Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 10

Speedup: 1.0×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-219}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 8.1 \cdot 10^{-84}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))))
   (if (<= t -7.5e-129)
     t_1
     (if (<= t 1.2e-219)
       (- x (* x y))
       (if (<= t 8.1e-84) (+ x (* x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -7.5e-129) {
		tmp = t_1;
	} else if (t <= 1.2e-219) {
		tmp = x - (x * y);
	} else if (t <= 8.1e-84) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * t)
    if (t <= (-7.5d-129)) then
        tmp = t_1
    else if (t <= 1.2d-219) then
        tmp = x - (x * y)
    else if (t <= 8.1d-84) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -7.5e-129) {
		tmp = t_1;
	} else if (t <= 1.2e-219) {
		tmp = x - (x * y);
	} else if (t <= 8.1e-84) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	tmp = 0
	if t <= -7.5e-129:
		tmp = t_1
	elif t <= 1.2e-219:
		tmp = x - (x * y)
	elif t <= 8.1e-84:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -7.5e-129)
		tmp = t_1;
	elseif (t <= 1.2e-219)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 8.1e-84)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -7.5e-129)
		tmp = t_1;
	elseif (t <= 1.2e-219)
		tmp = x - (x * y);
	elseif (t <= 8.1e-84)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e-129], t$95$1, If[LessEqual[t, 1.2e-219], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.1e-84], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.49999999999999944e-129 or 8.0999999999999997e-84 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.1%

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

   if -7.49999999999999944e-129 < t < 1.20000000000000007e-219

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.6%

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

      1. *-commutative 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 79.0%

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

      1. distribute-lft-in 79.0%

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

      2. *-rgt-identity 79.0%

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

      3. mul-1-neg 79.0%

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

      4. distribute-rgt-neg-in 79.0%

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

      5. unsub-neg 79.0%

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

   7. Simplified 79.0%

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

   if 1.20000000000000007e-219 < t < 8.0999999999999997e-84

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. distribute-lft-neg-out 78.5%

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

      3. *-commutative 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in t around 0 78.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-129}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-219}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 8.1 \cdot 10^{-84}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 3: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ \mathbf{if}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-220}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+59}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))))
   (if (<= t -9e-15)
     t_1
     (if (<= t 4.7e-220)
       (- x (* x y))
       (if (<= t 2.7e+59) (+ x (* x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double tmp;
	if (t <= -9e-15) {
		tmp = t_1;
	} else if (t <= 4.7e-220) {
		tmp = x - (x * y);
	} else if (t <= 2.7e+59) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * t)
    if (t <= (-9d-15)) then
        tmp = t_1
    else if (t <= 4.7d-220) then
        tmp = x - (x * y)
    else if (t <= 2.7d+59) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double tmp;
	if (t <= -9e-15) {
		tmp = t_1;
	} else if (t <= 4.7e-220) {
		tmp = x - (x * y);
	} else if (t <= 2.7e+59) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	tmp = 0
	if t <= -9e-15:
		tmp = t_1
	elif t <= 4.7e-220:
		tmp = x - (x * y)
	elif t <= 2.7e+59:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (t <= -9e-15)
		tmp = t_1;
	elseif (t <= 4.7e-220)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 2.7e+59)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	tmp = 0.0;
	if (t <= -9e-15)
		tmp = t_1;
	elseif (t <= 4.7e-220)
		tmp = x - (x * y);
	elseif (t <= 2.7e+59)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e-15], t$95$1, If[LessEqual[t, 4.7e-220], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+59], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.9999999999999995e-15 or 2.7000000000000001e59 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 57.1%

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

      1. *-commutative 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in t around inf 49.7%

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

      1. *-commutative 49.7%

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

   7. Simplified 49.7%

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

   if -8.9999999999999995e-15 < t < 4.7000000000000003e-220

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in x around inf 67.8%

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

      1. distribute-lft-in 67.8%

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

      2. *-rgt-identity 67.8%

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

      3. mul-1-neg 67.8%

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

      4. distribute-rgt-neg-in 67.8%

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

      5. unsub-neg 67.8%

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

   7. Simplified 67.8%

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

   if 4.7000000000000003e-220 < t < 2.7000000000000001e59

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-lft-neg-out 71.0%

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

      3. *-commutative 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in t around 0 55.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-15}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-220}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+59}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 4: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-221}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 10^{-60}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.36e-14)
   (+ x (* y t))
   (if (<= t 2.8e-221)
     (- x (* x y))
     (if (<= t 1e-60) (+ x (* x z)) (- x (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.36e-14) {
		tmp = x + (y * t);
	} else if (t <= 2.8e-221) {
		tmp = x - (x * y);
	} else if (t <= 1e-60) {
		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 (t <= (-1.36d-14)) then
        tmp = x + (y * t)
    else if (t <= 2.8d-221) then
        tmp = x - (x * y)
    else if (t <= 1d-60) 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 (t <= -1.36e-14) {
		tmp = x + (y * t);
	} else if (t <= 2.8e-221) {
		tmp = x - (x * y);
	} else if (t <= 1e-60) {
		tmp = x + (x * z);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.36e-14:
		tmp = x + (y * t)
	elif t <= 2.8e-221:
		tmp = x - (x * y)
	elif t <= 1e-60:
		tmp = x + (x * z)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.36e-14)
		tmp = Float64(x + Float64(y * t));
	elseif (t <= 2.8e-221)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 1e-60)
		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 (t <= -1.36e-14)
		tmp = x + (y * t);
	elseif (t <= 2.8e-221)
		tmp = x - (x * y);
	elseif (t <= 1e-60)
		tmp = x + (x * z);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.36e-14], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-221], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-60], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.36e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 65.3%

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

      1. *-commutative 65.3%

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

   4. Simplified 65.3%

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

   5. Taylor expanded in t around inf 57.2%

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

      1. *-commutative 57.2%

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

   7. Simplified 57.2%

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

   if -1.36e-14 < t < 2.80000000000000019e-221

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in x around inf 67.8%

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

      1. distribute-lft-in 67.8%

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

      2. *-rgt-identity 67.8%

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

      3. mul-1-neg 67.8%

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

      4. distribute-rgt-neg-in 67.8%

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

      5. unsub-neg 67.8%

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

   7. Simplified 67.8%

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

   if 2.80000000000000019e-221 < t < 9.9999999999999997e-61

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-lft-neg-out 70.7%

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

      3. *-commutative 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in t around 0 67.0%

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

   if 9.9999999999999997e-61 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.6%

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

   3. Taylor expanded in y around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

      3. *-commutative 59.8%

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

   5. Simplified 59.8%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-221}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 10^{-60}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 5: 79.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-16} \lor \neg \left(x \leq 2.4 \cdot 10^{-78}\right):\\ \;\;\;\;x - x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.9e-16) (not (<= x 2.4e-78)))
   (- x (* x (- y z)))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.9e-16) || !(x <= 2.4e-78)) {
		tmp = x - (x * (y - z));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.9d-16)) .or. (.not. (x <= 2.4d-78))) then
        tmp = x - (x * (y - z))
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.9e-16) || !(x <= 2.4e-78)) {
		tmp = x - (x * (y - z));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.9e-16) or not (x <= 2.4e-78):
		tmp = x - (x * (y - z))
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.9e-16) || !(x <= 2.4e-78))
		tmp = Float64(x - Float64(x * Float64(y - z)));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.9e-16) || ~((x <= 2.4e-78)))
		tmp = x - (x * (y - z));
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.9e-16], N[Not[LessEqual[x, 2.4e-78]], $MachinePrecision]], N[(x - N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.89999999999999977e-16 or 2.4e-78 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.2%

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

   3. Applied egg-rr 95.2%

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

   4. Taylor expanded in t around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. distribute-rgt-neg-in 74.5%

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

      3. mul-1-neg 74.5%

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

      4. distribute-lft-in 77.9%

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

      5. +-commutative 77.9%

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

      6. mul-1-neg 77.9%

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

      7. sub-neg 77.9%

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

   6. Simplified 77.9%

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

   if -3.89999999999999977e-16 < x < 2.4e-78

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 92.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-16} \lor \neg \left(x \leq 2.4 \cdot 10^{-78}\right):\\ \;\;\;\;x - x \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 6: 83.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+40} \lor \neg \left(z \leq 53\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e+40) (not (<= z 53.0)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e+40) || !(z <= 53.0)) {
		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 <= (-5d+40)) .or. (.not. (z <= 53.0d0))) 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 <= -5e+40) || !(z <= 53.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e+40) or not (z <= 53.0):
		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 <= -5e+40) || !(z <= 53.0))
		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 <= -5e+40) || ~((z <= 53.0)))
		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, -5e+40], N[Not[LessEqual[z, 53.0]], $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 < -5.00000000000000003e40 or 53 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. distribute-lft-neg-out 81.4%

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

      3. *-commutative 81.4%

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

   4. Simplified 81.4%

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

   if -5.00000000000000003e40 < z < 53

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   4. Simplified 91.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+40} \lor \neg \left(z \leq 53\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 48.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+88} \lor \neg \left(x \leq 2.4 \cdot 10^{-78}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.75e+88) (not (<= x 2.4e-78))) (+ x (* x z)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e+88) || !(x <= 2.4e-78)) {
		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 ((x <= (-1.75d+88)) .or. (.not. (x <= 2.4d-78))) 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 ((x <= -1.75e+88) || !(x <= 2.4e-78)) {
		tmp = x + (x * z);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.75e+88) or not (x <= 2.4e-78):
		tmp = x + (x * z)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.75e+88) || !(x <= 2.4e-78))
		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 ((x <= -1.75e+88) || ~((x <= 2.4e-78)))
		tmp = x + (x * z);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.75e+88], N[Not[LessEqual[x, 2.4e-78]], $MachinePrecision]], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7499999999999999e88 or 2.4e-78 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-lft-neg-out 60.0%

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

      3. *-commutative 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in t around 0 50.3%

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

   if -1.7499999999999999e88 < x < 2.4e-78

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 58.2%

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

      1. *-commutative 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. *-commutative 49.5%

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

   7. Simplified 49.5%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+88} \lor \neg \left(x \leq 2.4 \cdot 10^{-78}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 8: 37.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1250000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1250000000.0) (* x z) (if (<= z 1.0) x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1250000000.0) {
		tmp = x * z;
	} else if (z <= 1.0) {
		tmp = x;
	} 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 <= (-1250000000.0d0)) then
        tmp = x * z
    else if (z <= 1.0d0) then
        tmp = x
    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 <= -1250000000.0) {
		tmp = x * z;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1250000000.0:
		tmp = x * z
	elif z <= 1.0:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1250000000.0)
		tmp = Float64(x * z);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1250000000.0)
		tmp = x * z;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1250000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 1.0], x, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e9 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.4%

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

      1. mul-1-neg 79.4%

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

      2. distribute-lft-neg-out 79.4%

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

      3. *-commutative 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in t around 0 35.6%

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

   6. Taylor expanded in z around inf 35.6%

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

      1. *-commutative 35.6%

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

   8. Simplified 35.6%

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

   if -1.25e9 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.9%

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

   3. Taylor expanded in x around inf 25.5%

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

4. Final simplification 30.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1250000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 9: 37.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x + x \cdot z \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (x * 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 + (x * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 55.9%

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

   1. mul-1-neg 55.9%

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

   2. distribute-lft-neg-out 55.9%

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

   3. *-commutative 55.9%

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

4. Simplified 55.9%

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

5. Taylor expanded in t around 0 30.7%

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

6. Final simplification 30.7%

   \[\leadsto x + x \cdot z \]

Alternative 10: 17.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 66.0%

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

3. Taylor expanded in x around inf 14.0%

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

4. Final simplification 14.0%

   \[\leadsto x \]

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 2023290 
(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))))