Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.5s

Alternatives: 12

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. Final simplification 100.0%

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

Alternative 2: 62.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -3 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -3e+100)
     t_1
     (if (<= t -9.6e-21)
       (+ x (* y t))
       (if (<= t -5.3e-39)
         t_1
         (if (<= t -2.15e-72)
           (* x (- y))
           (if (<= t 5.6e-5) (+ x (* x z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -3e+100) {
		tmp = t_1;
	} else if (t <= -9.6e-21) {
		tmp = x + (y * t);
	} else if (t <= -5.3e-39) {
		tmp = t_1;
	} else if (t <= -2.15e-72) {
		tmp = x * -y;
	} else if (t <= 5.6e-5) {
		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 = (y - z) * t
    if (t <= (-3d+100)) then
        tmp = t_1
    else if (t <= (-9.6d-21)) then
        tmp = x + (y * t)
    else if (t <= (-5.3d-39)) then
        tmp = t_1
    else if (t <= (-2.15d-72)) then
        tmp = x * -y
    else if (t <= 5.6d-5) 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 = (y - z) * t;
	double tmp;
	if (t <= -3e+100) {
		tmp = t_1;
	} else if (t <= -9.6e-21) {
		tmp = x + (y * t);
	} else if (t <= -5.3e-39) {
		tmp = t_1;
	} else if (t <= -2.15e-72) {
		tmp = x * -y;
	} else if (t <= 5.6e-5) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -3e+100:
		tmp = t_1
	elif t <= -9.6e-21:
		tmp = x + (y * t)
	elif t <= -5.3e-39:
		tmp = t_1
	elif t <= -2.15e-72:
		tmp = x * -y
	elif t <= 5.6e-5:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -3e+100)
		tmp = t_1;
	elseif (t <= -9.6e-21)
		tmp = Float64(x + Float64(y * t));
	elseif (t <= -5.3e-39)
		tmp = t_1;
	elseif (t <= -2.15e-72)
		tmp = Float64(x * Float64(-y));
	elseif (t <= 5.6e-5)
		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 = (y - z) * t;
	tmp = 0.0;
	if (t <= -3e+100)
		tmp = t_1;
	elseif (t <= -9.6e-21)
		tmp = x + (y * t);
	elseif (t <= -5.3e-39)
		tmp = t_1;
	elseif (t <= -2.15e-72)
		tmp = x * -y;
	elseif (t <= 5.6e-5)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -3e+100], t$95$1, If[LessEqual[t, -9.6e-21], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.3e-39], t$95$1, If[LessEqual[t, -2.15e-72], N[(x * (-y)), $MachinePrecision], If[LessEqual[t, 5.6e-5], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.99999999999999985e100 or -9.5999999999999997e-21 < t < -5.30000000000000003e-39 or 5.59999999999999992e-5 < t

   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 90.1%

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

   4. Taylor expanded in y around 0 85.8%

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

   5. Taylor expanded in x around 0 75.3%

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

   6. Taylor expanded in t around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

   8. Simplified 79.5%

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

   if -2.99999999999999985e100 < t < -9.5999999999999997e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 63.7%

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

   4. Taylor expanded in z around 0 52.0%

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

   if -5.30000000000000003e-39 < t < -2.1499999999999999e-72

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. distribute-rgt-neg-in 79.0%

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

      3. sub-neg 79.0%

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

      4. +-commutative 79.0%

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

      5. distribute-neg-in 79.0%

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

      6. remove-double-neg 79.0%

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

      7. sub-neg 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. unsub-neg 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in y around inf 73.3%

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

       1. mul-1-neg 73.3%

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

       2. *-commutative 73.3%

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

       3. distribute-rgt-neg-in 73.3%

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

   11. Simplified 73.3%

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

   if -2.1499999999999999e-72 < t < 5.59999999999999992e-5

   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 91.5%

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

      1. mul-1-neg 91.5%

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

      2. distribute-rgt-neg-in 91.5%

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

      3. sub-neg 91.5%

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

      4. +-commutative 91.5%

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

      5. distribute-neg-in 91.5%

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

      6. remove-double-neg 91.5%

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

      7. sub-neg 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in y around 0 75.1%

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

      1. *-commutative 75.1%

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

   8. Simplified 75.1%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+100}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-21}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-39}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.38 \cdot 10^{+57}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 0.00095:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.3e+173)
     t_1
     (if (<= t -1.38e+57)
       (- x (* z t))
       (if (<= t -1.05e-39)
         (+ x (* y t))
         (if (<= t -2.15e-72)
           (* x (- y))
           (if (<= t 0.00095) (+ x (* x z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.3e+173) {
		tmp = t_1;
	} else if (t <= -1.38e+57) {
		tmp = x - (z * t);
	} else if (t <= -1.05e-39) {
		tmp = x + (y * t);
	} else if (t <= -2.15e-72) {
		tmp = x * -y;
	} else if (t <= 0.00095) {
		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 = (y - z) * t
    if (t <= (-1.3d+173)) then
        tmp = t_1
    else if (t <= (-1.38d+57)) then
        tmp = x - (z * t)
    else if (t <= (-1.05d-39)) then
        tmp = x + (y * t)
    else if (t <= (-2.15d-72)) then
        tmp = x * -y
    else if (t <= 0.00095d0) 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 = (y - z) * t;
	double tmp;
	if (t <= -1.3e+173) {
		tmp = t_1;
	} else if (t <= -1.38e+57) {
		tmp = x - (z * t);
	} else if (t <= -1.05e-39) {
		tmp = x + (y * t);
	} else if (t <= -2.15e-72) {
		tmp = x * -y;
	} else if (t <= 0.00095) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.3e+173:
		tmp = t_1
	elif t <= -1.38e+57:
		tmp = x - (z * t)
	elif t <= -1.05e-39:
		tmp = x + (y * t)
	elif t <= -2.15e-72:
		tmp = x * -y
	elif t <= 0.00095:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.3e+173)
		tmp = t_1;
	elseif (t <= -1.38e+57)
		tmp = Float64(x - Float64(z * t));
	elseif (t <= -1.05e-39)
		tmp = Float64(x + Float64(y * t));
	elseif (t <= -2.15e-72)
		tmp = Float64(x * Float64(-y));
	elseif (t <= 0.00095)
		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 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.3e+173)
		tmp = t_1;
	elseif (t <= -1.38e+57)
		tmp = x - (z * t);
	elseif (t <= -1.05e-39)
		tmp = x + (y * t);
	elseif (t <= -2.15e-72)
		tmp = x * -y;
	elseif (t <= 0.00095)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.3e+173], t$95$1, If[LessEqual[t, -1.38e+57], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-39], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.15e-72], N[(x * (-y)), $MachinePrecision], If[LessEqual[t, 0.00095], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.2999999999999999e173 or 9.49999999999999998e-4 < t

   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 89.0%

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

   4. Taylor expanded in y around 0 83.8%

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

   5. Taylor expanded in x around 0 75.2%

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

   6. Taylor expanded in t around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

   8. Simplified 80.4%

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

   if -1.2999999999999999e173 < t < -1.38e57

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 87.2%

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

   4. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

   6. Simplified 79.8%

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

   if -1.38e57 < t < -1.04999999999999997e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 65.7%

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

   4. Taylor expanded in z around 0 54.2%

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

   if -1.04999999999999997e-39 < t < -2.1499999999999999e-72

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. distribute-rgt-neg-in 79.0%

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

      3. sub-neg 79.0%

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

      4. +-commutative 79.0%

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

      5. distribute-neg-in 79.0%

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

      6. remove-double-neg 79.0%

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

      7. sub-neg 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. unsub-neg 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in y around inf 73.3%

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

       1. mul-1-neg 73.3%

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

       2. *-commutative 73.3%

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

       3. distribute-rgt-neg-in 73.3%

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

   11. Simplified 73.3%

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

   if -2.1499999999999999e-72 < t < 9.49999999999999998e-4

   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 91.5%

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

      1. mul-1-neg 91.5%

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

      2. distribute-rgt-neg-in 91.5%

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

      3. sub-neg 91.5%

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

      4. +-commutative 91.5%

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

      5. distribute-neg-in 91.5%

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

      6. remove-double-neg 91.5%

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

      7. sub-neg 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in y around 0 75.1%

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

      1. *-commutative 75.1%

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

   8. Simplified 75.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+173}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -1.38 \cdot 10^{+57}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 0.00095:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+54}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-87}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.5e+173)
     t_1
     (if (<= t -3.7e+54)
       (- x (* z t))
       (if (<= t -4.1e-39)
         (+ x (* y t))
         (if (<= t -5e-87)
           (- x (* x y))
           (if (<= t 5.9e-5) (+ x (* x z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.5e+173) {
		tmp = t_1;
	} else if (t <= -3.7e+54) {
		tmp = x - (z * t);
	} else if (t <= -4.1e-39) {
		tmp = x + (y * t);
	} else if (t <= -5e-87) {
		tmp = x - (x * y);
	} else if (t <= 5.9e-5) {
		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 = (y - z) * t
    if (t <= (-1.5d+173)) then
        tmp = t_1
    else if (t <= (-3.7d+54)) then
        tmp = x - (z * t)
    else if (t <= (-4.1d-39)) then
        tmp = x + (y * t)
    else if (t <= (-5d-87)) then
        tmp = x - (x * y)
    else if (t <= 5.9d-5) 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 = (y - z) * t;
	double tmp;
	if (t <= -1.5e+173) {
		tmp = t_1;
	} else if (t <= -3.7e+54) {
		tmp = x - (z * t);
	} else if (t <= -4.1e-39) {
		tmp = x + (y * t);
	} else if (t <= -5e-87) {
		tmp = x - (x * y);
	} else if (t <= 5.9e-5) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.5e+173:
		tmp = t_1
	elif t <= -3.7e+54:
		tmp = x - (z * t)
	elif t <= -4.1e-39:
		tmp = x + (y * t)
	elif t <= -5e-87:
		tmp = x - (x * y)
	elif t <= 5.9e-5:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.5e+173)
		tmp = t_1;
	elseif (t <= -3.7e+54)
		tmp = Float64(x - Float64(z * t));
	elseif (t <= -4.1e-39)
		tmp = Float64(x + Float64(y * t));
	elseif (t <= -5e-87)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 5.9e-5)
		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 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.5e+173)
		tmp = t_1;
	elseif (t <= -3.7e+54)
		tmp = x - (z * t);
	elseif (t <= -4.1e-39)
		tmp = x + (y * t);
	elseif (t <= -5e-87)
		tmp = x - (x * y);
	elseif (t <= 5.9e-5)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.5e+173], t$95$1, If[LessEqual[t, -3.7e+54], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.1e-39], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-87], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.9e-5], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.4999999999999999e173 or 5.8999999999999998e-5 < t

   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 89.0%

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

   4. Taylor expanded in y around 0 83.8%

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

   5. Taylor expanded in x around 0 75.2%

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

   6. Taylor expanded in t around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

   8. Simplified 80.4%

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

   if -1.4999999999999999e173 < t < -3.7000000000000002e54

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 87.2%

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

   4. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

   6. Simplified 79.8%

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

   if -3.7000000000000002e54 < t < -4.1e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 65.7%

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

   4. Taylor expanded in z around 0 54.2%

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

   if -4.1e-39 < t < -5.00000000000000042e-87

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

      3. sub-neg 83.4%

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

      4. +-commutative 83.4%

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

      5. distribute-neg-in 83.4%

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

      6. remove-double-neg 83.4%

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

      7. sub-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in z around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. unsub-neg 78.9%

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

   8. Simplified 78.9%

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

   if -5.00000000000000042e-87 < t < 5.8999999999999998e-5

   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 91.3%

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

      1. mul-1-neg 91.3%

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

      2. distribute-rgt-neg-in 91.3%

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

      3. sub-neg 91.3%

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

      4. +-commutative 91.3%

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

      5. distribute-neg-in 91.3%

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

      6. remove-double-neg 91.3%

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

      7. sub-neg 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. *-commutative 75.3%

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

   8. Simplified 75.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+173}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{+54}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-39}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-87}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-5}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+79}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2250000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -6e+79)
     (* y t)
     (if (<= y -8.5e+35)
       t_1
       (if (<= y -2250000000.0)
         (* y t)
         (if (<= y 1.3e-23) x (if (<= y 2e+104) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -6e+79) {
		tmp = y * t;
	} else if (y <= -8.5e+35) {
		tmp = t_1;
	} else if (y <= -2250000000.0) {
		tmp = y * t;
	} else if (y <= 1.3e-23) {
		tmp = x;
	} else if (y <= 2e+104) {
		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 * -y
    if (y <= (-6d+79)) then
        tmp = y * t
    else if (y <= (-8.5d+35)) then
        tmp = t_1
    else if (y <= (-2250000000.0d0)) then
        tmp = y * t
    else if (y <= 1.3d-23) then
        tmp = x
    else if (y <= 2d+104) 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 * -y;
	double tmp;
	if (y <= -6e+79) {
		tmp = y * t;
	} else if (y <= -8.5e+35) {
		tmp = t_1;
	} else if (y <= -2250000000.0) {
		tmp = y * t;
	} else if (y <= 1.3e-23) {
		tmp = x;
	} else if (y <= 2e+104) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -6e+79:
		tmp = y * t
	elif y <= -8.5e+35:
		tmp = t_1
	elif y <= -2250000000.0:
		tmp = y * t
	elif y <= 1.3e-23:
		tmp = x
	elif y <= 2e+104:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -6e+79)
		tmp = Float64(y * t);
	elseif (y <= -8.5e+35)
		tmp = t_1;
	elseif (y <= -2250000000.0)
		tmp = Float64(y * t);
	elseif (y <= 1.3e-23)
		tmp = x;
	elseif (y <= 2e+104)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -6e+79)
		tmp = y * t;
	elseif (y <= -8.5e+35)
		tmp = t_1;
	elseif (y <= -2250000000.0)
		tmp = y * t;
	elseif (y <= 1.3e-23)
		tmp = x;
	elseif (y <= 2e+104)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -6e+79], N[(y * t), $MachinePrecision], If[LessEqual[y, -8.5e+35], t$95$1, If[LessEqual[y, -2250000000.0], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.3e-23], x, If[LessEqual[y, 2e+104], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999948e79 or -8.4999999999999995e35 < y < -2.25e9 or 1.3e-23 < y < 2e104

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 68.3%

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

   4. Taylor expanded in y around 0 63.4%

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

   5. Taylor expanded in x around 0 63.3%

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

   6. Taylor expanded in z around 0 51.3%

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

   if -5.99999999999999948e79 < y < -8.4999999999999995e35 or 2e104 < y

   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 64.6%

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

      1. mul-1-neg 64.6%

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

      2. distribute-rgt-neg-in 64.6%

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

      3. sub-neg 64.6%

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

      4. +-commutative 64.6%

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

      5. distribute-neg-in 64.6%

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

      6. remove-double-neg 64.6%

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

      7. sub-neg 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in z around 0 49.7%

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

      1. mul-1-neg 49.7%

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

      2. unsub-neg 49.7%

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

   8. Simplified 49.7%

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

   9. Taylor expanded in y around inf 49.7%

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

       1. mul-1-neg 49.7%

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

       2. *-commutative 49.7%

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

       3. distribute-rgt-neg-in 49.7%

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

   11. Simplified 49.7%

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

   if -2.25e9 < y < 1.3e-23

   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 73.4%

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

   4. Taylor expanded in x around inf 38.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+79}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2250000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+49} \lor \neg \left(t \leq -2.2 \cdot 10^{-5} \lor \neg \left(t \leq -1.7 \cdot 10^{-38}\right) \land t \leq 1.15 \cdot 10^{-74}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e+49)
         (not (or (<= t -2.2e-5) (and (not (<= t -1.7e-38)) (<= t 1.15e-74)))))
   (+ x (* (- y z) t))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e+49) || !((t <= -2.2e-5) || (!(t <= -1.7e-38) && (t <= 1.15e-74)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (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 ((t <= (-1.65d+49)) .or. (.not. (t <= (-2.2d-5)) .or. (.not. (t <= (-1.7d-38))) .and. (t <= 1.15d-74))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e+49) || !((t <= -2.2e-5) || (!(t <= -1.7e-38) && (t <= 1.15e-74)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e+49) or not ((t <= -2.2e-5) or (not (t <= -1.7e-38) and (t <= 1.15e-74))):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e+49) || !((t <= -2.2e-5) || (!(t <= -1.7e-38) && (t <= 1.15e-74))))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65e+49) || ~(((t <= -2.2e-5) || (~((t <= -1.7e-38)) && (t <= 1.15e-74)))))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e+49], N[Not[Or[LessEqual[t, -2.2e-5], And[N[Not[LessEqual[t, -1.7e-38]], $MachinePrecision], LessEqual[t, 1.15e-74]]]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6499999999999999e49 or -2.1999999999999999e-5 < t < -1.7000000000000001e-38 or 1.1499999999999999e-74 < t

   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 89.8%

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

   if -1.6499999999999999e49 < t < -2.1999999999999999e-5 or -1.7000000000000001e-38 < t < 1.1499999999999999e-74

   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 90.2%

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

      1. mul-1-neg 90.2%

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

      2. distribute-rgt-neg-in 90.2%

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

      3. sub-neg 90.2%

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

      4. +-commutative 90.2%

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

      5. distribute-neg-in 90.2%

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

      6. remove-double-neg 90.2%

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

      7. sub-neg 90.2%

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

   5. Simplified 90.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+49} \lor \neg \left(t \leq -2.2 \cdot 10^{-5} \lor \neg \left(t \leq -1.7 \cdot 10^{-38}\right) \land t \leq 1.15 \cdot 10^{-74}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-88}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-81}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))))
   (if (<= t -1.08e-39)
     t_1
     (if (<= t -2.05e-88)
       (- x (* x y))
       (if (<= t 7.5e-81) (+ 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 <= -1.08e-39) {
		tmp = t_1;
	} else if (t <= -2.05e-88) {
		tmp = x - (x * y);
	} else if (t <= 7.5e-81) {
		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 <= (-1.08d-39)) then
        tmp = t_1
    else if (t <= (-2.05d-88)) then
        tmp = x - (x * y)
    else if (t <= 7.5d-81) 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 <= -1.08e-39) {
		tmp = t_1;
	} else if (t <= -2.05e-88) {
		tmp = x - (x * y);
	} else if (t <= 7.5e-81) {
		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 <= -1.08e-39:
		tmp = t_1
	elif t <= -2.05e-88:
		tmp = x - (x * y)
	elif t <= 7.5e-81:
		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 <= -1.08e-39)
		tmp = t_1;
	elseif (t <= -2.05e-88)
		tmp = Float64(x - Float64(x * y));
	elseif (t <= 7.5e-81)
		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 <= -1.08e-39)
		tmp = t_1;
	elseif (t <= -2.05e-88)
		tmp = x - (x * y);
	elseif (t <= 7.5e-81)
		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, -1.08e-39], t$95$1, If[LessEqual[t, -2.05e-88], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-81], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08e-39 or 7.50000000000000018e-81 < t

   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 85.5%

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

   if -1.08e-39 < t < -2.0500000000000001e-88

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

      3. sub-neg 83.4%

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

      4. +-commutative 83.4%

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

      5. distribute-neg-in 83.4%

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

      6. remove-double-neg 83.4%

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

      7. sub-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in z around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. unsub-neg 78.9%

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

   8. Simplified 78.9%

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

   if -2.0500000000000001e-88 < t < 7.50000000000000018e-81

   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 92.9%

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

      1. mul-1-neg 92.9%

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

      2. distribute-rgt-neg-in 92.9%

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

      3. sub-neg 92.9%

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

      4. +-commutative 92.9%

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

      5. distribute-neg-in 92.9%

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

      6. remove-double-neg 92.9%

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

      7. sub-neg 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in y around 0 76.1%

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

      1. *-commutative 76.1%

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

   8. Simplified 76.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-88}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-81}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-7} \lor \neg \left(y - z \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -5e-7) (not (<= (- y z) 1.3e-23))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-7) || !((y - z) <= 1.3e-23)) {
		tmp = (y - z) * 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 - z) <= (-5d-7)) .or. (.not. ((y - z) <= 1.3d-23))) then
        tmp = (y - z) * 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 - z) <= -5e-7) || !((y - z) <= 1.3e-23)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -5e-7) or not ((y - z) <= 1.3e-23):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -5e-7) || !(Float64(y - z) <= 1.3e-23))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -5e-7) || ~(((y - z) <= 1.3e-23)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -5e-7], N[Not[LessEqual[N[(y - z), $MachinePrecision], 1.3e-23]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -4.99999999999999977e-7 or 1.3e-23 < (-.f64 y 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 52.6%

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

   4. Taylor expanded in y around 0 49.9%

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

   5. Taylor expanded in x around 0 48.8%

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

   6. Taylor expanded in t around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

   8. Simplified 51.5%

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

   if -4.99999999999999977e-7 < (-.f64 y z) < 1.3e-23

   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 99.8%

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

   4. Taylor expanded in x around inf 72.5%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-7} \lor \neg \left(y - z \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+51} \lor \neg \left(z \leq 9 \cdot 10^{+23}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.8e+51) (not (<= z 9e+23)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e+51) || !(z <= 9e+23)) {
		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 <= (-9.8d+51)) .or. (.not. (z <= 9d+23))) 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 <= -9.8e+51) || !(z <= 9e+23)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.8e+51) or not (z <= 9e+23):
		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 <= -9.8e+51) || !(z <= 9e+23))
		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 <= -9.8e+51) || ~((z <= 9e+23)))
		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, -9.8e+51], N[Not[LessEqual[z, 9e+23]], $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 < -9.79999999999999967e51 or 8.99999999999999958e23 < 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 88.4%

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

      1. mul-1-neg 88.4%

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

      2. distribute-rgt-neg-in 88.4%

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

      3. sub-neg 88.4%

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

      4. +-commutative 88.4%

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

      5. distribute-neg-in 88.4%

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

      6. remove-double-neg 88.4%

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

      7. sub-neg 88.4%

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

   5. Simplified 88.4%

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

   if -9.79999999999999967e51 < z < 8.99999999999999958e23

   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 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+51} \lor \neg \left(z \leq 9 \cdot 10^{+23}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-16} \lor \neg \left(z \leq 2.4 \cdot 10^{-13}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e-16) (not (<= z 2.4e-13))) (* (- y z) t) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e-16) || !(z <= 2.4e-13)) {
		tmp = (y - z) * t;
	} 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 <= (-3.4d-16)) .or. (.not. (z <= 2.4d-13))) then
        tmp = (y - z) * t
    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 <= -3.4e-16) || !(z <= 2.4e-13)) {
		tmp = (y - z) * t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e-16) or not (z <= 2.4e-13):
		tmp = (y - z) * t
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e-16) || !(z <= 2.4e-13))
		tmp = Float64(Float64(y - z) * t);
	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 <= -3.4e-16) || ~((z <= 2.4e-13)))
		tmp = (y - z) * t;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e-16], N[Not[LessEqual[z, 2.4e-13]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e-16 or 2.3999999999999999e-13 < 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 50.7%

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

   4. Taylor expanded in y around 0 47.1%

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

   5. Taylor expanded in x around 0 46.5%

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

   6. Taylor expanded in t around 0 50.1%

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

      1. mul-1-neg 50.1%

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

      2. unsub-neg 50.1%

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

   8. Simplified 50.1%

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

   if -3.4e-16 < z < 2.3999999999999999e-13

   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 83.4%

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

   4. Taylor expanded in z around 0 76.0%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-16} \lor \neg \left(z \leq 2.4 \cdot 10^{-13}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2000000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2000000000000.0) (not (<= y 1.3e-23))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2000000000000.0) || !(y <= 1.3e-23)) {
		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 <= (-2000000000000.0d0)) .or. (.not. (y <= 1.3d-23))) 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 <= -2000000000000.0) || !(y <= 1.3e-23)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2000000000000.0) or not (y <= 1.3e-23):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2000000000000.0) || !(y <= 1.3e-23))
		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 <= -2000000000000.0) || ~((y <= 1.3e-23)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2000000000000.0], N[Not[LessEqual[y, 1.3e-23]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2e12 or 1.3e-23 < y

   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 55.7%

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

   4. Taylor expanded in y around 0 51.3%

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

   5. Taylor expanded in x around 0 51.0%

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

   6. Taylor expanded in z around 0 42.8%

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

   if -2e12 < y < 1.3e-23

   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 73.4%

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

   4. Taylor expanded in x around inf 38.2%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2000000000000 \lor \neg \left(y \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 65.7%

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

4. Taylor expanded in x around inf 22.8%

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

5. Final simplification 22.8%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.3% 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 2024059 
(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))))