Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 10

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-272}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (+ x (* (- y z) t))))
   (if (<= t -2.3e-35)
     t_2
     (if (<= t -5.4e-144)
       t_1
       (if (<= t -4.5e-170)
         t_2
         (if (<= t 1.4e-272) (- x (* x y)) (if (<= t 2.8e-37) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (t <= -2.3e-35) {
		tmp = t_2;
	} else if (t <= -5.4e-144) {
		tmp = t_1;
	} else if (t <= -4.5e-170) {
		tmp = t_2;
	} else if (t <= 1.4e-272) {
		tmp = x - (x * y);
	} else if (t <= 2.8e-37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = x + ((y - z) * t)
    if (t <= (-2.3d-35)) then
        tmp = t_2
    else if (t <= (-5.4d-144)) then
        tmp = t_1
    else if (t <= (-4.5d-170)) then
        tmp = t_2
    else if (t <= 1.4d-272) then
        tmp = x - (x * y)
    else if (t <= 2.8d-37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (t <= -2.3e-35) {
		tmp = t_2;
	} else if (t <= -5.4e-144) {
		tmp = t_1;
	} else if (t <= -4.5e-170) {
		tmp = t_2;
	} else if (t <= 1.4e-272) {
		tmp = x - (x * y);
	} else if (t <= 2.8e-37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if t <= -2.3e-35:
		tmp = t_2
	elif t <= -5.4e-144:
		tmp = t_1
	elif t <= -4.5e-170:
		tmp = t_2
	elif t <= 1.4e-272:
		tmp = x - (x * y)
	elif t <= 2.8e-37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -2.3e-35)
		tmp = t_2;
	elseif (t <= -5.4e-144)
		tmp = t_1;
	elseif (t <= -4.5e-170)
		tmp = t_2;
	elseif (t <= 1.4e-272)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 2.8e-37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -2.3e-35)
		tmp = t_2;
	elseif (t <= -5.4e-144)
		tmp = t_1;
	elseif (t <= -4.5e-170)
		tmp = t_2;
	elseif (t <= 1.4e-272)
		tmp = x - (x * y);
	elseif (t <= 2.8e-37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-35], t$95$2, If[LessEqual[t, -5.4e-144], t$95$1, If[LessEqual[t, -4.5e-170], t$95$2, If[LessEqual[t, 1.4e-272], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-37], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2999999999999999e-35 or -5.3999999999999995e-144 < t < -4.50000000000000002e-170 or 2.8000000000000001e-37 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.5%

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

   if -2.2999999999999999e-35 < t < -5.3999999999999995e-144 or 1.39999999999999997e-272 < t < 2.8000000000000001e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.1%

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

      1. mul-1-neg 76.1%

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

      2. distribute-lft-neg-out 76.1%

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

      3. *-commutative 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in t around 0 68.3%

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

   if -4.50000000000000002e-170 < t < 1.39999999999999997e-272

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-lft-neg-out 92.2%

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

      3. *-commutative 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in z around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-35}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-144}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-170}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-272}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-37}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 3: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+67} \lor \neg \left(z \leq -6.8 \cdot 10^{+34}\right) \land \left(z \leq -5.2 \cdot 10^{+19} \lor \neg \left(z \leq 2.2 \cdot 10^{+94}\right)\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.05e+67)
         (and (not (<= z -6.8e+34)) (or (<= z -5.2e+19) (not (<= z 2.2e+94)))))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.05e+67) || (!(z <= -6.8e+34) && ((z <= -5.2e+19) || !(z <= 2.2e+94)))) {
		tmp = x + (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 <= (-2.05d+67)) .or. (.not. (z <= (-6.8d+34))) .and. (z <= (-5.2d+19)) .or. (.not. (z <= 2.2d+94))) then
        tmp = x + (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 <= -2.05e+67) || (!(z <= -6.8e+34) && ((z <= -5.2e+19) || !(z <= 2.2e+94)))) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.05e+67) or (not (z <= -6.8e+34) and ((z <= -5.2e+19) or not (z <= 2.2e+94))):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.05e+67) || (!(z <= -6.8e+34) && ((z <= -5.2e+19) || !(z <= 2.2e+94))))
		tmp = Float64(x + 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 <= -2.05e+67) || (~((z <= -6.8e+34)) && ((z <= -5.2e+19) || ~((z <= 2.2e+94)))))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.05e+67], And[N[Not[LessEqual[z, -6.8e+34]], $MachinePrecision], Or[LessEqual[z, -5.2e+19], N[Not[LessEqual[z, 2.2e+94]], $MachinePrecision]]]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0499999999999999e67 or -6.7999999999999999e34 < z < -5.2e19 or 2.20000000000000012e94 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. distribute-lft-neg-out 85.4%

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

      3. *-commutative 85.4%

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

   4. Simplified 85.4%

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

   if -2.0499999999999999e67 < z < -6.7999999999999999e34 or -5.2e19 < z < 2.20000000000000012e94

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.6%

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

      1. *-commutative 90.6%

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

   4. Simplified 90.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+67} \lor \neg \left(z \leq -6.8 \cdot 10^{+34}\right) \land \left(z \leq -5.2 \cdot 10^{+19} \lor \neg \left(z \leq 2.2 \cdot 10^{+94}\right)\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 54.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= z -9.6e+68)
     t_1
     (if (<= z 1.75e+16)
       (+ x (* y t))
       (if (<= z 2.5e+96)
         (- x (* x y))
         (if (<= z 1.45e+165) t_1 (+ x (* x z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (z <= -9.6e+68) {
		tmp = t_1;
	} else if (z <= 1.75e+16) {
		tmp = x + (y * t);
	} else if (z <= 2.5e+96) {
		tmp = x - (x * y);
	} else if (z <= 1.45e+165) {
		tmp = t_1;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (z * t)
    if (z <= (-9.6d+68)) then
        tmp = t_1
    else if (z <= 1.75d+16) then
        tmp = x + (y * t)
    else if (z <= 2.5d+96) then
        tmp = x - (x * y)
    else if (z <= 1.45d+165) then
        tmp = t_1
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (z <= -9.6e+68) {
		tmp = t_1;
	} else if (z <= 1.75e+16) {
		tmp = x + (y * t);
	} else if (z <= 2.5e+96) {
		tmp = x - (x * y);
	} else if (z <= 1.45e+165) {
		tmp = t_1;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if z <= -9.6e+68:
		tmp = t_1
	elif z <= 1.75e+16:
		tmp = x + (y * t)
	elif z <= 2.5e+96:
		tmp = x - (x * y)
	elif z <= 1.45e+165:
		tmp = t_1
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (z <= -9.6e+68)
		tmp = t_1;
	elseif (z <= 1.75e+16)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 2.5e+96)
		tmp = Float64(x - Float64(x * y));
	elseif (z <= 1.45e+165)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	tmp = 0.0;
	if (z <= -9.6e+68)
		tmp = t_1;
	elseif (z <= 1.75e+16)
		tmp = x + (y * t);
	elseif (z <= 2.5e+96)
		tmp = x - (x * y);
	elseif (z <= 1.45e+165)
		tmp = t_1;
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+68], t$95$1, If[LessEqual[z, 1.75e+16], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+96], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+165], t$95$1, N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.60000000000000031e68 or 2.5000000000000002e96 < z < 1.45000000000000003e165

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 63.5%

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

   3. Taylor expanded in y around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. unsub-neg 52.7%

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

      3. *-commutative 52.7%

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

   5. Simplified 52.7%

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

   if -9.60000000000000031e68 < z < 1.75e16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.1%

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

      1. *-commutative 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in t around inf 71.3%

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

      1. *-commutative 71.3%

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

   7. Simplified 71.3%

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

   if 1.75e16 < z < 2.5000000000000002e96

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. distribute-lft-neg-out 70.4%

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

      3. *-commutative 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in z around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   7. Simplified 53.4%

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

   if 1.45000000000000003e165 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. distribute-lft-neg-out 88.5%

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

      3. *-commutative 88.5%

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

   4. Simplified 88.5%

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

   5. Taylor expanded in t around 0 54.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+68}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+165}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 5: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ \mathbf{if}\;t \leq -6 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-274}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))))
   (if (<= t -6e-63)
     t_1
     (if (<= t 2.1e-274)
       (- x (* x y))
       (if (<= t 1.3e+51) (+ x (* x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double tmp;
	if (t <= -6e-63) {
		tmp = t_1;
	} else if (t <= 2.1e-274) {
		tmp = x - (x * y);
	} else if (t <= 1.3e+51) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * t)
    if (t <= (-6d-63)) then
        tmp = t_1
    else if (t <= 2.1d-274) then
        tmp = x - (x * y)
    else if (t <= 1.3d+51) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double tmp;
	if (t <= -6e-63) {
		tmp = t_1;
	} else if (t <= 2.1e-274) {
		tmp = x - (x * y);
	} else if (t <= 1.3e+51) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	tmp = 0
	if t <= -6e-63:
		tmp = t_1
	elif t <= 2.1e-274:
		tmp = x - (x * y)
	elif t <= 1.3e+51:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (t <= -6e-63)
		tmp = t_1;
	elseif (t <= 2.1e-274)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 1.3e+51)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	tmp = 0.0;
	if (t <= -6e-63)
		tmp = t_1;
	elseif (t <= 2.1e-274)
		tmp = x - (x * y);
	elseif (t <= 1.3e+51)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6e-63], t$95$1, If[LessEqual[t, 2.1e-274], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+51], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.99999999999999959e-63 or 1.3000000000000001e51 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 62.1%

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

      1. *-commutative 62.1%

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

   4. Simplified 62.1%

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

   5. Taylor expanded in t around inf 54.3%

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

      1. *-commutative 54.3%

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

   7. Simplified 54.3%

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

   if -5.99999999999999959e-63 < t < 2.09999999999999994e-274

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. distribute-lft-neg-out 85.8%

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

      3. *-commutative 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   7. Simplified 67.2%

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

   if 2.09999999999999994e-274 < t < 1.3000000000000001e51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-lft-neg-out 75.5%

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

      3. *-commutative 75.5%

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

   4. Simplified 75.5%

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

   5. Taylor expanded in t around 0 62.7%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-274}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+51}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 6: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-13} \lor \neg \left(t \leq 1.95 \cdot 10^{+51}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-13) (not (<= t 1.95e+51)))
   (+ x (* t (- y z)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-13) || !(t <= 1.95e+51)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.5d-13)) .or. (.not. (t <= 1.95d+51))) then
        tmp = x + (t * (y - z))
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-13) || !(t <= 1.95e+51)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-13) or not (t <= 1.95e+51):
		tmp = x + (t * (y - z))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-13) || !(t <= 1.95e+51))
		tmp = Float64(x + Float64(t * Float64(y - z)));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e-13) || ~((t <= 1.95e+51)))
		tmp = x + (t * (y - z));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-13], N[Not[LessEqual[t, 1.95e+51]], $MachinePrecision]], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5000000000000002e-13 or 1.94999999999999992e51 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.9%

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

   if -3.5000000000000002e-13 < t < 1.94999999999999992e51

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.5%

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

   3. Applied egg-rr 95.5%

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

   4. Taylor expanded in t around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-in 76.2%

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

      3. mul-1-neg 76.2%

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

      4. distribute-lft-in 80.7%

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

      5. +-commutative 80.7%

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

      6. mul-1-neg 80.7%

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

      7. sub-neg 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-13} \lor \neg \left(t \leq 1.95 \cdot 10^{+51}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 7: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+25} \lor \neg \left(y \leq 5.5 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.4e+25) (not (<= y 5.5e+57))) (* y t) (+ x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e+25) || !(y <= 5.5e+57)) {
		tmp = y * t;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.4d+25)) .or. (.not. (y <= 5.5d+57))) then
        tmp = y * t
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e+25) || !(y <= 5.5e+57)) {
		tmp = y * t;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.4e+25) or not (y <= 5.5e+57):
		tmp = y * t
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.4e+25) || !(y <= 5.5e+57))
		tmp = Float64(y * t);
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.4e+25) || ~((y <= 5.5e+57)))
		tmp = y * t;
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.4e+25], N[Not[LessEqual[y, 5.5e+57]], $MachinePrecision]], N[(y * t), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3999999999999999e25 or 5.5000000000000002e57 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.2%

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

      1. *-commutative 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in t around inf 47.9%

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

      1. *-commutative 47.9%

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

   7. Simplified 47.9%

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

   8. Taylor expanded in x around 0 47.5%

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

   if -6.3999999999999999e25 < y < 5.5000000000000002e57

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-lft-neg-out 89.8%

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

      3. *-commutative 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in t around 0 61.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+25} \lor \neg \left(y \leq 5.5 \cdot 10^{+57}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 8: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-35} \lor \neg \left(t \leq 2.55 \cdot 10^{+51}\right):\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.4e-35) (not (<= t 2.55e+51))) (+ x (* y t)) (+ x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.4e-35) || !(t <= 2.55e+51)) {
		tmp = x + (y * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8.4d-35)) .or. (.not. (t <= 2.55d+51))) then
        tmp = x + (y * t)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.4e-35) || !(t <= 2.55e+51)) {
		tmp = x + (y * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.4e-35) or not (t <= 2.55e+51):
		tmp = x + (y * t)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.4e-35) || !(t <= 2.55e+51))
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.4e-35) || ~((t <= 2.55e+51)))
		tmp = x + (y * t);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.4e-35], N[Not[LessEqual[t, 2.55e+51]], $MachinePrecision]], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.3999999999999999e-35 or 2.55000000000000005e51 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 63.5%

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

      1. *-commutative 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in t around inf 55.2%

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

      1. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -8.3999999999999999e-35 < t < 2.55000000000000005e51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-lft-neg-out 69.9%

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

      3. *-commutative 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in t around 0 58.7%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{-35} \lor \neg \left(t \leq 2.55 \cdot 10^{+51}\right):\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 9: 37.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+22} \lor \neg \left(y \leq 0.0038\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+22) (not (<= y 0.0038))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+22) || !(y <= 0.0038)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.8d+22)) .or. (.not. (y <= 0.0038d0))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+22) || !(y <= 0.0038)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e+22) or not (y <= 0.0038):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+22) || !(y <= 0.0038))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.8e+22) || ~((y <= 0.0038)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+22], N[Not[LessEqual[y, 0.0038]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e22 or 0.00379999999999999999 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 74.4%

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

      1. *-commutative 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in t around inf 45.6%

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

      1. *-commutative 45.6%

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

   7. Simplified 45.6%

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

   8. Taylor expanded in x around 0 45.2%

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

   if -1.8e22 < y < 0.00379999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.8%

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

   3. Taylor expanded in x around inf 41.4%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+22} \lor \neg \left(y \leq 0.0038\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 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. Taylor expanded in t around inf 67.4%

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

3. Taylor expanded in x around inf 21.9%

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

4. Final simplification 21.9%

   \[\leadsto x \]

Developer target: 96.2% 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 2023332 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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