Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 11

Speedup: 1.0×

• 33.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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. Final simplification 100.0%

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

Alternative 2: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-147}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* (- y z) t))))
   (if (<= y -5.2e+47)
     t_1
     (if (<= y 1.8e-212)
       t_2
       (if (<= y 4.7e-147) (+ x (* x z)) (if (<= y 2.5e+38) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (y <= -5.2e+47) {
		tmp = t_1;
	} else if (y <= 1.8e-212) {
		tmp = t_2;
	} else if (y <= 4.7e-147) {
		tmp = x + (x * z);
	} else if (y <= 2.5e+38) {
		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 = y * (t - x)
    t_2 = x + ((y - z) * t)
    if (y <= (-5.2d+47)) then
        tmp = t_1
    else if (y <= 1.8d-212) then
        tmp = t_2
    else if (y <= 4.7d-147) then
        tmp = x + (x * z)
    else if (y <= 2.5d+38) 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 = y * (t - x);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (y <= -5.2e+47) {
		tmp = t_1;
	} else if (y <= 1.8e-212) {
		tmp = t_2;
	} else if (y <= 4.7e-147) {
		tmp = x + (x * z);
	} else if (y <= 2.5e+38) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if y <= -5.2e+47:
		tmp = t_1
	elif y <= 1.8e-212:
		tmp = t_2
	elif y <= 4.7e-147:
		tmp = x + (x * z)
	elif y <= 2.5e+38:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (y <= -5.2e+47)
		tmp = t_1;
	elseif (y <= 1.8e-212)
		tmp = t_2;
	elseif (y <= 4.7e-147)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 2.5e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x + ((y - z) * t);
	tmp = 0.0;
	if (y <= -5.2e+47)
		tmp = t_1;
	elseif (y <= 1.8e-212)
		tmp = t_2;
	elseif (y <= 4.7e-147)
		tmp = x + (x * z);
	elseif (y <= 2.5e+38)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+47], t$95$1, If[LessEqual[y, 1.8e-212], t$95$2, If[LessEqual[y, 4.7e-147], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+38], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.20000000000000007e47 or 2.49999999999999985e38 < 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 84.7%

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

      1. *-commutative 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around inf 84.7%

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

   if -5.20000000000000007e47 < y < 1.8e-212 or 4.69999999999999989e-147 < y < 2.49999999999999985e38

   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 77.5%

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

   if 1.8e-212 < y < 4.69999999999999989e-147

   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 93.1%

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

      1. mul-1-neg 93.1%

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

      2. distribute-rgt-neg-in 93.1%

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

      3. sub-neg 93.1%

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

      4. +-commutative 93.1%

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

      5. distribute-neg-in 93.1%

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

      6. remove-double-neg 93.1%

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

      7. sub-neg 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in t around 0 86.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-147}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+38}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -5 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-146}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* z t))))
   (if (<= y -5e-18)
     t_1
     (if (<= y 2.25e-212)
       t_2
       (if (<= y 3e-146) (+ x (* x z)) (if (<= y 1.3e-8) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -5e-18) {
		tmp = t_1;
	} else if (y <= 2.25e-212) {
		tmp = t_2;
	} else if (y <= 3e-146) {
		tmp = x + (x * z);
	} else if (y <= 1.3e-8) {
		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 = y * (t - x)
    t_2 = x - (z * t)
    if (y <= (-5d-18)) then
        tmp = t_1
    else if (y <= 2.25d-212) then
        tmp = t_2
    else if (y <= 3d-146) then
        tmp = x + (x * z)
    else if (y <= 1.3d-8) 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 = y * (t - x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -5e-18) {
		tmp = t_1;
	} else if (y <= 2.25e-212) {
		tmp = t_2;
	} else if (y <= 3e-146) {
		tmp = x + (x * z);
	} else if (y <= 1.3e-8) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x - (z * t)
	tmp = 0
	if y <= -5e-18:
		tmp = t_1
	elif y <= 2.25e-212:
		tmp = t_2
	elif y <= 3e-146:
		tmp = x + (x * z)
	elif y <= 1.3e-8:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -5e-18)
		tmp = t_1;
	elseif (y <= 2.25e-212)
		tmp = t_2;
	elseif (y <= 3e-146)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 1.3e-8)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x - (z * t);
	tmp = 0.0;
	if (y <= -5e-18)
		tmp = t_1;
	elseif (y <= 2.25e-212)
		tmp = t_2;
	elseif (y <= 3e-146)
		tmp = x + (x * z);
	elseif (y <= 1.3e-8)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-18], t$95$1, If[LessEqual[y, 2.25e-212], t$95$2, If[LessEqual[y, 3e-146], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-8], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000036e-18 or 1.3000000000000001e-8 < 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 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around inf 75.7%

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

   if -5.00000000000000036e-18 < y < 2.2499999999999999e-212 or 3.00000000000000019e-146 < y < 1.3000000000000001e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.3%

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

      1. mul-1-neg 93.3%

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

      2. distribute-rgt-neg-in 93.3%

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

      3. sub-neg 93.3%

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

      4. +-commutative 93.3%

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

      5. distribute-neg-in 93.3%

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

      6. remove-double-neg 93.3%

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

      7. sub-neg 93.3%

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

   5. Simplified 93.3%

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

      1. sub-neg 93.3%

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

      2. distribute-lft-in 90.5%

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

   7. Applied egg-rr 90.5%

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

   8. Taylor expanded in x around 0 70.6%

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

      1. associate-*r* 70.6%

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

      2. mul-1-neg 70.6%

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

   10. Simplified 70.6%

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

   if 2.2499999999999999e-212 < y < 3.00000000000000019e-146

   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 93.1%

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

      1. mul-1-neg 93.1%

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

      2. distribute-rgt-neg-in 93.1%

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

      3. sub-neg 93.1%

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

      4. +-commutative 93.1%

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

      5. distribute-neg-in 93.1%

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

      6. remove-double-neg 93.1%

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

      7. sub-neg 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in t around 0 86.2%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-212}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-146}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-20}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+69}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -5.5e+47)
     t_1
     (if (<= y -3.7e-20)
       (+ x (* (- y z) t))
       (if (<= y 2.25e+69) (+ x (* z (- x t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5.5e+47) {
		tmp = t_1;
	} else if (y <= -3.7e-20) {
		tmp = x + ((y - z) * t);
	} else if (y <= 2.25e+69) {
		tmp = x + (z * (x - 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 = y * (t - x)
    if (y <= (-5.5d+47)) then
        tmp = t_1
    else if (y <= (-3.7d-20)) then
        tmp = x + ((y - z) * t)
    else if (y <= 2.25d+69) then
        tmp = x + (z * (x - 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 = y * (t - x);
	double tmp;
	if (y <= -5.5e+47) {
		tmp = t_1;
	} else if (y <= -3.7e-20) {
		tmp = x + ((y - z) * t);
	} else if (y <= 2.25e+69) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -5.5e+47:
		tmp = t_1
	elif y <= -3.7e-20:
		tmp = x + ((y - z) * t)
	elif y <= 2.25e+69:
		tmp = x + (z * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -5.5e+47)
		tmp = t_1;
	elseif (y <= -3.7e-20)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	elseif (y <= 2.25e+69)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -5.5e+47)
		tmp = t_1;
	elseif (y <= -3.7e-20)
		tmp = x + ((y - z) * t);
	elseif (y <= 2.25e+69)
		tmp = x + (z * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+47], t$95$1, If[LessEqual[y, -3.7e-20], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+69], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999998e47 or 2.25e69 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 86.2%

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

      1. *-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around inf 86.2%

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

   if -5.4999999999999998e47 < y < -3.7000000000000001e-20

   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 83.9%

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

   if -3.7000000000000001e-20 < y < 2.25e69

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.4%

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

      1. mul-1-neg 88.4%

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

      2. distribute-rgt-neg-in 88.4%

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

      3. sub-neg 88.4%

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

      4. +-commutative 88.4%

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

      5. distribute-neg-in 88.4%

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

      6. remove-double-neg 88.4%

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

      7. sub-neg 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-20}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+69}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -5.8e+47)
     t_1
     (if (<= y -3.5e-20)
       (+ x (* (- y z) t))
       (if (<= y 1.8e-8) (+ x (* z (- x t))) (+ x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5.8e+47) {
		tmp = t_1;
	} else if (y <= -3.5e-20) {
		tmp = x + ((y - z) * t);
	} else if (y <= 1.8e-8) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-5.8d+47)) then
        tmp = t_1
    else if (y <= (-3.5d-20)) then
        tmp = x + ((y - z) * t)
    else if (y <= 1.8d-8) then
        tmp = x + (z * (x - t))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5.8e+47) {
		tmp = t_1;
	} else if (y <= -3.5e-20) {
		tmp = x + ((y - z) * t);
	} else if (y <= 1.8e-8) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -5.8e+47:
		tmp = t_1
	elif y <= -3.5e-20:
		tmp = x + ((y - z) * t)
	elif y <= 1.8e-8:
		tmp = x + (z * (x - t))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -5.8e+47)
		tmp = t_1;
	elseif (y <= -3.5e-20)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	elseif (y <= 1.8e-8)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -5.8e+47)
		tmp = t_1;
	elseif (y <= -3.5e-20)
		tmp = x + ((y - z) * t);
	elseif (y <= 1.8e-8)
		tmp = x + (z * (x - t));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+47], t$95$1, If[LessEqual[y, -3.5e-20], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-8], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999961e47

   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 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in y around inf 88.1%

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

   if -5.79999999999999961e47 < y < -3.50000000000000003e-20

   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 83.9%

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

   if -3.50000000000000003e-20 < y < 1.79999999999999991e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.3%

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

      1. mul-1-neg 93.3%

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

      2. distribute-rgt-neg-in 93.3%

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

      3. sub-neg 93.3%

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

      4. +-commutative 93.3%

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

      5. distribute-neg-in 93.3%

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

      6. remove-double-neg 93.3%

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

      7. sub-neg 93.3%

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

   5. Simplified 93.3%

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

   if 1.79999999999999991e-8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+56} \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.4e+56) (not (<= x 4.2e-9)))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.4e+56) || !(x <= 4.2e-9)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - 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 ((x <= (-6.4d+56)) .or. (.not. (x <= 4.2d-9))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.4e+56) || !(x <= 4.2e-9)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.4e+56) or not (x <= 4.2e-9):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.4e+56) || !(x <= 4.2e-9))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6.4e+56) || ~((x <= 4.2e-9)))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.4e+56], N[Not[LessEqual[x, 4.2e-9]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.40000000000000007e56 or 4.20000000000000039e-9 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 88.2%

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

      1. mul-1-neg 88.2%

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

      2. distribute-rgt-neg-in 88.2%

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

      3. sub-neg 88.2%

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

      4. +-commutative 88.2%

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

      5. distribute-neg-in 88.2%

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

      6. remove-double-neg 88.2%

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

      7. sub-neg 88.2%

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

   5. Simplified 88.2%

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

   if -6.40000000000000007e56 < x < 4.20000000000000039e-9

   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 81.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+56} \lor \neg \left(x \leq 4.2 \cdot 10^{-9}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-26} \lor \neg \left(y \leq 3.9 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e-26) (not (<= y 3.9e-32))) (* y (- t x)) (* x z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-26) || !(y <= 3.9e-32)) {
		tmp = y * (t - x);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.5d-26)) .or. (.not. (y <= 3.9d-32))) then
        tmp = y * (t - x)
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-26) || !(y <= 3.9e-32)) {
		tmp = y * (t - x);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.5e-26) or not (y <= 3.9e-32):
		tmp = y * (t - x)
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e-26) || !(y <= 3.9e-32))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e-26) || ~((y <= 3.9e-32)))
		tmp = y * (t - x);
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e-26], N[Not[LessEqual[y, 3.9e-32]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e-26 or 3.9000000000000001e-32 < 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 76.6%

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

      1. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in y around inf 74.2%

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

   if -4.4999999999999999e-26 < y < 3.9000000000000001e-32

   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 93.5%

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

      1. mul-1-neg 93.5%

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

      2. distribute-rgt-neg-in 93.5%

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

      3. sub-neg 93.5%

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

      4. +-commutative 93.5%

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

      5. distribute-neg-in 93.5%

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

      6. remove-double-neg 93.5%

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

      7. sub-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in t around 0 55.9%

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

   7. Taylor expanded in z around inf 29.7%

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

      1. *-commutative 29.7%

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

   9. Simplified 29.7%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-26} \lor \neg \left(y \leq 3.9 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-22} \lor \neg \left(y \leq 1.5 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.8e-22) (not (<= y 1.5e-31))) (* y (- t x)) (+ x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-22) || !(y <= 1.5e-31)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.8d-22)) .or. (.not. (y <= 1.5d-31))) then
        tmp = y * (t - x)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-22) || !(y <= 1.5e-31)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.8e-22) or not (y <= 1.5e-31):
		tmp = y * (t - x)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.8e-22) || !(y <= 1.5e-31))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.8e-22) || ~((y <= 1.5e-31)))
		tmp = y * (t - x);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.8e-22], N[Not[LessEqual[y, 1.5e-31]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000005e-22 or 1.49999999999999991e-31 < 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 76.5%

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

      1. *-commutative 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in y around inf 74.7%

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

   if -4.80000000000000005e-22 < y < 1.49999999999999991e-31

   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 93.5%

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

      1. mul-1-neg 93.5%

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

      2. distribute-rgt-neg-in 93.5%

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

      3. sub-neg 93.5%

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

      4. +-commutative 93.5%

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

      5. distribute-neg-in 93.5%

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

      6. remove-double-neg 93.5%

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

      7. sub-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in t around 0 56.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-22} \lor \neg \left(y \leq 1.5 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+47} \lor \neg \left(y \leq 1.95 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.95e+47) (not (<= y 1.95e+73))) (* x (- y)) (* x z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95e+47) || !(y <= 1.95e+73)) {
		tmp = x * -y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.95d+47)) .or. (.not. (y <= 1.95d+73))) then
        tmp = x * -y
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95e+47) || !(y <= 1.95e+73)) {
		tmp = x * -y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.95e+47) or not (y <= 1.95e+73):
		tmp = x * -y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.95e+47) || !(y <= 1.95e+73))
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.95e+47) || ~((y <= 1.95e+73)))
		tmp = x * -y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.95e+47], N[Not[LessEqual[y, 1.95e+73]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], N[(x * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95000000000000013e47 or 1.95e73 < 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 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-rgt-neg-in 61.4%

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

      3. sub-neg 61.4%

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

      4. +-commutative 61.4%

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

      5. distribute-neg-in 61.4%

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

      6. remove-double-neg 61.4%

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

      7. sub-neg 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. distribute-rgt-neg-out 56.1%

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

   8. Simplified 56.1%

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

   9. Taylor expanded in y around inf 56.1%

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

       1. associate-*r* 56.1%

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

       2. mul-1-neg 56.1%

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

   11. Simplified 56.1%

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

   if -1.95000000000000013e47 < y < 1.95e73

   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 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-in 83.5%

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

      3. sub-neg 83.5%

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

      4. +-commutative 83.5%

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

      5. distribute-neg-in 83.5%

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

      6. remove-double-neg 83.5%

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

      7. sub-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in t around 0 48.5%

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

   7. Taylor expanded in z around inf 27.4%

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

      1. *-commutative 27.4%

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

   9. Simplified 27.4%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+47} \lor \neg \left(y \leq 1.95 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 8.6 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 8.6e-5))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 8.6e-5)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 8.6d-5))) then
        tmp = x * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 8.6e-5)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 8.6e-5):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 8.6e-5))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 8.6e-5)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 8.6e-5]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 8.6000000000000003e-5 < 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 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-in 78.6%

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

      3. sub-neg 78.6%

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

      4. +-commutative 78.6%

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

      5. distribute-neg-in 78.6%

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

      6. remove-double-neg 78.6%

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

      7. sub-neg 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in t around 0 40.5%

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

   7. Taylor expanded in z around inf 39.6%

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

      1. *-commutative 39.6%

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

   9. Simplified 39.6%

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

   if -1 < z < 8.6000000000000003e-5

   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 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-rgt-neg-in 40.2%

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

      3. sub-neg 40.2%

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

      4. +-commutative 40.2%

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

      5. distribute-neg-in 40.2%

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

      6. remove-double-neg 40.2%

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

      7. sub-neg 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in z around 0 28.8%

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

4. Final simplification 34.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 8.6 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 18.1% 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 0 61.1%

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

   1. mul-1-neg 61.1%

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

   2. distribute-rgt-neg-in 61.1%

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

   3. sub-neg 61.1%

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

   4. +-commutative 61.1%

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

   5. distribute-neg-in 61.1%

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

   6. remove-double-neg 61.1%

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

   7. sub-neg 61.1%

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

5. Simplified 61.1%

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

6. Taylor expanded in z around 0 14.7%

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

7. Final simplification 14.7%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.7% 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 2024079 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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