Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 11

Speedup: 1.0×

• 33.8% 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

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

FPCore

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

C

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

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) * (z - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot y\\ t_2 := x + x \cdot z\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.007:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+251} \lor \neg \left(x \leq 3.3 \cdot 10^{+280}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* x y))) (t_2 (+ x (* x z))))
   (if (<= x -1.15e+223)
     t_1
     (if (<= x -3.2e+124)
       t_2
       (if (<= x -1.5e+69)
         t_1
         (if (<= x 0.007)
           (- x (* z t))
           (if (or (<= x 3.3e+251) (not (<= x 3.3e+280))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double t_2 = x + (x * z);
	double tmp;
	if (x <= -1.15e+223) {
		tmp = t_1;
	} else if (x <= -3.2e+124) {
		tmp = t_2;
	} else if (x <= -1.5e+69) {
		tmp = t_1;
	} else if (x <= 0.007) {
		tmp = x - (z * t);
	} else if ((x <= 3.3e+251) || !(x <= 3.3e+280)) {
		tmp = t_2;
	} 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 * y)
    t_2 = x + (x * z)
    if (x <= (-1.15d+223)) then
        tmp = t_1
    else if (x <= (-3.2d+124)) then
        tmp = t_2
    else if (x <= (-1.5d+69)) then
        tmp = t_1
    else if (x <= 0.007d0) then
        tmp = x - (z * t)
    else if ((x <= 3.3d+251) .or. (.not. (x <= 3.3d+280))) then
        tmp = t_2
    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 * y);
	double t_2 = x + (x * z);
	double tmp;
	if (x <= -1.15e+223) {
		tmp = t_1;
	} else if (x <= -3.2e+124) {
		tmp = t_2;
	} else if (x <= -1.5e+69) {
		tmp = t_1;
	} else if (x <= 0.007) {
		tmp = x - (z * t);
	} else if ((x <= 3.3e+251) || !(x <= 3.3e+280)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x * y)
	t_2 = x + (x * z)
	tmp = 0
	if x <= -1.15e+223:
		tmp = t_1
	elif x <= -3.2e+124:
		tmp = t_2
	elif x <= -1.5e+69:
		tmp = t_1
	elif x <= 0.007:
		tmp = x - (z * t)
	elif (x <= 3.3e+251) or not (x <= 3.3e+280):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x * y))
	t_2 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (x <= -1.15e+223)
		tmp = t_1;
	elseif (x <= -3.2e+124)
		tmp = t_2;
	elseif (x <= -1.5e+69)
		tmp = t_1;
	elseif (x <= 0.007)
		tmp = Float64(x - Float64(z * t));
	elseif ((x <= 3.3e+251) || !(x <= 3.3e+280))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x * y);
	t_2 = x + (x * z);
	tmp = 0.0;
	if (x <= -1.15e+223)
		tmp = t_1;
	elseif (x <= -3.2e+124)
		tmp = t_2;
	elseif (x <= -1.5e+69)
		tmp = t_1;
	elseif (x <= 0.007)
		tmp = x - (z * t);
	elseif ((x <= 3.3e+251) || ~((x <= 3.3e+280)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+223], t$95$1, If[LessEqual[x, -3.2e+124], t$95$2, If[LessEqual[x, -1.5e+69], t$95$1, If[LessEqual[x, 0.007], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.3e+251], N[Not[LessEqual[x, 3.3e+280]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000002e223 or -3.19999999999999993e124 < x < -1.49999999999999992e69 or 3.30000000000000018e251 < x < 3.30000000000000003e280

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

   7. Simplified 85.6%

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

   if -1.15000000000000002e223 < x < -3.19999999999999993e124 or 0.00700000000000000015 < x < 3.30000000000000018e251 or 3.30000000000000003e280 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. distribute-lft-neg-out 68.0%

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

      3. *-commutative 68.0%

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

   4. Simplified 68.0%

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

   5. Taylor expanded in t around 0 60.2%

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

   if -1.49999999999999992e69 < x < 0.00700000000000000015

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-lft-neg-out 67.8%

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

      3. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in t around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. distribute-rgt-neg-in 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. sub-neg 57.9%

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

   10. Simplified 57.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+223}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+124}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{+69}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 0.007:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+251} \lor \neg \left(x \leq 3.3 \cdot 10^{+280}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 3: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot y\\ t_2 := x + x \cdot z\\ \mathbf{if}\;x \leq -1.14 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+187}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+255} \lor \neg \left(x \leq 3.8 \cdot 10^{+280}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* x y))) (t_2 (+ x (* x z))))
   (if (<= x -1.14e+223)
     t_1
     (if (<= x -1.22e+124)
       t_2
       (if (<= x -3.4e+69)
         t_1
         (if (<= x 1.08e+187)
           (- x (* t (- z y)))
           (if (or (<= x 1.45e+255) (not (<= x 3.8e+280))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double t_2 = x + (x * z);
	double tmp;
	if (x <= -1.14e+223) {
		tmp = t_1;
	} else if (x <= -1.22e+124) {
		tmp = t_2;
	} else if (x <= -3.4e+69) {
		tmp = t_1;
	} else if (x <= 1.08e+187) {
		tmp = x - (t * (z - y));
	} else if ((x <= 1.45e+255) || !(x <= 3.8e+280)) {
		tmp = t_2;
	} 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 * y)
    t_2 = x + (x * z)
    if (x <= (-1.14d+223)) then
        tmp = t_1
    else if (x <= (-1.22d+124)) then
        tmp = t_2
    else if (x <= (-3.4d+69)) then
        tmp = t_1
    else if (x <= 1.08d+187) then
        tmp = x - (t * (z - y))
    else if ((x <= 1.45d+255) .or. (.not. (x <= 3.8d+280))) then
        tmp = t_2
    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 * y);
	double t_2 = x + (x * z);
	double tmp;
	if (x <= -1.14e+223) {
		tmp = t_1;
	} else if (x <= -1.22e+124) {
		tmp = t_2;
	} else if (x <= -3.4e+69) {
		tmp = t_1;
	} else if (x <= 1.08e+187) {
		tmp = x - (t * (z - y));
	} else if ((x <= 1.45e+255) || !(x <= 3.8e+280)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x * y)
	t_2 = x + (x * z)
	tmp = 0
	if x <= -1.14e+223:
		tmp = t_1
	elif x <= -1.22e+124:
		tmp = t_2
	elif x <= -3.4e+69:
		tmp = t_1
	elif x <= 1.08e+187:
		tmp = x - (t * (z - y))
	elif (x <= 1.45e+255) or not (x <= 3.8e+280):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x * y))
	t_2 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (x <= -1.14e+223)
		tmp = t_1;
	elseif (x <= -1.22e+124)
		tmp = t_2;
	elseif (x <= -3.4e+69)
		tmp = t_1;
	elseif (x <= 1.08e+187)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	elseif ((x <= 1.45e+255) || !(x <= 3.8e+280))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x * y);
	t_2 = x + (x * z);
	tmp = 0.0;
	if (x <= -1.14e+223)
		tmp = t_1;
	elseif (x <= -1.22e+124)
		tmp = t_2;
	elseif (x <= -3.4e+69)
		tmp = t_1;
	elseif (x <= 1.08e+187)
		tmp = x - (t * (z - y));
	elseif ((x <= 1.45e+255) || ~((x <= 3.8e+280)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.14e+223], t$95$1, If[LessEqual[x, -1.22e+124], t$95$2, If[LessEqual[x, -3.4e+69], t$95$1, If[LessEqual[x, 1.08e+187], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.45e+255], N[Not[LessEqual[x, 3.8e+280]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.13999999999999999e223 or -1.22e124 < x < -3.39999999999999986e69 or 1.4500000000000001e255 < x < 3.79999999999999964e280

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

   7. Simplified 85.6%

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

   if -1.13999999999999999e223 < x < -1.22e124 or 1.08e187 < x < 1.4500000000000001e255 or 3.79999999999999964e280 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-lft-neg-out 70.8%

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

      3. *-commutative 70.8%

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

   4. Simplified 70.8%

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

   5. Taylor expanded in t around 0 66.5%

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

   if -3.39999999999999986e69 < x < 1.08e187

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{+223}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{+124}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+69}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+187}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+255} \lor \neg \left(x \leq 3.8 \cdot 10^{+280}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot y\\ \end{array} \]

Alternative 4: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+42} \lor \neg \left(x \leq 6.7 \cdot 10^{+66}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.3e+42) (not (<= x 6.7e+66)))
   (+ x (* x (- z y)))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.3e+42) || !(x <= 6.7e+66)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.3d+42)) .or. (.not. (x <= 6.7d+66))) then
        tmp = x + (x * (z - y))
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.3e+42) || !(x <= 6.7e+66)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.3e+42) or not (x <= 6.7e+66):
		tmp = x + (x * (z - y))
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.3e+42) || !(x <= 6.7e+66))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.3e+42) || ~((x <= 6.7e+66)))
		tmp = x + (x * (z - y));
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.3e+42], N[Not[LessEqual[x, 6.7e+66]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e42 or 6.69999999999999969e66 < 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 93.4%

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

   3. Applied egg-rr 93.4%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-rgt-neg-in 80.0%

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

      3. mul-1-neg 80.0%

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

      4. distribute-lft-in 85.8%

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

      5. +-commutative 85.8%

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

      6. mul-1-neg 85.8%

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

      7. sub-neg 85.8%

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

   6. Simplified 85.8%

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

   if -2.3e42 < x < 6.69999999999999969e66

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.1%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+42} \lor \neg \left(x \leq 6.7 \cdot 10^{+66}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]

Alternative 5: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-6} \lor \neg \left(z \leq 1.4 \cdot 10^{-8}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e-6) (not (<= z 1.4e-8)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-6) || !(z <= 1.4e-8)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1d-6)) .or. (.not. (z <= 1.4d-8))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-6) || !(z <= 1.4e-8)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e-6) or not (z <= 1.4e-8):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e-6) || !(z <= 1.4e-8))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e-6) || ~((z <= 1.4e-8)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e-6], N[Not[LessEqual[z, 1.4e-8]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999955e-7 or 1.4e-8 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. distribute-lft-neg-out 82.3%

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

      3. *-commutative 82.3%

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

   4. Simplified 82.3%

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

   if -9.99999999999999955e-7 < z < 1.4e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 94.0%

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

      1. *-commutative 94.0%

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

   4. Simplified 94.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-6} \lor \neg \left(z \leq 1.4 \cdot 10^{-8}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 37.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* x z)
   (if (<= z 4.5e-192) x (if (<= z 2.05e+73) (* x (- y)) (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 4.5e-192) {
		tmp = x;
	} else if (z <= 2.05e+73) {
		tmp = x * -y;
	} 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 <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 4.5d-192) then
        tmp = x
    else if (z <= 2.05d+73) then
        tmp = x * -y
    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 <= -1.0) {
		tmp = x * z;
	} else if (z <= 4.5e-192) {
		tmp = x;
	} else if (z <= 2.05e+73) {
		tmp = x * -y;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 4.5e-192:
		tmp = x
	elif z <= 2.05e+73:
		tmp = x * -y
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 4.5e-192)
		tmp = x;
	elseif (z <= 2.05e+73)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * z;
	elseif (z <= 4.5e-192)
		tmp = x;
	elseif (z <= 2.05e+73)
		tmp = x * -y;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 4.5e-192], x, If[LessEqual[z, 2.05e+73], N[(x * (-y)), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 2.0499999999999999e73 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.3%

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

      1. mul-1-neg 85.3%

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

      2. distribute-lft-neg-out 85.3%

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

      3. *-commutative 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in t around 0 44.5%

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

   6. Taylor expanded in z around inf 44.4%

      \[\leadsto \color{blue}{x \cdot z} \]
   7. Step-by-step derivation

      1. *-commutative 44.4%

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

   8. Simplified 44.4%

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

   if -1 < z < 4.50000000000000024e-192

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 41.4%

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

      1. mul-1-neg 41.4%

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

      2. distribute-lft-neg-out 41.4%

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

      3. *-commutative 41.4%

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

   4. Simplified 41.4%

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

   5. Taylor expanded in z around 0 34.5%

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

   if 4.50000000000000024e-192 < z < 2.0499999999999999e73

   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 97.9%

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

   3. Applied egg-rr 97.9%

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

   4. Taylor expanded in t around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. distribute-rgt-neg-in 57.9%

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

      3. mul-1-neg 57.9%

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

      4. distribute-lft-in 57.9%

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

      5. +-commutative 57.9%

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

      6. mul-1-neg 57.9%

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

      7. sub-neg 57.9%

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

   6. Simplified 57.9%

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

   7. Taylor expanded in y around inf 33.2%

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

      1. mul-1-neg 33.2%

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

      2. *-commutative 33.2%

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

      3. distribute-lft-neg-in 33.2%

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

   9. Simplified 33.2%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 7: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+36} \lor \neg \left(y \leq 3 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e+36) (not (<= y 3e+19))) (* x (- y)) (+ x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+36) || !(y <= 3e+19)) {
		tmp = x * -y;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8d+36)) .or. (.not. (y <= 3d+19))) then
        tmp = x * -y
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+36) || !(y <= 3e+19)) {
		tmp = x * -y;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e+36) or not (y <= 3e+19):
		tmp = x * -y
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e+36) || !(y <= 3e+19))
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e+36) || ~((y <= 3e+19)))
		tmp = x * -y;
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e+36], N[Not[LessEqual[y, 3e+19]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000034e36 or 3e19 < 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 89.2%

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

   3. Applied egg-rr 89.2%

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

   4. Taylor expanded in t around 0 45.5%

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

      1. mul-1-neg 45.5%

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

      2. distribute-rgt-neg-in 45.5%

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

      3. mul-1-neg 45.5%

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

      4. distribute-lft-in 51.8%

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

      5. +-commutative 51.8%

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

      6. mul-1-neg 51.8%

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

      7. sub-neg 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in y around inf 39.9%

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

      1. mul-1-neg 39.9%

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

      2. *-commutative 39.9%

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

      3. distribute-lft-neg-in 39.9%

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

   9. Simplified 39.9%

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

   if -8.00000000000000034e36 < y < 3e19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. distribute-lft-neg-out 88.1%

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

      3. *-commutative 88.1%

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

   4. Simplified 88.1%

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

   5. Taylor expanded in t around 0 53.7%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+36} \lor \neg \left(y \leq 3 \cdot 10^{+19}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 8: 54.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-8} \lor \neg \left(z \leq 2.15 \cdot 10^{+73}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e-8) (not (<= z 2.15e+73))) (+ x (* x z)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e-8) || !(z <= 2.15e+73)) {
		tmp = x + (x * z);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.8d-8)) .or. (.not. (z <= 2.15d+73))) then
        tmp = x + (x * z)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e-8) || !(z <= 2.15e+73)) {
		tmp = x + (x * z);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e-8) or not (z <= 2.15e+73):
		tmp = x + (x * z)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e-8) || !(z <= 2.15e+73))
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e-8) || ~((z <= 2.15e+73)))
		tmp = x + (x * z);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e-8], N[Not[LessEqual[z, 2.15e+73]], $MachinePrecision]], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999997e-8 or 2.15000000000000007e73 < 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 44.0%

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

   if -4.79999999999999997e-8 < z < 2.15000000000000007e73

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.2%

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

      1. *-commutative 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in t around inf 63.2%

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

      1. *-commutative 63.2%

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

   7. Simplified 63.2%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-8} \lor \neg \left(z \leq 2.15 \cdot 10^{+73}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 9: 51.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1950000000000 \lor \neg \left(x \leq 1.1\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1950000000000.0) (not (<= x 1.1)))
   (+ x (* x z))
   (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1950000000000.0) || !(x <= 1.1)) {
		tmp = x + (x * z);
	} else {
		tmp = x - (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 <= (-1950000000000.0d0)) .or. (.not. (x <= 1.1d0))) then
        tmp = x + (x * z)
    else
        tmp = x - (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 <= -1950000000000.0) || !(x <= 1.1)) {
		tmp = x + (x * z);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1950000000000.0) or not (x <= 1.1):
		tmp = x + (x * z)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1950000000000.0) || !(x <= 1.1))
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1950000000000.0) || ~((x <= 1.1)))
		tmp = x + (x * z);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1950000000000.0], N[Not[LessEqual[x, 1.1]], $MachinePrecision]], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95e12 or 1.1000000000000001 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-lft-neg-out 62.1%

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

      3. *-commutative 62.1%

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

   4. Simplified 62.1%

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

   5. Taylor expanded in t around 0 55.6%

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

   if -1.95e12 < x < 1.1000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.0%

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

      1. mul-1-neg 67.0%

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

      2. distribute-lft-neg-out 67.0%

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

      3. *-commutative 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in t around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. *-commutative 58.4%

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

      3. distribute-rgt-neg-in 58.4%

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

   7. Simplified 58.4%

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

   8. Taylor expanded in x around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. sub-neg 58.4%

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

   10. Simplified 58.4%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1950000000000 \lor \neg \left(x \leq 1.1\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 10: 37.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5600000000000\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 5600000000000.0))) (* x z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 5600000000000.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 5600000000000.0d0))) then
        tmp = x * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 5600000000000.0)) {
		tmp = x * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 5600000000000.0):
		tmp = x * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 5600000000000.0))
		tmp = Float64(x * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 5600000000000.0)))
		tmp = x * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 5600000000000.0]], $MachinePrecision]], N[(x * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 5.6e12 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. distribute-lft-neg-out 82.5%

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

      3. *-commutative 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in t around 0 42.3%

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

   6. Taylor expanded in z around inf 42.3%

      \[\leadsto \color{blue}{x \cdot z} \]
   7. Step-by-step derivation

      1. *-commutative 42.3%

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

   8. Simplified 42.3%

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

   if -1 < z < 5.6e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-lft-neg-out 40.2%

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

      3. *-commutative 40.2%

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

   4. Simplified 40.2%

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

   5. Taylor expanded in z around 0 31.3%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 5600000000000\right):\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 18.2% 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 y around 0 64.4%

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

   1. mul-1-neg 64.4%

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

   2. distribute-lft-neg-out 64.4%

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

   3. *-commutative 64.4%

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

4. Simplified 64.4%

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

5. Taylor expanded in z around 0 15.0%

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

6. Final simplification 15.0%

   \[\leadsto x \]

Developer target: 96.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(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))))