Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.5s

Alternatives: 12

Speedup: 1.0×

• 33.7% 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: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + x \cdot z\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -8000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+278}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* x z))) (t_3 (+ x (* y t))))
   (if (<= z -8000000.0)
     t_2
     (if (<= z -4.7e-228)
       t_3
       (if (<= z 4.4e-129)
         t_1
         (if (<= z 4e-61)
           t_3
           (if (<= z 1.1e+72) t_1 (if (<= z 2.65e+278) (* t (- z)) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -8000000.0) {
		tmp = t_2;
	} else if (z <= -4.7e-228) {
		tmp = t_3;
	} else if (z <= 4.4e-129) {
		tmp = t_1;
	} else if (z <= 4e-61) {
		tmp = t_3;
	} else if (z <= 1.1e+72) {
		tmp = t_1;
	} else if (z <= 2.65e+278) {
		tmp = t * -z;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (x * z)
    t_3 = x + (y * t)
    if (z <= (-8000000.0d0)) then
        tmp = t_2
    else if (z <= (-4.7d-228)) then
        tmp = t_3
    else if (z <= 4.4d-129) then
        tmp = t_1
    else if (z <= 4d-61) then
        tmp = t_3
    else if (z <= 1.1d+72) then
        tmp = t_1
    else if (z <= 2.65d+278) then
        tmp = t * -z
    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 * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -8000000.0) {
		tmp = t_2;
	} else if (z <= -4.7e-228) {
		tmp = t_3;
	} else if (z <= 4.4e-129) {
		tmp = t_1;
	} else if (z <= 4e-61) {
		tmp = t_3;
	} else if (z <= 1.1e+72) {
		tmp = t_1;
	} else if (z <= 2.65e+278) {
		tmp = t * -z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (x * z)
	t_3 = x + (y * t)
	tmp = 0
	if z <= -8000000.0:
		tmp = t_2
	elif z <= -4.7e-228:
		tmp = t_3
	elif z <= 4.4e-129:
		tmp = t_1
	elif z <= 4e-61:
		tmp = t_3
	elif z <= 1.1e+72:
		tmp = t_1
	elif z <= 2.65e+278:
		tmp = t * -z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(x * z))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -8000000.0)
		tmp = t_2;
	elseif (z <= -4.7e-228)
		tmp = t_3;
	elseif (z <= 4.4e-129)
		tmp = t_1;
	elseif (z <= 4e-61)
		tmp = t_3;
	elseif (z <= 1.1e+72)
		tmp = t_1;
	elseif (z <= 2.65e+278)
		tmp = Float64(t * Float64(-z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (x * z);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -8000000.0)
		tmp = t_2;
	elseif (z <= -4.7e-228)
		tmp = t_3;
	elseif (z <= 4.4e-129)
		tmp = t_1;
	elseif (z <= 4e-61)
		tmp = t_3;
	elseif (z <= 1.1e+72)
		tmp = t_1;
	elseif (z <= 2.65e+278)
		tmp = t * -z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8000000.0], t$95$2, If[LessEqual[z, -4.7e-228], t$95$3, If[LessEqual[z, 4.4e-129], t$95$1, If[LessEqual[z, 4e-61], t$95$3, If[LessEqual[z, 1.1e+72], t$95$1, If[LessEqual[z, 2.65e+278], N[(t * (-z)), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8e6 or 2.64999999999999996e278 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-lft-neg-out 84.6%

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

      3. *-commutative 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in t around 0 54.2%

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

   if -8e6 < z < -4.7000000000000002e-228 or 4.40000000000000006e-129 < z < 4.0000000000000002e-61

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 88.8%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   if -4.7000000000000002e-228 < z < 4.40000000000000006e-129 or 4.0000000000000002e-61 < z < 1.1e72

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.6%

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

      1. *-commutative 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in x around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

   7. Simplified 71.2%

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

   if 1.1e72 < z < 2.64999999999999996e278

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.0%

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

   3. Taylor expanded in y around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

      3. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in x around 0 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8000000:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-228}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-129}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+278}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 3: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + x \cdot z\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+280}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* x z))) (t_3 (+ x (* y t))))
   (if (<= z -0.42)
     t_2
     (if (<= z -1.12e-225)
       t_3
       (if (<= z 1.8e-128)
         t_1
         (if (<= z 3.1e-61)
           t_3
           (if (<= z 1.4e+78) t_1 (if (<= z 1.1e+280) (- x (* z t)) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -0.42) {
		tmp = t_2;
	} else if (z <= -1.12e-225) {
		tmp = t_3;
	} else if (z <= 1.8e-128) {
		tmp = t_1;
	} else if (z <= 3.1e-61) {
		tmp = t_3;
	} else if (z <= 1.4e+78) {
		tmp = t_1;
	} else if (z <= 1.1e+280) {
		tmp = x - (z * t);
	} 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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (x * z)
    t_3 = x + (y * t)
    if (z <= (-0.42d0)) then
        tmp = t_2
    else if (z <= (-1.12d-225)) then
        tmp = t_3
    else if (z <= 1.8d-128) then
        tmp = t_1
    else if (z <= 3.1d-61) then
        tmp = t_3
    else if (z <= 1.4d+78) then
        tmp = t_1
    else if (z <= 1.1d+280) then
        tmp = x - (z * t)
    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 * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -0.42) {
		tmp = t_2;
	} else if (z <= -1.12e-225) {
		tmp = t_3;
	} else if (z <= 1.8e-128) {
		tmp = t_1;
	} else if (z <= 3.1e-61) {
		tmp = t_3;
	} else if (z <= 1.4e+78) {
		tmp = t_1;
	} else if (z <= 1.1e+280) {
		tmp = x - (z * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (x * z)
	t_3 = x + (y * t)
	tmp = 0
	if z <= -0.42:
		tmp = t_2
	elif z <= -1.12e-225:
		tmp = t_3
	elif z <= 1.8e-128:
		tmp = t_1
	elif z <= 3.1e-61:
		tmp = t_3
	elif z <= 1.4e+78:
		tmp = t_1
	elif z <= 1.1e+280:
		tmp = x - (z * t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(x * z))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -0.42)
		tmp = t_2;
	elseif (z <= -1.12e-225)
		tmp = t_3;
	elseif (z <= 1.8e-128)
		tmp = t_1;
	elseif (z <= 3.1e-61)
		tmp = t_3;
	elseif (z <= 1.4e+78)
		tmp = t_1;
	elseif (z <= 1.1e+280)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (x * z);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -0.42)
		tmp = t_2;
	elseif (z <= -1.12e-225)
		tmp = t_3;
	elseif (z <= 1.8e-128)
		tmp = t_1;
	elseif (z <= 3.1e-61)
		tmp = t_3;
	elseif (z <= 1.4e+78)
		tmp = t_1;
	elseif (z <= 1.1e+280)
		tmp = x - (z * t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.42], t$95$2, If[LessEqual[z, -1.12e-225], t$95$3, If[LessEqual[z, 1.8e-128], t$95$1, If[LessEqual[z, 3.1e-61], t$95$3, If[LessEqual[z, 1.4e+78], t$95$1, If[LessEqual[z, 1.1e+280], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.419999999999999984 or 1.10000000000000008e280 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-lft-neg-out 84.6%

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

      3. *-commutative 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in t around 0 54.2%

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

   if -0.419999999999999984 < z < -1.12000000000000003e-225 or 1.80000000000000012e-128 < z < 3.09999999999999995e-61

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 88.8%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   if -1.12000000000000003e-225 < z < 1.80000000000000012e-128 or 3.09999999999999995e-61 < z < 1.4000000000000001e78

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.6%

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

      1. *-commutative 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in x around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

   7. Simplified 71.2%

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

   if 1.4000000000000001e78 < z < 1.10000000000000008e280

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.0%

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

   3. Taylor expanded in y around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

      3. *-commutative 52.1%

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

   5. Simplified 52.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-225}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+280}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 4: 51.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -22000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-128}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+279}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (+ x (* y t))))
   (if (<= z -22000000.0)
     t_1
     (if (<= z -7.5e-231)
       t_2
       (if (<= z 1.55e-128)
         (- x (* x y))
         (if (<= z 3.6e-61)
           t_2
           (if (<= z 3.1e+62)
             (* x (- 1.0 y))
             (if (<= z 1.5e+279) (- x (* z t)) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -22000000.0) {
		tmp = t_1;
	} else if (z <= -7.5e-231) {
		tmp = t_2;
	} else if (z <= 1.55e-128) {
		tmp = x - (x * y);
	} else if (z <= 3.6e-61) {
		tmp = t_2;
	} else if (z <= 3.1e+62) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.5e+279) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = x + (y * t)
    if (z <= (-22000000.0d0)) then
        tmp = t_1
    else if (z <= (-7.5d-231)) then
        tmp = t_2
    else if (z <= 1.55d-128) then
        tmp = x - (x * y)
    else if (z <= 3.6d-61) then
        tmp = t_2
    else if (z <= 3.1d+62) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1.5d+279) then
        tmp = x - (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -22000000.0) {
		tmp = t_1;
	} else if (z <= -7.5e-231) {
		tmp = t_2;
	} else if (z <= 1.55e-128) {
		tmp = x - (x * y);
	} else if (z <= 3.6e-61) {
		tmp = t_2;
	} else if (z <= 3.1e+62) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.5e+279) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -22000000.0:
		tmp = t_1
	elif z <= -7.5e-231:
		tmp = t_2
	elif z <= 1.55e-128:
		tmp = x - (x * y)
	elif z <= 3.6e-61:
		tmp = t_2
	elif z <= 3.1e+62:
		tmp = x * (1.0 - y)
	elif z <= 1.5e+279:
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -22000000.0)
		tmp = t_1;
	elseif (z <= -7.5e-231)
		tmp = t_2;
	elseif (z <= 1.55e-128)
		tmp = Float64(x - Float64(x * y));
	elseif (z <= 3.6e-61)
		tmp = t_2;
	elseif (z <= 3.1e+62)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1.5e+279)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -22000000.0)
		tmp = t_1;
	elseif (z <= -7.5e-231)
		tmp = t_2;
	elseif (z <= 1.55e-128)
		tmp = x - (x * y);
	elseif (z <= 3.6e-61)
		tmp = t_2;
	elseif (z <= 3.1e+62)
		tmp = x * (1.0 - y);
	elseif (z <= 1.5e+279)
		tmp = x - (z * t);
	else
		tmp = t_1;
	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[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -22000000.0], t$95$1, If[LessEqual[z, -7.5e-231], t$95$2, If[LessEqual[z, 1.55e-128], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-61], t$95$2, If[LessEqual[z, 3.1e+62], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+279], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2e7 or 1.4999999999999999e279 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-lft-neg-out 84.6%

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

      3. *-commutative 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in t around 0 54.2%

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

   if -2.2e7 < z < -7.5000000000000001e-231 or 1.55000000000000001e-128 < z < 3.60000000000000014e-61

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 88.8%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   if -7.5000000000000001e-231 < z < 1.55000000000000001e-128

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.4%

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

      1. *-commutative 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-lft-neg-out 78.1%

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

      3. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   if 3.60000000000000014e-61 < z < 3.10000000000000014e62

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 84.6%

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

      1. *-commutative 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

   7. Simplified 58.3%

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

   if 3.10000000000000014e62 < z < 1.4999999999999999e279

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.0%

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

   3. Taylor expanded in y around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

      3. *-commutative 52.1%

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

   5. Simplified 52.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22000000:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-231}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-128}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-61}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+62}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+279}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 5: 45.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-14}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-226}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* t (- z))))
   (if (<= z -1.8e+146)
     t_2
     (if (<= z -2.8e-14)
       (* y t)
       (if (<= z -7.5e-106)
         t_1
         (if (<= z -6.2e-226) (* y t) (if (<= z 5.8e+71) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = t * -z;
	double tmp;
	if (z <= -1.8e+146) {
		tmp = t_2;
	} else if (z <= -2.8e-14) {
		tmp = y * t;
	} else if (z <= -7.5e-106) {
		tmp = t_1;
	} else if (z <= -6.2e-226) {
		tmp = y * t;
	} else if (z <= 5.8e+71) {
		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 * (1.0d0 - y)
    t_2 = t * -z
    if (z <= (-1.8d+146)) then
        tmp = t_2
    else if (z <= (-2.8d-14)) then
        tmp = y * t
    else if (z <= (-7.5d-106)) then
        tmp = t_1
    else if (z <= (-6.2d-226)) then
        tmp = y * t
    else if (z <= 5.8d+71) 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 * (1.0 - y);
	double t_2 = t * -z;
	double tmp;
	if (z <= -1.8e+146) {
		tmp = t_2;
	} else if (z <= -2.8e-14) {
		tmp = y * t;
	} else if (z <= -7.5e-106) {
		tmp = t_1;
	} else if (z <= -6.2e-226) {
		tmp = y * t;
	} else if (z <= 5.8e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = t * -z
	tmp = 0
	if z <= -1.8e+146:
		tmp = t_2
	elif z <= -2.8e-14:
		tmp = y * t
	elif z <= -7.5e-106:
		tmp = t_1
	elif z <= -6.2e-226:
		tmp = y * t
	elif z <= 5.8e+71:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -1.8e+146)
		tmp = t_2;
	elseif (z <= -2.8e-14)
		tmp = Float64(y * t);
	elseif (z <= -7.5e-106)
		tmp = t_1;
	elseif (z <= -6.2e-226)
		tmp = Float64(y * t);
	elseif (z <= 5.8e+71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = t * -z;
	tmp = 0.0;
	if (z <= -1.8e+146)
		tmp = t_2;
	elseif (z <= -2.8e-14)
		tmp = y * t;
	elseif (z <= -7.5e-106)
		tmp = t_1;
	elseif (z <= -6.2e-226)
		tmp = y * t;
	elseif (z <= 5.8e+71)
		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[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.8e+146], t$95$2, If[LessEqual[z, -2.8e-14], N[(y * t), $MachinePrecision], If[LessEqual[z, -7.5e-106], t$95$1, If[LessEqual[z, -6.2e-226], N[(y * t), $MachinePrecision], If[LessEqual[z, 5.8e+71], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e146 or 5.80000000000000014e71 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 56.2%

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

   3. Taylor expanded in y around 0 50.2%

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

      1. mul-1-neg 50.2%

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

      2. unsub-neg 50.2%

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

      3. *-commutative 50.2%

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

   5. Simplified 50.2%

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

   6. Taylor expanded in x around 0 49.7%

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

      1. associate-*r* 49.7%

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

      2. neg-mul-1 49.7%

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

   8. Simplified 49.7%

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

   if -1.7999999999999999e146 < z < -2.8000000000000001e-14 or -7.5000000000000002e-106 < z < -6.19999999999999978e-226

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 61.0%

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

      1. *-commutative 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in x around 0 48.7%

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

   if -2.8000000000000001e-14 < z < -7.5000000000000002e-106 or -6.19999999999999978e-226 < z < 5.80000000000000014e71

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.2%

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

      1. *-commutative 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in x around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. unsub-neg 64.8%

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

   7. Simplified 64.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-14}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-226}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]

Alternative 6: 44.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-222}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+279}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))))
   (if (<= z -2.25e-46)
     t_1
     (if (<= z -2.45e-222)
       (* y t)
       (if (<= z 9.5e+78)
         (* x (- 1.0 y))
         (if (<= z 3.2e+279) (* t (- z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double tmp;
	if (z <= -2.25e-46) {
		tmp = t_1;
	} else if (z <= -2.45e-222) {
		tmp = y * t;
	} else if (z <= 9.5e+78) {
		tmp = x * (1.0 - y);
	} else if (z <= 3.2e+279) {
		tmp = t * -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 + (x * z)
    if (z <= (-2.25d-46)) then
        tmp = t_1
    else if (z <= (-2.45d-222)) then
        tmp = y * t
    else if (z <= 9.5d+78) then
        tmp = x * (1.0d0 - y)
    else if (z <= 3.2d+279) then
        tmp = t * -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 + (x * z);
	double tmp;
	if (z <= -2.25e-46) {
		tmp = t_1;
	} else if (z <= -2.45e-222) {
		tmp = y * t;
	} else if (z <= 9.5e+78) {
		tmp = x * (1.0 - y);
	} else if (z <= 3.2e+279) {
		tmp = t * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	tmp = 0
	if z <= -2.25e-46:
		tmp = t_1
	elif z <= -2.45e-222:
		tmp = y * t
	elif z <= 9.5e+78:
		tmp = x * (1.0 - y)
	elif z <= 3.2e+279:
		tmp = t * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (z <= -2.25e-46)
		tmp = t_1;
	elseif (z <= -2.45e-222)
		tmp = Float64(y * t);
	elseif (z <= 9.5e+78)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 3.2e+279)
		tmp = Float64(t * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	tmp = 0.0;
	if (z <= -2.25e-46)
		tmp = t_1;
	elseif (z <= -2.45e-222)
		tmp = y * t;
	elseif (z <= 9.5e+78)
		tmp = x * (1.0 - y);
	elseif (z <= 3.2e+279)
		tmp = t * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-46], t$95$1, If[LessEqual[z, -2.45e-222], N[(y * t), $MachinePrecision], If[LessEqual[z, 9.5e+78], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+279], N[(t * (-z)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.25e-46 or 3.19999999999999988e279 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. distribute-lft-neg-out 81.0%

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

      3. *-commutative 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in t around 0 52.3%

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

   if -2.25e-46 < z < -2.45e-222

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.0%

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

      1. *-commutative 78.0%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in x around 0 54.8%

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

   if -2.45e-222 < z < 9.5000000000000006e78

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in x around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

   7. Simplified 65.9%

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

   if 9.5000000000000006e78 < z < 3.19999999999999988e279

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.0%

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

   3. Taylor expanded in y around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

      3. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in x around 0 51.4%

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

      1. associate-*r* 51.4%

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

      2. neg-mul-1 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-222}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+279}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 7: 69.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+85}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e+241)
   (* x (- 1.0 y))
   (if (<= x -1.75e+85)
     (+ x (* x z))
     (if (<= x 1.3e+21) (+ x (* t (- y z))) (- x (* x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e+241) {
		tmp = x * (1.0 - y);
	} else if (x <= -1.75e+85) {
		tmp = x + (x * z);
	} else if (x <= 1.3e+21) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.55d+241)) then
        tmp = x * (1.0d0 - y)
    else if (x <= (-1.75d+85)) then
        tmp = x + (x * z)
    else if (x <= 1.3d+21) then
        tmp = x + (t * (y - z))
    else
        tmp = x - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e+241) {
		tmp = x * (1.0 - y);
	} else if (x <= -1.75e+85) {
		tmp = x + (x * z);
	} else if (x <= 1.3e+21) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x - (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e+241:
		tmp = x * (1.0 - y)
	elif x <= -1.75e+85:
		tmp = x + (x * z)
	elif x <= 1.3e+21:
		tmp = x + (t * (y - z))
	else:
		tmp = x - (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e+241)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= -1.75e+85)
		tmp = Float64(x + Float64(x * z));
	elseif (x <= 1.3e+21)
		tmp = Float64(x + Float64(t * Float64(y - z)));
	else
		tmp = Float64(x - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.55e+241)
		tmp = x * (1.0 - y);
	elseif (x <= -1.75e+85)
		tmp = x + (x * z);
	elseif (x <= 1.3e+21)
		tmp = x + (t * (y - z));
	else
		tmp = x - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e+241], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.75e+85], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+21], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.55e241

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.6%

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

      1. *-commutative 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in x around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

   7. Simplified 78.6%

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

   if -1.55e241 < x < -1.75000000000000003e85

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.2%

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

      1. mul-1-neg 74.2%

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

      2. distribute-lft-neg-out 74.2%

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

      3. *-commutative 74.2%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in t around 0 66.3%

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

   if -1.75000000000000003e85 < x < 1.3e21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.3%

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

   if 1.3e21 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in t around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-lft-neg-out 61.2%

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

      3. *-commutative 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+85}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 8: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -26000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-170}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (- x t)))))
   (if (<= z -26000000.0)
     t_1
     (if (<= z -2.05e-170)
       (+ x (* t (- y z)))
       (if (<= z 2.4e+106) (+ x (* y (- t x))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (x - t));
	double tmp;
	if (z <= -26000000.0) {
		tmp = t_1;
	} else if (z <= -2.05e-170) {
		tmp = x + (t * (y - z));
	} else if (z <= 2.4e+106) {
		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 = x + (z * (x - t))
    if (z <= (-26000000.0d0)) then
        tmp = t_1
    else if (z <= (-2.05d-170)) then
        tmp = x + (t * (y - z))
    else if (z <= 2.4d+106) 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 = x + (z * (x - t));
	double tmp;
	if (z <= -26000000.0) {
		tmp = t_1;
	} else if (z <= -2.05e-170) {
		tmp = x + (t * (y - z));
	} else if (z <= 2.4e+106) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (x - t))
	tmp = 0
	if z <= -26000000.0:
		tmp = t_1
	elif z <= -2.05e-170:
		tmp = x + (t * (y - z))
	elif z <= 2.4e+106:
		tmp = x + (y * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(x - t)))
	tmp = 0.0
	if (z <= -26000000.0)
		tmp = t_1;
	elseif (z <= -2.05e-170)
		tmp = Float64(x + Float64(t * Float64(y - z)));
	elseif (z <= 2.4e+106)
		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 = x + (z * (x - t));
	tmp = 0.0;
	if (z <= -26000000.0)
		tmp = t_1;
	elseif (z <= -2.05e-170)
		tmp = x + (t * (y - z));
	elseif (z <= 2.4e+106)
		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[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -26000000.0], t$95$1, If[LessEqual[z, -2.05e-170], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+106], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6e7 or 2.4000000000000001e106 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.1%

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

      1. mul-1-neg 89.1%

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

      2. distribute-lft-neg-out 89.1%

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

      3. *-commutative 89.1%

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

   4. Simplified 89.1%

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

      1. distribute-rgt-neg-out 89.1%

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

      2. unsub-neg 89.1%

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

   6. Applied egg-rr 89.1%

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

   if -2.6e7 < z < -2.04999999999999983e-170

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 91.6%

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

   if -2.04999999999999983e-170 < z < 2.4000000000000001e106

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.8%

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

      1. *-commutative 90.8%

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

   4. Simplified 90.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000000:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-170}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+85} \lor \neg \left(x \leq 1.16 \cdot 10^{+21}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.5e+85) (not (<= x 1.16e+21)))
   (+ x (* x (- z y)))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e+85) || !(x <= 1.16e+21)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.5d+85)) .or. (.not. (x <= 1.16d+21))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.5e+85) || !(x <= 1.16e+21)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.5e+85) or not (x <= 1.16e+21):
		tmp = x + (x * (z - y))
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.5e+85) || !(x <= 1.16e+21))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.5e+85) || ~((x <= 1.16e+21)))
		tmp = x + (x * (z - y));
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.5e+85], N[Not[LessEqual[x, 1.16e+21]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000008e85 or 1.16e21 < x

   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%

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

      4. fma-def 98.2%

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

   3. Applied egg-rr 98.2%

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

   4. Taylor expanded in t around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. distribute-rgt-neg-in 86.6%

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

      3. mul-1-neg 86.6%

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

      4. distribute-lft-in 91.1%

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

      5. +-commutative 91.1%

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

      6. mul-1-neg 91.1%

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

      7. sub-neg 91.1%

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

   6. Simplified 91.1%

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

   if -5.50000000000000008e85 < x < 1.16e21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+85} \lor \neg \left(x \leq 1.16 \cdot 10^{+21}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 10: 38.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+73} \lor \neg \left(y \leq 3.5 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.06e+73) (not (<= y 3.5e-29))) (* y t) (* t (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e+73) || !(y <= 3.5e-29)) {
		tmp = y * t;
	} else {
		tmp = t * -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 <= (-1.06d+73)) .or. (.not. (y <= 3.5d-29))) then
        tmp = y * t
    else
        tmp = t * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e+73) || !(y <= 3.5e-29)) {
		tmp = y * t;
	} else {
		tmp = t * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.06e+73) or not (y <= 3.5e-29):
		tmp = y * t
	else:
		tmp = t * -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.06e+73) || !(y <= 3.5e-29))
		tmp = Float64(y * t);
	else
		tmp = Float64(t * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.06e+73) || ~((y <= 3.5e-29)))
		tmp = y * t;
	else
		tmp = t * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.06e+73], N[Not[LessEqual[y, 3.5e-29]], $MachinePrecision]], N[(y * t), $MachinePrecision], N[(t * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0600000000000001e73 or 3.4999999999999997e-29 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.5%

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

      1. *-commutative 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in x around 0 43.5%

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

   if -1.0600000000000001e73 < y < 3.4999999999999997e-29

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 71.2%

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

   3. Taylor expanded in y around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. unsub-neg 61.0%

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

      3. *-commutative 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in x around 0 38.4%

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

      1. associate-*r* 38.4%

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

      2. neg-mul-1 38.4%

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

   8. Simplified 38.4%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+73} \lor \neg \left(y \leq 3.5 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]

Alternative 11: 37.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-57} \lor \neg \left(y \leq 5.2 \cdot 10^{-63}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e-57) (not (<= y 5.2e-63))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-57) || !(y <= 5.2e-63)) {
		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 <= (-6.5d-57)) .or. (.not. (y <= 5.2d-63))) 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 <= -6.5e-57) || !(y <= 5.2e-63)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e-57) or not (y <= 5.2e-63):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e-57) || !(y <= 5.2e-63))
		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 <= -6.5e-57) || ~((y <= 5.2e-63)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e-57], N[Not[LessEqual[y, 5.2e-63]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999992e-57 or 5.2000000000000003e-63 < 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 x around 0 38.3%

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

   if -6.49999999999999992e-57 < y < 5.2000000000000003e-63

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.4%

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

   3. Taylor expanded in x around inf 30.7%

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

4. Final simplification 35.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-57} \lor \neg \left(y \leq 5.2 \cdot 10^{-63}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 17.7% 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 60.6%

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

3. Taylor expanded in x around inf 14.2%

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

4. Final simplification 14.2%

   \[\leadsto x \]

Developer target: 96.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023336 
(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))))