg 93.3%

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

      7. mul-1-neg 93.3%

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

      8. mul-1-neg 93.3%

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

      9. *-rgt-identity 93.3%

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

      10. distribute-rgt-neg-in 93.3%

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

      11. mul-1-neg 93.3%

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

      12. distribute-lft-in 93.3%

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

      13. mul-1-neg 93.3%

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

      14. unsub-neg 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in x around 0 51.4%

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

   7. Taylor expanded in y around inf 41.9%

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

   if 3.00000000000000013e89 < z < 1.8499999999999999e161

   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 94.0%

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

      1. associate--l+ 93.9%

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

      2. +-commutative 93.9%

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

      3. mul-1-neg 93.9%

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

      4. unsub-neg 93.9%

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

      5. div-sub 93.9%

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

      6. unsub-neg 93.9%

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

      7. mul-1-neg 93.9%

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

      8. mul-1-neg 93.9%

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

      9. *-rgt-identity 93.9%

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

      10. distribute-rgt-neg-in 93.9%

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

      11. mul-1-neg 93.9%

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

      12. distribute-lft-in 93.9%

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

      13. mul-1-neg 93.9%

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

      14. unsub-neg 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in x around 0 74.6%

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

   7. Taylor expanded in y around 0 74.7%

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

      1. neg-mul-1 74.7%

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

   9. Simplified 74.7%

      \[\leadsto t \cdot \color{blue}{\left(-z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+68}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+161}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-59}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+163}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e+49)
   (* z x)
   (if (<= z -9e-59)
     (* y t)
     (if (<= z -6.2e-270)
       x
       (if (<= z 5.1e+89)
         (* y t)
         (if (<= z 1.95e+163) (* z (- t)) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+49) {
		tmp = z * x;
	} else if (z <= -9e-59) {
		tmp = y * t;
	} else if (z <= -6.2e-270) {
		tmp = x;
	} else if (z <= 5.1e+89) {
		tmp = y * t;
	} else if (z <= 1.95e+163) {
		tmp = z * -t;
	} else {
		tmp = z * 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 <= (-4.5d+49)) then
        tmp = z * x
    else if (z <= (-9d-59)) then
        tmp = y * t
    else if (z <= (-6.2d-270)) then
        tmp = x
    else if (z <= 5.1d+89) then
        tmp = y * t
    else if (z <= 1.95d+163) then
        tmp = z * -t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+49) {
		tmp = z * x;
	} else if (z <= -9e-59) {
		tmp = y * t;
	} else if (z <= -6.2e-270) {
		tmp = x;
	} else if (z <= 5.1e+89) {
		tmp = y * t;
	} else if (z <= 1.95e+163) {
		tmp = z * -t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e+49:
		tmp = z * x
	elif z <= -9e-59:
		tmp = y * t
	elif z <= -6.2e-270:
		tmp = x
	elif z <= 5.1e+89:
		tmp = y * t
	elif z <= 1.95e+163:
		tmp = z * -t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e+49)
		tmp = Float64(z * x);
	elseif (z <= -9e-59)
		tmp = Float64(y * t);
	elseif (z <= -6.2e-270)
		tmp = x;
	elseif (z <= 5.1e+89)
		tmp = Float64(y * t);
	elseif (z <= 1.95e+163)
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e+49)
		tmp = z * x;
	elseif (z <= -9e-59)
		tmp = y * t;
	elseif (z <= -6.2e-270)
		tmp = x;
	elseif (z <= 5.1e+89)
		tmp = y * t;
	elseif (z <= 1.95e+163)
		tmp = z * -t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e+49], N[(z * x), $MachinePrecision], If[LessEqual[z, -9e-59], N[(y * t), $MachinePrecision], If[LessEqual[z, -6.2e-270], x, If[LessEqual[z, 5.1e+89], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.95e+163], N[(z * (-t)), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.49999999999999982e49 or 1.95000000000000012e163 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in z around inf 53.1%

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

   if -4.49999999999999982e49 < z < -9.00000000000000023e-59 or -6.2e-270 < z < 5.10000000000000027e89

   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 91.9%

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

      1. associate--l+ 91.9%

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

      2. +-commutative 91.9%

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

      3. mul-1-neg 91.9%

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

      4. unsub-neg 91.9%

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

      5. div-sub 92.9%

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

      6. unsub-neg 92.9%

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

      7. mul-1-neg 92.9%

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

      8. mul-1-neg 92.9%

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

      9. *-rgt-identity 92.9%

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

      10. distribute-rgt-neg-in 92.9%

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

      11. mul-1-neg 92.9%

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

      12. distribute-lft-in 93.0%

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

      13. mul-1-neg 93.0%

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

      14. unsub-neg 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around 0 54.4%

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

   7. Taylor expanded in y around inf 40.1%

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

   if -9.00000000000000023e-59 < z < -6.2e-270

   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 95.3%

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

      1. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around 0 46.0%

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

   if 5.10000000000000027e89 < z < 1.95000000000000012e163

   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 94.0%

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

      1. associate--l+ 93.9%

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

      2. +-commutative 93.9%

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

      3. mul-1-neg 93.9%

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

      4. unsub-neg 93.9%

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

      5. div-sub 93.9%

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

      6. unsub-neg 93.9%

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

      7. mul-1-neg 93.9%

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

      8. mul-1-neg 93.9%

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

      9. *-rgt-identity 93.9%

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

      10. distribute-rgt-neg-in 93.9%

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

      11. mul-1-neg 93.9%

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

      12. distribute-lft-in 93.9%

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

      13. mul-1-neg 93.9%

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

      14. unsub-neg 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in x around 0 74.6%

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

   7. Taylor expanded in y around 0 74.7%

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

      1. neg-mul-1 74.7%

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

   9. Simplified 74.7%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-59}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-270}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+163}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-272}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e+49)
   (* z x)
   (if (<= z -8.5e-63)
     (* y t)
     (if (<= z -1e-272) x (if (<= z 5.6e+28) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+49) {
		tmp = z * x;
	} else if (z <= -8.5e-63) {
		tmp = y * t;
	} else if (z <= -1e-272) {
		tmp = x;
	} else if (z <= 5.6e+28) {
		tmp = y * t;
	} else {
		tmp = z * 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 <= (-4.2d+49)) then
        tmp = z * x
    else if (z <= (-8.5d-63)) then
        tmp = y * t
    else if (z <= (-1d-272)) then
        tmp = x
    else if (z <= 5.6d+28) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+49) {
		tmp = z * x;
	} else if (z <= -8.5e-63) {
		tmp = y * t;
	} else if (z <= -1e-272) {
		tmp = x;
	} else if (z <= 5.6e+28) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+49:
		tmp = z * x
	elif z <= -8.5e-63:
		tmp = y * t
	elif z <= -1e-272:
		tmp = x
	elif z <= 5.6e+28:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e+49)
		tmp = Float64(z * x);
	elseif (z <= -8.5e-63)
		tmp = Float64(y * t);
	elseif (z <= -1e-272)
		tmp = x;
	elseif (z <= 5.6e+28)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e+49)
		tmp = z * x;
	elseif (z <= -8.5e-63)
		tmp = y * t;
	elseif (z <= -1e-272)
		tmp = x;
	elseif (z <= 5.6e+28)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e+49], N[(z * x), $MachinePrecision], If[LessEqual[z, -8.5e-63], N[(y * t), $MachinePrecision], If[LessEqual[z, -1e-272], x, If[LessEqual[z, 5.6e+28], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000022e49 or 5.6000000000000003e28 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. unsub-neg 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in z around inf 46.9%

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

   if -4.20000000000000022e49 < z < -8.49999999999999969e-63 or -9.9999999999999993e-273 < z < 5.6000000000000003e28

   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 91.9%

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

      1. associate--l+ 91.9%

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

      2. +-commutative 91.9%

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

      3. mul-1-neg 91.9%

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

      4. unsub-neg 91.9%

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

      5. div-sub 93.1%

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

      6. unsub-neg 93.1%

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

      7. mul-1-neg 93.1%

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

      8. mul-1-neg 93.1%

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

      9. *-rgt-identity 93.1%

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

      10. distribute-rgt-neg-in 93.1%

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

      11. mul-1-neg 93.1%

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

      12. distribute-lft-in 93.1%

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

      13. mul-1-neg 93.1%

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

      14. unsub-neg 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in x around 0 56.4%

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

   7. Taylor expanded in y around inf 41.4%

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

   if -8.49999999999999969e-63 < z < -9.9999999999999993e-273

   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 95.3%

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

      1. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around 0 46.0%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-272}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+28}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.82 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+41}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.82e-7)
     t_1
     (if (<= t -1.3e-262)
       (* x (+ z 1.0))
       (if (<= t 8.5e+41) (- x (* y x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.82e-7) {
		tmp = t_1;
	} else if (t <= -1.3e-262) {
		tmp = x * (z + 1.0);
	} else if (t <= 8.5e+41) {
		tmp = x - (y * x);
	} 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 - z) * t
    if (t <= (-1.82d-7)) then
        tmp = t_1
    else if (t <= (-1.3d-262)) then
        tmp = x * (z + 1.0d0)
    else if (t <= 8.5d+41) then
        tmp = x - (y * x)
    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 - z) * t;
	double tmp;
	if (t <= -1.82e-7) {
		tmp = t_1;
	} else if (t <= -1.3e-262) {
		tmp = x * (z + 1.0);
	} else if (t <= 8.5e+41) {
		tmp = x - (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.82e-7:
		tmp = t_1
	elif t <= -1.3e-262:
		tmp = x * (z + 1.0)
	elif t <= 8.5e+41:
		tmp = x - (y * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.82e-7)
		tmp = t_1;
	elseif (t <= -1.3e-262)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (t <= 8.5e+41)
		tmp = Float64(x - Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.82e-7)
		tmp = t_1;
	elseif (t <= -1.3e-262)
		tmp = x * (z + 1.0);
	elseif (t <= 8.5e+41)
		tmp = x - (y * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.82e-7], t$95$1, If[LessEqual[t, -1.3e-262], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+41], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.81999999999999989e-7 or 8.49999999999999938e41 < 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 97.6%

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

      1. associate--l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. unsub-neg 97.6%

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

      5. div-sub 97.6%

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

      6. unsub-neg 97.6%

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

      7. mul-1-neg 97.6%

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

      8. mul-1-neg 97.6%

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

      9. *-rgt-identity 97.6%

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

      10. distribute-rgt-neg-in 97.6%

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

      11. mul-1-neg 97.6%

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

      12. distribute-lft-in 97.6%

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

      13. mul-1-neg 97.6%

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

      14. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in x around 0 79.4%

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

   if -1.81999999999999989e-7 < t < -1.2999999999999999e-262

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in y around 0 64.9%

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

      1. +-commutative 64.9%

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

   8. Simplified 64.9%

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

   if -1.2999999999999999e-262 < t < 8.49999999999999938e41

   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 80.4%

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

      1. mul-1-neg 80.4%

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

      2. distribute-rgt-neg-in 80.4%

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

      3. sub-neg 80.4%

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

      4. +-commutative 80.4%

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

      5. distribute-neg-in 80.4%

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

      6. remove-double-neg 80.4%

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

      7. sub-neg 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in z around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. *-commutative 64.0%

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

      3. unsub-neg 64.0%

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

   8. Simplified 64.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.82 \cdot 10^{-7}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-262}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+41}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -4.8e-7)
     t_1
     (if (<= t -9e-257)
       (* x (+ z 1.0))
       (if (<= t 2.8e+41) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -4.8e-7) {
		tmp = t_1;
	} else if (t <= -9e-257) {
		tmp = x * (z + 1.0);
	} else if (t <= 2.8e+41) {
		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 - z) * t
    if (t <= (-4.8d-7)) then
        tmp = t_1
    else if (t <= (-9d-257)) then
        tmp = x * (z + 1.0d0)
    else if (t <= 2.8d+41) 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 - z) * t;
	double tmp;
	if (t <= -4.8e-7) {
		tmp = t_1;
	} else if (t <= -9e-257) {
		tmp = x * (z + 1.0);
	} else if (t <= 2.8e+41) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -4.8e-7:
		tmp = t_1
	elif t <= -9e-257:
		tmp = x * (z + 1.0)
	elif t <= 2.8e+41:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -4.8e-7)
		tmp = t_1;
	elseif (t <= -9e-257)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (t <= 2.8e+41)
		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 - z) * t;
	tmp = 0.0;
	if (t <= -4.8e-7)
		tmp = t_1;
	elseif (t <= -9e-257)
		tmp = x * (z + 1.0);
	elseif (t <= 2.8e+41)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.8e-7], t$95$1, If[LessEqual[t, -9e-257], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+41], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999957e-7 or 2.7999999999999999e41 < 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 97.6%

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

      1. associate--l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. unsub-neg 97.6%

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

      5. div-sub 97.6%

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

      6. unsub-neg 97.6%

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

      7. mul-1-neg 97.6%

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

      8. mul-1-neg 97.6%

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

      9. *-rgt-identity 97.6%

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

      10. distribute-rgt-neg-in 97.6%

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

      11. mul-1-neg 97.6%

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

      12. distribute-lft-in 97.6%

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

      13. mul-1-neg 97.6%

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

      14. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in x around 0 79.4%

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

   if -4.79999999999999957e-7 < t < -9.0000000000000005e-257

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in y around 0 64.9%

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

      1. +-commutative 64.9%

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

   8. Simplified 64.9%

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

   if -9.0000000000000005e-257 < t < 2.7999999999999999e41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in z around 0 64.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-39}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(x + \frac{x}{z}\right) - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.4e-39)
   (+ x (* z (- x t)))
   (if (<= z 6.5e+23) (+ x (* y (- t x))) (* z (- (+ x (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.4e-39) {
		tmp = x + (z * (x - t));
	} else if (z <= 6.5e+23) {
		tmp = x + (y * (t - x));
	} else {
		tmp = z * ((x + (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 (z <= (-4.4d-39)) then
        tmp = x + (z * (x - t))
    else if (z <= 6.5d+23) then
        tmp = x + (y * (t - x))
    else
        tmp = z * ((x + (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 (z <= -4.4e-39) {
		tmp = x + (z * (x - t));
	} else if (z <= 6.5e+23) {
		tmp = x + (y * (t - x));
	} else {
		tmp = z * ((x + (x / z)) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.4e-39:
		tmp = x + (z * (x - t))
	elif z <= 6.5e+23:
		tmp = x + (y * (t - x))
	else:
		tmp = z * ((x + (x / z)) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.4e-39)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	elseif (z <= 6.5e+23)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(z * Float64(Float64(x + Float64(x / z)) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.4e-39)
		tmp = x + (z * (x - t));
	elseif (z <= 6.5e+23)
		tmp = x + (y * (t - x));
	else
		tmp = z * ((x + (x / z)) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.4e-39], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+23], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(x + N[(x / z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000002e-39

   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 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   5. Simplified 78.4%

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

   if -4.40000000000000002e-39 < z < 6.4999999999999996e23

   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 92.8%

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

      1. *-commutative 92.8%

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

   5. Simplified 92.8%

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

   if 6.4999999999999996e23 < 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 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in z around inf 87.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-39}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+23}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(x + \frac{x}{z}\right) - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-38} \lor \neg \left(z \leq 8.5 \cdot 10^{+23}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-38) (not (<= z 8.5e+23)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-38) || !(z <= 8.5e+23)) {
		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 <= (-1.95d-38)) .or. (.not. (z <= 8.5d+23))) 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 <= -1.95e-38) || !(z <= 8.5e+23)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-38) or not (z <= 8.5e+23):
		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 <= -1.95e-38) || !(z <= 8.5e+23))
		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 <= -1.95e-38) || ~((z <= 8.5e+23)))
		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, -1.95e-38], N[Not[LessEqual[z, 8.5e+23]], $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 < -1.95e-38 or 8.5000000000000001e23 < 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 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

   5. Simplified 82.2%

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

   if -1.95e-38 < z < 8.5000000000000001e23

   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 92.8%

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

      1. *-commutative 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-38} \lor \neg \left(z \leq 8.5 \cdot 10^{+23}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-7} \lor \neg \left(t \leq 8.5 \cdot 10^{+41}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e-7) (not (<= t 8.5e+41)))
   (* (- y z) t)
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e-7) || !(t <= 8.5e+41)) {
		tmp = (y - z) * t;
	} 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 <= (-1.35d-7)) .or. (.not. (t <= 8.5d+41))) then
        tmp = (y - z) * t
    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 <= -1.35e-7) || !(t <= 8.5e+41)) {
		tmp = (y - z) * t;
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e-7) or not (t <= 8.5e+41):
		tmp = (y - z) * t
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e-7) || !(t <= 8.5e+41))
		tmp = Float64(Float64(y - z) * t);
	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 <= -1.35e-7) || ~((t <= 8.5e+41)))
		tmp = (y - z) * t;
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.35e-7], N[Not[LessEqual[t, 8.5e+41]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35000000000000004e-7 or 8.49999999999999938e41 < 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 97.6%

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

      1. associate--l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. unsub-neg 97.6%

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

      5. div-sub 97.6%

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

      6. unsub-neg 97.6%

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

      7. mul-1-neg 97.6%

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

      8. mul-1-neg 97.6%

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

      9. *-rgt-identity 97.6%

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

      10. distribute-rgt-neg-in 97.6%

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

      11. mul-1-neg 97.6%

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

      12. distribute-lft-in 97.6%

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

      13. mul-1-neg 97.6%

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

      14. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in x around 0 79.4%

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

   if -1.35000000000000004e-7 < t < 8.49999999999999938e41

   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 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-rgt-neg-in 82.6%

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

      3. sub-neg 82.6%

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

      4. +-commutative 82.6%

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

      5. distribute-neg-in 82.6%

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

      6. remove-double-neg 82.6%

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

      7. sub-neg 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-7} \lor \neg \left(t \leq 8.5 \cdot 10^{+41}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-6} \lor \neg \left(t \leq 2.05 \cdot 10^{+42}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.3e-6) (not (<= t 2.05e+42)))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e-6) || !(t <= 2.05e+42)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 <= (-3.3d-6)) .or. (.not. (t <= 2.05d+42))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e-6) || !(t <= 2.05e+42)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.3e-6) or not (t <= 2.05e+42):
		tmp = (y - z) * t
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.3e-6) || !(t <= 2.05e+42))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.3e-6) || ~((t <= 2.05e+42)))
		tmp = (y - z) * t;
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.3e-6], N[Not[LessEqual[t, 2.05e+42]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.30000000000000017e-6 or 2.05e42 < 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 97.6%

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

      1. associate--l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. unsub-neg 97.6%

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

      5. div-sub 97.6%

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

      6. unsub-neg 97.6%

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

      7. mul-1-neg 97.6%

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

      8. mul-1-neg 97.6%

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

      9. *-rgt-identity 97.6%

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

      10. distribute-rgt-neg-in 97.6%

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

      11. mul-1-neg 97.6%

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

      12. distribute-lft-in 97.6%

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

      13. mul-1-neg 97.6%

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

      14. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in x around 0 79.4%

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

   if -3.30000000000000017e-6 < t < 2.05e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-6} \lor \neg \left(t \leq 2.05 \cdot 10^{+42}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+33}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+154}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.35e+33)
   (+ x (* x (- z y)))
   (if (<= x 6.8e+154) (- x (* t (- z y))) (* x (+ (- z y) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e+33) {
		tmp = x + (x * (z - y));
	} else if (x <= 6.8e+154) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 <= (-2.35d+33)) then
        tmp = x + (x * (z - y))
    else if (x <= 6.8d+154) then
        tmp = x - (t * (z - y))
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e+33) {
		tmp = x + (x * (z - y));
	} else if (x <= 6.8e+154) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.35e+33:
		tmp = x + (x * (z - y))
	elif x <= 6.8e+154:
		tmp = x - (t * (z - y))
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.35e+33)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	elseif (x <= 6.8e+154)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.35e+33)
		tmp = x + (x * (z - y));
	elseif (x <= 6.8e+154)
		tmp = x - (t * (z - y));
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.35e+33], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+154], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3499999999999999e33

   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 87.9%

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

      1. mul-1-neg 87.9%

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

      2. distribute-rgt-neg-in 87.9%

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

      3. sub-neg 87.9%

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

      4. +-commutative 87.9%

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

      5. distribute-neg-in 87.9%

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

      6. remove-double-neg 87.9%

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

      7. sub-neg 87.9%

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

   5. Simplified 87.9%

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

   if -2.3499999999999999e33 < x < 6.79999999999999948e154

   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 82.5%

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

   if 6.79999999999999948e154 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+33}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+154}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-6} \lor \neg \left(t \leq 8.2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-6) (not (<= t 8.2e+41))) (* (- y z) t) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-6) || !(t <= 8.2e+41)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	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 <= (-3.5d-6)) .or. (.not. (t <= 8.2d+41))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-6) || !(t <= 8.2e+41)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-6) or not (t <= 8.2e+41):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-6) || !(t <= 8.2e+41))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e-6) || ~((t <= 8.2e+41)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-6], N[Not[LessEqual[t, 8.2e+41]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.49999999999999995e-6 or 8.2000000000000007e41 < 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 97.6%

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

      1. associate--l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. unsub-neg 97.6%

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

      5. div-sub 97.6%

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

      6. unsub-neg 97.6%

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

      7. mul-1-neg 97.6%

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

      8. mul-1-neg 97.6%

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

      9. *-rgt-identity 97.6%

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

      10. distribute-rgt-neg-in 97.6%

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

      11. mul-1-neg 97.6%

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

      12. distribute-lft-in 97.6%

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

      13. mul-1-neg 97.6%

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

      14. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in x around 0 79.4%

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

   if -3.49999999999999995e-6 < t < 8.2000000000000007e41

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in y around 0 56.7%

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

      1. +-commutative 56.7%

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

   8. Simplified 56.7%

      \[\leadsto x \cdot \color{blue}{\left(z + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-6} \lor \neg \left(t \leq 8.2 \cdot 10^{+41}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+62}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+195}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2e+62) (* z x) (if (<= x 1.16e+195) (* (- y z) t) (* y (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e+62) {
		tmp = z * x;
	} else if (x <= 1.16e+195) {
		tmp = (y - z) * t;
	} else {
		tmp = y * -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 (x <= (-2d+62)) then
        tmp = z * x
    else if (x <= 1.16d+195) then
        tmp = (y - z) * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e+62) {
		tmp = z * x;
	} else if (x <= 1.16e+195) {
		tmp = (y - z) * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2e+62:
		tmp = z * x
	elif x <= 1.16e+195:
		tmp = (y - z) * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2e+62)
		tmp = Float64(z * x);
	elseif (x <= 1.16e+195)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2e+62)
		tmp = z * x;
	elseif (x <= 1.16e+195)
		tmp = (y - z) * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2e+62], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.16e+195], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.00000000000000007e62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around inf 46.9%

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

   if -2.00000000000000007e62 < x < 1.16e195

   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 90.3%

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

      1. associate--l+ 90.3%

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

      2. +-commutative 90.3%

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

      3. mul-1-neg 90.3%

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

      4. unsub-neg 90.3%

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

      5. div-sub 90.9%

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

      6. unsub-neg 90.9%

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

      7. mul-1-neg 90.9%

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

      8. mul-1-neg 90.9%

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

      9. *-rgt-identity 90.9%

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

      10. distribute-rgt-neg-in 90.9%

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

      11. mul-1-neg 90.9%

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

      12. distribute-lft-in 90.9%

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

      13. mul-1-neg 90.9%

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

      14. unsub-neg 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in x around 0 62.6%

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

   if 1.16e195 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in y around inf 58.9%

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

      1. neg-mul-1 58.9%

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

   8. Simplified 58.9%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+62}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+195}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-58} \lor \neg \left(y \leq 2.15 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e-58) (not (<= y 2.15e-30))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-58) || !(y <= 2.15e-30)) {
		tmp = y * t;
	} 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 ((y <= (-3.5d-58)) .or. (.not. (y <= 2.15d-30))) then
        tmp = y * t
    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 ((y <= -3.5e-58) || !(y <= 2.15e-30)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e-58) or not (y <= 2.15e-30):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e-58) || !(y <= 2.15e-30))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5e-58) || ~((y <= 2.15e-30)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e-58], N[Not[LessEqual[y, 2.15e-30]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999999e-58 or 2.14999999999999983e-30 < y

   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 82.7%

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

      1. associate--l+ 82.6%

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

      2. +-commutative 82.6%

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

      3. mul-1-neg 82.6%

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

      4. unsub-neg 82.6%

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

      5. div-sub 84.8%

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

      6. unsub-neg 84.8%

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

      7. mul-1-neg 84.8%

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

      8. mul-1-neg 84.8%

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

      9. *-rgt-identity 84.8%

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

      10. distribute-rgt-neg-in 84.8%

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

      11. mul-1-neg 84.8%

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

      12. distribute-lft-in 84.8%

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

      13. mul-1-neg 84.8%

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

      14. unsub-neg 84.8%

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

   5. Simplified 84.8%

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

   6. Taylor expanded in x around 0 52.7%

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

   7. Taylor expanded in y around inf 40.6%

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

   if -3.4999999999999999e-58 < y < 2.14999999999999983e-30

   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 45.7%

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

      1. *-commutative 45.7%

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

   5. Simplified 45.7%

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

   6. Taylor expanded in y around 0 37.3%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-58} \lor \neg \left(y \leq 2.15 \cdot 10^{-30}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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]

Derivation

1. Initial program 100.0%

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

Alternative 16: 18.4% 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 62.4%

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

   1. *-commutative 62.4%

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

5. Simplified 62.4%

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

6. Taylor expanded in y around 0 19.9%

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

Developer Target 1: 96.2% 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 2024191 
(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))))