Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.3s

Alternatives: 15

Speedup: 1.0×

• 34.5% 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-def 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. Final simplification 100.0%

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

Alternative 2: 54.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+157} \lor \neg \left(z \leq 1.5 \cdot 10^{+265}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= z -3.6e+139)
     t_1
     (if (<= z -6.2e+56)
       (* z x)
       (if (<= z -1.85e+30)
         t_1
         (if (<= z -2.1e-31)
           (* x (- 1.0 y))
           (if (<= z 2.2e-15)
             (+ x (* y t))
             (if (or (<= z 6.5e+157) (not (<= z 1.5e+265))) t_1 (* z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (z <= -3.6e+139) {
		tmp = t_1;
	} else if (z <= -6.2e+56) {
		tmp = z * x;
	} else if (z <= -1.85e+30) {
		tmp = t_1;
	} else if (z <= -2.1e-31) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.2e-15) {
		tmp = x + (y * t);
	} else if ((z <= 6.5e+157) || !(z <= 1.5e+265)) {
		tmp = t_1;
	} 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 = x - (z * t)
    if (z <= (-3.6d+139)) then
        tmp = t_1
    else if (z <= (-6.2d+56)) then
        tmp = z * x
    else if (z <= (-1.85d+30)) then
        tmp = t_1
    else if (z <= (-2.1d-31)) then
        tmp = x * (1.0d0 - y)
    else if (z <= 2.2d-15) then
        tmp = x + (y * t)
    else if ((z <= 6.5d+157) .or. (.not. (z <= 1.5d+265))) then
        tmp = t_1
    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 = x - (z * t);
	double tmp;
	if (z <= -3.6e+139) {
		tmp = t_1;
	} else if (z <= -6.2e+56) {
		tmp = z * x;
	} else if (z <= -1.85e+30) {
		tmp = t_1;
	} else if (z <= -2.1e-31) {
		tmp = x * (1.0 - y);
	} else if (z <= 2.2e-15) {
		tmp = x + (y * t);
	} else if ((z <= 6.5e+157) || !(z <= 1.5e+265)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if z <= -3.6e+139:
		tmp = t_1
	elif z <= -6.2e+56:
		tmp = z * x
	elif z <= -1.85e+30:
		tmp = t_1
	elif z <= -2.1e-31:
		tmp = x * (1.0 - y)
	elif z <= 2.2e-15:
		tmp = x + (y * t)
	elif (z <= 6.5e+157) or not (z <= 1.5e+265):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (z <= -3.6e+139)
		tmp = t_1;
	elseif (z <= -6.2e+56)
		tmp = Float64(z * x);
	elseif (z <= -1.85e+30)
		tmp = t_1;
	elseif (z <= -2.1e-31)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 2.2e-15)
		tmp = Float64(x + Float64(y * t));
	elseif ((z <= 6.5e+157) || !(z <= 1.5e+265))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	tmp = 0.0;
	if (z <= -3.6e+139)
		tmp = t_1;
	elseif (z <= -6.2e+56)
		tmp = z * x;
	elseif (z <= -1.85e+30)
		tmp = t_1;
	elseif (z <= -2.1e-31)
		tmp = x * (1.0 - y);
	elseif (z <= 2.2e-15)
		tmp = x + (y * t);
	elseif ((z <= 6.5e+157) || ~((z <= 1.5e+265)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+139], t$95$1, If[LessEqual[z, -6.2e+56], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.85e+30], t$95$1, If[LessEqual[z, -2.1e-31], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-15], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6.5e+157], N[Not[LessEqual[z, 1.5e+265]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.59999999999999985e139 or -6.20000000000000009e56 < z < -1.85000000000000008e30 or 2.19999999999999986e-15 < z < 6.5e157 or 1.50000000000000001e265 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 72.9%

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

   3. Taylor expanded in y around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. *-commutative 60.4%

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

      3. distribute-rgt-neg-in 60.4%

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

   5. Simplified 60.4%

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

   if -3.59999999999999985e139 < z < -6.20000000000000009e56 or 6.5e157 < z < 1.50000000000000001e265

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. mul-1-neg 65.1%

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

      3. unsub-neg 65.1%

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

      4. distribute-lft-out-- 65.1%

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

      5. *-rgt-identity 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in z around inf 57.4%

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

   if -1.85000000000000008e30 < z < -2.09999999999999991e-31

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 69.5%

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

      1. *-commutative 69.5%

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

      2. mul-1-neg 69.5%

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

      3. unsub-neg 69.5%

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

      4. distribute-lft-out-- 69.5%

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

      5. *-rgt-identity 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in x around 0 69.5%

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

   6. Taylor expanded in z around 0 57.3%

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

   if -2.09999999999999991e-31 < z < 2.19999999999999986e-15

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 78.6%

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

   3. Taylor expanded in y around inf 75.1%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+139}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+30}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+157} \lor \neg \left(z \leq 1.5 \cdot 10^{+265}\right):\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ t_2 := x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))) (t_2 (* x (- (+ z 1.0) y))))
   (if (<= x -8.8e+35)
     t_2
     (if (<= x -8e-274)
       t_1
       (if (<= x 1.36e-301)
         (* y t)
         (if (<= x 5.3e-266) t_1 (if (<= x 5.3e-40) (+ x (* y t)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = x * ((z + 1.0) - y);
	double tmp;
	if (x <= -8.8e+35) {
		tmp = t_2;
	} else if (x <= -8e-274) {
		tmp = t_1;
	} else if (x <= 1.36e-301) {
		tmp = y * t;
	} else if (x <= 5.3e-266) {
		tmp = t_1;
	} else if (x <= 5.3e-40) {
		tmp = x + (y * t);
	} else {
		tmp = t_2;
	}
	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 = x - (z * t)
    t_2 = x * ((z + 1.0d0) - y)
    if (x <= (-8.8d+35)) then
        tmp = t_2
    else if (x <= (-8d-274)) then
        tmp = t_1
    else if (x <= 1.36d-301) then
        tmp = y * t
    else if (x <= 5.3d-266) then
        tmp = t_1
    else if (x <= 5.3d-40) then
        tmp = x + (y * t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = x * ((z + 1.0) - y);
	double tmp;
	if (x <= -8.8e+35) {
		tmp = t_2;
	} else if (x <= -8e-274) {
		tmp = t_1;
	} else if (x <= 1.36e-301) {
		tmp = y * t;
	} else if (x <= 5.3e-266) {
		tmp = t_1;
	} else if (x <= 5.3e-40) {
		tmp = x + (y * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	t_2 = x * ((z + 1.0) - y)
	tmp = 0
	if x <= -8.8e+35:
		tmp = t_2
	elif x <= -8e-274:
		tmp = t_1
	elif x <= 1.36e-301:
		tmp = y * t
	elif x <= 5.3e-266:
		tmp = t_1
	elif x <= 5.3e-40:
		tmp = x + (y * t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	t_2 = Float64(x * Float64(Float64(z + 1.0) - y))
	tmp = 0.0
	if (x <= -8.8e+35)
		tmp = t_2;
	elseif (x <= -8e-274)
		tmp = t_1;
	elseif (x <= 1.36e-301)
		tmp = Float64(y * t);
	elseif (x <= 5.3e-266)
		tmp = t_1;
	elseif (x <= 5.3e-40)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	t_2 = x * ((z + 1.0) - y);
	tmp = 0.0;
	if (x <= -8.8e+35)
		tmp = t_2;
	elseif (x <= -8e-274)
		tmp = t_1;
	elseif (x <= 1.36e-301)
		tmp = y * t;
	elseif (x <= 5.3e-266)
		tmp = t_1;
	elseif (x <= 5.3e-40)
		tmp = x + (y * t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.8e+35], t$95$2, If[LessEqual[x, -8e-274], t$95$1, If[LessEqual[x, 1.36e-301], N[(y * t), $MachinePrecision], If[LessEqual[x, 5.3e-266], t$95$1, If[LessEqual[x, 5.3e-40], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.7999999999999994e35 or 5.3000000000000002e-40 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 84.5%

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

      1. *-commutative 84.5%

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

      2. mul-1-neg 84.5%

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

      3. unsub-neg 84.5%

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

      4. distribute-lft-out-- 84.5%

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

      5. *-rgt-identity 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in x around 0 84.5%

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

   if -8.7999999999999994e35 < x < -7.99999999999999973e-274 or 1.36e-301 < x < 5.3000000000000003e-266

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 91.5%

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

   3. Taylor expanded in y around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. *-commutative 58.9%

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

      3. distribute-rgt-neg-in 58.9%

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

   5. Simplified 58.9%

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

   if -7.99999999999999973e-274 < x < 1.36e-301

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in y around inf 82.3%

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

   4. Taylor expanded in x around 0 82.3%

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

   if 5.3000000000000003e-266 < x < 5.3000000000000002e-40

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 83.6%

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

   3. Taylor expanded in y around inf 58.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-274}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-266}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-40}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \]

Alternative 4: 45.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+260}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+78} \lor \neg \left(x \leq 2.3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.8e+260)
   (* x (+ z 1.0))
   (if (or (<= x -4.6e+78) (not (<= x 2.3e-36))) (* x (- 1.0 y)) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e+260) {
		tmp = x * (z + 1.0);
	} else if ((x <= -4.6e+78) || !(x <= 2.3e-36)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.8d+260)) then
        tmp = x * (z + 1.0d0)
    else if ((x <= (-4.6d+78)) .or. (.not. (x <= 2.3d-36))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e+260) {
		tmp = x * (z + 1.0);
	} else if ((x <= -4.6e+78) || !(x <= 2.3e-36)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.8e+260:
		tmp = x * (z + 1.0)
	elif (x <= -4.6e+78) or not (x <= 2.3e-36):
		tmp = x * (1.0 - y)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.8e+260)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((x <= -4.6e+78) || !(x <= 2.3e-36))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.8e+260)
		tmp = x * (z + 1.0);
	elseif ((x <= -4.6e+78) || ~((x <= 2.3e-36)))
		tmp = x * (1.0 - y);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.8e+260], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -4.6e+78], N[Not[LessEqual[x, 2.3e-36]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.7999999999999995e260

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   if -6.7999999999999995e260 < x < -4.6000000000000004e78 or 2.29999999999999996e-36 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 85.2%

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

      1. *-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

      4. distribute-lft-out-- 85.3%

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

      5. *-rgt-identity 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in x around 0 85.2%

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

   6. Taylor expanded in z around 0 63.5%

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

   if -4.6000000000000004e78 < x < 2.29999999999999996e-36

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 88.0%

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

   3. Taylor expanded in y around inf 51.4%

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

   4. Taylor expanded in x around 0 47.6%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+260}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+78} \lor \neg \left(x \leq 2.3 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 5: 51.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+78} \lor \neg \left(x \leq 1.12 \cdot 10^{+79}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.45e+261)
   (* x (+ z 1.0))
   (if (or (<= x -7.5e+78) (not (<= x 1.12e+79)))
     (* x (- 1.0 y))
     (+ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+261) {
		tmp = x * (z + 1.0);
	} else if ((x <= -7.5e+78) || !(x <= 1.12e+79)) {
		tmp = x * (1.0 - y);
	} 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 (x <= (-1.45d+261)) then
        tmp = x * (z + 1.0d0)
    else if ((x <= (-7.5d+78)) .or. (.not. (x <= 1.12d+79))) then
        tmp = x * (1.0d0 - y)
    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 (x <= -1.45e+261) {
		tmp = x * (z + 1.0);
	} else if ((x <= -7.5e+78) || !(x <= 1.12e+79)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.45e+261:
		tmp = x * (z + 1.0)
	elif (x <= -7.5e+78) or not (x <= 1.12e+79):
		tmp = x * (1.0 - y)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.45e+261)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((x <= -7.5e+78) || !(x <= 1.12e+79))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.45e+261)
		tmp = x * (z + 1.0);
	elseif ((x <= -7.5e+78) || ~((x <= 1.12e+79)))
		tmp = x * (1.0 - y);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.45e+261], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -7.5e+78], N[Not[LessEqual[x, 1.12e+79]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45e261

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   if -1.45e261 < x < -7.49999999999999934e78 or 1.12e79 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 92.0%

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

      1. *-commutative 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

      4. distribute-lft-out-- 92.1%

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

      5. *-rgt-identity 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in x around 0 92.0%

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

   6. Taylor expanded in z around 0 71.6%

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

   if -7.49999999999999934e78 < x < 1.12e79

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 83.4%

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

   3. Taylor expanded in y around inf 50.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+261}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+78} \lor \neg \left(x \leq 1.12 \cdot 10^{+79}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 6: 51.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.6e+253)
   (* x (+ z 1.0))
   (if (<= x -3.5e+79)
     (* x (- 1.0 y))
     (if (<= x 1.95e+79) (+ x (* y t)) (- x (* y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.6e+253) {
		tmp = x * (z + 1.0);
	} else if (x <= -3.5e+79) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.95e+79) {
		tmp = x + (y * t);
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9.6d+253)) then
        tmp = x * (z + 1.0d0)
    else if (x <= (-3.5d+79)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 1.95d+79) then
        tmp = x + (y * t)
    else
        tmp = x - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.6e+253) {
		tmp = x * (z + 1.0);
	} else if (x <= -3.5e+79) {
		tmp = x * (1.0 - y);
	} else if (x <= 1.95e+79) {
		tmp = x + (y * t);
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.6e+253:
		tmp = x * (z + 1.0)
	elif x <= -3.5e+79:
		tmp = x * (1.0 - y)
	elif x <= 1.95e+79:
		tmp = x + (y * t)
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.6e+253)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (x <= -3.5e+79)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 1.95e+79)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.6e+253)
		tmp = x * (z + 1.0);
	elseif (x <= -3.5e+79)
		tmp = x * (1.0 - y);
	elseif (x <= 1.95e+79)
		tmp = x + (y * t);
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.6e+253], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.5e+79], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+79], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.59999999999999965e253

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

   if -9.59999999999999965e253 < x < -3.4999999999999998e79

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 90.2%

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

      1. *-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

      4. distribute-lft-out-- 90.2%

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

      5. *-rgt-identity 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in x around 0 90.2%

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

   6. Taylor expanded in z around 0 73.8%

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

   if -3.4999999999999998e79 < x < 1.9499999999999999e79

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 83.4%

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

   3. Taylor expanded in y around inf 50.5%

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

   if 1.9499999999999999e79 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 93.4%

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

      1. *-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. unsub-neg 93.4%

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

      4. distribute-lft-out-- 93.4%

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

      5. *-rgt-identity 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in z around 0 70.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 7: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+79} \lor \neg \left(x \leq 6.4 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.35e+79) (not (<= x 6.4e-40)))
   (* x (- (+ z 1.0) y))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.35e+79) || !(x <= 6.4e-40)) {
		tmp = x * ((z + 1.0) - 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 <= (-2.35d+79)) .or. (.not. (x <= 6.4d-40))) then
        tmp = x * ((z + 1.0d0) - 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 <= -2.35e+79) || !(x <= 6.4e-40)) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.35e+79) or not (x <= 6.4e-40):
		tmp = x * ((z + 1.0) - y)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.35e+79) || !(x <= 6.4e-40))
		tmp = Float64(x * Float64(Float64(z + 1.0) - 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 <= -2.35e+79) || ~((x <= 6.4e-40)))
		tmp = x * ((z + 1.0) - y);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.35e+79], N[Not[LessEqual[x, 6.4e-40]], $MachinePrecision]], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.35000000000000011e79 or 6.40000000000000004e-40 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. mul-1-neg 86.2%

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

      3. unsub-neg 86.2%

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

      4. distribute-lft-out-- 86.2%

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

      5. *-rgt-identity 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in x around 0 86.2%

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

   if -2.35000000000000011e79 < x < 6.40000000000000004e-40

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 88.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+79} \lor \neg \left(x \leq 6.4 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 8: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-8} \lor \neg \left(y \leq 2.4 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.8e-8) (not (<= y 2.4e-6)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e-8) || !(y <= 2.4e-6)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.8d-8)) .or. (.not. (y <= 2.4d-6))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e-8) || !(y <= 2.4e-6)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.8e-8) or not (y <= 2.4e-6):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.8e-8) || !(y <= 2.4e-6))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.8e-8) || ~((y <= 2.4e-6)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.8e-8], N[Not[LessEqual[y, 2.4e-6]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e-8 or 2.3999999999999999e-6 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 86.5%

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

   if -2.7999999999999999e-8 < y < 2.3999999999999999e-6

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. mul-1-neg 93.1%

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

      3. unsub-neg 93.1%

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

      4. *-commutative 93.1%

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

   4. Simplified 93.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-8} \lor \neg \left(y \leq 2.4 \cdot 10^{-6}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.2e+78)
   (* x (- (+ z 1.0) y))
   (if (<= x 1.22e-39) (+ x (* (- y z) t)) (+ x (* x (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e+78) {
		tmp = x * ((z + 1.0) - y);
	} else if (x <= 1.22e-39) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.2d+78)) then
        tmp = x * ((z + 1.0d0) - y)
    else if (x <= 1.22d-39) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e+78) {
		tmp = x * ((z + 1.0) - y);
	} else if (x <= 1.22e-39) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.2e+78:
		tmp = x * ((z + 1.0) - y)
	elif x <= 1.22e-39:
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.2e+78)
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	elseif (x <= 1.22e-39)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.2e+78)
		tmp = x * ((z + 1.0) - y);
	elseif (x <= 1.22e-39)
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.2e+78], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e-39], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000002e78

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 92.7%

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

      1. *-commutative 92.7%

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

      2. mul-1-neg 92.7%

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

      3. unsub-neg 92.7%

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

      4. distribute-lft-out-- 92.7%

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

      5. *-rgt-identity 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in x around 0 92.7%

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

   if -4.2000000000000002e78 < x < 1.2200000000000001e-39

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 88.6%

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

   if 1.2200000000000001e-39 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 82.0%

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

      1. *-commutative 82.0%

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

      2. mul-1-neg 82.0%

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

      3. unsub-neg 82.0%

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

      4. distribute-lft-out-- 82.1%

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

      5. *-rgt-identity 82.1%

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

   4. Simplified 82.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 10: 34.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+78} \lor \neg \left(x \leq 1.35 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.95e+211)
   x
   (if (or (<= x -7.5e+78) (not (<= x 1.35e+79))) (* y (- x)) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.95e+211) {
		tmp = x;
	} else if ((x <= -7.5e+78) || !(x <= 1.35e+79)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.95d+211)) then
        tmp = x
    else if ((x <= (-7.5d+78)) .or. (.not. (x <= 1.35d+79))) then
        tmp = y * -x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.95e+211) {
		tmp = x;
	} else if ((x <= -7.5e+78) || !(x <= 1.35e+79)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.95e+211:
		tmp = x
	elif (x <= -7.5e+78) or not (x <= 1.35e+79):
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.95e+211)
		tmp = x;
	elseif ((x <= -7.5e+78) || !(x <= 1.35e+79))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.95e+211)
		tmp = x;
	elseif ((x <= -7.5e+78) || ~((x <= 1.35e+79)))
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.95e+211], x, If[Or[LessEqual[x, -7.5e+78], N[Not[LessEqual[x, 1.35e+79]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.95000000000000011e211

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 51.9%

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

   3. Taylor expanded in y around inf 47.2%

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

   4. Taylor expanded in x around inf 47.2%

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

   if -1.95000000000000011e211 < x < -7.49999999999999934e78 or 1.35e79 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. mul-1-neg 91.4%

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

      3. unsub-neg 91.4%

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

      4. distribute-lft-out-- 91.4%

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

      5. *-rgt-identity 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. distribute-rgt-neg-in 50.5%

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

   7. Simplified 50.5%

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

   if -7.49999999999999934e78 < x < 1.35e79

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 83.4%

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

   3. Taylor expanded in y around inf 50.5%

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

   4. Taylor expanded in x around 0 43.7%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+78} \lor \neg \left(x \leq 1.35 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 11: 36.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-157}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-24)
   (* y t)
   (if (<= y -3.9e-157) (* z x) (if (<= y 1.12e-32) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-24) {
		tmp = y * t;
	} else if (y <= -3.9e-157) {
		tmp = z * x;
	} else if (y <= 1.12e-32) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d-24)) then
        tmp = y * t
    else if (y <= (-3.9d-157)) then
        tmp = z * x
    else if (y <= 1.12d-32) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-24) {
		tmp = y * t;
	} else if (y <= -3.9e-157) {
		tmp = z * x;
	} else if (y <= 1.12e-32) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-24:
		tmp = y * t
	elif y <= -3.9e-157:
		tmp = z * x
	elif y <= 1.12e-32:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-24)
		tmp = Float64(y * t);
	elseif (y <= -3.9e-157)
		tmp = Float64(z * x);
	elseif (y <= 1.12e-32)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e-24)
		tmp = y * t;
	elseif (y <= -3.9e-157)
		tmp = z * x;
	elseif (y <= 1.12e-32)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-24], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.9e-157], N[(z * x), $MachinePrecision], If[LessEqual[y, 1.12e-32], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000007e-24 or 1.12e-32 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 62.6%

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

   3. Taylor expanded in y around inf 50.0%

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

   4. Taylor expanded in x around 0 48.6%

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

   if -7.50000000000000007e-24 < y < -3.89999999999999999e-157

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. distribute-lft-out-- 70.0%

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

      5. *-rgt-identity 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in z around inf 47.6%

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

   if -3.89999999999999999e-157 < y < 1.12e-32

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 81.0%

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

   3. Taylor expanded in y around inf 39.6%

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

   4. Taylor expanded in x around inf 35.8%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-157}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 12: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-19}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e-19) (* y t) (if (<= y 2.5e-6) (* x (+ z 1.0)) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-19) {
		tmp = y * t;
	} else if (y <= 2.5e-6) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.2d-19)) then
        tmp = y * t
    else if (y <= 2.5d-6) then
        tmp = x * (z + 1.0d0)
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-19) {
		tmp = y * t;
	} else if (y <= 2.5e-6) {
		tmp = x * (z + 1.0);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e-19:
		tmp = y * t
	elif y <= 2.5e-6:
		tmp = x * (z + 1.0)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e-19)
		tmp = Float64(y * t);
	elseif (y <= 2.5e-6)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e-19)
		tmp = y * t;
	elseif (y <= 2.5e-6)
		tmp = x * (z + 1.0);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e-19], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.5e-6], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.20000000000000011e-19 or 2.5000000000000002e-6 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 62.1%

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

   3. Taylor expanded in y around inf 50.4%

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

   4. Taylor expanded in x around 0 49.7%

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

   if -1.20000000000000011e-19 < y < 2.5000000000000002e-6

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. distribute-rgt-neg-in 57.9%

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

      3. +-commutative 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around 0 57.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-19}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 13: 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. Final simplification 100.0%

   \[\leadsto x + \left(y - z\right) \cdot \left(t - x\right) \]

Alternative 14: 36.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-48}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.1e-48) (* y t) (if (<= y 4.3e-32) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-48) {
		tmp = y * t;
	} else if (y <= 4.3e-32) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.1d-48)) then
        tmp = y * t
    else if (y <= 4.3d-32) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.1e-48) {
		tmp = y * t;
	} else if (y <= 4.3e-32) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.1e-48:
		tmp = y * t
	elif y <= 4.3e-32:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.1e-48)
		tmp = Float64(y * t);
	elseif (y <= 4.3e-32)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.1e-48)
		tmp = y * t;
	elseif (y <= 4.3e-32)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.1e-48], N[(y * t), $MachinePrecision], If[LessEqual[y, 4.3e-32], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.10000000000000014e-48 or 4.2999999999999999e-32 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 61.7%

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

   3. Taylor expanded in y around inf 49.4%

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

   4. Taylor expanded in x around 0 48.0%

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

   if -4.10000000000000014e-48 < y < 4.2999999999999999e-32

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 77.3%

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

   3. Taylor expanded in y around inf 38.9%

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

   4. Taylor expanded in x around inf 34.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-48}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 15: 18.5% 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. Taylor expanded in t around inf 67.8%

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

3. Taylor expanded in y around inf 45.4%

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

4. Taylor expanded in x around inf 15.5%

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

5. Final simplification 15.5%

   \[\leadsto x \]

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 2023176 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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