Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

Alternatives: 11

Speedup: 1.0×

• 34.7% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 36.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-101}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-264}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+159}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -10000000000.0)
   (* x z)
   (if (<= z -5.2e-101)
     (* y t)
     (if (<= z -1.2e-295)
       x
       (if (<= z 1.9e-264)
         (* y t)
         (if (<= z 6.4e-184) x (if (<= z 8.5e+159) (* y t) (* x z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -10000000000.0) {
		tmp = x * z;
	} else if (z <= -5.2e-101) {
		tmp = y * t;
	} else if (z <= -1.2e-295) {
		tmp = x;
	} else if (z <= 1.9e-264) {
		tmp = y * t;
	} else if (z <= 6.4e-184) {
		tmp = x;
	} else if (z <= 8.5e+159) {
		tmp = y * t;
	} else {
		tmp = 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 (z <= (-10000000000.0d0)) then
        tmp = x * z
    else if (z <= (-5.2d-101)) then
        tmp = y * t
    else if (z <= (-1.2d-295)) then
        tmp = x
    else if (z <= 1.9d-264) then
        tmp = y * t
    else if (z <= 6.4d-184) then
        tmp = x
    else if (z <= 8.5d+159) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -10000000000.0) {
		tmp = x * z;
	} else if (z <= -5.2e-101) {
		tmp = y * t;
	} else if (z <= -1.2e-295) {
		tmp = x;
	} else if (z <= 1.9e-264) {
		tmp = y * t;
	} else if (z <= 6.4e-184) {
		tmp = x;
	} else if (z <= 8.5e+159) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -10000000000.0:
		tmp = x * z
	elif z <= -5.2e-101:
		tmp = y * t
	elif z <= -1.2e-295:
		tmp = x
	elif z <= 1.9e-264:
		tmp = y * t
	elif z <= 6.4e-184:
		tmp = x
	elif z <= 8.5e+159:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -10000000000.0)
		tmp = Float64(x * z);
	elseif (z <= -5.2e-101)
		tmp = Float64(y * t);
	elseif (z <= -1.2e-295)
		tmp = x;
	elseif (z <= 1.9e-264)
		tmp = Float64(y * t);
	elseif (z <= 6.4e-184)
		tmp = x;
	elseif (z <= 8.5e+159)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -10000000000.0)
		tmp = x * z;
	elseif (z <= -5.2e-101)
		tmp = y * t;
	elseif (z <= -1.2e-295)
		tmp = x;
	elseif (z <= 1.9e-264)
		tmp = y * t;
	elseif (z <= 6.4e-184)
		tmp = x;
	elseif (z <= 8.5e+159)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -10000000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -5.2e-101], N[(y * t), $MachinePrecision], If[LessEqual[z, -1.2e-295], x, If[LessEqual[z, 1.9e-264], N[(y * t), $MachinePrecision], If[LessEqual[z, 6.4e-184], x, If[LessEqual[z, 8.5e+159], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e10 or 8.50000000000000076e159 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   4. Simplified 58.2%

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

      1. associate--r- 58.2%

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

      2. distribute-rgt-in 55.4%

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

   6. Applied egg-rr 55.4%

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

   7. Taylor expanded in z around inf 50.0%

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

   if -1e10 < z < -5.2000000000000002e-101 or -1.1999999999999999e-295 < z < 1.90000000000000007e-264 or 6.4e-184 < z < 8.50000000000000076e159

   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 99.0%

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

   3. Applied egg-rr 99.0%

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

   4. Taylor expanded in x around 0 66.0%

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

   5. Taylor expanded in x around 0 57.0%

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

   6. Taylor expanded in z around 0 39.7%

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

   if -5.2000000000000002e-101 < z < -1.1999999999999999e-295 or 1.90000000000000007e-264 < z < 6.4e-184

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 71.8%

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

   3. Taylor expanded in x around inf 45.3%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10000000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-101}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-264}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+159}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 3: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-300}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-75}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))) (t_2 (* (- y z) t)))
   (if (<= t -1.15e-125)
     t_2
     (if (<= t -3.1e-300)
       (* x z)
       (if (<= t 8.5e-110)
         t_1
         (if (<= t 4.5e-75) (* x z) (if (<= t 3.7e-35) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double t_2 = (y - z) * t;
	double tmp;
	if (t <= -1.15e-125) {
		tmp = t_2;
	} else if (t <= -3.1e-300) {
		tmp = x * z;
	} else if (t <= 8.5e-110) {
		tmp = t_1;
	} else if (t <= 4.5e-75) {
		tmp = x * z;
	} else if (t <= 3.7e-35) {
		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 * -y
    t_2 = (y - z) * t
    if (t <= (-1.15d-125)) then
        tmp = t_2
    else if (t <= (-3.1d-300)) then
        tmp = x * z
    else if (t <= 8.5d-110) then
        tmp = t_1
    else if (t <= 4.5d-75) then
        tmp = x * z
    else if (t <= 3.7d-35) 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 * -y;
	double t_2 = (y - z) * t;
	double tmp;
	if (t <= -1.15e-125) {
		tmp = t_2;
	} else if (t <= -3.1e-300) {
		tmp = x * z;
	} else if (t <= 8.5e-110) {
		tmp = t_1;
	} else if (t <= 4.5e-75) {
		tmp = x * z;
	} else if (t <= 3.7e-35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	t_2 = (y - z) * t
	tmp = 0
	if t <= -1.15e-125:
		tmp = t_2
	elif t <= -3.1e-300:
		tmp = x * z
	elif t <= 8.5e-110:
		tmp = t_1
	elif t <= 4.5e-75:
		tmp = x * z
	elif t <= 3.7e-35:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.15e-125)
		tmp = t_2;
	elseif (t <= -3.1e-300)
		tmp = Float64(x * z);
	elseif (t <= 8.5e-110)
		tmp = t_1;
	elseif (t <= 4.5e-75)
		tmp = Float64(x * z);
	elseif (t <= 3.7e-35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.15e-125)
		tmp = t_2;
	elseif (t <= -3.1e-300)
		tmp = x * z;
	elseif (t <= 8.5e-110)
		tmp = t_1;
	elseif (t <= 4.5e-75)
		tmp = x * z;
	elseif (t <= 3.7e-35)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.15e-125], t$95$2, If[LessEqual[t, -3.1e-300], N[(x * z), $MachinePrecision], If[LessEqual[t, 8.5e-110], t$95$1, If[LessEqual[t, 4.5e-75], N[(x * z), $MachinePrecision], If[LessEqual[t, 3.7e-35], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-125 or 3.6999999999999999e-35 < t

   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 96.1%

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

   3. Applied egg-rr 96.1%

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

   4. Taylor expanded in x around 0 80.6%

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

   5. Taylor expanded in x around 0 69.5%

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

   6. Taylor expanded in t around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. sub-neg 72.1%

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

   8. Simplified 72.1%

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

   if -1.15e-125 < t < -3.1000000000000002e-300 or 8.50000000000000029e-110 < t < 4.5000000000000003e-75

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   4. Simplified 89.7%

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

      1. associate--r- 89.7%

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

      2. distribute-rgt-in 87.4%

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

   6. Applied egg-rr 87.4%

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

   7. Taylor expanded in z around inf 52.8%

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

   if -3.1000000000000002e-300 < t < 8.50000000000000029e-110 or 4.5000000000000003e-75 < t < 3.6999999999999999e-35

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   4. Simplified 89.5%

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

   5. Taylor expanded in z around 0 65.9%

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

   6. Taylor expanded in y around inf 50.7%

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

      1. associate-*r* 50.7%

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

      2. neg-mul-1 50.7%

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

      3. *-commutative 50.7%

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

   8. Simplified 50.7%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-125}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-300}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-75}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-121} \lor \neg \left(t \leq 1060000000000\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.1e-121) (not (<= t 1060000000000.0)))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e-121) || !(t <= 1060000000000.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.1d-121)) .or. (.not. (t <= 1060000000000.0d0))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e-121) || !(t <= 1060000000000.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.1e-121) or not (t <= 1060000000000.0):
		tmp = (y - z) * t
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.1e-121) || !(t <= 1060000000000.0))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.1e-121) || ~((t <= 1060000000000.0)))
		tmp = (y - z) * t;
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.1e-121], N[Not[LessEqual[t, 1060000000000.0]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0999999999999999e-121 or 1.06e12 < t

   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 96.0%

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

   3. Applied egg-rr 96.0%

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

   4. Taylor expanded in x around 0 81.0%

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

   5. Taylor expanded in x around 0 71.3%

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

   6. Taylor expanded in t around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. sub-neg 74.0%

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

   8. Simplified 74.0%

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

   if -2.0999999999999999e-121 < t < 1.06e12

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

   4. Simplified 88.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-121} \lor \neg \left(t \leq 1060000000000\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]

Alternative 5: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-121} \lor \neg \left(t \leq 1.3 \cdot 10^{-34}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.1e-121) (not (<= t 1.3e-34)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e-121) || !(t <= 1.3e-34)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.1d-121)) .or. (.not. (t <= 1.3d-34))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e-121) || !(t <= 1.3e-34)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.1e-121) or not (t <= 1.3e-34):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.1e-121) || !(t <= 1.3e-34))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.1e-121) || ~((t <= 1.3e-34)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.1e-121], N[Not[LessEqual[t, 1.3e-34]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0999999999999999e-121 or 1.3e-34 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.2%

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

   if -2.0999999999999999e-121 < t < 1.3e-34

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. unsub-neg 89.6%

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

   4. Simplified 89.6%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-121} \lor \neg \left(t \leq 1.3 \cdot 10^{-34}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]

Alternative 6: 36.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+140}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-144}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 0.0014:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.95e+140)
   (* y t)
   (if (<= y -5.1e-144) (* x z) (if (<= y 0.0014) (* t (- z)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.95e+140) {
		tmp = y * t;
	} else if (y <= -5.1e-144) {
		tmp = x * z;
	} else if (y <= 0.0014) {
		tmp = t * -z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.95d+140)) then
        tmp = y * t
    else if (y <= (-5.1d-144)) then
        tmp = x * z
    else if (y <= 0.0014d0) then
        tmp = t * -z
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.95e+140) {
		tmp = y * t;
	} else if (y <= -5.1e-144) {
		tmp = x * z;
	} else if (y <= 0.0014) {
		tmp = t * -z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.95e+140:
		tmp = y * t
	elif y <= -5.1e-144:
		tmp = x * z
	elif y <= 0.0014:
		tmp = t * -z
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.95e+140)
		tmp = Float64(y * t);
	elseif (y <= -5.1e-144)
		tmp = Float64(x * z);
	elseif (y <= 0.0014)
		tmp = Float64(t * Float64(-z));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.95e+140)
		tmp = y * t;
	elseif (y <= -5.1e-144)
		tmp = x * z;
	elseif (y <= 0.0014)
		tmp = t * -z;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.95e+140], N[(y * t), $MachinePrecision], If[LessEqual[y, -5.1e-144], N[(x * z), $MachinePrecision], If[LessEqual[y, 0.0014], N[(t * (-z)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9500000000000001e140 or 0.00139999999999999999 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 95.3%

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

   3. Applied egg-rr 95.3%

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

   4. Taylor expanded in x around 0 50.1%

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

   5. Taylor expanded in x around 0 49.9%

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

   6. Taylor expanded in z around 0 44.1%

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

   if -2.9500000000000001e140 < y < -5.1e-144

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

   4. Simplified 65.1%

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

      1. associate--r- 65.1%

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

      2. distribute-rgt-in 63.4%

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

   6. Applied egg-rr 63.4%

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

   7. Taylor expanded in z around inf 39.2%

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

   if -5.1e-144 < y < 0.00139999999999999999

   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 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 76.6%

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

   5. Taylor expanded in x around 0 51.1%

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

   6. Taylor expanded in z around inf 50.2%

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

      1. mul-1-neg 50.2%

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

      2. distribute-rgt-neg-in 50.2%

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

   8. Simplified 50.2%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+140}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-144}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 0.0014:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 7: 37.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-144}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 0.0007:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+131)
   (* x (- y))
   (if (<= y -3.6e-144) (* x z) (if (<= y 0.0007) (* t (- z)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+131) {
		tmp = x * -y;
	} else if (y <= -3.6e-144) {
		tmp = x * z;
	} else if (y <= 0.0007) {
		tmp = t * -z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.05d+131)) then
        tmp = x * -y
    else if (y <= (-3.6d-144)) then
        tmp = x * z
    else if (y <= 0.0007d0) then
        tmp = t * -z
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+131) {
		tmp = x * -y;
	} else if (y <= -3.6e-144) {
		tmp = x * z;
	} else if (y <= 0.0007) {
		tmp = t * -z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+131:
		tmp = x * -y
	elif y <= -3.6e-144:
		tmp = x * z
	elif y <= 0.0007:
		tmp = t * -z
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+131)
		tmp = Float64(x * Float64(-y));
	elseif (y <= -3.6e-144)
		tmp = Float64(x * z);
	elseif (y <= 0.0007)
		tmp = Float64(t * Float64(-z));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e+131)
		tmp = x * -y;
	elseif (y <= -3.6e-144)
		tmp = x * z;
	elseif (y <= 0.0007)
		tmp = t * -z;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+131], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, -3.6e-144], N[(x * z), $MachinePrecision], If[LessEqual[y, 0.0007], N[(t * (-z)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.04999999999999993e131

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

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

   4. Simplified 62.7%

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

   5. Taylor expanded in z around 0 54.2%

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

   6. Taylor expanded in y around inf 54.2%

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

      1. associate-*r* 54.2%

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

      2. neg-mul-1 54.2%

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

      3. *-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -1.04999999999999993e131 < y < -3.6e-144

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

   4. Simplified 64.5%

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

      1. associate--r- 64.5%

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

      2. distribute-rgt-in 62.8%

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

   6. Applied egg-rr 62.8%

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

   7. Taylor expanded in z around inf 39.9%

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

   if -3.6e-144 < y < 6.99999999999999993e-4

   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 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 76.6%

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

   5. Taylor expanded in x around 0 51.1%

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

   6. Taylor expanded in z around inf 50.2%

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

      1. mul-1-neg 50.2%

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

      2. distribute-rgt-neg-in 50.2%

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

   8. Simplified 50.2%

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

   if 6.99999999999999993e-4 < y

   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 x around 0 56.0%

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

   5. Taylor expanded in x around 0 56.3%

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

   6. Taylor expanded in z around 0 50.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-144}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 0.0007:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 8: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+56} \lor \neg \left(x \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.45e+56) (not (<= x 4.8e+43))) (* x (+ z 1.0)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.45e+56) || !(x <= 4.8e+43)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.45d+56)) .or. (.not. (x <= 4.8d+43))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.45e+56) || !(x <= 4.8e+43)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.45e+56) or not (x <= 4.8e+43):
		tmp = x * (z + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.45e+56) || !(x <= 4.8e+43))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.45e+56) || ~((x <= 4.8e+43)))
		tmp = x * (z + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.45e+56], N[Not[LessEqual[x, 4.8e+43]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45000000000000004e56 or 4.80000000000000046e43 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in y around 0 62.2%

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

      1. +-commutative 62.2%

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

   7. Simplified 62.2%

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

   if -1.45000000000000004e56 < x < 4.80000000000000046e43

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 97.4%

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

   3. Applied egg-rr 97.4%

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

   4. Taylor expanded in x around 0 72.3%

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

   5. Taylor expanded in x around 0 63.4%

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

   6. Taylor expanded in t around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. sub-neg 65.9%

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

   8. Simplified 65.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+56} \lor \neg \left(x \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 9: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e+56)
   (* x (+ z 1.0))
   (if (<= x 2.5e+126) (* (- y z) t) (* x (- 1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e+56) {
		tmp = x * (z + 1.0);
	} else if (x <= 2.5e+126) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.8d+56)) then
        tmp = x * (z + 1.0d0)
    else if (x <= 2.5d+126) then
        tmp = (y - z) * t
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e+56) {
		tmp = x * (z + 1.0);
	} else if (x <= 2.5e+126) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e+56:
		tmp = x * (z + 1.0)
	elif x <= 2.5e+126:
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e+56)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (x <= 2.5e+126)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8e+56)
		tmp = x * (z + 1.0);
	elseif (x <= 2.5e+126)
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e+56], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+126], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999999e56

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in y around 0 65.8%

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

      1. +-commutative 65.8%

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

   7. Simplified 65.8%

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

   if -1.79999999999999999e56 < x < 2.49999999999999989e126

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 97.6%

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

   3. Applied egg-rr 97.6%

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

   4. Taylor expanded in x around 0 71.4%

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

   5. Taylor expanded in x around 0 62.5%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. mul-1-neg 64.9%

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

      2. sub-neg 64.9%

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

   8. Simplified 64.9%

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

   if 2.49999999999999989e126 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.1%

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

      1. mul-1-neg 92.1%

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

      2. unsub-neg 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in z around 0 70.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+126}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 10: 36.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-9} \lor \neg \left(y \leq 0.00045\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.6e-9) (not (<= y 0.00045))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e-9) || !(y <= 0.00045)) {
		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 <= (-4.6d-9)) .or. (.not. (y <= 0.00045d0))) 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 <= -4.6e-9) || !(y <= 0.00045)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.6e-9) or not (y <= 0.00045):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.6e-9) || !(y <= 0.00045))
		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 <= -4.6e-9) || ~((y <= 0.00045)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.6e-9], N[Not[LessEqual[y, 0.00045]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.5999999999999998e-9 or 4.4999999999999999e-4 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 94.9%

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

   3. Applied egg-rr 94.9%

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

   4. Taylor expanded in x around 0 48.2%

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

   5. Taylor expanded in x around 0 47.5%

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

   6. Taylor expanded in z around 0 39.5%

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

   if -4.5999999999999998e-9 < y < 4.4999999999999999e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 73.0%

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

   3. Taylor expanded in x around inf 27.7%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-9} \lor \neg \left(y \leq 0.00045\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 18.1% 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 61.2%

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

3. Taylor expanded in x around inf 14.6%

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

4. Final simplification 14.6%

   \[\leadsto x \]

Developer target: 96.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023310 
(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))))