Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.9s

Alternatives: 15

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 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 99.9%

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

   1. +-commutative 99.9%

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

   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: 69.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-235}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-109}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -6e-11)
     t_1
     (if (<= z 1.3e-235)
       (+ x (* y t))
       (if (<= z 3.7e-109)
         (- x (* y x))
         (if (<= z 6.2e+40) (* t (- y z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -6e-11) {
		tmp = t_1;
	} else if (z <= 1.3e-235) {
		tmp = x + (y * t);
	} else if (z <= 3.7e-109) {
		tmp = x - (y * x);
	} else if (z <= 6.2e+40) {
		tmp = t * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-6d-11)) then
        tmp = t_1
    else if (z <= 1.3d-235) then
        tmp = x + (y * t)
    else if (z <= 3.7d-109) then
        tmp = x - (y * x)
    else if (z <= 6.2d+40) then
        tmp = t * (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -6e-11) {
		tmp = t_1;
	} else if (z <= 1.3e-235) {
		tmp = x + (y * t);
	} else if (z <= 3.7e-109) {
		tmp = x - (y * x);
	} else if (z <= 6.2e+40) {
		tmp = t * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -6e-11:
		tmp = t_1
	elif z <= 1.3e-235:
		tmp = x + (y * t)
	elif z <= 3.7e-109:
		tmp = x - (y * x)
	elif z <= 6.2e+40:
		tmp = t * (y - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -6e-11)
		tmp = t_1;
	elseif (z <= 1.3e-235)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.7e-109)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 6.2e+40)
		tmp = Float64(t * Float64(y - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -6e-11)
		tmp = t_1;
	elseif (z <= 1.3e-235)
		tmp = x + (y * t);
	elseif (z <= 3.7e-109)
		tmp = x - (y * x);
	elseif (z <= 6.2e+40)
		tmp = t * (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-11], t$95$1, If[LessEqual[z, 1.3e-235], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-109], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+40], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6e-11 or 6.1999999999999995e40 < 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 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in z around inf 75.8%

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

   if -6e-11 < z < 1.3e-235

   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 81.1%

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

   4. Taylor expanded in y around inf 73.0%

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

   if 1.3e-235 < z < 3.69999999999999981e-109

   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 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-in 78.6%

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

      3. sub-neg 78.6%

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

      4. +-commutative 78.6%

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

      5. distribute-neg-in 78.6%

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

      6. remove-double-neg 78.6%

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

      7. sub-neg 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

   8. Simplified 78.6%

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

   if 3.69999999999999981e-109 < z < 6.1999999999999995e40

   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 86.1%

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

   4. Taylor expanded in t around inf 86.1%

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

      1. associate--l+ 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 85.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-235}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-109}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-205}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* (- y z) t)))
   (if (<= z -6.5e+27)
     t_1
     (if (<= z -4.2e-205)
       t_2
       (if (<= z 3.4e-150) x (if (<= z 1.1e+41) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -6.5e+27) {
		tmp = t_1;
	} else if (z <= -4.2e-205) {
		tmp = t_2;
	} else if (z <= 3.4e-150) {
		tmp = x;
	} else if (z <= 1.1e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = (y - z) * t
    if (z <= (-6.5d+27)) then
        tmp = t_1
    else if (z <= (-4.2d-205)) then
        tmp = t_2
    else if (z <= 3.4d-150) then
        tmp = x
    else if (z <= 1.1d+41) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -6.5e+27) {
		tmp = t_1;
	} else if (z <= -4.2e-205) {
		tmp = t_2;
	} else if (z <= 3.4e-150) {
		tmp = x;
	} else if (z <= 1.1e+41) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -6.5e+27:
		tmp = t_1
	elif z <= -4.2e-205:
		tmp = t_2
	elif z <= 3.4e-150:
		tmp = x
	elif z <= 1.1e+41:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -6.5e+27)
		tmp = t_1;
	elseif (z <= -4.2e-205)
		tmp = t_2;
	elseif (z <= 3.4e-150)
		tmp = x;
	elseif (z <= 1.1e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (z <= -6.5e+27)
		tmp = t_1;
	elseif (z <= -4.2e-205)
		tmp = t_2;
	elseif (z <= 3.4e-150)
		tmp = x;
	elseif (z <= 1.1e+41)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -6.5e+27], t$95$1, If[LessEqual[z, -4.2e-205], t$95$2, If[LessEqual[z, 3.4e-150], x, If[LessEqual[z, 1.1e+41], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5000000000000005e27 or 1.09999999999999995e41 < 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 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in z around inf 82.3%

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

   if -6.5000000000000005e27 < z < -4.19999999999999965e-205 or 3.39999999999999999e-150 < z < 1.09999999999999995e41

   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 75.2%

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

   4. Taylor expanded in t around inf 76.1%

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

      1. associate--l+ 76.1%

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

   6. Simplified 76.1%

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

   7. Taylor expanded in x around 0 59.7%

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

   if -4.19999999999999965e-205 < z < 3.39999999999999999e-150

   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 79.0%

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

   4. Taylor expanded in x around inf 51.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-205}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+41}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(y - z\right)\\ \mathbf{if}\;t \leq -2.1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-245}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-180}:\\ \;\;\;\;-y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- y z))))
   (if (<= t -2.1)
     t_1
     (if (<= t -2.35e-181)
       x
       (if (<= t 1.32e-245) (* z x) (if (<= t 2.9e-180) (- (* y x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y - z);
	double tmp;
	if (t <= -2.1) {
		tmp = t_1;
	} else if (t <= -2.35e-181) {
		tmp = x;
	} else if (t <= 1.32e-245) {
		tmp = z * x;
	} else if (t <= 2.9e-180) {
		tmp = -(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 = t * (y - z)
    if (t <= (-2.1d0)) then
        tmp = t_1
    else if (t <= (-2.35d-181)) then
        tmp = x
    else if (t <= 1.32d-245) then
        tmp = z * x
    else if (t <= 2.9d-180) then
        tmp = -(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 = t * (y - z);
	double tmp;
	if (t <= -2.1) {
		tmp = t_1;
	} else if (t <= -2.35e-181) {
		tmp = x;
	} else if (t <= 1.32e-245) {
		tmp = z * x;
	} else if (t <= 2.9e-180) {
		tmp = -(y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y - z)
	tmp = 0
	if t <= -2.1:
		tmp = t_1
	elif t <= -2.35e-181:
		tmp = x
	elif t <= 1.32e-245:
		tmp = z * x
	elif t <= 2.9e-180:
		tmp = -(y * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y - z))
	tmp = 0.0
	if (t <= -2.1)
		tmp = t_1;
	elseif (t <= -2.35e-181)
		tmp = x;
	elseif (t <= 1.32e-245)
		tmp = Float64(z * x);
	elseif (t <= 2.9e-180)
		tmp = Float64(-Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y - z);
	tmp = 0.0;
	if (t <= -2.1)
		tmp = t_1;
	elseif (t <= -2.35e-181)
		tmp = x;
	elseif (t <= 1.32e-245)
		tmp = z * x;
	elseif (t <= 2.9e-180)
		tmp = -(y * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1], t$95$1, If[LessEqual[t, -2.35e-181], x, If[LessEqual[t, 1.32e-245], N[(z * x), $MachinePrecision], If[LessEqual[t, 2.9e-180], (-N[(y * x), $MachinePrecision]), t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.10000000000000009 or 2.8999999999999998e-180 < t

   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 81.3%

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

   4. Taylor expanded in t around inf 81.9%

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

      1. associate--l+ 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in x around 0 71.3%

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

   if -2.10000000000000009 < t < -2.3499999999999999e-181

   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 61.1%

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

   4. Taylor expanded in x around inf 42.5%

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

   if -2.3499999999999999e-181 < t < 1.32e-245

   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 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in z around inf 60.4%

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

   7. Taylor expanded in x around inf 60.2%

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

      1. *-commutative 60.2%

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

   9. Simplified 60.2%

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

   if 1.32e-245 < t < 2.8999999999999998e-180

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 89.0%

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

      1. mul-1-neg 89.0%

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

      2. distribute-rgt-neg-in 89.0%

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

      3. sub-neg 89.0%

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

      4. +-commutative 89.0%

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

      5. distribute-neg-in 89.0%

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

      6. remove-double-neg 89.0%

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

      7. sub-neg 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in z around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. unsub-neg 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in y around inf 42.3%

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

       1. associate-*r* 42.3%

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

       2. neg-mul-1 42.3%

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

       3. *-commutative 42.3%

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

   11. Simplified 42.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-245}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-180}:\\ \;\;\;\;-y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-109}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -4.7e+29)
     t_1
     (if (<= z 6.6e-109)
       (+ x (* y (- t x)))
       (if (<= z 9.5e+40) (* t (- y z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.7e+29) {
		tmp = t_1;
	} else if (z <= 6.6e-109) {
		tmp = x + (y * (t - x));
	} else if (z <= 9.5e+40) {
		tmp = t * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-4.7d+29)) then
        tmp = t_1
    else if (z <= 6.6d-109) then
        tmp = x + (y * (t - x))
    else if (z <= 9.5d+40) then
        tmp = t * (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.7e+29) {
		tmp = t_1;
	} else if (z <= 6.6e-109) {
		tmp = x + (y * (t - x));
	} else if (z <= 9.5e+40) {
		tmp = t * (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -4.7e+29:
		tmp = t_1
	elif z <= 6.6e-109:
		tmp = x + (y * (t - x))
	elif z <= 9.5e+40:
		tmp = t * (y - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -4.7e+29)
		tmp = t_1;
	elseif (z <= 6.6e-109)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	elseif (z <= 9.5e+40)
		tmp = Float64(t * Float64(y - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -4.7e+29)
		tmp = t_1;
	elseif (z <= 6.6e-109)
		tmp = x + (y * (t - x));
	elseif (z <= 9.5e+40)
		tmp = t * (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.7e+29], t$95$1, If[LessEqual[z, 6.6e-109], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+40], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7000000000000002e29 or 9.5000000000000003e40 < 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 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in z around inf 82.3%

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

   if -4.7000000000000002e29 < z < 6.59999999999999981e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.2%

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

      1. *-commutative 88.2%

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

   5. Simplified 88.2%

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

   if 6.59999999999999981e-109 < z < 9.5000000000000003e40

   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 86.1%

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

   4. Taylor expanded in t around inf 86.1%

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

      1. associate--l+ 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 85.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-109}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-109}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7.5e-11)
     t_1
     (if (<= z 6.6e-109)
       (+ x (* y t))
       (if (<= z 6.4e+40) (* (- y z) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.5e-11) {
		tmp = t_1;
	} else if (z <= 6.6e-109) {
		tmp = x + (y * t);
	} else if (z <= 6.4e+40) {
		tmp = (y - z) * t;
	} 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 = z * (x - t)
    if (z <= (-7.5d-11)) then
        tmp = t_1
    else if (z <= 6.6d-109) then
        tmp = x + (y * t)
    else if (z <= 6.4d+40) then
        tmp = (y - z) * t
    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 = z * (x - t);
	double tmp;
	if (z <= -7.5e-11) {
		tmp = t_1;
	} else if (z <= 6.6e-109) {
		tmp = x + (y * t);
	} else if (z <= 6.4e+40) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7.5e-11:
		tmp = t_1
	elif z <= 6.6e-109:
		tmp = x + (y * t)
	elif z <= 6.4e+40:
		tmp = (y - z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7.5e-11)
		tmp = t_1;
	elseif (z <= 6.6e-109)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 6.4e+40)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -7.5e-11)
		tmp = t_1;
	elseif (z <= 6.6e-109)
		tmp = x + (y * t);
	elseif (z <= 6.4e+40)
		tmp = (y - z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-11], t$95$1, If[LessEqual[z, 6.6e-109], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+40], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e-11 or 6.39999999999999961e40 < 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 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in z around inf 75.8%

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

   if -7.5e-11 < z < 6.59999999999999981e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.7%

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

   4. Taylor expanded in y around inf 70.6%

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

   if 6.59999999999999981e-109 < z < 6.39999999999999961e40

   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 86.1%

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

   4. Taylor expanded in t around inf 86.1%

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

      1. associate--l+ 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in x around 0 85.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-109}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+40}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-212}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e-7)
   (* y t)
   (if (<= y -2.1e-212) (* z x) (if (<= y 6.2e+61) (* t (- z)) (- (* y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e-7) {
		tmp = y * t;
	} else if (y <= -2.1e-212) {
		tmp = z * x;
	} else if (y <= 6.2e+61) {
		tmp = t * -z;
	} 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 (y <= (-4.5d-7)) then
        tmp = y * t
    else if (y <= (-2.1d-212)) then
        tmp = z * x
    else if (y <= 6.2d+61) then
        tmp = t * -z
    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 (y <= -4.5e-7) {
		tmp = y * t;
	} else if (y <= -2.1e-212) {
		tmp = z * x;
	} else if (y <= 6.2e+61) {
		tmp = t * -z;
	} else {
		tmp = -(y * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e-7:
		tmp = y * t
	elif y <= -2.1e-212:
		tmp = z * x
	elif y <= 6.2e+61:
		tmp = t * -z
	else:
		tmp = -(y * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.5e-7)
		tmp = Float64(y * t);
	elseif (y <= -2.1e-212)
		tmp = Float64(z * x);
	elseif (y <= 6.2e+61)
		tmp = Float64(t * Float64(-z));
	else
		tmp = Float64(-Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.5e-7)
		tmp = y * t;
	elseif (y <= -2.1e-212)
		tmp = z * x;
	elseif (y <= 6.2e+61)
		tmp = t * -z;
	else
		tmp = -(y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.5e-7], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.1e-212], N[(z * x), $MachinePrecision], If[LessEqual[y, 6.2e+61], N[(t * (-z)), $MachinePrecision], (-N[(y * x), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999998e-7

   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 58.9%

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

   4. Taylor expanded in t around inf 65.8%

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

      1. associate--l+ 65.8%

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

   6. Simplified 65.8%

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

   7. Taylor expanded in y around inf 50.4%

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

   if -4.4999999999999998e-7 < y < -2.1e-212

   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 91.8%

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

      1. mul-1-neg 91.8%

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

      2. unsub-neg 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in z around inf 70.2%

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

   7. Taylor expanded in x around inf 42.1%

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

      1. *-commutative 42.1%

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

   9. Simplified 42.1%

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

   if -2.1e-212 < y < 6.1999999999999998e61

   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 82.1%

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

   4. Taylor expanded in t around inf 77.4%

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

      1. associate--l+ 77.4%

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

   6. Simplified 77.4%

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

   7. Taylor expanded in z around inf 43.1%

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

      1. neg-mul-1 43.1%

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

   9. Simplified 43.1%

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

   if 6.1999999999999998e61 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. distribute-rgt-neg-in 62.2%

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

      3. sub-neg 62.2%

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

      4. +-commutative 62.2%

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

      5. distribute-neg-in 62.2%

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

      6. remove-double-neg 62.2%

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

      7. sub-neg 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in z around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. unsub-neg 60.0%

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

   8. Simplified 60.0%

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

   9. Taylor expanded in y around inf 60.0%

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

       1. associate-*r* 60.0%

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

       2. neg-mul-1 60.0%

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

       3. *-commutative 60.0%

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

   11. Simplified 60.0%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-212}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-211}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 0.0042:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e-12)
   (* y t)
   (if (<= y -3.5e-211) (* z x) (if (<= y 0.0042) (* t (- z)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-12) {
		tmp = y * t;
	} else if (y <= -3.5e-211) {
		tmp = z * x;
	} else if (y <= 0.0042) {
		tmp = t * -z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.8d-12)) then
        tmp = y * t
    else if (y <= (-3.5d-211)) then
        tmp = z * x
    else if (y <= 0.0042d0) then
        tmp = t * -z
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-12) {
		tmp = y * t;
	} else if (y <= -3.5e-211) {
		tmp = z * x;
	} else if (y <= 0.0042) {
		tmp = t * -z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e-12:
		tmp = y * t
	elif y <= -3.5e-211:
		tmp = z * x
	elif y <= 0.0042:
		tmp = t * -z
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e-12)
		tmp = Float64(y * t);
	elseif (y <= -3.5e-211)
		tmp = Float64(z * x);
	elseif (y <= 0.0042)
		tmp = Float64(t * Float64(-z));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e-12)
		tmp = y * t;
	elseif (y <= -3.5e-211)
		tmp = z * x;
	elseif (y <= 0.0042)
		tmp = t * -z;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e-12], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.5e-211], N[(z * x), $MachinePrecision], If[LessEqual[y, 0.0042], N[(t * (-z)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.79999999999999996e-12 or 0.00419999999999999974 < y

   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 55.2%

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

   4. Taylor expanded in t around inf 58.4%

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

      1. associate--l+ 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in y around inf 47.0%

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

   if -3.79999999999999996e-12 < y < -3.5e-211

   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 91.8%

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

      1. mul-1-neg 91.8%

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

      2. unsub-neg 91.8%

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

   5. Simplified 91.8%

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

   6. Taylor expanded in z around inf 70.2%

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

   7. Taylor expanded in x around inf 42.1%

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

      1. *-commutative 42.1%

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

   9. Simplified 42.1%

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

   if -3.5e-211 < y < 0.00419999999999999974

   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 85.4%

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

   4. Taylor expanded in t around inf 79.7%

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

      1. associate--l+ 79.8%

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

   6. Simplified 79.8%

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

   7. Taylor expanded in z around inf 46.6%

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

      1. neg-mul-1 46.6%

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

   9. Simplified 46.6%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-211}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 0.0042:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-228}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-12)
   (* y t)
   (if (<= y -6.5e-228) (* z x) (if (<= y 5.2e-12) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-12) {
		tmp = y * t;
	} else if (y <= -6.5e-228) {
		tmp = z * x;
	} else if (y <= 5.2e-12) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.15d-12)) then
        tmp = y * t
    else if (y <= (-6.5d-228)) then
        tmp = z * x
    else if (y <= 5.2d-12) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-12) {
		tmp = y * t;
	} else if (y <= -6.5e-228) {
		tmp = z * x;
	} else if (y <= 5.2e-12) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-12:
		tmp = y * t
	elif y <= -6.5e-228:
		tmp = z * x
	elif y <= 5.2e-12:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-12)
		tmp = Float64(y * t);
	elseif (y <= -6.5e-228)
		tmp = Float64(z * x);
	elseif (y <= 5.2e-12)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e-12)
		tmp = y * t;
	elseif (y <= -6.5e-228)
		tmp = z * x;
	elseif (y <= 5.2e-12)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-12], N[(y * t), $MachinePrecision], If[LessEqual[y, -6.5e-228], N[(z * x), $MachinePrecision], If[LessEqual[y, 5.2e-12], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.14999999999999995e-12 or 5.19999999999999965e-12 < y

   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 55.2%

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

   4. Taylor expanded in t around inf 58.4%

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

      1. associate--l+ 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in y around inf 47.0%

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

   if -1.14999999999999995e-12 < y < -6.50000000000000029e-228

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in z around inf 72.2%

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

   7. Taylor expanded in x around inf 41.1%

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

      1. *-commutative 41.1%

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

   9. Simplified 41.1%

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

   if -6.50000000000000029e-228 < y < 5.19999999999999965e-12

   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 85.9%

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

   4. Taylor expanded in x around inf 36.7%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-228}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-32} \lor \neg \left(y \leq 220000000000\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.45e-32) (not (<= y 220000000000.0)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.45e-32) || !(y <= 220000000000.0)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.45d-32)) .or. (.not. (y <= 220000000000.0d0))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.45e-32) || !(y <= 220000000000.0)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.45e-32) or not (y <= 220000000000.0):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.45e-32) || !(y <= 220000000000.0))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.45e-32) || ~((y <= 220000000000.0)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.45e-32], N[Not[LessEqual[y, 220000000000.0]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4499999999999999e-32 or 2.2e11 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.9%

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

      1. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -2.4499999999999999e-32 < y < 2.2e11

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-32} \lor \neg \left(y \leq 220000000000\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -20.5 \lor \neg \left(t \leq 4.5 \cdot 10^{-116}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -20.5) (not (<= t 4.5e-116)))
   (- x (* t (- z y)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -20.5) || !(t <= 4.5e-116)) {
		tmp = x - (t * (z - y));
	} 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 <= (-20.5d0)) .or. (.not. (t <= 4.5d-116))) then
        tmp = x - (t * (z - y))
    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 <= -20.5) || !(t <= 4.5e-116)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -20.5) or not (t <= 4.5e-116):
		tmp = x - (t * (z - y))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -20.5) || !(t <= 4.5e-116))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	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 <= -20.5) || ~((t <= 4.5e-116)))
		tmp = x - (t * (z - y));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -20.5], N[Not[LessEqual[t, 4.5e-116]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -20.5 or 4.50000000000000012e-116 < t

   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 83.5%

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

   if -20.5 < t < 4.50000000000000012e-116

   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 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-in 87.3%

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

      3. sub-neg 87.3%

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

      4. +-commutative 87.3%

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

      5. distribute-neg-in 87.3%

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

      6. remove-double-neg 87.3%

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

      7. sub-neg 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -20.5 \lor \neg \left(t \leq 4.5 \cdot 10^{-116}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2400 \lor \neg \left(t \leq 1.8 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2400.0) (not (<= t 1.8e+26)))
   (* t (- y z))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2400.0) || !(t <= 1.8e+26)) {
		tmp = t * (y - z);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2400.0d0)) .or. (.not. (t <= 1.8d+26))) then
        tmp = t * (y - z)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2400.0) || !(t <= 1.8e+26)) {
		tmp = t * (y - z);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2400.0) or not (t <= 1.8e+26):
		tmp = t * (y - z)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2400.0) || !(t <= 1.8e+26))
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2400.0) || ~((t <= 1.8e+26)))
		tmp = t * (y - z);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2400.0], N[Not[LessEqual[t, 1.8e+26]], $MachinePrecision]], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2400 or 1.80000000000000012e26 < t

   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 86.0%

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

   4. Taylor expanded in t around inf 86.0%

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

      1. associate--l+ 86.0%

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

   6. Simplified 86.0%

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

   7. Taylor expanded in x around 0 79.5%

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

   if -2400 < t < 1.80000000000000012e26

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2400 \lor \neg \left(t \leq 1.8 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-35} \lor \neg \left(y \leq 4.6 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.8e-35) (not (<= y 4.6e-11))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-35) || !(y <= 4.6e-11)) {
		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 <= (-4.8d-35)) .or. (.not. (y <= 4.6d-11))) 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 <= -4.8e-35) || !(y <= 4.6e-11)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.8e-35) or not (y <= 4.6e-11):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.8e-35) || !(y <= 4.6e-11))
		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 <= -4.8e-35) || ~((y <= 4.6e-11)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.8e-35], N[Not[LessEqual[y, 4.6e-11]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000003e-35 or 4.60000000000000027e-11 < y

   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 55.5%

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

   4. Taylor expanded in t around inf 59.4%

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

      1. associate--l+ 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in y around inf 46.1%

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

   if -4.8000000000000003e-35 < y < 4.60000000000000027e-11

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.1%

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

   4. Taylor expanded in x around inf 31.3%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-35} \lor \neg \left(y \leq 4.6 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 15: 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 99.9%

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

3. Taylor expanded in t around inf 66.5%

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

4. Taylor expanded in x around inf 18.3%

   \[\leadsto \color{blue}{x} \]
5. 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 2024186 
(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))))