Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 15

Speedup: 1.0×

• 34.0% 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: 38.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+187}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7500:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+130} \lor \neg \left(z \leq 5.5 \cdot 10^{+282}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -7.2e+187)
     (* z x)
     (if (<= z -1.75e-28)
       t_1
       (if (<= z 1.8e-271)
         x
         (if (<= z 7500.0)
           (* y t)
           (if (or (<= z 5.5e+130) (not (<= z 5.5e+282))) (* z x) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -7.2e+187) {
		tmp = z * x;
	} else if (z <= -1.75e-28) {
		tmp = t_1;
	} else if (z <= 1.8e-271) {
		tmp = x;
	} else if (z <= 7500.0) {
		tmp = y * t;
	} else if ((z <= 5.5e+130) || !(z <= 5.5e+282)) {
		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 = z * -t
    if (z <= (-7.2d+187)) then
        tmp = z * x
    else if (z <= (-1.75d-28)) then
        tmp = t_1
    else if (z <= 1.8d-271) then
        tmp = x
    else if (z <= 7500.0d0) then
        tmp = y * t
    else if ((z <= 5.5d+130) .or. (.not. (z <= 5.5d+282))) 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 = z * -t;
	double tmp;
	if (z <= -7.2e+187) {
		tmp = z * x;
	} else if (z <= -1.75e-28) {
		tmp = t_1;
	} else if (z <= 1.8e-271) {
		tmp = x;
	} else if (z <= 7500.0) {
		tmp = y * t;
	} else if ((z <= 5.5e+130) || !(z <= 5.5e+282)) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -7.2e+187:
		tmp = z * x
	elif z <= -1.75e-28:
		tmp = t_1
	elif z <= 1.8e-271:
		tmp = x
	elif z <= 7500.0:
		tmp = y * t
	elif (z <= 5.5e+130) or not (z <= 5.5e+282):
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -7.2e+187)
		tmp = Float64(z * x);
	elseif (z <= -1.75e-28)
		tmp = t_1;
	elseif (z <= 1.8e-271)
		tmp = x;
	elseif (z <= 7500.0)
		tmp = Float64(y * t);
	elseif ((z <= 5.5e+130) || !(z <= 5.5e+282))
		tmp = Float64(z * x);
	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 <= -7.2e+187)
		tmp = z * x;
	elseif (z <= -1.75e-28)
		tmp = t_1;
	elseif (z <= 1.8e-271)
		tmp = x;
	elseif (z <= 7500.0)
		tmp = y * t;
	elseif ((z <= 5.5e+130) || ~((z <= 5.5e+282)))
		tmp = z * x;
	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, -7.2e+187], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.75e-28], t$95$1, If[LessEqual[z, 1.8e-271], x, If[LessEqual[z, 7500.0], N[(y * t), $MachinePrecision], If[Or[LessEqual[z, 5.5e+130], N[Not[LessEqual[z, 5.5e+282]], $MachinePrecision]], N[(z * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.20000000000000072e187 or 7500 < z < 5.4999999999999997e130 or 5.4999999999999999e282 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in z around inf 62.1%

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

   if -7.20000000000000072e187 < z < -1.75e-28 or 5.4999999999999997e130 < z < 5.4999999999999999e282

   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 74.5%

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

      1. mul-1-neg 74.5%

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

      2. unsub-neg 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in x around 0 71.6%

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

   7. Taylor expanded in x around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. *-commutative 49.9%

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

      3. distribute-rgt-neg-in 49.9%

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

   9. Simplified 49.9%

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

   if -1.75e-28 < z < 1.7999999999999999e-271

   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 94.0%

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

      1. *-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in y around 0 42.7%

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

   if 1.7999999999999999e-271 < z < 7500

   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 92.0%

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

      1. *-commutative 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in x around 0 85.5%

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

   7. Taylor expanded in t around inf 43.5%

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

      1. *-commutative 43.5%

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

   9. Simplified 43.5%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+187}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7500:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+130} \lor \neg \left(z \leq 5.5 \cdot 10^{+282}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+118}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-222}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6500:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.18e+118)
   (* z x)
   (if (<= z -3.6e-222)
     (* y t)
     (if (<= z 1.75e-269) x (if (<= z 6500.0) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.18e+118) {
		tmp = z * x;
	} else if (z <= -3.6e-222) {
		tmp = y * t;
	} else if (z <= 1.75e-269) {
		tmp = x;
	} else if (z <= 6500.0) {
		tmp = y * t;
	} 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 <= (-1.18d+118)) then
        tmp = z * x
    else if (z <= (-3.6d-222)) then
        tmp = y * t
    else if (z <= 1.75d-269) then
        tmp = x
    else if (z <= 6500.0d0) then
        tmp = y * t
    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 <= -1.18e+118) {
		tmp = z * x;
	} else if (z <= -3.6e-222) {
		tmp = y * t;
	} else if (z <= 1.75e-269) {
		tmp = x;
	} else if (z <= 6500.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.18e+118:
		tmp = z * x
	elif z <= -3.6e-222:
		tmp = y * t
	elif z <= 1.75e-269:
		tmp = x
	elif z <= 6500.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.18e+118)
		tmp = Float64(z * x);
	elseif (z <= -3.6e-222)
		tmp = Float64(y * t);
	elseif (z <= 1.75e-269)
		tmp = x;
	elseif (z <= 6500.0)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.18e+118)
		tmp = z * x;
	elseif (z <= -3.6e-222)
		tmp = y * t;
	elseif (z <= 1.75e-269)
		tmp = x;
	elseif (z <= 6500.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.18e+118], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.6e-222], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.75e-269], x, If[LessEqual[z, 6500.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1799999999999999e118 or 6500 < 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 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in z around inf 49.0%

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

   if -1.1799999999999999e118 < z < -3.59999999999999974e-222 or 1.75000000000000009e-269 < z < 6500

   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 83.0%

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

      1. *-commutative 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in x around 0 79.8%

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

   7. Taylor expanded in t around inf 38.3%

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

      1. *-commutative 38.3%

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

   9. Simplified 38.3%

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

   if -3.59999999999999974e-222 < z < 1.75000000000000009e-269

   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 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 55.0%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+118}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-222}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-269}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6500:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 420:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.35e-6)
     t_1
     (if (<= z 3.3e-278)
       (* x (- 1.0 y))
       (if (<= z 420.0) (* 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 <= -1.35e-6) {
		tmp = t_1;
	} else if (z <= 3.3e-278) {
		tmp = x * (1.0 - y);
	} else if (z <= 420.0) {
		tmp = 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 <= (-1.35d-6)) then
        tmp = t_1
    else if (z <= 3.3d-278) then
        tmp = x * (1.0d0 - y)
    else if (z <= 420.0d0) then
        tmp = 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 <= -1.35e-6) {
		tmp = t_1;
	} else if (z <= 3.3e-278) {
		tmp = x * (1.0 - y);
	} else if (z <= 420.0) {
		tmp = 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 <= -1.35e-6:
		tmp = t_1
	elif z <= 3.3e-278:
		tmp = x * (1.0 - y)
	elif z <= 420.0:
		tmp = 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 <= -1.35e-6)
		tmp = t_1;
	elseif (z <= 3.3e-278)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 420.0)
		tmp = 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 <= -1.35e-6)
		tmp = t_1;
	elseif (z <= 3.3e-278)
		tmp = x * (1.0 - y);
	elseif (z <= 420.0)
		tmp = 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, -1.35e-6], t$95$1, If[LessEqual[z, 3.3e-278], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 420.0], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999999e-6 or 420 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in x around 0 78.3%

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

   7. Taylor expanded in z around inf 82.4%

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

   if -1.34999999999999999e-6 < z < 3.2999999999999998e-278

   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 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in z around 0 65.6%

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

   if 3.2999999999999998e-278 < z < 420

   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 92.1%

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

      1. *-commutative 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in x around 0 85.7%

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

   7. Taylor expanded in y around inf 69.6%

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

      1. neg-mul-1 69.6%

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

      2. unsub-neg 69.6%

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

   9. Simplified 69.6%

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

Alternative 5: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+35}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.5e+35)
   (* y t)
   (if (<= t -6.5e-245)
     (* x (+ z 1.0))
     (if (<= t 1.3e+74) (* x (- 1.0 y)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.5e+35) {
		tmp = y * t;
	} else if (t <= -6.5e-245) {
		tmp = x * (z + 1.0);
	} else if (t <= 1.3e+74) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-9.5d+35)) then
        tmp = y * t
    else if (t <= (-6.5d-245)) then
        tmp = x * (z + 1.0d0)
    else if (t <= 1.3d+74) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.5e+35) {
		tmp = y * t;
	} else if (t <= -6.5e-245) {
		tmp = x * (z + 1.0);
	} else if (t <= 1.3e+74) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.5e+35:
		tmp = y * t
	elif t <= -6.5e-245:
		tmp = x * (z + 1.0)
	elif t <= 1.3e+74:
		tmp = x * (1.0 - y)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.5e+35)
		tmp = Float64(y * t);
	elseif (t <= -6.5e-245)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (t <= 1.3e+74)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.5e+35)
		tmp = y * t;
	elseif (t <= -6.5e-245)
		tmp = x * (z + 1.0);
	elseif (t <= 1.3e+74)
		tmp = x * (1.0 - y);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.5e+35], N[(y * t), $MachinePrecision], If[LessEqual[t, -6.5e-245], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+74], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000062e35 or 1.3e74 < t

   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 59.9%

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

      1. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in x around 0 53.2%

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

   7. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

   9. Simplified 49.5%

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

   if -9.50000000000000062e35 < t < -6.5000000000000004e-245

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 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%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around 0 57.1%

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

      1. +-commutative 57.1%

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

   8. Simplified 57.1%

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

   if -6.5000000000000004e-245 < t < 1.3e74

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in z around 0 63.8%

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

Alternative 6: 50.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e+44)
   (* y t)
   (if (<= y 5.8e+23)
     (* x (+ z 1.0))
     (if (<= y 1.25e+168) (* y (- x)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e+44) {
		tmp = y * t;
	} else if (y <= 5.8e+23) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.25e+168) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d+44)) then
        tmp = y * t
    else if (y <= 5.8d+23) then
        tmp = x * (z + 1.0d0)
    else if (y <= 1.25d+168) then
        tmp = y * -x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e+44) {
		tmp = y * t;
	} else if (y <= 5.8e+23) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.25e+168) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e+44:
		tmp = y * t
	elif y <= 5.8e+23:
		tmp = x * (z + 1.0)
	elif y <= 1.25e+168:
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e+44)
		tmp = Float64(y * t);
	elseif (y <= 5.8e+23)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 1.25e+168)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e+44)
		tmp = y * t;
	elseif (y <= 5.8e+23)
		tmp = x * (z + 1.0);
	elseif (y <= 1.25e+168)
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e+44], N[(y * t), $MachinePrecision], If[LessEqual[y, 5.8e+23], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+168], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e44 or 1.24999999999999992e168 < 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 84.2%

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

      1. *-commutative 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in x around 0 76.9%

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

   7. Taylor expanded in t around inf 58.4%

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

      1. *-commutative 58.4%

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

   9. Simplified 58.4%

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

   if -3.4e44 < y < 5.80000000000000025e23

   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 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in y around 0 57.5%

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

      1. +-commutative 57.5%

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

   8. Simplified 57.5%

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

   if 5.80000000000000025e23 < y < 1.24999999999999992e168

   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 65.3%

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

      1. mul-1-neg 65.3%

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

      2. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

   8. Simplified 47.6%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-63}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e-63)
   (* y t)
   (if (<= y 5.8e+22) x (if (<= y 5.7e+169) (* y (- x)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-63) {
		tmp = y * t;
	} else if (y <= 5.8e+22) {
		tmp = x;
	} else if (y <= 5.7e+169) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.9d-63)) then
        tmp = y * t
    else if (y <= 5.8d+22) then
        tmp = x
    else if (y <= 5.7d+169) then
        tmp = y * -x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e-63) {
		tmp = y * t;
	} else if (y <= 5.8e+22) {
		tmp = x;
	} else if (y <= 5.7e+169) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.9e-63:
		tmp = y * t
	elif y <= 5.8e+22:
		tmp = x
	elif y <= 5.7e+169:
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e-63)
		tmp = Float64(y * t);
	elseif (y <= 5.8e+22)
		tmp = x;
	elseif (y <= 5.7e+169)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.9e-63)
		tmp = y * t;
	elseif (y <= 5.8e+22)
		tmp = x;
	elseif (y <= 5.7e+169)
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e-63], N[(y * t), $MachinePrecision], If[LessEqual[y, 5.8e+22], x, If[LessEqual[y, 5.7e+169], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.90000000000000022e-63 or 5.7000000000000002e169 < 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 79.4%

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

      1. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in x around 0 73.7%

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

   7. Taylor expanded in t around inf 50.9%

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

      1. *-commutative 50.9%

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

   9. Simplified 50.9%

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

   if -3.90000000000000022e-63 < y < 5.8e22

   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 43.9%

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

      1. *-commutative 43.9%

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

   5. Simplified 43.9%

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

   6. Taylor expanded in y around 0 37.5%

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

   if 5.8e22 < y < 5.7000000000000002e169

   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 65.3%

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

      1. mul-1-neg 65.3%

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

      2. unsub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

   8. Simplified 47.6%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-63}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+54} \lor \neg \left(z \leq 1800\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+54) (not (<= z 1800.0)))
   (* z (- x t))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+54) || !(z <= 1800.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.8d+54)) .or. (.not. (z <= 1800.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+54) || !(z <= 1800.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+54) or not (z <= 1800.0):
		tmp = z * (x - t)
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+54) || !(z <= 1800.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e+54) || ~((z <= 1800.0)))
		tmp = z * (x - t);
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e+54], N[Not[LessEqual[z, 1800.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e54 or 1800 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in x around 0 81.1%

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

   7. Taylor expanded in z around inf 85.7%

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

   if -1.8000000000000001e54 < z < 1800

   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 89.0%

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

      1. *-commutative 89.0%

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

   5. Simplified 89.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+54} \lor \neg \left(z \leq 1800\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.2e+61) t_1 (if (<= z 10.5) (- x (* y (- x 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 <= -1.2e+61) {
		tmp = t_1;
	} else if (z <= 10.5) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-1.2d+61)) then
        tmp = t_1
    else if (z <= 10.5d0) then
        tmp = x - (y * (x - t))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.2e+61) {
		tmp = t_1;
	} else if (z <= 10.5) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.2e+61:
		tmp = t_1
	elif z <= 10.5:
		tmp = x - (y * (x - t))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.2e+61)
		tmp = t_1;
	elseif (z <= 10.5)
		tmp = Float64(x - Float64(y * Float64(x - t)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.2e+61)
		tmp = t_1;
	elseif (z <= 10.5)
		tmp = x - (y * (x - t));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+61], t$95$1, If[LessEqual[z, 10.5], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1999999999999999e61

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in x around 0 81.0%

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

   7. Taylor expanded in z around inf 86.3%

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

   if -1.1999999999999999e61 < z < 10.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.0%

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

      1. *-commutative 89.0%

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

   5. Simplified 89.0%

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

   if 10.5 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. unsub-neg 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-6} \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.35e-6) (not (<= z 1.12e-8))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e-6) || !(z <= 1.12e-8)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.35d-6)) .or. (.not. (z <= 1.12d-8))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e-6) || !(z <= 1.12e-8)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.35e-6) or not (z <= 1.12e-8):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.35e-6) || !(z <= 1.12e-8))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.35e-6) || ~((z <= 1.12e-8)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.35e-6], N[Not[LessEqual[z, 1.12e-8]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999999e-6 or 1.11999999999999994e-8 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around 0 77.7%

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

   7. Taylor expanded in z around inf 81.7%

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

   if -1.34999999999999999e-6 < z < 1.11999999999999994e-8

   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 75.8%

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

   4. Taylor expanded in y around inf 68.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-6} \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -85000 \lor \neg \left(y \leq 3.8 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -85000.0) (not (<= y 3.8e+21))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -85000.0) || !(y <= 3.8e+21)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-85000.0d0)) .or. (.not. (y <= 3.8d+21))) then
        tmp = y * (t - x)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -85000.0) || !(y <= 3.8e+21)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -85000.0) or not (y <= 3.8e+21):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -85000.0) || !(y <= 3.8e+21))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -85000.0) || ~((y <= 3.8e+21)))
		tmp = y * (t - x);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -85000.0], N[Not[LessEqual[y, 3.8e+21]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -85000 or 3.8e21 < 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 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in x around 0 72.8%

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

   7. Taylor expanded in y around inf 78.3%

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

      1. neg-mul-1 78.3%

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

      2. unsub-neg 78.3%

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

   9. Simplified 78.3%

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

   if -85000 < y < 3.8e21

   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 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in y around 0 60.0%

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

      1. +-commutative 60.0%

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

   8. Simplified 60.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -85000 \lor \neg \left(y \leq 3.8 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -380000 \lor \neg \left(z \leq 6 \cdot 10^{-7}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -380000.0) (not (<= z 6e-7))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -380000.0) || !(z <= 6e-7)) {
		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 <= (-380000.0d0)) .or. (.not. (z <= 6d-7))) 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 <= -380000.0) || !(z <= 6e-7)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -380000.0) or not (z <= 6e-7):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -380000.0) || !(z <= 6e-7))
		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 <= -380000.0) || ~((z <= 6e-7)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -380000.0], N[Not[LessEqual[z, 6e-7]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e5 or 5.9999999999999997e-7 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. unsub-neg 51.9%

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

   5. Simplified 51.9%

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

   6. Taylor expanded in z around inf 43.8%

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

   if -3.8e5 < z < 5.9999999999999997e-7

   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 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in y around 0 33.9%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -380000 \lor \neg \left(z \leq 6 \cdot 10^{-7}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 14: 18.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -82000:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y -82000.0) (* y x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -82000.0) {
		tmp = y * 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 (y <= (-82000.0d0)) then
        tmp = y * 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 (y <= -82000.0) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -82000.0:
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -82000.0)
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -82000.0)
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -82000.0], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -82000

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 43.5%

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

      1. mul-1-neg 43.5%

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

      2. unsub-neg 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in y around inf 32.4%

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

      1. mul-1-neg 32.4%

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

   8. Simplified 32.4%

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

      1. add-sqr-sqrt 32.4%

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

      2. sqrt-unprod 33.9%

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

      3. sqr-neg 33.9%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 9.9%

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

      6. pow1 9.9%

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

   10. Applied egg-rr 9.9%

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

       1. unpow1 9.9%

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

   12. Simplified 9.9%

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

   if -82000 < 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 55.6%

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

      1. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in y around 0 24.7%

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

4. Final simplification 21.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -82000:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 17.8% 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 61.6%

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

   1. *-commutative 61.6%

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

5. Simplified 61.6%

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

6. Taylor expanded in y around 0 19.5%

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

Developer Target 1: 96.1% 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 2024152 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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