Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 9

Speedup: 1.0×

• 34.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 54.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-101}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+166} \lor \neg \left(z \leq 5.7 \cdot 10^{+232}\right):\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))))
   (if (<= z -0.52)
     t_1
     (if (<= z 3.2e-101)
       (+ x (* y t))
       (if (<= z 1.6e+26)
         (* x (- 1.0 y))
         (if (or (<= z 6e+166) (not (<= z 5.7e+232))) (- x (* z t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double tmp;
	if (z <= -0.52) {
		tmp = t_1;
	} else if (z <= 3.2e-101) {
		tmp = x + (y * t);
	} else if (z <= 1.6e+26) {
		tmp = x * (1.0 - y);
	} else if ((z <= 6e+166) || !(z <= 5.7e+232)) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (x * z)
    if (z <= (-0.52d0)) then
        tmp = t_1
    else if (z <= 3.2d-101) then
        tmp = x + (y * t)
    else if (z <= 1.6d+26) then
        tmp = x * (1.0d0 - y)
    else if ((z <= 6d+166) .or. (.not. (z <= 5.7d+232))) then
        tmp = x - (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double tmp;
	if (z <= -0.52) {
		tmp = t_1;
	} else if (z <= 3.2e-101) {
		tmp = x + (y * t);
	} else if (z <= 1.6e+26) {
		tmp = x * (1.0 - y);
	} else if ((z <= 6e+166) || !(z <= 5.7e+232)) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	tmp = 0
	if z <= -0.52:
		tmp = t_1
	elif z <= 3.2e-101:
		tmp = x + (y * t)
	elif z <= 1.6e+26:
		tmp = x * (1.0 - y)
	elif (z <= 6e+166) or not (z <= 5.7e+232):
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (z <= -0.52)
		tmp = t_1;
	elseif (z <= 3.2e-101)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 1.6e+26)
		tmp = Float64(x * Float64(1.0 - y));
	elseif ((z <= 6e+166) || !(z <= 5.7e+232))
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	tmp = 0.0;
	if (z <= -0.52)
		tmp = t_1;
	elseif (z <= 3.2e-101)
		tmp = x + (y * t);
	elseif (z <= 1.6e+26)
		tmp = x * (1.0 - y);
	elseif ((z <= 6e+166) || ~((z <= 5.7e+232)))
		tmp = x - (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.52], t$95$1, If[LessEqual[z, 3.2e-101], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+26], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6e+166], N[Not[LessEqual[z, 5.7e+232]], $MachinePrecision]], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.52000000000000002 or 5.99999999999999997e166 < z < 5.69999999999999956e232

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. distribute-rgt-neg-in 85.8%

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

      3. sub-neg 85.8%

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

      4. +-commutative 85.8%

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

      5. distribute-neg-in 85.8%

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

      6. remove-double-neg 85.8%

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

      7. sub-neg 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in t around 0 60.0%

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

   if -0.52000000000000002 < z < 3.19999999999999978e-101

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 94.1%

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

      1. *-commutative 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in t around inf 74.5%

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

      1. *-commutative 74.5%

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

   8. Simplified 74.5%

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

   if 3.19999999999999978e-101 < z < 1.60000000000000014e26

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in x around inf 60.7%

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

      1. neg-mul-1 60.7%

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

      2. unsub-neg 60.7%

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

   8. Simplified 60.7%

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

   if 1.60000000000000014e26 < z < 5.99999999999999997e166 or 5.69999999999999956e232 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.2%

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

   4. Taylor expanded in y around 0 54.3%

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

      1. mul-1-neg 54.3%

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

      2. unsub-neg 54.3%

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

      3. *-commutative 54.3%

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

   6. Simplified 54.3%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-101}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+166} \lor \neg \left(z \leq 5.7 \cdot 10^{+232}\right):\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ \mathbf{if}\;z \leq -750:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-102}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))))
   (if (<= z -750.0)
     t_1
     (if (<= z 6.6e-102)
       (+ x (* y t))
       (if (<= z 1.6e+26) (* x (- 1.0 y)) (if (<= z 1.2e+29) (* y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double tmp;
	if (z <= -750.0) {
		tmp = t_1;
	} else if (z <= 6.6e-102) {
		tmp = x + (y * t);
	} else if (z <= 1.6e+26) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.2e+29) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (x * z)
    if (z <= (-750.0d0)) then
        tmp = t_1
    else if (z <= 6.6d-102) then
        tmp = x + (y * t)
    else if (z <= 1.6d+26) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1.2d+29) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double tmp;
	if (z <= -750.0) {
		tmp = t_1;
	} else if (z <= 6.6e-102) {
		tmp = x + (y * t);
	} else if (z <= 1.6e+26) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.2e+29) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	tmp = 0
	if z <= -750.0:
		tmp = t_1
	elif z <= 6.6e-102:
		tmp = x + (y * t)
	elif z <= 1.6e+26:
		tmp = x * (1.0 - y)
	elif z <= 1.2e+29:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	tmp = 0.0
	if (z <= -750.0)
		tmp = t_1;
	elseif (z <= 6.6e-102)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 1.6e+26)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1.2e+29)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	tmp = 0.0;
	if (z <= -750.0)
		tmp = t_1;
	elseif (z <= 6.6e-102)
		tmp = x + (y * t);
	elseif (z <= 1.6e+26)
		tmp = x * (1.0 - y);
	elseif (z <= 1.2e+29)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -750.0], t$95$1, If[LessEqual[z, 6.6e-102], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+26], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+29], N[(y * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -750 or 1.2e29 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-rgt-neg-in 85.0%

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

      3. sub-neg 85.0%

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

      4. +-commutative 85.0%

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

      5. distribute-neg-in 85.0%

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

      6. remove-double-neg 85.0%

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

      7. sub-neg 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in t around 0 52.5%

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

   if -750 < z < 6.6e-102

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 94.1%

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

      1. *-commutative 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in t around inf 74.5%

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

      1. *-commutative 74.5%

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

   8. Simplified 74.5%

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

   if 6.6e-102 < z < 1.60000000000000014e26

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in x around inf 60.7%

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

      1. neg-mul-1 60.7%

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

      2. unsub-neg 60.7%

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

   8. Simplified 60.7%

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

   if 1.60000000000000014e26 < z < 1.2e29

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

       1. *-commutative 100.0%

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

   11. Simplified 100.0%

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

Alternative 4: 50.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-298}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (* x (- 1.0 y))))
   (if (<= z -1.9e+20)
     t_1
     (if (<= z -6e-298)
       t_2
       (if (<= z 6.5e-258) (* y t) (if (<= z 1.2e+32) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.9e+20) {
		tmp = t_1;
	} else if (z <= -6e-298) {
		tmp = t_2;
	} else if (z <= 6.5e-258) {
		tmp = y * t;
	} else if (z <= 1.2e+32) {
		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 * z)
    t_2 = x * (1.0d0 - y)
    if (z <= (-1.9d+20)) then
        tmp = t_1
    else if (z <= (-6d-298)) then
        tmp = t_2
    else if (z <= 6.5d-258) then
        tmp = y * t
    else if (z <= 1.2d+32) 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 * z);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.9e+20) {
		tmp = t_1;
	} else if (z <= -6e-298) {
		tmp = t_2;
	} else if (z <= 6.5e-258) {
		tmp = y * t;
	} else if (z <= 1.2e+32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -1.9e+20:
		tmp = t_1
	elif z <= -6e-298:
		tmp = t_2
	elif z <= 6.5e-258:
		tmp = y * t
	elif z <= 1.2e+32:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.9e+20)
		tmp = t_1;
	elseif (z <= -6e-298)
		tmp = t_2;
	elseif (z <= 6.5e-258)
		tmp = Float64(y * t);
	elseif (z <= 1.2e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.9e+20)
		tmp = t_1;
	elseif (z <= -6e-298)
		tmp = t_2;
	elseif (z <= 6.5e-258)
		tmp = y * t;
	elseif (z <= 1.2e+32)
		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 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+20], t$95$1, If[LessEqual[z, -6e-298], t$95$2, If[LessEqual[z, 6.5e-258], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.2e+32], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e20 or 1.19999999999999996e32 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. distribute-rgt-neg-in 87.7%

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

      3. sub-neg 87.7%

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

      4. +-commutative 87.7%

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

      5. distribute-neg-in 87.7%

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

      6. remove-double-neg 87.7%

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

      7. sub-neg 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in t around 0 54.0%

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

   if -1.9e20 < z < -5.9999999999999999e-298 or 6.5000000000000002e-258 < z < 1.19999999999999996e32

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 89.0%

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

      1. *-commutative 89.0%

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

   5. Simplified 89.0%

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

   6. Taylor expanded in x around inf 62.4%

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

      1. neg-mul-1 62.4%

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

      2. unsub-neg 62.4%

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

   8. Simplified 62.4%

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

   if -5.9999999999999999e-298 < z < 6.5000000000000002e-258

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 95.9%

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

      1. *-commutative 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in t around inf 95.9%

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

      1. *-commutative 95.9%

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

   8. Simplified 95.9%

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

   9. Taylor expanded in x around 0 78.2%

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

       1. *-commutative 78.2%

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

   11. Simplified 78.2%

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

Alternative 5: 80.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+17} \lor \neg \left(x \leq 4.9 \cdot 10^{-57}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.25e+17) (not (<= x 4.9e-57)))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.25e+17) || !(x <= 4.9e-57)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.25d+17)) .or. (.not. (x <= 4.9d-57))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.25e+17) || !(x <= 4.9e-57)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.25e+17) or not (x <= 4.9e-57):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.25e+17) || !(x <= 4.9e-57))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.25e+17) || ~((x <= 4.9e-57)))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.25e+17], N[Not[LessEqual[x, 4.9e-57]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e17 or 4.89999999999999988e-57 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. distribute-rgt-neg-in 88.1%

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

      3. sub-neg 88.1%

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

      4. +-commutative 88.1%

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

      5. distribute-neg-in 88.1%

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

      6. remove-double-neg 88.1%

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

      7. sub-neg 88.1%

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

   5. Simplified 88.1%

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

   if -2.25e17 < x < 4.89999999999999988e-57

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 87.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+17} \lor \neg \left(x \leq 4.9 \cdot 10^{-57}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.6e+88)
   (* x (- 1.0 y))
   (if (<= x 5e-8) (+ x (* (- y z) t)) (+ x (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e+88) {
		tmp = x * (1.0 - y);
	} else if (x <= 5e-8) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.6d+88)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 5d-8) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.6e+88) {
		tmp = x * (1.0 - y);
	} else if (x <= 5e-8) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.6e+88:
		tmp = x * (1.0 - y)
	elif x <= 5e-8:
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.6e+88)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 5e-8)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.6e+88)
		tmp = x * (1.0 - y);
	elseif (x <= 5e-8)
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.6e+88], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-8], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6000000000000002e88

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 66.3%

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

      1. *-commutative 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in x around inf 66.3%

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

      1. neg-mul-1 66.3%

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

      2. unsub-neg 66.3%

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

   8. Simplified 66.3%

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

   if -3.6000000000000002e88 < x < 4.9999999999999998e-8

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.5%

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

   if 4.9999999999999998e-8 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-rgt-neg-in 68.3%

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

      3. sub-neg 68.3%

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

      4. +-commutative 68.3%

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

      5. distribute-neg-in 68.3%

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

      6. remove-double-neg 68.3%

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

      7. sub-neg 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 68.3%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 45.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-179} \lor \neg \left(x \leq 2.1 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.5e-179) (not (<= x 2.1e-112))) (* x (- 1.0 y)) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e-179) || !(x <= 2.1e-112)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.5d-179)) .or. (.not. (x <= 2.1d-112))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e-179) || !(x <= 2.1e-112)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.5e-179) or not (x <= 2.1e-112):
		tmp = x * (1.0 - y)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.5e-179) || !(x <= 2.1e-112))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.5e-179) || ~((x <= 2.1e-112)))
		tmp = x * (1.0 - y);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.5e-179], N[Not[LessEqual[x, 2.1e-112]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.50000000000000003e-179 or 2.1000000000000001e-112 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.6%

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

      1. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in x around inf 49.9%

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

      1. neg-mul-1 49.9%

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

      2. unsub-neg 49.9%

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

   8. Simplified 49.9%

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

   if -1.50000000000000003e-179 < x < 2.1000000000000001e-112

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.4%

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

      1. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in t around inf 60.7%

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

      1. *-commutative 60.7%

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

   8. Simplified 60.7%

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

   9. Taylor expanded in x around 0 51.9%

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

       1. *-commutative 51.9%

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

   11. Simplified 51.9%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-179} \lor \neg \left(x \leq 2.1 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-18} \lor \neg \left(y \leq 6.5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e-18) (not (<= y 6.5e-26))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-18) || !(y <= 6.5e-26)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4d-18)) .or. (.not. (y <= 6.5d-26))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-18) || !(y <= 6.5e-26)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e-18) or not (y <= 6.5e-26):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e-18) || !(y <= 6.5e-26))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4e-18) || ~((y <= 6.5e-26)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4e-18], N[Not[LessEqual[y, 6.5e-26]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000003e-18 or 6.5e-26 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.6%

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

      1. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around inf 39.5%

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

      1. *-commutative 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in x around 0 38.7%

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

       1. *-commutative 38.7%

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

   11. Simplified 38.7%

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

   if -4.0000000000000003e-18 < y < 6.5e-26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 72.1%

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

   4. Taylor expanded in x around inf 37.7%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-18} \lor \neg \left(y \leq 6.5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 17.9% 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. Add Preprocessing

3. Taylor expanded in t around inf 61.9%

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

4. Taylor expanded in x around inf 20.7%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Developer target: 96.0% 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 2024087 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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