Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.0s

Alternatives: 13

Speedup: 1.0×

• 35.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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: 38.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+230}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-272}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-64}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2e+230)
     (* z x)
     (if (<= z -2.2e+70)
       t_1
       (if (<= z -8e-272)
         (* y t)
         (if (<= z 1.65e-271)
           x
           (if (<= z 8.8e-189)
             (* y t)
             (if (<= z 1.2e-163) x (if (<= z 7.2e-64) (* y t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2e+230) {
		tmp = z * x;
	} else if (z <= -2.2e+70) {
		tmp = t_1;
	} else if (z <= -8e-272) {
		tmp = y * t;
	} else if (z <= 1.65e-271) {
		tmp = x;
	} else if (z <= 8.8e-189) {
		tmp = y * t;
	} else if (z <= 1.2e-163) {
		tmp = x;
	} else if (z <= 7.2e-64) {
		tmp = 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 * -t
    if (z <= (-2d+230)) then
        tmp = z * x
    else if (z <= (-2.2d+70)) then
        tmp = t_1
    else if (z <= (-8d-272)) then
        tmp = y * t
    else if (z <= 1.65d-271) then
        tmp = x
    else if (z <= 8.8d-189) then
        tmp = y * t
    else if (z <= 1.2d-163) then
        tmp = x
    else if (z <= 7.2d-64) then
        tmp = 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 * -t;
	double tmp;
	if (z <= -2e+230) {
		tmp = z * x;
	} else if (z <= -2.2e+70) {
		tmp = t_1;
	} else if (z <= -8e-272) {
		tmp = y * t;
	} else if (z <= 1.65e-271) {
		tmp = x;
	} else if (z <= 8.8e-189) {
		tmp = y * t;
	} else if (z <= 1.2e-163) {
		tmp = x;
	} else if (z <= 7.2e-64) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -2e+230:
		tmp = z * x
	elif z <= -2.2e+70:
		tmp = t_1
	elif z <= -8e-272:
		tmp = y * t
	elif z <= 1.65e-271:
		tmp = x
	elif z <= 8.8e-189:
		tmp = y * t
	elif z <= 1.2e-163:
		tmp = x
	elif z <= 7.2e-64:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2e+230)
		tmp = Float64(z * x);
	elseif (z <= -2.2e+70)
		tmp = t_1;
	elseif (z <= -8e-272)
		tmp = Float64(y * t);
	elseif (z <= 1.65e-271)
		tmp = x;
	elseif (z <= 8.8e-189)
		tmp = Float64(y * t);
	elseif (z <= 1.2e-163)
		tmp = x;
	elseif (z <= 7.2e-64)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -2e+230)
		tmp = z * x;
	elseif (z <= -2.2e+70)
		tmp = t_1;
	elseif (z <= -8e-272)
		tmp = y * t;
	elseif (z <= 1.65e-271)
		tmp = x;
	elseif (z <= 8.8e-189)
		tmp = y * t;
	elseif (z <= 1.2e-163)
		tmp = x;
	elseif (z <= 7.2e-64)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -2e+230], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.2e+70], t$95$1, If[LessEqual[z, -8e-272], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.65e-271], x, If[LessEqual[z, 8.8e-189], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.2e-163], x, If[LessEqual[z, 7.2e-64], N[(y * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0000000000000002e230

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-in 77.4%

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

      3. neg-sub0 77.4%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 77.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 77.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 77.4%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 77.4%

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

      8. remove-double-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in z around inf 71.1%

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

   7. Taylor expanded in z around inf 71.1%

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

   if -2.0000000000000002e230 < z < -2.20000000000000001e70 or 7.1999999999999996e-64 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 59.5%

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

   4. Taylor expanded in t around inf 63.7%

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

   5. Taylor expanded in z around inf 45.7%

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

      1. associate-*r* 45.7%

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

      2. *-commutative 45.7%

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

      3. mul-1-neg 45.7%

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

   7. Simplified 45.7%

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

   if -2.20000000000000001e70 < z < -7.99999999999999944e-272 or 1.6500000000000001e-271 < z < 8.80000000000000076e-189 or 1.2e-163 < 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 t around inf 68.8%

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

   4. Taylor expanded in z around 0 61.7%

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

   5. Taylor expanded in x around 0 44.6%

      \[\leadsto \color{blue}{t \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 44.6%

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

   7. Simplified 44.6%

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

   if -7.99999999999999944e-272 < z < 1.6500000000000001e-271 or 8.80000000000000076e-189 < z < 1.2e-163

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 78.7%

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

   4. Taylor expanded in x around inf 59.9%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+230}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-272}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-189}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-163}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-64}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+14} \lor \neg \left(t \leq -7.2 \cdot 10^{-15}\right) \land \left(t \leq -5.5 \cdot 10^{-131} \lor \neg \left(t \leq 8 \cdot 10^{+75}\right)\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.6e+14)
         (and (not (<= t -7.2e-15)) (or (<= t -5.5e-131) (not (<= t 8e+75)))))
   (- x (* t (- z y)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.6e+14) || (!(t <= -7.2e-15) && ((t <= -5.5e-131) || !(t <= 8e+75)))) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.6d+14)) .or. (.not. (t <= (-7.2d-15))) .and. (t <= (-5.5d-131)) .or. (.not. (t <= 8d+75))) then
        tmp = x - (t * (z - y))
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.6e+14) || (!(t <= -7.2e-15) && ((t <= -5.5e-131) || !(t <= 8e+75)))) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.6e+14) or (not (t <= -7.2e-15) and ((t <= -5.5e-131) or not (t <= 8e+75))):
		tmp = x - (t * (z - y))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.6e+14) || (!(t <= -7.2e-15) && ((t <= -5.5e-131) || !(t <= 8e+75))))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.6e+14) || (~((t <= -7.2e-15)) && ((t <= -5.5e-131) || ~((t <= 8e+75)))))
		tmp = x - (t * (z - y));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.6e+14], And[N[Not[LessEqual[t, -7.2e-15]], $MachinePrecision], Or[LessEqual[t, -5.5e-131], N[Not[LessEqual[t, 8e+75]], $MachinePrecision]]]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e14 or -7.2000000000000002e-15 < t < -5.4999999999999997e-131 or 7.99999999999999941e75 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 86.0%

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

   if -2.6e14 < t < -7.2000000000000002e-15 or -5.4999999999999997e-131 < t < 7.99999999999999941e75

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. distribute-rgt-neg-in 83.2%

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

      3. neg-sub0 83.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 83.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 83.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 83.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 83.2%

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

      8. remove-double-neg 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+14} \lor \neg \left(t \leq -7.2 \cdot 10^{-15}\right) \land \left(t \leq -5.5 \cdot 10^{-131} \lor \neg \left(t \leq 8 \cdot 10^{+75}\right)\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-131} \lor \neg \left(t \leq 2.3 \cdot 10^{+74}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* t (- z y)))))
   (if (<= t -4.7e+58)
     t_1
     (if (<= t -1.25e-15)
       (+ x (* y (- t x)))
       (if (or (<= t -5.5e-131) (not (<= t 2.3e+74)))
         t_1
         (+ x (* x (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (t * (z - y));
	double tmp;
	if (t <= -4.7e+58) {
		tmp = t_1;
	} else if (t <= -1.25e-15) {
		tmp = x + (y * (t - x));
	} else if ((t <= -5.5e-131) || !(t <= 2.3e+74)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (z - y))
    if (t <= (-4.7d+58)) then
        tmp = t_1
    else if (t <= (-1.25d-15)) then
        tmp = x + (y * (t - x))
    else if ((t <= (-5.5d-131)) .or. (.not. (t <= 2.3d+74))) then
        tmp = t_1
    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 t_1 = x - (t * (z - y));
	double tmp;
	if (t <= -4.7e+58) {
		tmp = t_1;
	} else if (t <= -1.25e-15) {
		tmp = x + (y * (t - x));
	} else if ((t <= -5.5e-131) || !(t <= 2.3e+74)) {
		tmp = t_1;
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (t * (z - y))
	tmp = 0
	if t <= -4.7e+58:
		tmp = t_1
	elif t <= -1.25e-15:
		tmp = x + (y * (t - x))
	elif (t <= -5.5e-131) or not (t <= 2.3e+74):
		tmp = t_1
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(t * Float64(z - y)))
	tmp = 0.0
	if (t <= -4.7e+58)
		tmp = t_1;
	elseif (t <= -1.25e-15)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	elseif ((t <= -5.5e-131) || !(t <= 2.3e+74))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (t * (z - y));
	tmp = 0.0;
	if (t <= -4.7e+58)
		tmp = t_1;
	elseif (t <= -1.25e-15)
		tmp = x + (y * (t - x));
	elseif ((t <= -5.5e-131) || ~((t <= 2.3e+74)))
		tmp = t_1;
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e+58], t$95$1, If[LessEqual[t, -1.25e-15], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -5.5e-131], N[Not[LessEqual[t, 2.3e+74]], $MachinePrecision]], t$95$1, N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.69999999999999972e58 or -1.25e-15 < t < -5.4999999999999997e-131 or 2.2999999999999999e74 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 87.3%

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

   if -4.69999999999999972e58 < t < -1.25e-15

   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 86.5%

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

      1. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   if -5.4999999999999997e-131 < t < 2.2999999999999999e74

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. distribute-rgt-neg-in 82.2%

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

      3. neg-sub0 82.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 82.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 82.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 82.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 82.2%

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

      8. remove-double-neg 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+58}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-131} \lor \neg \left(t \leq 2.3 \cdot 10^{+74}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+32} \lor \neg \left(t \leq -9 \cdot 10^{-13}\right) \land \left(t \leq -3.8 \cdot 10^{-103} \lor \neg \left(t \leq 2.9 \cdot 10^{-11}\right)\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e+32)
         (and (not (<= t -9e-13)) (or (<= t -3.8e-103) (not (<= t 2.9e-11)))))
   (* t (- y z))
   (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e+32) || (!(t <= -9e-13) && ((t <= -3.8e-103) || !(t <= 2.9e-11)))) {
		tmp = t * (y - z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.5d+32)) .or. (.not. (t <= (-9d-13))) .and. (t <= (-3.8d-103)) .or. (.not. (t <= 2.9d-11))) then
        tmp = t * (y - z)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e+32) || (!(t <= -9e-13) && ((t <= -3.8e-103) || !(t <= 2.9e-11)))) {
		tmp = t * (y - z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e+32) or (not (t <= -9e-13) and ((t <= -3.8e-103) or not (t <= 2.9e-11))):
		tmp = t * (y - z)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e+32) || (!(t <= -9e-13) && ((t <= -3.8e-103) || !(t <= 2.9e-11))))
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e+32) || (~((t <= -9e-13)) && ((t <= -3.8e-103) || ~((t <= 2.9e-11)))))
		tmp = t * (y - z);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e+32], And[N[Not[LessEqual[t, -9e-13]], $MachinePrecision], Or[LessEqual[t, -3.8e-103], N[Not[LessEqual[t, 2.9e-11]], $MachinePrecision]]]], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5000000000000001e32 or -9e-13 < t < -3.8000000000000001e-103 or 2.9e-11 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.4%

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

   4. Taylor expanded in t around inf 85.2%

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

   5. Taylor expanded in t around inf 73.2%

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

   if -3.5000000000000001e32 < t < -9e-13 or -3.8000000000000001e-103 < t < 2.9e-11

   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 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in x around inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

   8. Simplified 58.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+32} \lor \neg \left(t \leq -9 \cdot 10^{-13}\right) \land \left(t \leq -3.8 \cdot 10^{-103} \lor \neg \left(t \leq 2.9 \cdot 10^{-11}\right)\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-78}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (- t x)))))
   (if (<= y -4.8e+161)
     t_1
     (if (<= y -2e-78)
       (- x (* t (- z y)))
       (if (<= y 1.8e-12) (+ x (* z (- x t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -4.8e+161) {
		tmp = t_1;
	} else if (y <= -2e-78) {
		tmp = x - (t * (z - y));
	} else if (y <= 1.8e-12) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t - x))
    if (y <= (-4.8d+161)) then
        tmp = t_1
    else if (y <= (-2d-78)) then
        tmp = x - (t * (z - y))
    else if (y <= 1.8d-12) then
        tmp = x + (z * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -4.8e+161) {
		tmp = t_1;
	} else if (y <= -2e-78) {
		tmp = x - (t * (z - y));
	} else if (y <= 1.8e-12) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (t - x))
	tmp = 0
	if y <= -4.8e+161:
		tmp = t_1
	elif y <= -2e-78:
		tmp = x - (t * (z - y))
	elif y <= 1.8e-12:
		tmp = x + (z * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -4.8e+161)
		tmp = t_1;
	elseif (y <= -2e-78)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	elseif (y <= 1.8e-12)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -4.8e+161)
		tmp = t_1;
	elseif (y <= -2e-78)
		tmp = x - (t * (z - y));
	elseif (y <= 1.8e-12)
		tmp = x + (z * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+161], t$95$1, If[LessEqual[y, -2e-78], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-12], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999998e161 or 1.8e-12 < 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 85.0%

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

      1. *-commutative 85.0%

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

   5. Simplified 85.0%

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

   if -4.7999999999999998e161 < y < -2e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.8%

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

   if -2e-78 < y < 1.8e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 93.2%

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

      1. mul-1-neg 93.2%

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

      2. unsub-neg 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+161}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-78}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))))
   (if (<= x -2.4e+17)
     t_1
     (if (<= x 4.3e+42)
       (* t (- y z))
       (if (<= x 1.5e+145) t_1 (* x (- 1.0 y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double tmp;
	if (x <= -2.4e+17) {
		tmp = t_1;
	} else if (x <= 4.3e+42) {
		tmp = t * (y - z);
	} else if (x <= 1.5e+145) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * x)
    if (x <= (-2.4d+17)) then
        tmp = t_1
    else if (x <= 4.3d+42) then
        tmp = t * (y - z)
    else if (x <= 1.5d+145) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double tmp;
	if (x <= -2.4e+17) {
		tmp = t_1;
	} else if (x <= 4.3e+42) {
		tmp = t * (y - z);
	} else if (x <= 1.5e+145) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	tmp = 0
	if x <= -2.4e+17:
		tmp = t_1
	elif x <= 4.3e+42:
		tmp = t * (y - z)
	elif x <= 1.5e+145:
		tmp = t_1
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	tmp = 0.0
	if (x <= -2.4e+17)
		tmp = t_1;
	elseif (x <= 4.3e+42)
		tmp = Float64(t * Float64(y - z));
	elseif (x <= 1.5e+145)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	tmp = 0.0;
	if (x <= -2.4e+17)
		tmp = t_1;
	elseif (x <= 4.3e+42)
		tmp = t * (y - z);
	elseif (x <= 1.5e+145)
		tmp = t_1;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+17], t$95$1, If[LessEqual[x, 4.3e+42], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+145], t$95$1, N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e17 or 4.2999999999999998e42 < x < 1.5000000000000001e145

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-rgt-neg-in 82.6%

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

      3. neg-sub0 82.6%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 82.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 82.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 82.6%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 82.6%

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

      8. remove-double-neg 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in z around inf 60.8%

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

   if -2.4e17 < x < 4.2999999999999998e42

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 81.4%

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

   4. Taylor expanded in t around inf 81.4%

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

   5. Taylor expanded in t around inf 71.5%

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

   if 1.5000000000000001e145 < x

   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 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in x around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

   8. Simplified 68.2%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+145}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+170}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.8e+47)
   (+ x (* z x))
   (if (<= x 2.3e+170) (- x (* t (- z y))) (* x (- 1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e+47) {
		tmp = x + (z * x);
	} else if (x <= 2.3e+170) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.8d+47)) then
        tmp = x + (z * x)
    else if (x <= 2.3d+170) then
        tmp = x - (t * (z - y))
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e+47) {
		tmp = x + (z * x);
	} else if (x <= 2.3e+170) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.8e+47:
		tmp = x + (z * x)
	elif x <= 2.3e+170:
		tmp = x - (t * (z - y))
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.8e+47)
		tmp = Float64(x + Float64(z * x));
	elseif (x <= 2.3e+170)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.8e+47)
		tmp = x + (z * x);
	elseif (x <= 2.3e+170)
		tmp = x - (t * (z - y));
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.8e+47], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+170], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999988e47

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-rgt-neg-in 85.0%

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

      3. neg-sub0 85.0%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 85.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 85.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 85.0%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 85.0%

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

      8. remove-double-neg 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around inf 58.7%

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

   if -2.79999999999999988e47 < x < 2.3000000000000001e170

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 77.6%

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

   if 2.3000000000000001e170 < x

   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 78.7%

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

      1. *-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in x around inf 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+47}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+170}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+47} \lor \neg \left(x \leq 1.5 \cdot 10^{+201}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.12e+47) (not (<= x 1.5e+201))) (* z x) (* t (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.12e+47) || !(x <= 1.5e+201)) {
		tmp = z * x;
	} else {
		tmp = t * (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.12d+47)) .or. (.not. (x <= 1.5d+201))) then
        tmp = z * x
    else
        tmp = t * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.12e+47) || !(x <= 1.5e+201)) {
		tmp = z * x;
	} else {
		tmp = t * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.12e+47) or not (x <= 1.5e+201):
		tmp = z * x
	else:
		tmp = t * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.12e+47) || !(x <= 1.5e+201))
		tmp = Float64(z * x);
	else
		tmp = Float64(t * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.12e+47) || ~((x <= 1.5e+201)))
		tmp = z * x;
	else
		tmp = t * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.12e+47], N[Not[LessEqual[x, 1.5e+201]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.12000000000000007e47 or 1.50000000000000012e201 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.4%

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

      1. mul-1-neg 89.4%

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

      2. distribute-rgt-neg-in 89.4%

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

      3. neg-sub0 89.4%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 89.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 89.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 89.4%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 89.4%

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

      8. remove-double-neg 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in z around inf 59.1%

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

   7. Taylor expanded in z around inf 40.1%

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

   if -1.12000000000000007e47 < x < 1.50000000000000012e201

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 76.9%

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

   4. Taylor expanded in t around inf 76.9%

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

   5. Taylor expanded in t around inf 65.4%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+47} \lor \neg \left(x \leq 1.5 \cdot 10^{+201}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+16} \lor \neg \left(x \leq 1.55 \cdot 10^{+46}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6e+16) (not (<= x 1.55e+46))) (* z x) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6e+16) || !(x <= 1.55e+46)) {
		tmp = z * 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 <= (-6d+16)) .or. (.not. (x <= 1.55d+46))) then
        tmp = z * 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 <= -6e+16) || !(x <= 1.55e+46)) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6e+16) or not (x <= 1.55e+46):
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6e+16) || !(x <= 1.55e+46))
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6e+16) || ~((x <= 1.55e+46)))
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6e+16], N[Not[LessEqual[x, 1.55e+46]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6e16 or 1.54999999999999988e46 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. distribute-rgt-neg-in 83.7%

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

      3. neg-sub0 83.7%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 83.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 83.7%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 83.7%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 83.7%

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

      8. remove-double-neg 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in z around inf 55.5%

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

   7. Taylor expanded in z around inf 37.6%

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

   if -6e16 < x < 1.54999999999999988e46

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 81.5%

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

   4. Taylor expanded in z around 0 49.0%

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

   5. Taylor expanded in x around 0 38.7%

      \[\leadsto \color{blue}{t \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 38.7%

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

   7. Simplified 38.7%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+16} \lor \neg \left(x \leq 1.55 \cdot 10^{+46}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+36} \lor \neg \left(z \leq 0.034\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.65e+36) (not (<= z 0.034))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.65e+36) || !(z <= 0.034)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.65d+36)) .or. (.not. (z <= 0.034d0))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.65e+36) || !(z <= 0.034)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.65e+36) or not (z <= 0.034):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.65e+36) || !(z <= 0.034))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.65e+36) || ~((z <= 0.034)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.65e+36], N[Not[LessEqual[z, 0.034]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.65e36 or 0.034000000000000002 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-rgt-neg-in 51.4%

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

      3. neg-sub0 51.4%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 51.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 51.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 51.4%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 51.4%

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

      8. remove-double-neg 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in z around inf 40.7%

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

   7. Taylor expanded in z around inf 40.7%

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

   if -2.65e36 < z < 0.034000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 73.3%

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

   4. Taylor expanded in x around inf 29.2%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+36} \lor \neg \left(z \leq 0.034\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 13: 17.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 64.3%

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

4. Taylor expanded in x around inf 16.2%

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

Developer target: 96.4% 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 2024088 
(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))))