Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

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-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 36.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{+272}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.0011:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-155}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+65}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 10^{+233}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -4e+272)
     (* y t)
     (if (<= y -3.8e+126)
       t_1
       (if (<= y -0.0011)
         (* y t)
         (if (<= y 1.02e-286)
           x
           (if (<= y 3.55e-155)
             (* z x)
             (if (<= y 4.2e-52)
               x
               (if (<= y 5.2e+65)
                 (* z x)
                 (if (<= y 1e+233) t_1 (* y t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -4e+272) {
		tmp = y * t;
	} else if (y <= -3.8e+126) {
		tmp = t_1;
	} else if (y <= -0.0011) {
		tmp = y * t;
	} else if (y <= 1.02e-286) {
		tmp = x;
	} else if (y <= 3.55e-155) {
		tmp = z * x;
	} else if (y <= 4.2e-52) {
		tmp = x;
	} else if (y <= 5.2e+65) {
		tmp = z * x;
	} else if (y <= 1e+233) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (y <= (-4d+272)) then
        tmp = y * t
    else if (y <= (-3.8d+126)) then
        tmp = t_1
    else if (y <= (-0.0011d0)) then
        tmp = y * t
    else if (y <= 1.02d-286) then
        tmp = x
    else if (y <= 3.55d-155) then
        tmp = z * x
    else if (y <= 4.2d-52) then
        tmp = x
    else if (y <= 5.2d+65) then
        tmp = z * x
    else if (y <= 1d+233) then
        tmp = t_1
    else
        tmp = y * t
    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 (y <= -4e+272) {
		tmp = y * t;
	} else if (y <= -3.8e+126) {
		tmp = t_1;
	} else if (y <= -0.0011) {
		tmp = y * t;
	} else if (y <= 1.02e-286) {
		tmp = x;
	} else if (y <= 3.55e-155) {
		tmp = z * x;
	} else if (y <= 4.2e-52) {
		tmp = x;
	} else if (y <= 5.2e+65) {
		tmp = z * x;
	} else if (y <= 1e+233) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -4e+272:
		tmp = y * t
	elif y <= -3.8e+126:
		tmp = t_1
	elif y <= -0.0011:
		tmp = y * t
	elif y <= 1.02e-286:
		tmp = x
	elif y <= 3.55e-155:
		tmp = z * x
	elif y <= 4.2e-52:
		tmp = x
	elif y <= 5.2e+65:
		tmp = z * x
	elif y <= 1e+233:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -4e+272)
		tmp = Float64(y * t);
	elseif (y <= -3.8e+126)
		tmp = t_1;
	elseif (y <= -0.0011)
		tmp = Float64(y * t);
	elseif (y <= 1.02e-286)
		tmp = x;
	elseif (y <= 3.55e-155)
		tmp = Float64(z * x);
	elseif (y <= 4.2e-52)
		tmp = x;
	elseif (y <= 5.2e+65)
		tmp = Float64(z * x);
	elseif (y <= 1e+233)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -4e+272)
		tmp = y * t;
	elseif (y <= -3.8e+126)
		tmp = t_1;
	elseif (y <= -0.0011)
		tmp = y * t;
	elseif (y <= 1.02e-286)
		tmp = x;
	elseif (y <= 3.55e-155)
		tmp = z * x;
	elseif (y <= 4.2e-52)
		tmp = x;
	elseif (y <= 5.2e+65)
		tmp = z * x;
	elseif (y <= 1e+233)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -4e+272], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.8e+126], t$95$1, If[LessEqual[y, -0.0011], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.02e-286], x, If[LessEqual[y, 3.55e-155], N[(z * x), $MachinePrecision], If[LessEqual[y, 4.2e-52], x, If[LessEqual[y, 5.2e+65], N[(z * x), $MachinePrecision], If[LessEqual[y, 1e+233], t$95$1, N[(y * t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.0000000000000003e272 or -3.80000000000000017e126 < y < -0.00110000000000000007 or 9.99999999999999974e232 < 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 0 70.1%

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

   4. Taylor expanded in y around inf 49.2%

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

   if -4.0000000000000003e272 < y < -3.80000000000000017e126 or 5.20000000000000005e65 < y < 9.99999999999999974e232

   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 89.3%

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

   4. Taylor expanded in t around 0 56.5%

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

      1. mul-1-neg 56.5%

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

      2. distribute-rgt-neg-in 56.5%

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

   6. Simplified 56.5%

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

   if -0.00110000000000000007 < y < 1.01999999999999996e-286 or 3.55e-155 < y < 4.1999999999999997e-52

   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 53.8%

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

      1. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in y around 0 45.0%

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

   if 1.01999999999999996e-286 < y < 3.55e-155 or 4.1999999999999997e-52 < y < 5.20000000000000005e65

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

      3. distribute-lft-out-- 62.7%

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

      4. *-rgt-identity 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in z around inf 46.8%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+272}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -0.0011:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-155}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+65}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 10^{+233}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -65000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-116}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-230}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -4.5e+77)
     t_1
     (if (<= z -3.8e+37)
       (* y (- t x))
       (if (<= z -65000000.0)
         t_1
         (if (<= z -9.5e-116)
           (* (- y z) t)
           (if (<= z 3.4e-230)
             (- x (* y x))
             (if (<= z 5.8e+17) (+ x (* y t)) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.5e+77) {
		tmp = t_1;
	} else if (z <= -3.8e+37) {
		tmp = y * (t - x);
	} else if (z <= -65000000.0) {
		tmp = t_1;
	} else if (z <= -9.5e-116) {
		tmp = (y - z) * t;
	} else if (z <= 3.4e-230) {
		tmp = x - (y * x);
	} else if (z <= 5.8e+17) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-4.5d+77)) then
        tmp = t_1
    else if (z <= (-3.8d+37)) then
        tmp = y * (t - x)
    else if (z <= (-65000000.0d0)) then
        tmp = t_1
    else if (z <= (-9.5d-116)) then
        tmp = (y - z) * t
    else if (z <= 3.4d-230) then
        tmp = x - (y * x)
    else if (z <= 5.8d+17) then
        tmp = x + (y * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -4.5e+77) {
		tmp = t_1;
	} else if (z <= -3.8e+37) {
		tmp = y * (t - x);
	} else if (z <= -65000000.0) {
		tmp = t_1;
	} else if (z <= -9.5e-116) {
		tmp = (y - z) * t;
	} else if (z <= 3.4e-230) {
		tmp = x - (y * x);
	} else if (z <= 5.8e+17) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -4.5e+77:
		tmp = t_1
	elif z <= -3.8e+37:
		tmp = y * (t - x)
	elif z <= -65000000.0:
		tmp = t_1
	elif z <= -9.5e-116:
		tmp = (y - z) * t
	elif z <= 3.4e-230:
		tmp = x - (y * x)
	elif z <= 5.8e+17:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -4.5e+77)
		tmp = t_1;
	elseif (z <= -3.8e+37)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= -65000000.0)
		tmp = t_1;
	elseif (z <= -9.5e-116)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 3.4e-230)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 5.8e+17)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -4.5e+77)
		tmp = t_1;
	elseif (z <= -3.8e+37)
		tmp = y * (t - x);
	elseif (z <= -65000000.0)
		tmp = t_1;
	elseif (z <= -9.5e-116)
		tmp = (y - z) * t;
	elseif (z <= 3.4e-230)
		tmp = x - (y * x);
	elseif (z <= 5.8e+17)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+77], t$95$1, If[LessEqual[z, -3.8e+37], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -65000000.0], t$95$1, If[LessEqual[z, -9.5e-116], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 3.4e-230], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+17], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.50000000000000024e77 or -3.7999999999999999e37 < z < -6.5e7 or 5.8e17 < 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 inf 84.1%

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

      1. sub-neg 84.1%

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

      2. +-commutative 84.1%

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

      3. associate-+l+ 84.1%

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

      4. +-commutative 84.1%

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

      5. mul-1-neg 84.1%

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

      6. unsub-neg 84.1%

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

      7. div-sub 90.5%

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

      8. unsub-neg 90.5%

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

      9. mul-1-neg 90.5%

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

      10. sub-neg 90.5%

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

      11. +-commutative 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around -inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-in 84.5%

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

      3. sub-neg 84.5%

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

      4. distribute-neg-in 84.5%

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

      5. remove-double-neg 84.5%

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

   8. Simplified 84.5%

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

   if -4.50000000000000024e77 < z < -3.7999999999999999e37

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.7%

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

   if -6.5e7 < z < -9.4999999999999998e-116

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 68.8%

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

   if -9.4999999999999998e-116 < z < 3.4e-230

   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 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. distribute-lft-out-- 81.1%

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

      4. *-rgt-identity 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in z around 0 81.1%

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

   if 3.4e-230 < z < 5.8e17

   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 90.0%

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

      1. *-commutative 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in t around inf 77.3%

      \[\leadsto x + \color{blue}{t \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -65000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-116}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-230}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4300000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-64}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* y (- t x))))
   (if (<= z -1.45e+77)
     t_1
     (if (<= z -4e+37)
       t_2
       (if (<= z -4300000000.0)
         t_1
         (if (<= z -7.2e-64)
           (* (- y z) t)
           (if (<= z 2.9e+18) (+ x t_2) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -1.45e+77) {
		tmp = t_1;
	} else if (z <= -4e+37) {
		tmp = t_2;
	} else if (z <= -4300000000.0) {
		tmp = t_1;
	} else if (z <= -7.2e-64) {
		tmp = (y - z) * t;
	} else if (z <= 2.9e+18) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = y * (t - x)
    if (z <= (-1.45d+77)) then
        tmp = t_1
    else if (z <= (-4d+37)) then
        tmp = t_2
    else if (z <= (-4300000000.0d0)) then
        tmp = t_1
    else if (z <= (-7.2d-64)) then
        tmp = (y - z) * t
    else if (z <= 2.9d+18) then
        tmp = x + t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -1.45e+77) {
		tmp = t_1;
	} else if (z <= -4e+37) {
		tmp = t_2;
	} else if (z <= -4300000000.0) {
		tmp = t_1;
	} else if (z <= -7.2e-64) {
		tmp = (y - z) * t;
	} else if (z <= 2.9e+18) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = y * (t - x)
	tmp = 0
	if z <= -1.45e+77:
		tmp = t_1
	elif z <= -4e+37:
		tmp = t_2
	elif z <= -4300000000.0:
		tmp = t_1
	elif z <= -7.2e-64:
		tmp = (y - z) * t
	elif z <= 2.9e+18:
		tmp = x + t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -1.45e+77)
		tmp = t_1;
	elseif (z <= -4e+37)
		tmp = t_2;
	elseif (z <= -4300000000.0)
		tmp = t_1;
	elseif (z <= -7.2e-64)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 2.9e+18)
		tmp = Float64(x + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = y * (t - x);
	tmp = 0.0;
	if (z <= -1.45e+77)
		tmp = t_1;
	elseif (z <= -4e+37)
		tmp = t_2;
	elseif (z <= -4300000000.0)
		tmp = t_1;
	elseif (z <= -7.2e-64)
		tmp = (y - z) * t;
	elseif (z <= 2.9e+18)
		tmp = x + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+77], t$95$1, If[LessEqual[z, -4e+37], t$95$2, If[LessEqual[z, -4300000000.0], t$95$1, If[LessEqual[z, -7.2e-64], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 2.9e+18], N[(x + t$95$2), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4500000000000001e77 or -3.99999999999999982e37 < z < -4.3e9 or 2.9e18 < 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 inf 84.1%

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

      1. sub-neg 84.1%

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

      2. +-commutative 84.1%

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

      3. associate-+l+ 84.1%

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

      4. +-commutative 84.1%

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

      5. mul-1-neg 84.1%

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

      6. unsub-neg 84.1%

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

      7. div-sub 90.5%

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

      8. unsub-neg 90.5%

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

      9. mul-1-neg 90.5%

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

      10. sub-neg 90.5%

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

      11. +-commutative 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around -inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-in 84.5%

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

      3. sub-neg 84.5%

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

      4. distribute-neg-in 84.5%

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

      5. remove-double-neg 84.5%

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

   8. Simplified 84.5%

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

   if -1.4500000000000001e77 < z < -3.99999999999999982e37

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.7%

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

   if -4.3e9 < z < -7.1999999999999996e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.1%

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

   if -7.1999999999999996e-64 < z < 2.9e18

   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 95.1%

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

      1. *-commutative 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -4300000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-64}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+42} \lor \neg \left(z \leq 3.7 \cdot 10^{+171}\right) \land z \leq 6.3 \cdot 10^{+246}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= z -4.3e-65)
     t_1
     (if (<= z 8.5e+17)
       (+ x (* y t))
       (if (or (<= z 9e+42) (and (not (<= z 3.7e+171)) (<= z 6.3e+246)))
         (* z x)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (z <= -4.3e-65) {
		tmp = t_1;
	} else if (z <= 8.5e+17) {
		tmp = x + (y * t);
	} else if ((z <= 9e+42) || (!(z <= 3.7e+171) && (z <= 6.3e+246))) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (z <= (-4.3d-65)) then
        tmp = t_1
    else if (z <= 8.5d+17) then
        tmp = x + (y * t)
    else if ((z <= 9d+42) .or. (.not. (z <= 3.7d+171)) .and. (z <= 6.3d+246)) then
        tmp = z * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (z <= -4.3e-65) {
		tmp = t_1;
	} else if (z <= 8.5e+17) {
		tmp = x + (y * t);
	} else if ((z <= 9e+42) || (!(z <= 3.7e+171) && (z <= 6.3e+246))) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if z <= -4.3e-65:
		tmp = t_1
	elif z <= 8.5e+17:
		tmp = x + (y * t)
	elif (z <= 9e+42) or (not (z <= 3.7e+171) and (z <= 6.3e+246)):
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -4.3e-65)
		tmp = t_1;
	elseif (z <= 8.5e+17)
		tmp = Float64(x + Float64(y * t));
	elseif ((z <= 9e+42) || (!(z <= 3.7e+171) && (z <= 6.3e+246)))
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (z <= -4.3e-65)
		tmp = t_1;
	elseif (z <= 8.5e+17)
		tmp = x + (y * t);
	elseif ((z <= 9e+42) || (~((z <= 3.7e+171)) && (z <= 6.3e+246)))
		tmp = z * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -4.3e-65], t$95$1, If[LessEqual[z, 8.5e+17], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 9e+42], And[N[Not[LessEqual[z, 3.7e+171]], $MachinePrecision], LessEqual[z, 6.3e+246]]], N[(z * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.30000000000000024e-65 or 9.00000000000000025e42 < z < 3.69999999999999998e171 or 6.3e246 < 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 0 64.5%

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

   if -4.30000000000000024e-65 < z < 8.5e17

   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 95.1%

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

      1. *-commutative 95.1%

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

   5. Simplified 95.1%

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

   6. Taylor expanded in t around inf 71.7%

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

   if 8.5e17 < z < 9.00000000000000025e42 or 3.69999999999999998e171 < z < 6.3e246

   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 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

      3. distribute-lft-out-- 75.8%

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

      4. *-rgt-identity 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in z around inf 76.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-65}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+42} \lor \neg \left(z \leq 3.7 \cdot 10^{+171}\right) \land z \leq 6.3 \cdot 10^{+246}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-232}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-190}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* (- y z) t)))
   (if (<= y -2e+54)
     t_1
     (if (<= y -6.8e-232)
       t_2
       (if (<= y 9e-287)
         x
         (if (<= y 5e-190) (* z x) (if (<= y 7.2e+66) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -2e+54) {
		tmp = t_1;
	} else if (y <= -6.8e-232) {
		tmp = t_2;
	} else if (y <= 9e-287) {
		tmp = x;
	} else if (y <= 5e-190) {
		tmp = z * x;
	} else if (y <= 7.2e+66) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = (y - z) * t
    if (y <= (-2d+54)) then
        tmp = t_1
    else if (y <= (-6.8d-232)) then
        tmp = t_2
    else if (y <= 9d-287) then
        tmp = x
    else if (y <= 5d-190) then
        tmp = z * x
    else if (y <= 7.2d+66) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -2e+54) {
		tmp = t_1;
	} else if (y <= -6.8e-232) {
		tmp = t_2;
	} else if (y <= 9e-287) {
		tmp = x;
	} else if (y <= 5e-190) {
		tmp = z * x;
	} else if (y <= 7.2e+66) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = (y - z) * t
	tmp = 0
	if y <= -2e+54:
		tmp = t_1
	elif y <= -6.8e-232:
		tmp = t_2
	elif y <= 9e-287:
		tmp = x
	elif y <= 5e-190:
		tmp = z * x
	elif y <= 7.2e+66:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -2e+54)
		tmp = t_1;
	elseif (y <= -6.8e-232)
		tmp = t_2;
	elseif (y <= 9e-287)
		tmp = x;
	elseif (y <= 5e-190)
		tmp = Float64(z * x);
	elseif (y <= 7.2e+66)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (y <= -2e+54)
		tmp = t_1;
	elseif (y <= -6.8e-232)
		tmp = t_2;
	elseif (y <= 9e-287)
		tmp = x;
	elseif (y <= 5e-190)
		tmp = z * x;
	elseif (y <= 7.2e+66)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -2e+54], t$95$1, If[LessEqual[y, -6.8e-232], t$95$2, If[LessEqual[y, 9e-287], x, If[LessEqual[y, 5e-190], N[(z * x), $MachinePrecision], If[LessEqual[y, 7.2e+66], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.0000000000000002e54 or 7.2e66 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.5%

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

   if -2.0000000000000002e54 < y < -6.8000000000000004e-232 or 5.00000000000000034e-190 < y < 7.2e66

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 50.7%

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

   if -6.8000000000000004e-232 < y < 9.00000000000000034e-287

   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 55.1%

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

      1. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in y around 0 54.9%

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

   if 9.00000000000000034e-287 < y < 5.00000000000000034e-190

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

      3. distribute-lft-out-- 82.1%

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

      4. *-rgt-identity 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in z around inf 61.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-232}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-190}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+66}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-61}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+66}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -2e+54)
     t_1
     (if (<= y -3.4e+40)
       (* z (- x t))
       (if (<= y -2.15e-61)
         (+ x t_1)
         (if (<= y 2.5e+66) (- x (* z (- t x))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2e+54) {
		tmp = t_1;
	} else if (y <= -3.4e+40) {
		tmp = z * (x - t);
	} else if (y <= -2.15e-61) {
		tmp = x + t_1;
	} else if (y <= 2.5e+66) {
		tmp = x - (z * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-2d+54)) then
        tmp = t_1
    else if (y <= (-3.4d+40)) then
        tmp = z * (x - t)
    else if (y <= (-2.15d-61)) then
        tmp = x + t_1
    else if (y <= 2.5d+66) then
        tmp = x - (z * (t - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2e+54) {
		tmp = t_1;
	} else if (y <= -3.4e+40) {
		tmp = z * (x - t);
	} else if (y <= -2.15e-61) {
		tmp = x + t_1;
	} else if (y <= 2.5e+66) {
		tmp = x - (z * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -2e+54:
		tmp = t_1
	elif y <= -3.4e+40:
		tmp = z * (x - t)
	elif y <= -2.15e-61:
		tmp = x + t_1
	elif y <= 2.5e+66:
		tmp = x - (z * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -2e+54)
		tmp = t_1;
	elseif (y <= -3.4e+40)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= -2.15e-61)
		tmp = Float64(x + t_1);
	elseif (y <= 2.5e+66)
		tmp = Float64(x - Float64(z * Float64(t - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -2e+54)
		tmp = t_1;
	elseif (y <= -3.4e+40)
		tmp = z * (x - t);
	elseif (y <= -2.15e-61)
		tmp = x + t_1;
	elseif (y <= 2.5e+66)
		tmp = x - (z * (t - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+54], t$95$1, If[LessEqual[y, -3.4e+40], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-61], N[(x + t$95$1), $MachinePrecision], If[LessEqual[y, 2.5e+66], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.0000000000000002e54 or 2.49999999999999996e66 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.5%

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

   if -2.0000000000000002e54 < y < -3.39999999999999989e40

   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 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. div-sub 100.0%

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

      8. unsub-neg 100.0%

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

      9. mul-1-neg 100.0%

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

      10. sub-neg 100.0%

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

      11. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. remove-double-neg 100.0%

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

   8. Simplified 100.0%

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

   if -3.39999999999999989e40 < y < -2.1500000000000002e-61

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.3%

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

      1. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -2.1500000000000002e-61 < y < 2.49999999999999996e66

   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 94.5%

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

      1. mul-1-neg 94.5%

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

      2. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+40}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+66}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -29000:\\ \;\;\;\;x - \left(y - z\right) \cdot x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-30}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.65e+77)
     t_1
     (if (<= z -29000.0)
       (- x (* (- y z) x))
       (if (<= z -2.9e-30)
         (* (- y z) t)
         (if (<= z 4.3e+18) (+ x (* y (- t x))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.65e+77) {
		tmp = t_1;
	} else if (z <= -29000.0) {
		tmp = x - ((y - z) * x);
	} else if (z <= -2.9e-30) {
		tmp = (y - z) * t;
	} else if (z <= 4.3e+18) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-1.65d+77)) then
        tmp = t_1
    else if (z <= (-29000.0d0)) then
        tmp = x - ((y - z) * x)
    else if (z <= (-2.9d-30)) then
        tmp = (y - z) * t
    else if (z <= 4.3d+18) then
        tmp = x + (y * (t - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.65e+77) {
		tmp = t_1;
	} else if (z <= -29000.0) {
		tmp = x - ((y - z) * x);
	} else if (z <= -2.9e-30) {
		tmp = (y - z) * t;
	} else if (z <= 4.3e+18) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.65e+77:
		tmp = t_1
	elif z <= -29000.0:
		tmp = x - ((y - z) * x)
	elif z <= -2.9e-30:
		tmp = (y - z) * t
	elif z <= 4.3e+18:
		tmp = x + (y * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.65e+77)
		tmp = t_1;
	elseif (z <= -29000.0)
		tmp = Float64(x - Float64(Float64(y - z) * x));
	elseif (z <= -2.9e-30)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 4.3e+18)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.65e+77)
		tmp = t_1;
	elseif (z <= -29000.0)
		tmp = x - ((y - z) * x);
	elseif (z <= -2.9e-30)
		tmp = (y - z) * t;
	elseif (z <= 4.3e+18)
		tmp = x + (y * (t - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+77], t$95$1, If[LessEqual[z, -29000.0], N[(x - N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-30], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 4.3e+18], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6499999999999999e77 or 4.3e18 < 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 inf 84.0%

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

      1. sub-neg 84.0%

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

      2. +-commutative 84.0%

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

      3. associate-+l+ 84.0%

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

      4. +-commutative 84.0%

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

      5. mul-1-neg 84.0%

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

      6. unsub-neg 84.0%

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

      7. div-sub 90.7%

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

      8. unsub-neg 90.7%

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

      9. mul-1-neg 90.7%

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

      10. sub-neg 90.7%

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

      11. +-commutative 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in z around -inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. distribute-rgt-neg-in 86.1%

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

      3. sub-neg 86.1%

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

      4. distribute-neg-in 86.1%

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

      5. remove-double-neg 86.1%

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

   8. Simplified 86.1%

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

   if -1.6499999999999999e77 < z < -29000

   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 69.9%

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

      1. mul-1-neg 69.9%

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

      2. unsub-neg 69.9%

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

      3. distribute-lft-out-- 69.9%

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

      4. *-rgt-identity 69.9%

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

   5. Simplified 69.9%

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

   if -29000 < z < -2.89999999999999989e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.5%

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

   if -2.89999999999999989e-30 < z < 4.3e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.7%

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

      1. *-commutative 92.7%

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

   5. Simplified 92.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -29000:\\ \;\;\;\;x - \left(y - z\right) \cdot x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-30}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := x - y \cdot x\\ \mathbf{if}\;t \leq -7 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-44}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (- x (* y x))))
   (if (<= t -7e-119)
     t_1
     (if (<= t 1.6e-71)
       t_2
       (if (<= t 1.65e-44) (* z x) (if (<= t 1000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x - (y * x);
	double tmp;
	if (t <= -7e-119) {
		tmp = t_1;
	} else if (t <= 1.6e-71) {
		tmp = t_2;
	} else if (t <= 1.65e-44) {
		tmp = z * x;
	} else if (t <= 1000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * t
    t_2 = x - (y * x)
    if (t <= (-7d-119)) then
        tmp = t_1
    else if (t <= 1.6d-71) then
        tmp = t_2
    else if (t <= 1.65d-44) then
        tmp = z * x
    else if (t <= 1000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x - (y * x);
	double tmp;
	if (t <= -7e-119) {
		tmp = t_1;
	} else if (t <= 1.6e-71) {
		tmp = t_2;
	} else if (t <= 1.65e-44) {
		tmp = z * x;
	} else if (t <= 1000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = x - (y * x)
	tmp = 0
	if t <= -7e-119:
		tmp = t_1
	elif t <= 1.6e-71:
		tmp = t_2
	elif t <= 1.65e-44:
		tmp = z * x
	elif t <= 1000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(x - Float64(y * x))
	tmp = 0.0
	if (t <= -7e-119)
		tmp = t_1;
	elseif (t <= 1.6e-71)
		tmp = t_2;
	elseif (t <= 1.65e-44)
		tmp = Float64(z * x);
	elseif (t <= 1000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = x - (y * x);
	tmp = 0.0;
	if (t <= -7e-119)
		tmp = t_1;
	elseif (t <= 1.6e-71)
		tmp = t_2;
	elseif (t <= 1.65e-44)
		tmp = z * x;
	elseif (t <= 1000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7e-119], t$95$1, If[LessEqual[t, 1.6e-71], t$95$2, If[LessEqual[t, 1.65e-44], N[(z * x), $MachinePrecision], If[LessEqual[t, 1000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7e-119 or 1e6 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.5%

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

   if -7e-119 < t < 1.5999999999999999e-71 or 1.65000000000000003e-44 < t < 1e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.6%

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

      1. mul-1-neg 88.6%

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

      2. unsub-neg 88.6%

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

      3. distribute-lft-out-- 88.6%

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

      4. *-rgt-identity 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in z around 0 66.8%

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

   if 1.5999999999999999e-71 < t < 1.65000000000000003e-44

   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 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

      3. distribute-lft-out-- 63.3%

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

      4. *-rgt-identity 63.3%

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

   5. Simplified 63.3%

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

   6. Taylor expanded in z around inf 63.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-119}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-71}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-44}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1000000:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0027:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-156}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 0.0013:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.0027)
   (* y t)
   (if (<= y 9.5e-288)
     x
     (if (<= y 1.2e-156) (* z x) (if (<= y 0.0013) x (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.0027) {
		tmp = y * t;
	} else if (y <= 9.5e-288) {
		tmp = x;
	} else if (y <= 1.2e-156) {
		tmp = z * x;
	} else if (y <= 0.0013) {
		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 <= (-0.0027d0)) then
        tmp = y * t
    else if (y <= 9.5d-288) then
        tmp = x
    else if (y <= 1.2d-156) then
        tmp = z * x
    else if (y <= 0.0013d0) 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 <= -0.0027) {
		tmp = y * t;
	} else if (y <= 9.5e-288) {
		tmp = x;
	} else if (y <= 1.2e-156) {
		tmp = z * x;
	} else if (y <= 0.0013) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.0027:
		tmp = y * t
	elif y <= 9.5e-288:
		tmp = x
	elif y <= 1.2e-156:
		tmp = z * x
	elif y <= 0.0013:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.0027)
		tmp = Float64(y * t);
	elseif (y <= 9.5e-288)
		tmp = x;
	elseif (y <= 1.2e-156)
		tmp = Float64(z * x);
	elseif (y <= 0.0013)
		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 <= -0.0027)
		tmp = y * t;
	elseif (y <= 9.5e-288)
		tmp = x;
	elseif (y <= 1.2e-156)
		tmp = z * x;
	elseif (y <= 0.0013)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.0027], N[(y * t), $MachinePrecision], If[LessEqual[y, 9.5e-288], x, If[LessEqual[y, 1.2e-156], N[(z * x), $MachinePrecision], If[LessEqual[y, 0.0013], x, N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0027000000000000001 or 0.0012999999999999999 < 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 0 57.7%

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

   4. Taylor expanded in y around inf 41.6%

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

   if -0.0027000000000000001 < y < 9.49999999999999955e-288 or 1.2e-156 < y < 0.0012999999999999999

   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 51.8%

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

      1. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y around 0 43.1%

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

   if 9.49999999999999955e-288 < y < 1.2e-156

   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 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

      3. distribute-lft-out-- 74.0%

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

      4. *-rgt-identity 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in z around inf 53.9%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0027:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-156}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 0.0013:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-8} \lor \neg \left(y - z \leq 2 \cdot 10^{-76}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -5e-8) (not (<= (- y z) 2e-76))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-8) || !((y - z) <= 2e-76)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y - z) <= (-5d-8)) .or. (.not. ((y - z) <= 2d-76))) then
        tmp = (y - z) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-8) || !((y - z) <= 2e-76)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -5e-8) or not ((y - z) <= 2e-76):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -5e-8) || !(Float64(y - z) <= 2e-76))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -5e-8) || ~(((y - z) <= 2e-76)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -5e-8], N[Not[LessEqual[N[(y - z), $MachinePrecision], 2e-76]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -4.9999999999999998e-8 or 1.99999999999999985e-76 < (-.f64 y 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 0 56.5%

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

   if -4.9999999999999998e-8 < (-.f64 y z) < 1.99999999999999985e-76

   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 91.1%

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

      1. *-commutative 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in y around 0 78.5%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-8} \lor \neg \left(y - z \leq 2 \cdot 10^{-76}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1700000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e-56)
   (* z (- t))
   (if (<= z -8.5e-116) (* y t) (if (<= z 1700000000000.0) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-56) {
		tmp = z * -t;
	} else if (z <= -8.5e-116) {
		tmp = y * t;
	} else if (z <= 1700000000000.0) {
		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) :: tmp
    if (z <= (-6d-56)) then
        tmp = z * -t
    else if (z <= (-8.5d-116)) then
        tmp = y * t
    else if (z <= 1700000000000.0d0) 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 tmp;
	if (z <= -6e-56) {
		tmp = z * -t;
	} else if (z <= -8.5e-116) {
		tmp = y * t;
	} else if (z <= 1700000000000.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e-56:
		tmp = z * -t
	elif z <= -8.5e-116:
		tmp = y * t
	elif z <= 1700000000000.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e-56)
		tmp = Float64(z * Float64(-t));
	elseif (z <= -8.5e-116)
		tmp = Float64(y * t);
	elseif (z <= 1700000000000.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6e-56)
		tmp = z * -t;
	elseif (z <= -8.5e-116)
		tmp = y * t;
	elseif (z <= 1700000000000.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e-56], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, -8.5e-116], N[(y * t), $MachinePrecision], If[LessEqual[z, 1700000000000.0], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.99999999999999979e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 60.2%

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

   4. Taylor expanded in y around 0 49.0%

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

      1. mul-1-neg 49.0%

         \[\leadsto \color{blue}{-t \cdot z} \]

      2. *-commutative 49.0%

         \[\leadsto -\color{blue}{z \cdot t} \]

      3. distribute-rgt-neg-in 49.0%

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

   6. Simplified 49.0%

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

   if -5.99999999999999979e-56 < z < -8.4999999999999995e-116

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 69.7%

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

   4. Taylor expanded in y around inf 60.4%

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

   if -8.4999999999999995e-116 < z < 1.7e12

   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 94.3%

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

      1. *-commutative 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in y around 0 43.4%

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

   if 1.7e12 < 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 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

      3. distribute-lft-out-- 53.4%

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

      4. *-rgt-identity 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in z around inf 48.2%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-116}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1700000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00125 \lor \neg \left(y \leq 9.8 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.00125) (not (<= y 9.8e-6))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00125) || !(y <= 9.8e-6)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.00125d0)) .or. (.not. (y <= 9.8d-6))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00125) || !(y <= 9.8e-6)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.00125) or not (y <= 9.8e-6):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.00125) || !(y <= 9.8e-6))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.00125) || ~((y <= 9.8e-6)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.00125], N[Not[LessEqual[y, 9.8e-6]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.00125000000000000003 or 9.79999999999999934e-6 < 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 0 57.7%

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

   4. Taylor expanded in y around inf 41.6%

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

   if -0.00125000000000000003 < y < 9.79999999999999934e-6

   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 46.1%

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

      1. *-commutative 46.1%

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

   5. Simplified 46.1%

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

   6. Taylor expanded in y around 0 39.0%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00125 \lor \neg \left(y \leq 9.8 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 100.0% accurate, 1.0× speedup

Math

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

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 15: 17.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 61.0%

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

   1. *-commutative 61.0%

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

5. Simplified 61.0%

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

6. Taylor expanded in y around 0 21.4%

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

Developer target: 96.6% 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 2024097 
(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))))