Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.4s

Alternatives: 14

Speedup: 1.0×

• 35.0% 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: 35.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+48}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1.2e+262)
     t_1
     (if (<= z -2.25e+48)
       (* z x)
       (if (<= z -1.15e-125)
         t_1
         (if (<= z 5e-157) x (if (<= z 3.1e+87) (* y (- x)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.2e+262) {
		tmp = t_1;
	} else if (z <= -2.25e+48) {
		tmp = z * x;
	} else if (z <= -1.15e-125) {
		tmp = t_1;
	} else if (z <= 5e-157) {
		tmp = x;
	} else if (z <= 3.1e+87) {
		tmp = y * -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 <= (-1.2d+262)) then
        tmp = t_1
    else if (z <= (-2.25d+48)) then
        tmp = z * x
    else if (z <= (-1.15d-125)) then
        tmp = t_1
    else if (z <= 5d-157) then
        tmp = x
    else if (z <= 3.1d+87) then
        tmp = y * -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 <= -1.2e+262) {
		tmp = t_1;
	} else if (z <= -2.25e+48) {
		tmp = z * x;
	} else if (z <= -1.15e-125) {
		tmp = t_1;
	} else if (z <= 5e-157) {
		tmp = x;
	} else if (z <= 3.1e+87) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1.2e+262:
		tmp = t_1
	elif z <= -2.25e+48:
		tmp = z * x
	elif z <= -1.15e-125:
		tmp = t_1
	elif z <= 5e-157:
		tmp = x
	elif z <= 3.1e+87:
		tmp = y * -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 <= -1.2e+262)
		tmp = t_1;
	elseif (z <= -2.25e+48)
		tmp = Float64(z * x);
	elseif (z <= -1.15e-125)
		tmp = t_1;
	elseif (z <= 5e-157)
		tmp = x;
	elseif (z <= 3.1e+87)
		tmp = Float64(y * Float64(-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 <= -1.2e+262)
		tmp = t_1;
	elseif (z <= -2.25e+48)
		tmp = z * x;
	elseif (z <= -1.15e-125)
		tmp = t_1;
	elseif (z <= 5e-157)
		tmp = x;
	elseif (z <= 3.1e+87)
		tmp = y * -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, -1.2e+262], t$95$1, If[LessEqual[z, -2.25e+48], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.15e-125], t$95$1, If[LessEqual[z, 5e-157], x, If[LessEqual[z, 3.1e+87], N[(y * (-x)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.19999999999999991e262 or -2.24999999999999998e48 < z < -1.15e-125 or 3.1e87 < 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 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around inf 51.5%

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

   7. Taylor expanded in x around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. *-commutative 47.6%

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

      3. distribute-rgt-neg-in 47.6%

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

   9. Simplified 47.6%

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

   if -1.19999999999999991e262 < z < -2.24999999999999998e48

   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 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in z around inf 54.6%

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

   if -1.15e-125 < z < 5.0000000000000002e-157

   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 96.6%

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

      1. *-commutative 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in y around 0 42.6%

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

   if 5.0000000000000002e-157 < z < 3.1e87

   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 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around inf 43.3%

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

      1. mul-1-neg 43.3%

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

   8. Simplified 43.3%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+262}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+48}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-157}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -13500:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= z -13500.0)
     (* z x)
     (if (<= z -2.45e-101)
       t_1
       (if (<= z 2.7e-159) x (if (<= z 6e+21) t_1 (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -13500.0) {
		tmp = z * x;
	} else if (z <= -2.45e-101) {
		tmp = t_1;
	} else if (z <= 2.7e-159) {
		tmp = x;
	} else if (z <= 6e+21) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (z <= (-13500.0d0)) then
        tmp = z * x
    else if (z <= (-2.45d-101)) then
        tmp = t_1
    else if (z <= 2.7d-159) then
        tmp = x
    else if (z <= 6d+21) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -13500.0) {
		tmp = z * x;
	} else if (z <= -2.45e-101) {
		tmp = t_1;
	} else if (z <= 2.7e-159) {
		tmp = x;
	} else if (z <= 6e+21) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if z <= -13500.0:
		tmp = z * x
	elif z <= -2.45e-101:
		tmp = t_1
	elif z <= 2.7e-159:
		tmp = x
	elif z <= 6e+21:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (z <= -13500.0)
		tmp = Float64(z * x);
	elseif (z <= -2.45e-101)
		tmp = t_1;
	elseif (z <= 2.7e-159)
		tmp = x;
	elseif (z <= 6e+21)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (z <= -13500.0)
		tmp = z * x;
	elseif (z <= -2.45e-101)
		tmp = t_1;
	elseif (z <= 2.7e-159)
		tmp = x;
	elseif (z <= 6e+21)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[z, -13500.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.45e-101], t$95$1, If[LessEqual[z, 2.7e-159], x, If[LessEqual[z, 6e+21], t$95$1, N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -13500 or 6e21 < 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 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in z around inf 46.0%

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

   if -13500 < z < -2.45e-101 or 2.7e-159 < z < 6e21

   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 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in y around inf 46.2%

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

      1. mul-1-neg 46.2%

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

   8. Simplified 46.2%

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

   if -2.45e-101 < z < 2.7e-159

   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 94.5%

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

      1. *-commutative 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in y around 0 40.9%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13500:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -6.4e+28)
     t_1
     (if (<= z 4.5e-173)
       (+ x (* y t))
       (if (<= z 3.5e+24) (* x (+ (- z y) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -6.4e+28) {
		tmp = t_1;
	} else if (z <= 4.5e-173) {
		tmp = x + (y * t);
	} else if (z <= 3.5e+24) {
		tmp = x * ((z - y) + 1.0);
	} 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 <= (-6.4d+28)) then
        tmp = t_1
    else if (z <= 4.5d-173) then
        tmp = x + (y * t)
    else if (z <= 3.5d+24) then
        tmp = x * ((z - y) + 1.0d0)
    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 <= -6.4e+28) {
		tmp = t_1;
	} else if (z <= 4.5e-173) {
		tmp = x + (y * t);
	} else if (z <= 3.5e+24) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -6.4e+28:
		tmp = t_1
	elif z <= 4.5e-173:
		tmp = x + (y * t)
	elif z <= 3.5e+24:
		tmp = x * ((z - y) + 1.0)
	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 <= -6.4e+28)
		tmp = t_1;
	elseif (z <= 4.5e-173)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.5e+24)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	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 <= -6.4e+28)
		tmp = t_1;
	elseif (z <= 4.5e-173)
		tmp = x + (y * t);
	elseif (z <= 3.5e+24)
		tmp = x * ((z - y) + 1.0);
	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, -6.4e+28], t$95$1, If[LessEqual[z, 4.5e-173], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+24], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4000000000000001e28 or 3.5000000000000002e24 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in x around 0 76.2%

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

   7. Taylor expanded in z around inf 84.1%

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

   if -6.4000000000000001e28 < z < 4.50000000000000018e-173

   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 78.8%

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

   4. Taylor expanded in y around inf 70.1%

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

   if 4.50000000000000018e-173 < z < 3.5000000000000002e24

   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 79.4%

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

      1. mul-1-neg 79.4%

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

      2. unsub-neg 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-173}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -6.4e+28)
     t_1
     (if (<= z 2.7e-173)
       (+ x (* y t))
       (if (<= z 3.8e+18) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -6.4e+28) {
		tmp = t_1;
	} else if (z <= 2.7e-173) {
		tmp = x + (y * t);
	} else if (z <= 3.8e+18) {
		tmp = x * (1.0 - y);
	} 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 <= (-6.4d+28)) then
        tmp = t_1
    else if (z <= 2.7d-173) then
        tmp = x + (y * t)
    else if (z <= 3.8d+18) then
        tmp = x * (1.0d0 - y)
    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 <= -6.4e+28) {
		tmp = t_1;
	} else if (z <= 2.7e-173) {
		tmp = x + (y * t);
	} else if (z <= 3.8e+18) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -6.4e+28:
		tmp = t_1
	elif z <= 2.7e-173:
		tmp = x + (y * t)
	elif z <= 3.8e+18:
		tmp = x * (1.0 - y)
	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 <= -6.4e+28)
		tmp = t_1;
	elseif (z <= 2.7e-173)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.8e+18)
		tmp = Float64(x * Float64(1.0 - y));
	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 <= -6.4e+28)
		tmp = t_1;
	elseif (z <= 2.7e-173)
		tmp = x + (y * t);
	elseif (z <= 3.8e+18)
		tmp = x * (1.0 - y);
	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, -6.4e+28], t$95$1, If[LessEqual[z, 2.7e-173], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+18], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4000000000000001e28 or 3.8e18 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in x around 0 76.2%

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

   7. Taylor expanded in z around inf 84.1%

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

   if -6.4000000000000001e28 < z < 2.7e-173

   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 78.8%

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

   4. Taylor expanded in y around inf 70.1%

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

   if 2.7e-173 < z < 3.8e18

   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 79.4%

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

      1. mul-1-neg 79.4%

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

      2. unsub-neg 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in z around 0 76.6%

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

Alternative 6: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-166}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7.2e+28)
     t_1
     (if (<= z -9.5e-166)
       (* y (- t x))
       (if (<= z 3.8e+18) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.2e+28) {
		tmp = t_1;
	} else if (z <= -9.5e-166) {
		tmp = y * (t - x);
	} else if (z <= 3.8e+18) {
		tmp = x * (1.0 - y);
	} 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 <= (-7.2d+28)) then
        tmp = t_1
    else if (z <= (-9.5d-166)) then
        tmp = y * (t - x)
    else if (z <= 3.8d+18) then
        tmp = x * (1.0d0 - y)
    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 <= -7.2e+28) {
		tmp = t_1;
	} else if (z <= -9.5e-166) {
		tmp = y * (t - x);
	} else if (z <= 3.8e+18) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7.2e+28:
		tmp = t_1
	elif z <= -9.5e-166:
		tmp = y * (t - x)
	elif z <= 3.8e+18:
		tmp = x * (1.0 - y)
	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 <= -7.2e+28)
		tmp = t_1;
	elseif (z <= -9.5e-166)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 3.8e+18)
		tmp = Float64(x * Float64(1.0 - y));
	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 <= -7.2e+28)
		tmp = t_1;
	elseif (z <= -9.5e-166)
		tmp = y * (t - x);
	elseif (z <= 3.8e+18)
		tmp = x * (1.0 - y);
	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, -7.2e+28], t$95$1, If[LessEqual[z, -9.5e-166], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+18], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999999e28 or 3.8e18 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in x around 0 76.2%

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

   7. Taylor expanded in z around inf 84.1%

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

   if -7.1999999999999999e28 < z < -9.50000000000000046e-166

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf 94.2%

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

      1. associate-*r* 94.2%

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

      2. mul-1-neg 94.2%

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

   7. Simplified 94.2%

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

      1. associate-+r+ 94.2%

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

      2. distribute-lft-neg-out 94.2%

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

      3. unsub-neg 94.2%

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

      4. *-commutative 94.2%

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

   9. Applied egg-rr 94.2%

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

   10. Taylor expanded in y around inf 58.9%

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

   if -9.50000000000000046e-166 < z < 3.8e18

   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 68.0%

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

      1. mul-1-neg 68.0%

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

      2. unsub-neg 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in z around 0 67.1%

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

Alternative 7: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -9.4 \cdot 10^{+262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.72 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -9.4e+262)
     t_1
     (if (<= z -1.72e-6)
       (* x (+ z 1.0))
       (if (<= z 2.2e+87) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -9.4e+262) {
		tmp = t_1;
	} else if (z <= -1.72e-6) {
		tmp = x * (z + 1.0);
	} else if (z <= 2.2e+87) {
		tmp = x * (1.0 - y);
	} 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 <= (-9.4d+262)) then
        tmp = t_1
    else if (z <= (-1.72d-6)) then
        tmp = x * (z + 1.0d0)
    else if (z <= 2.2d+87) then
        tmp = x * (1.0d0 - y)
    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 <= -9.4e+262) {
		tmp = t_1;
	} else if (z <= -1.72e-6) {
		tmp = x * (z + 1.0);
	} else if (z <= 2.2e+87) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -9.4e+262:
		tmp = t_1
	elif z <= -1.72e-6:
		tmp = x * (z + 1.0)
	elif z <= 2.2e+87:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -9.4e+262)
		tmp = t_1;
	elseif (z <= -1.72e-6)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (z <= 2.2e+87)
		tmp = Float64(x * Float64(1.0 - y));
	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 <= -9.4e+262)
		tmp = t_1;
	elseif (z <= -1.72e-6)
		tmp = x * (z + 1.0);
	elseif (z <= 2.2e+87)
		tmp = x * (1.0 - y);
	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, -9.4e+262], t$95$1, If[LessEqual[z, -1.72e-6], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+87], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.40000000000000029e262 or 2.2000000000000001e87 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in t around inf 55.0%

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

   7. Taylor expanded in x around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. *-commutative 54.6%

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

      3. distribute-rgt-neg-in 54.6%

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

   9. Simplified 54.6%

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

   if -9.40000000000000029e262 < z < -1.72e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. unsub-neg 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 50.7%

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

      1. +-commutative 50.7%

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

   8. Simplified 50.7%

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

   if -1.72e-6 < z < 2.2000000000000001e87

   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 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in z around 0 60.3%

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

Alternative 8: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+28} \lor \neg \left(z \leq 1.56 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.8e+28) (not (<= z 1.56e+22)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e+28) || !(z <= 1.56e+22)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.8d+28)) .or. (.not. (z <= 1.56d+22))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e+28) || !(z <= 1.56e+22)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.8e+28) or not (z <= 1.56e+22):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.8e+28) || !(z <= 1.56e+22))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.8e+28) || ~((z <= 1.56e+22)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.8e+28], N[Not[LessEqual[z, 1.56e+22]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8e28 or 1.56e22 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in x around 0 76.2%

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

   7. Taylor expanded in z around inf 84.1%

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

   if -6.8e28 < z < 1.56e22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.3%

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

      1. *-commutative 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+28} \lor \neg \left(z \leq 1.56 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -0.175:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -0.175) (+ x t_1) (if (<= z 3.9e+20) (+ x (* y (- t x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -0.175) {
		tmp = x + t_1;
	} else if (z <= 3.9e+20) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-0.175d0)) then
        tmp = x + t_1
    else if (z <= 3.9d+20) then
        tmp = x + (y * (t - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -0.175) {
		tmp = x + t_1;
	} else if (z <= 3.9e+20) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -0.175:
		tmp = x + t_1
	elif z <= 3.9e+20:
		tmp = x + (y * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -0.175)
		tmp = Float64(x + t_1);
	elseif (z <= 3.9e+20)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -0.175)
		tmp = x + t_1;
	elseif (z <= 3.9e+20)
		tmp = x + (y * (t - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.175], N[(x + t$95$1), $MachinePrecision], If[LessEqual[z, 3.9e+20], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.17499999999999999

   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 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

   5. Simplified 80.7%

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

   if -0.17499999999999999 < z < 3.9e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.1%

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

      1. *-commutative 91.1%

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

   5. Simplified 91.1%

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

   if 3.9e20 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

   5. Simplified 85.9%

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

   6. Taylor expanded in x around 0 74.8%

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

   7. Taylor expanded in z around inf 85.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.175:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -150000 \lor \neg \left(y \leq 5.4 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -150000.0) (not (<= y 5.4e+63))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -150000.0) || !(y <= 5.4e+63)) {
		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 <= (-150000.0d0)) .or. (.not. (y <= 5.4d+63))) 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 <= -150000.0) || !(y <= 5.4e+63)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -150000.0) or not (y <= 5.4e+63):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -150000.0) || !(y <= 5.4e+63))
		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 <= -150000.0) || ~((y <= 5.4e+63)))
		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, -150000.0], N[Not[LessEqual[y, 5.4e+63]], $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 < -1.5e5 or 5.40000000000000035e63 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 95.5%

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

   4. Applied egg-rr 95.5%

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

   5. Taylor expanded in y around inf 88.3%

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

      1. associate-*r* 88.3%

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

      2. mul-1-neg 88.3%

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

   7. Simplified 88.3%

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

      1. associate-+r+ 88.3%

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

      2. distribute-lft-neg-out 88.3%

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

      3. unsub-neg 88.3%

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

      4. *-commutative 88.3%

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

   9. Applied egg-rr 88.3%

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

   10. Taylor expanded in y around inf 79.8%

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

   if -1.5e5 < y < 5.40000000000000035e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in y around 0 59.4%

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

      1. +-commutative 59.4%

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

   8. Simplified 59.4%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -150000 \lor \neg \left(y \leq 5.4 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-50} \lor \neg \left(t \leq 1.4 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.5e-50) (not (<= t 1.4e+54))) (* z (- t)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.5e-50) || !(t <= 1.4e+54)) {
		tmp = z * -t;
	} 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 ((t <= (-2.5d-50)) .or. (.not. (t <= 1.4d+54))) then
        tmp = z * -t
    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 ((t <= -2.5e-50) || !(t <= 1.4e+54)) {
		tmp = z * -t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.5e-50) or not (t <= 1.4e+54):
		tmp = z * -t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.5e-50) || !(t <= 1.4e+54))
		tmp = Float64(z * Float64(-t));
	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 ((t <= -2.5e-50) || ~((t <= 1.4e+54)))
		tmp = z * -t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.5e-50], N[Not[LessEqual[t, 1.4e+54]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.49999999999999984e-50 or 1.40000000000000008e54 < 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 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in t around inf 49.9%

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

   7. Taylor expanded in x around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

   9. Simplified 44.4%

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

   if -2.49999999999999984e-50 < t < 1.40000000000000008e54

   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 83.5%

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

      1. mul-1-neg 83.5%

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

      2. unsub-neg 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in y around 0 62.2%

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

      1. +-commutative 62.2%

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

   8. Simplified 62.2%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-50} \lor \neg \left(t \leq 1.4 \cdot 10^{+54}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \lor \neg \left(z \leq 1.6 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02) (not (<= z 1.6e-15))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02) || !(z <= 1.6e-15)) {
		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 <= (-1.02d0)) .or. (.not. (z <= 1.6d-15))) 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 <= -1.02) || !(z <= 1.6e-15)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02) or not (z <= 1.6e-15):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02) || !(z <= 1.6e-15))
		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 <= -1.02) || ~((z <= 1.6e-15)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02], N[Not[LessEqual[z, 1.6e-15]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.02 or 1.6e-15 < 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 54.3%

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

      1. mul-1-neg 54.3%

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

      2. unsub-neg 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in z around inf 44.3%

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

   if -1.02 < z < 1.6e-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 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in y around 0 37.0%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \lor \neg \left(z \leq 1.6 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 17.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 58.2%

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

   1. *-commutative 58.2%

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

5. Simplified 58.2%

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

6. Taylor expanded in y around 0 18.8%

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

Developer Target 1: 96.0% 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 2024130 
(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))))