Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 12

Speedup: 1.0×

• 34.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 35.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-259}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= z -6.6e+28)
     (* z x)
     (if (<= z -3.7e-152)
       t_1
       (if (<= z 3e-259)
         x
         (if (<= z 2.5e-181) t_1 (if (<= z 4.4e-9) x (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -6.6e+28) {
		tmp = z * x;
	} else if (z <= -3.7e-152) {
		tmp = t_1;
	} else if (z <= 3e-259) {
		tmp = x;
	} else if (z <= 2.5e-181) {
		tmp = t_1;
	} else if (z <= 4.4e-9) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (z <= (-6.6d+28)) then
        tmp = z * x
    else if (z <= (-3.7d-152)) then
        tmp = t_1
    else if (z <= 3d-259) then
        tmp = x
    else if (z <= 2.5d-181) then
        tmp = t_1
    else if (z <= 4.4d-9) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -6.6e+28) {
		tmp = z * x;
	} else if (z <= -3.7e-152) {
		tmp = t_1;
	} else if (z <= 3e-259) {
		tmp = x;
	} else if (z <= 2.5e-181) {
		tmp = t_1;
	} else if (z <= 4.4e-9) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if z <= -6.6e+28:
		tmp = z * x
	elif z <= -3.7e-152:
		tmp = t_1
	elif z <= 3e-259:
		tmp = x
	elif z <= 2.5e-181:
		tmp = t_1
	elif z <= 4.4e-9:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (z <= -6.6e+28)
		tmp = Float64(z * x);
	elseif (z <= -3.7e-152)
		tmp = t_1;
	elseif (z <= 3e-259)
		tmp = x;
	elseif (z <= 2.5e-181)
		tmp = t_1;
	elseif (z <= 4.4e-9)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (z <= -6.6e+28)
		tmp = z * x;
	elseif (z <= -3.7e-152)
		tmp = t_1;
	elseif (z <= 3e-259)
		tmp = x;
	elseif (z <= 2.5e-181)
		tmp = t_1;
	elseif (z <= 4.4e-9)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[z, -6.6e+28], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.7e-152], t$95$1, If[LessEqual[z, 3e-259], x, If[LessEqual[z, 2.5e-181], t$95$1, If[LessEqual[z, 4.4e-9], x, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.6e28 or 4.3999999999999997e-9 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in z around inf 48.5%

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

      1. *-commutative 48.5%

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

   8. Simplified 48.5%

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

   if -6.6e28 < z < -3.6999999999999998e-152 or 3.0000000000000002e-259 < z < 2.5000000000000001e-181

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. unsub-neg 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf 44.3%

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

      1. mul-1-neg 44.3%

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

      2. distribute-lft-neg-out 44.3%

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

      3. *-commutative 44.3%

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

   8. Simplified 44.3%

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

   if -3.6999999999999998e-152 < z < 3.0000000000000002e-259 or 2.5000000000000001e-181 < z < 4.3999999999999997e-9

   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 49.7%

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

      1. mul-1-neg 49.7%

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

      2. unsub-neg 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in z around 0 44.6%

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

Alternative 3: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+19} \lor \neg \left(z \leq 4.4 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e+19) (not (<= z 4.4e-9)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+19) || !(z <= 4.4e-9)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.8d+19)) .or. (.not. (z <= 4.4d-9))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+19) || !(z <= 4.4e-9)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e+19) or not (z <= 4.4e-9):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e+19) || !(z <= 4.4e-9))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e+19) || ~((z <= 4.4e-9)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e+19], N[Not[LessEqual[z, 4.4e-9]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e19 or 4.3999999999999997e-9 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around inf 85.0%

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

   if -4.8e19 < z < 4.3999999999999997e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 94.4%

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

      1. *-commutative 94.4%

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

   5. Simplified 94.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+19} \lor \neg \left(z \leq 4.4 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+87} \lor \neg \left(x \leq 2 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.1e+87) (not (<= x 2e+59)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.1e+87) || !(x <= 2e+59)) {
		tmp = x * ((z - y) + 1.0);
	} 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 <= (-2.1d+87)) .or. (.not. (x <= 2d+59))) then
        tmp = x * ((z - y) + 1.0d0)
    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 <= -2.1e+87) || !(x <= 2e+59)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.1e+87) or not (x <= 2e+59):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.1e+87) || !(x <= 2e+59))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	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 <= -2.1e+87) || ~((x <= 2e+59)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.1e+87], N[Not[LessEqual[x, 2e+59]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e87 or 1.99999999999999994e59 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.4%

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

      1. mul-1-neg 91.4%

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

      2. unsub-neg 91.4%

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

   5. Simplified 91.4%

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

   if -2.1e87 < x < 1.99999999999999994e59

   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 83.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+87} \lor \neg \left(x \leq 2 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -4.6e+19) t_1 (if (<= z 1.8e-31) (+ x (* y (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.6e+19) {
		tmp = t_1;
	} else if (z <= 1.8e-31) {
		tmp = x + (y * (t - x));
	} 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 = z * (x - t)
    if (z <= (-4.6d+19)) then
        tmp = t_1
    else if (z <= 1.8d-31) then
        tmp = x + (y * (t - x))
    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 = z * (x - t);
	double tmp;
	if (z <= -4.6e+19) {
		tmp = t_1;
	} else if (z <= 1.8e-31) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -4.6e+19:
		tmp = t_1
	elif z <= 1.8e-31:
		tmp = x + (y * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -4.6e+19)
		tmp = t_1;
	elseif (z <= 1.8e-31)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + 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 <= -4.6e+19)
		tmp = t_1;
	elseif (z <= 1.8e-31)
		tmp = x + (y * (t - x));
	else
		tmp = x + 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, -4.6e+19], t$95$1, If[LessEqual[z, 1.8e-31], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6e19

   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 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around inf 86.8%

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

   if -4.6e19 < z < 1.80000000000000002e-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 inf 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   if 1.80000000000000002e-31 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

   5. Simplified 82.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-25} \lor \neg \left(z \leq 1.8 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-25) (not (<= z 1.8e-31))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-25) || !(z <= 1.8e-31)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (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 ((z <= (-1.8d-25)) .or. (.not. (z <= 1.8d-31))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-25) || !(z <= 1.8e-31)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e-25) or not (z <= 1.8e-31):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-25) || !(z <= 1.8e-31))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e-25) || ~((z <= 1.8e-31)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-25], N[Not[LessEqual[z, 1.8e-31]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-25 or 1.80000000000000002e-31 < 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 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in z around inf 80.9%

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

   if -1.8e-25 < z < 1.80000000000000002e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.4%

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

   4. Taylor expanded in y around inf 79.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-25} \lor \neg \left(z \leq 1.8 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+19} \lor \neg \left(z \leq 6.5 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e+19) (not (<= z 6.5e-12))) (* z (- x t)) (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+19) || !(z <= 6.5e-12)) {
		tmp = z * (x - t);
	} else {
		tmp = x * (1.0 - 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 ((z <= (-2.6d+19)) .or. (.not. (z <= 6.5d-12))) then
        tmp = z * (x - t)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+19) || !(z <= 6.5e-12)) {
		tmp = z * (x - t);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e+19) or not (z <= 6.5e-12):
		tmp = z * (x - t)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e+19) || !(z <= 6.5e-12))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.6e+19) || ~((z <= 6.5e-12)))
		tmp = z * (x - t);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e+19], N[Not[LessEqual[z, 6.5e-12]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e19 or 6.5000000000000002e-12 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. unsub-neg 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around inf 85.0%

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

   if -2.6e19 < z < 6.5000000000000002e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in z around 0 57.6%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+19} \lor \neg \left(z \leq 6.5 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \lor \neg \left(y \leq 9 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.95) (not (<= y 9e+67))) (* x (- 1.0 y)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95) || !(y <= 9e+67)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.95d0)) .or. (.not. (y <= 9d+67))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.95) || !(y <= 9e+67)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.95) or not (y <= 9e+67):
		tmp = x * (1.0 - y)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.95) || !(y <= 9e+67))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.95) || ~((y <= 9e+67)))
		tmp = x * (1.0 - y);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.95], N[Not[LessEqual[y, 9e+67]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.94999999999999996 or 8.9999999999999997e67 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in z around 0 45.3%

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

   if -1.94999999999999996 < y < 8.9999999999999997e67

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. +-commutative 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \lor \neg \left(y \leq 9 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \lor \neg \left(y \leq 1.22 \cdot 10^{+68}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.0) (not (<= y 1.22e+68))) (* y (- x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.0) || !(y <= 1.22e+68)) {
		tmp = y * -x;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.0d0)) .or. (.not. (y <= 1.22d+68))) then
        tmp = y * -x
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.0) || !(y <= 1.22e+68)) {
		tmp = y * -x;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.0) or not (y <= 1.22e+68):
		tmp = y * -x
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.0) || !(y <= 1.22e+68))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.0) || ~((y <= 1.22e+68)))
		tmp = y * -x;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.0], N[Not[LessEqual[y, 1.22e+68]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2 or 1.22e68 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in y around inf 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-lft-neg-out 45.3%

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

      3. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   if -2 < y < 1.22e68

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0 61.0%

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

      1. +-commutative 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \lor \neg \left(y \leq 1.22 \cdot 10^{+68}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -820000000 \lor \neg \left(z \leq 4.4 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -820000000.0) (not (<= z 4.4e-9))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -820000000.0) || !(z <= 4.4e-9)) {
		tmp = z * x;
	} 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 <= (-820000000.0d0)) .or. (.not. (z <= 4.4d-9))) then
        tmp = z * x
    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 <= -820000000.0) || !(z <= 4.4e-9)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -820000000.0) or not (z <= 4.4e-9):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -820000000.0) || !(z <= 4.4e-9))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -820000000.0) || ~((z <= 4.4e-9)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -820000000.0], N[Not[LessEqual[z, 4.4e-9]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e8 or 4.3999999999999997e-9 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in z around inf 47.7%

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

      1. *-commutative 47.7%

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

   8. Simplified 47.7%

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

   if -8.2e8 < z < 4.3999999999999997e-9

   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 40.9%

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

      1. mul-1-neg 40.9%

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

      2. unsub-neg 40.9%

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

   5. Simplified 40.9%

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

   6. Taylor expanded in z around 0 36.4%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -820000000 \lor \neg \left(z \leq 4.4 \cdot 10^{-9}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 12: 17.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 60.6%

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

   1. mul-1-neg 60.6%

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

   2. unsub-neg 60.6%

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

5. Simplified 60.6%

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

6. Taylor expanded in z around 0 21.4%

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

Developer target: 96.5% 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 2024091 
(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))))