Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 16

Speedup: 1.0×

• 34.4% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right) \]
6. Add Preprocessing

Alternative 2: 36.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := y \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* y (- x))))
   (if (<= z -3.4e+34)
     t_1
     (if (<= z -1.5e-26)
       t_2
       (if (<= z -2.3e-57)
         t_1
         (if (<= z -8e-289)
           x
           (if (<= z 1.35e-231)
             t_2
             (if (<= z 1.25e-96) x (if (<= z 2.7e+72) (* y t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = y * -x;
	double tmp;
	if (z <= -3.4e+34) {
		tmp = t_1;
	} else if (z <= -1.5e-26) {
		tmp = t_2;
	} else if (z <= -2.3e-57) {
		tmp = t_1;
	} else if (z <= -8e-289) {
		tmp = x;
	} else if (z <= 1.35e-231) {
		tmp = t_2;
	} else if (z <= 1.25e-96) {
		tmp = x;
	} else if (z <= 2.7e+72) {
		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) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = y * -x
    if (z <= (-3.4d+34)) then
        tmp = t_1
    else if (z <= (-1.5d-26)) then
        tmp = t_2
    else if (z <= (-2.3d-57)) then
        tmp = t_1
    else if (z <= (-8d-289)) then
        tmp = x
    else if (z <= 1.35d-231) then
        tmp = t_2
    else if (z <= 1.25d-96) then
        tmp = x
    else if (z <= 2.7d+72) 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 = z * -t;
	double t_2 = y * -x;
	double tmp;
	if (z <= -3.4e+34) {
		tmp = t_1;
	} else if (z <= -1.5e-26) {
		tmp = t_2;
	} else if (z <= -2.3e-57) {
		tmp = t_1;
	} else if (z <= -8e-289) {
		tmp = x;
	} else if (z <= 1.35e-231) {
		tmp = t_2;
	} else if (z <= 1.25e-96) {
		tmp = x;
	} else if (z <= 2.7e+72) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = y * -x
	tmp = 0
	if z <= -3.4e+34:
		tmp = t_1
	elif z <= -1.5e-26:
		tmp = t_2
	elif z <= -2.3e-57:
		tmp = t_1
	elif z <= -8e-289:
		tmp = x
	elif z <= 1.35e-231:
		tmp = t_2
	elif z <= 1.25e-96:
		tmp = x
	elif z <= 2.7e+72:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(y * Float64(-x))
	tmp = 0.0
	if (z <= -3.4e+34)
		tmp = t_1;
	elseif (z <= -1.5e-26)
		tmp = t_2;
	elseif (z <= -2.3e-57)
		tmp = t_1;
	elseif (z <= -8e-289)
		tmp = x;
	elseif (z <= 1.35e-231)
		tmp = t_2;
	elseif (z <= 1.25e-96)
		tmp = x;
	elseif (z <= 2.7e+72)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = y * -x;
	tmp = 0.0;
	if (z <= -3.4e+34)
		tmp = t_1;
	elseif (z <= -1.5e-26)
		tmp = t_2;
	elseif (z <= -2.3e-57)
		tmp = t_1;
	elseif (z <= -8e-289)
		tmp = x;
	elseif (z <= 1.35e-231)
		tmp = t_2;
	elseif (z <= 1.25e-96)
		tmp = x;
	elseif (z <= 2.7e+72)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[z, -3.4e+34], t$95$1, If[LessEqual[z, -1.5e-26], t$95$2, If[LessEqual[z, -2.3e-57], t$95$1, If[LessEqual[z, -8e-289], x, If[LessEqual[z, 1.35e-231], t$95$2, If[LessEqual[z, 1.25e-96], x, If[LessEqual[z, 2.7e+72], N[(y * t), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999999e34 or -1.50000000000000006e-26 < z < -2.3e-57 or 2.7000000000000001e72 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.2%

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in x around 0 55.4%

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

      1. associate-+r+ 55.4%

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

      2. mul-1-neg 55.4%

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

      3. *-commutative 55.4%

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

      4. sub-neg 55.4%

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

      5. associate-+l- 55.4%

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

      6. *-commutative 55.4%

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

   7. Applied egg-rr 55.4%

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

   8. Taylor expanded in z around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. distribute-rgt-neg-out 53.5%

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

   10. Simplified 53.5%

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

   if -3.3999999999999999e34 < z < -1.50000000000000006e-26 or -8.0000000000000001e-289 < z < 1.35000000000000011e-231

   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 94.7%

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

      1. *-commutative 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in x around inf 67.9%

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

      1. neg-mul-1 67.9%

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

      2. unsub-neg 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in y around inf 53.2%

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

       1. associate-*r* 53.2%

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

       2. mul-1-neg 53.2%

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

       3. *-commutative 53.2%

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

   11. Simplified 53.2%

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

   if -2.3e-57 < z < -8.0000000000000001e-289 or 1.35000000000000011e-231 < z < 1.24999999999999999e-96

   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 76.3%

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

   4. Taylor expanded in x around inf 48.9%

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

   if 1.24999999999999999e-96 < z < 2.7000000000000001e72

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in x around 0 61.3%

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

      1. associate-+r+ 61.3%

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

      2. mul-1-neg 61.3%

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

      3. *-commutative 61.3%

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

      4. sub-neg 61.3%

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

      5. associate-+l- 61.3%

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

      6. *-commutative 61.3%

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

   7. Applied egg-rr 61.3%

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

   8. Taylor expanded in y around inf 45.7%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-96}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2.4e-56)
     t_1
     (if (<= z -5.1e-198)
       x
       (if (<= z 7.5e-258)
         (* y t)
         (if (<= z 1.9e-95) x (if (<= z 3.4e+72) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.4e-56) {
		tmp = t_1;
	} else if (z <= -5.1e-198) {
		tmp = x;
	} else if (z <= 7.5e-258) {
		tmp = y * t;
	} else if (z <= 1.9e-95) {
		tmp = x;
	} else if (z <= 3.4e+72) {
		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 = z * -t
    if (z <= (-2.4d-56)) then
        tmp = t_1
    else if (z <= (-5.1d-198)) then
        tmp = x
    else if (z <= 7.5d-258) then
        tmp = y * t
    else if (z <= 1.9d-95) then
        tmp = x
    else if (z <= 3.4d+72) 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 = z * -t;
	double tmp;
	if (z <= -2.4e-56) {
		tmp = t_1;
	} else if (z <= -5.1e-198) {
		tmp = x;
	} else if (z <= 7.5e-258) {
		tmp = y * t;
	} else if (z <= 1.9e-95) {
		tmp = x;
	} else if (z <= 3.4e+72) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -2.4e-56:
		tmp = t_1
	elif z <= -5.1e-198:
		tmp = x
	elif z <= 7.5e-258:
		tmp = y * t
	elif z <= 1.9e-95:
		tmp = x
	elif z <= 3.4e+72:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2.4e-56)
		tmp = t_1;
	elseif (z <= -5.1e-198)
		tmp = x;
	elseif (z <= 7.5e-258)
		tmp = Float64(y * t);
	elseif (z <= 1.9e-95)
		tmp = x;
	elseif (z <= 3.4e+72)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -2.4e-56)
		tmp = t_1;
	elseif (z <= -5.1e-198)
		tmp = x;
	elseif (z <= 7.5e-258)
		tmp = y * t;
	elseif (z <= 1.9e-95)
		tmp = x;
	elseif (z <= 3.4e+72)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -2.4e-56], t$95$1, If[LessEqual[z, -5.1e-198], x, If[LessEqual[z, 7.5e-258], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.9e-95], x, If[LessEqual[z, 3.4e+72], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000001e-56 or 3.3999999999999998e72 < z

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in x around 0 54.7%

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

      1. associate-+r+ 54.7%

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

      2. mul-1-neg 54.7%

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

      3. *-commutative 54.7%

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

      4. sub-neg 54.7%

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

      5. associate-+l- 54.7%

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

      6. *-commutative 54.7%

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

   7. Applied egg-rr 54.7%

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

   8. Taylor expanded in z around inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. distribute-rgt-neg-out 49.1%

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

   10. Simplified 49.1%

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

   if -2.40000000000000001e-56 < z < -5.0999999999999997e-198 or 7.4999999999999998e-258 < z < 1.8999999999999999e-95

   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 71.1%

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

   4. Taylor expanded in x around inf 49.0%

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

   if -5.0999999999999997e-198 < z < 7.4999999999999998e-258 or 1.8999999999999999e-95 < z < 3.3999999999999998e72

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in x around 0 65.6%

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

      1. associate-+r+ 65.6%

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

      2. mul-1-neg 65.6%

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

      3. *-commutative 65.6%

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

      4. sub-neg 65.6%

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

      5. associate-+l- 65.6%

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

      6. *-commutative 65.6%

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

   7. Applied egg-rr 65.6%

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

   8. Taylor expanded in y around inf 42.6%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+72}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.042 \lor \neg \left(t \leq -7.8 \cdot 10^{-51}\right) \land \left(t \leq -4.5 \cdot 10^{-113} \lor \neg \left(t \leq 6.2 \cdot 10^{+74}\right)\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.042)
         (and (not (<= t -7.8e-51))
              (or (<= t -4.5e-113) (not (<= t 6.2e+74)))))
   (+ x (* t (- y z)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.042) || (!(t <= -7.8e-51) && ((t <= -4.5e-113) || !(t <= 6.2e+74)))) {
		tmp = x + (t * (y - z));
	} 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 <= (-0.042d0)) .or. (.not. (t <= (-7.8d-51))) .and. (t <= (-4.5d-113)) .or. (.not. (t <= 6.2d+74))) then
        tmp = x + (t * (y - z))
    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 <= -0.042) || (!(t <= -7.8e-51) && ((t <= -4.5e-113) || !(t <= 6.2e+74)))) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.042) or (not (t <= -7.8e-51) and ((t <= -4.5e-113) or not (t <= 6.2e+74))):
		tmp = x + (t * (y - z))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.042) || (!(t <= -7.8e-51) && ((t <= -4.5e-113) || !(t <= 6.2e+74))))
		tmp = Float64(x + Float64(t * Float64(y - z)));
	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 <= -0.042) || (~((t <= -7.8e-51)) && ((t <= -4.5e-113) || ~((t <= 6.2e+74)))))
		tmp = x + (t * (y - z));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.042], And[N[Not[LessEqual[t, -7.8e-51]], $MachinePrecision], Or[LessEqual[t, -4.5e-113], N[Not[LessEqual[t, 6.2e+74]], $MachinePrecision]]]], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0420000000000000026 or -7.7999999999999995e-51 < t < -4.5000000000000001e-113 or 6.20000000000000043e74 < 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 86.1%

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

   if -0.0420000000000000026 < t < -7.7999999999999995e-51 or -4.5000000000000001e-113 < t < 6.20000000000000043e74

   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 86.6%

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

      1. mul-1-neg 86.6%

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

      2. distribute-rgt-neg-in 86.6%

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

      3. neg-sub0 86.6%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 86.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 86.6%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 86.6%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 86.6%

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

      8. remove-double-neg 86.6%

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

   5. Simplified 86.6%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.042 \lor \neg \left(t \leq -7.8 \cdot 10^{-51}\right) \land \left(t \leq -4.5 \cdot 10^{-113} \lor \neg \left(t \leq 6.2 \cdot 10^{+74}\right)\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-265}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* (- y z) t))))
   (if (<= z -1.85e+81)
     t_1
     (if (<= z 9e-265)
       t_2
       (if (<= z 1.85e-97) (* x (- 1.0 y)) (if (<= z 1.42e+31) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (z <= -1.85e+81) {
		tmp = t_1;
	} else if (z <= 9e-265) {
		tmp = t_2;
	} else if (z <= 1.85e-97) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.42e+31) {
		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 = z * (x - t)
    t_2 = x + ((y - z) * t)
    if (z <= (-1.85d+81)) then
        tmp = t_1
    else if (z <= 9d-265) then
        tmp = t_2
    else if (z <= 1.85d-97) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1.42d+31) 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 = z * (x - t);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (z <= -1.85e+81) {
		tmp = t_1;
	} else if (z <= 9e-265) {
		tmp = t_2;
	} else if (z <= 1.85e-97) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.42e+31) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if z <= -1.85e+81:
		tmp = t_1
	elif z <= 9e-265:
		tmp = t_2
	elif z <= 1.85e-97:
		tmp = x * (1.0 - y)
	elif z <= 1.42e+31:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -1.85e+81)
		tmp = t_1;
	elseif (z <= 9e-265)
		tmp = t_2;
	elseif (z <= 1.85e-97)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1.42e+31)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + ((y - z) * t);
	tmp = 0.0;
	if (z <= -1.85e+81)
		tmp = t_1;
	elseif (z <= 9e-265)
		tmp = t_2;
	elseif (z <= 1.85e-97)
		tmp = x * (1.0 - y);
	elseif (z <= 1.42e+31)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+81], t$95$1, If[LessEqual[z, 9e-265], t$95$2, If[LessEqual[z, 1.85e-97], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e+31], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85e81 or 1.41999999999999997e31 < 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 82.9%

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

      1. mul-1-neg 82.9%

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

      2. unsub-neg 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in z around inf 82.9%

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

   7. Taylor expanded in z around inf 82.9%

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

   if -1.85e81 < z < 9.0000000000000006e-265 or 1.84999999999999988e-97 < z < 1.41999999999999997e31

   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 74.5%

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

   if 9.0000000000000006e-265 < z < 1.84999999999999988e-97

   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 97.7%

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

      1. *-commutative 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in x around inf 83.0%

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

      1. neg-mul-1 83.0%

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

      2. unsub-neg 83.0%

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

   8. Simplified 83.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-265}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+31}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.16 \lor \neg \left(t \leq -1.4 \cdot 10^{-48}\right) \land \left(t \leq -4.7 \cdot 10^{-113} \lor \neg \left(t \leq 6.8 \cdot 10^{+74}\right)\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.16)
         (and (not (<= t -1.4e-48))
              (or (<= t -4.7e-113) (not (<= t 6.8e+74)))))
   (* t (- y z))
   (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.16) || (!(t <= -1.4e-48) && ((t <= -4.7e-113) || !(t <= 6.8e+74)))) {
		tmp = t * (y - z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-0.16d0)) .or. (.not. (t <= (-1.4d-48))) .and. (t <= (-4.7d-113)) .or. (.not. (t <= 6.8d+74))) then
        tmp = t * (y - z)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.16) || (!(t <= -1.4e-48) && ((t <= -4.7e-113) || !(t <= 6.8e+74)))) {
		tmp = t * (y - z);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.16) or (not (t <= -1.4e-48) and ((t <= -4.7e-113) or not (t <= 6.8e+74))):
		tmp = t * (y - z)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.16) || (!(t <= -1.4e-48) && ((t <= -4.7e-113) || !(t <= 6.8e+74))))
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.16) || (~((t <= -1.4e-48)) && ((t <= -4.7e-113) || ~((t <= 6.8e+74)))))
		tmp = t * (y - z);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.16], And[N[Not[LessEqual[t, -1.4e-48]], $MachinePrecision], Or[LessEqual[t, -4.7e-113], N[Not[LessEqual[t, 6.8e+74]], $MachinePrecision]]]], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.160000000000000003 or -1.40000000000000002e-48 < t < -4.7000000000000002e-113 or 6.7999999999999998e74 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.2%

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in x around 0 82.9%

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

      1. associate-+r+ 82.9%

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

      2. mul-1-neg 82.9%

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

      3. *-commutative 82.9%

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

      4. sub-neg 82.9%

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

      5. associate-+l- 82.9%

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

      6. *-commutative 82.9%

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

   7. Applied egg-rr 82.9%

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

   8. Taylor expanded in x around 0 74.0%

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

      1. distribute-lft-out-- 77.2%

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

   10. Simplified 77.2%

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

   if -0.160000000000000003 < t < -1.40000000000000002e-48 or -4.7000000000000002e-113 < t < 6.7999999999999998e74

   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 67.6%

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

      1. *-commutative 67.6%

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

   5. Simplified 67.6%

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

   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%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.16 \lor \neg \left(t \leq -1.4 \cdot 10^{-48}\right) \land \left(t \leq -4.7 \cdot 10^{-113} \lor \neg \left(t \leq 6.8 \cdot 10^{+74}\right)\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-18}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* x (- 1.0 y))))
   (if (<= z -3.9e+33)
     t_1
     (if (<= z 2.3e-96)
       t_2
       (if (<= z 5.4e-18) (* (- y z) t) (if (<= z 1.5e+32) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -3.9e+33) {
		tmp = t_1;
	} else if (z <= 2.3e-96) {
		tmp = t_2;
	} else if (z <= 5.4e-18) {
		tmp = (y - z) * t;
	} else if (z <= 1.5e+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 = z * (x - t)
    t_2 = x * (1.0d0 - y)
    if (z <= (-3.9d+33)) then
        tmp = t_1
    else if (z <= 2.3d-96) then
        tmp = t_2
    else if (z <= 5.4d-18) then
        tmp = (y - z) * t
    else if (z <= 1.5d+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 = z * (x - t);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -3.9e+33) {
		tmp = t_1;
	} else if (z <= 2.3e-96) {
		tmp = t_2;
	} else if (z <= 5.4e-18) {
		tmp = (y - z) * t;
	} else if (z <= 1.5e+32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -3.9e+33:
		tmp = t_1
	elif z <= 2.3e-96:
		tmp = t_2
	elif z <= 5.4e-18:
		tmp = (y - z) * t
	elif z <= 1.5e+32:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -3.9e+33)
		tmp = t_1;
	elseif (z <= 2.3e-96)
		tmp = t_2;
	elseif (z <= 5.4e-18)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 1.5e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -3.9e+33)
		tmp = t_1;
	elseif (z <= 2.3e-96)
		tmp = t_2;
	elseif (z <= 5.4e-18)
		tmp = (y - z) * t;
	elseif (z <= 1.5e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+33], t$95$1, If[LessEqual[z, 2.3e-96], t$95$2, If[LessEqual[z, 5.4e-18], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.5e+32], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9000000000000002e33 or 1.5e32 < 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 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around inf 82.0%

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

   7. Taylor expanded in z around inf 82.0%

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

   if -3.9000000000000002e33 < z < 2.3e-96 or 5.39999999999999977e-18 < z < 1.5e32

   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 89.8%

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

      1. *-commutative 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in x around inf 67.1%

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

      1. neg-mul-1 67.1%

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

      2. unsub-neg 67.1%

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

   8. Simplified 67.1%

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

   if 2.3e-96 < z < 5.39999999999999977e-18

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 91.4%

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

      1. associate-+r+ 91.4%

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

      2. mul-1-neg 91.4%

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

      3. *-commutative 91.4%

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

      4. sub-neg 91.4%

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

      5. associate-+l- 91.4%

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

      6. *-commutative 91.4%

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

   7. Applied egg-rr 91.4%

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

   8. Taylor expanded in x around 0 77.5%

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

      1. distribute-lft-out-- 77.5%

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

   10. Simplified 77.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-96}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-18}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-265}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.3e+79)
     t_1
     (if (<= z -7.5e-57)
       (* (- y z) t)
       (if (<= z 5.5e-265)
         (+ x (* y t))
         (if (<= z 1.5e+32) (* x (- 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.3e+79) {
		tmp = t_1;
	} else if (z <= -7.5e-57) {
		tmp = (y - z) * t;
	} else if (z <= 5.5e-265) {
		tmp = x + (y * t);
	} else if (z <= 1.5e+32) {
		tmp = x * (1.0 - y);
	} 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 = z * (x - t)
    if (z <= (-1.3d+79)) then
        tmp = t_1
    else if (z <= (-7.5d-57)) then
        tmp = (y - z) * t
    else if (z <= 5.5d-265) then
        tmp = x + (y * t)
    else if (z <= 1.5d+32) then
        tmp = x * (1.0d0 - y)
    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 = z * (x - t);
	double tmp;
	if (z <= -1.3e+79) {
		tmp = t_1;
	} else if (z <= -7.5e-57) {
		tmp = (y - z) * t;
	} else if (z <= 5.5e-265) {
		tmp = x + (y * t);
	} else if (z <= 1.5e+32) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.3e+79:
		tmp = t_1
	elif z <= -7.5e-57:
		tmp = (y - z) * t
	elif z <= 5.5e-265:
		tmp = x + (y * t)
	elif z <= 1.5e+32:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.3e+79)
		tmp = t_1;
	elseif (z <= -7.5e-57)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 5.5e-265)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 1.5e+32)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.3e+79)
		tmp = t_1;
	elseif (z <= -7.5e-57)
		tmp = (y - z) * t;
	elseif (z <= 5.5e-265)
		tmp = x + (y * t);
	elseif (z <= 1.5e+32)
		tmp = x * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+79], t$95$1, If[LessEqual[z, -7.5e-57], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 5.5e-265], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+32], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.30000000000000007e79 or 1.5e32 < 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 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in z around inf 83.6%

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

   7. Taylor expanded in z around inf 83.6%

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

   if -1.30000000000000007e79 < z < -7.49999999999999973e-57

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 91.7%

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

   4. Applied egg-rr 91.7%

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

   5. Taylor expanded in x around 0 62.2%

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

      1. associate-+r+ 62.2%

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

      2. mul-1-neg 62.2%

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

      3. *-commutative 62.2%

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

      4. sub-neg 62.2%

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

      5. associate-+l- 62.2%

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

      6. *-commutative 62.2%

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

   7. Applied egg-rr 62.2%

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

   8. Taylor expanded in x around 0 59.1%

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

      1. distribute-lft-out-- 63.3%

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

   10. Simplified 63.3%

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

   if -7.49999999999999973e-57 < z < 5.49999999999999985e-265

   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 92.9%

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

      1. *-commutative 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in t around inf 69.9%

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

      1. *-commutative 69.9%

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

   8. Simplified 69.9%

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

   if 5.49999999999999985e-265 < z < 1.5e32

   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 90.9%

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

      1. *-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in x around inf 70.0%

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

      1. neg-mul-1 70.0%

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

      2. unsub-neg 70.0%

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

   8. Simplified 70.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-265}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+63}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e-19)
   (* y t)
   (if (<= y 1.35e-117) x (if (<= y 1.45e+63) (* z x) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-19) {
		tmp = y * t;
	} else if (y <= 1.35e-117) {
		tmp = x;
	} else if (y <= 1.45e+63) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.5d-19)) then
        tmp = y * t
    else if (y <= 1.35d-117) then
        tmp = x
    else if (y <= 1.45d+63) then
        tmp = z * x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-19) {
		tmp = y * t;
	} else if (y <= 1.35e-117) {
		tmp = x;
	} else if (y <= 1.45e+63) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e-19:
		tmp = y * t
	elif y <= 1.35e-117:
		tmp = x
	elif y <= 1.45e+63:
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e-19)
		tmp = Float64(y * t);
	elseif (y <= 1.35e-117)
		tmp = x;
	elseif (y <= 1.45e+63)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.5e-19)
		tmp = y * t;
	elseif (y <= 1.35e-117)
		tmp = x;
	elseif (y <= 1.45e+63)
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e-19], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.35e-117], x, If[LessEqual[y, 1.45e+63], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.4999999999999995e-19 or 1.45e63 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.0%

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

   4. Applied egg-rr 95.0%

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

   5. Taylor expanded in x around 0 48.0%

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

      1. associate-+r+ 48.0%

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

      2. mul-1-neg 48.0%

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

      3. *-commutative 48.0%

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

      4. sub-neg 48.0%

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

      5. associate-+l- 48.0%

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

      6. *-commutative 48.0%

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

   7. Applied egg-rr 48.0%

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

   8. Taylor expanded in y around inf 42.5%

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

   if -9.4999999999999995e-19 < y < 1.35000000000000001e-117

   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 79.8%

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

   4. Taylor expanded in x around inf 41.4%

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

   if 1.35000000000000001e-117 < y < 1.45e63

   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 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in z around inf 78.1%

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

   7. Taylor expanded in z around inf 64.6%

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

   8. Taylor expanded in x around inf 32.9%

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

      1. *-commutative 32.9%

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

   10. Simplified 32.9%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-117}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+63}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+67} \lor \neg \left(z \leq 1.3 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+67) (not (<= z 1.3e+47)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+67) || !(z <= 1.3e+47)) {
		tmp = 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 <= (-2.2d+67)) .or. (.not. (z <= 1.3d+47))) then
        tmp = 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 <= -2.2e+67) || !(z <= 1.3e+47)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+67) or not (z <= 1.3e+47):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+67) || !(z <= 1.3e+47))
		tmp = 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 <= -2.2e+67) || ~((z <= 1.3e+47)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+67], N[Not[LessEqual[z, 1.3e+47]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e67 or 1.30000000000000002e47 < 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 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in z around inf 84.5%

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

   7. Taylor expanded in z around inf 84.5%

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

   if -2.2e67 < z < 1.30000000000000002e47

   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 88.5%

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

      1. *-commutative 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+67} \lor \neg \left(z \leq 1.3 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.058 \lor \neg \left(y \leq 1.4 \cdot 10^{+63}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.058) (not (<= y 1.4e+63)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.058) || !(y <= 1.4e+63)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.058d0)) .or. (.not. (y <= 1.4d+63))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.058) || !(y <= 1.4e+63)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.058) or not (y <= 1.4e+63):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.058) || !(y <= 1.4e+63))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.058) || ~((y <= 1.4e+63)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.058], N[Not[LessEqual[y, 1.4e+63]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0580000000000000029 or 1.39999999999999993e63 < 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 87.2%

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

      1. *-commutative 87.2%

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

   5. Simplified 87.2%

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

   if -0.0580000000000000029 < y < 1.39999999999999993e63

   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 91.9%

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

      1. mul-1-neg 91.9%

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

      2. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.058 \lor \neg \left(y \leq 1.4 \cdot 10^{+63}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{-114} \lor \neg \left(t \leq 2.9 \cdot 10^{-104}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.52e-114) (not (<= t 2.9e-104))) (* t (- y z)) (* y (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.52e-114) || !(t <= 2.9e-104)) {
		tmp = t * (y - z);
	} else {
		tmp = y * -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 ((t <= (-1.52d-114)) .or. (.not. (t <= 2.9d-104))) then
        tmp = t * (y - z)
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.52e-114) || !(t <= 2.9e-104)) {
		tmp = t * (y - z);
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.52e-114) or not (t <= 2.9e-104):
		tmp = t * (y - z)
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.52e-114) || !(t <= 2.9e-104))
		tmp = Float64(t * Float64(y - z));
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.52e-114) || ~((t <= 2.9e-104)))
		tmp = t * (y - z);
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.52e-114], N[Not[LessEqual[t, 2.9e-104]], $MachinePrecision]], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.51999999999999997e-114 or 2.9000000000000001e-104 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in x around 0 76.1%

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

      1. associate-+r+ 76.1%

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

      2. mul-1-neg 76.1%

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

      3. *-commutative 76.1%

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

      4. sub-neg 76.1%

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

      5. associate-+l- 76.1%

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

      6. *-commutative 76.1%

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

   7. Applied egg-rr 76.1%

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

   8. Taylor expanded in x around 0 60.7%

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

      1. distribute-lft-out-- 63.0%

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

   10. Simplified 63.0%

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

   if -1.51999999999999997e-114 < t < 2.9000000000000001e-104

   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 69.7%

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

      1. *-commutative 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in x around inf 66.6%

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

      1. neg-mul-1 66.6%

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

      2. unsub-neg 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in y around inf 43.6%

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

       1. associate-*r* 43.6%

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

       2. mul-1-neg 43.6%

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

       3. *-commutative 43.6%

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

   11. Simplified 43.6%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{-114} \lor \neg \left(t \leq 2.9 \cdot 10^{-104}\right):\\ \;\;\;\;t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-5} \lor \neg \left(x \leq 0.00225\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.32e-5) (not (<= x 0.00225))) (* x (+ z 1.0)) (* t (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.32e-5) || !(x <= 0.00225)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t * (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.32d-5)) .or. (.not. (x <= 0.00225d0))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = t * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.32e-5) || !(x <= 0.00225)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.32e-5) or not (x <= 0.00225):
		tmp = x * (z + 1.0)
	else:
		tmp = t * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.32e-5) || !(x <= 0.00225))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(t * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.32e-5) || ~((x <= 0.00225)))
		tmp = x * (z + 1.0);
	else
		tmp = t * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.32e-5], N[Not[LessEqual[x, 0.00225]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.32000000000000007e-5 or 0.00224999999999999983 < 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 59.7%

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

      1. mul-1-neg 59.7%

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

      2. unsub-neg 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in x around inf 54.2%

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

      1. sub-neg 54.2%

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

      2. mul-1-neg 54.2%

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

      3. remove-double-neg 54.2%

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

      4. +-commutative 54.2%

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

   8. Simplified 54.2%

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

   if -1.32000000000000007e-5 < x < 0.00224999999999999983

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in x around 0 76.9%

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

      1. associate-+r+ 76.9%

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

      2. mul-1-neg 76.9%

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

      3. *-commutative 76.9%

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

      4. sub-neg 76.9%

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

      5. associate-+l- 76.9%

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

      6. *-commutative 76.9%

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

   7. Applied egg-rr 76.9%

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

   8. Taylor expanded in x around 0 68.6%

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

      1. distribute-lft-out-- 72.0%

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

   10. Simplified 72.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-5} \lor \neg \left(x \leq 0.00225\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-27} \lor \neg \left(y \leq 1.4 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-27) (not (<= y 1.4e+63))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-27) || !(y <= 1.4e+63)) {
		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 <= (-1.02d-27)) .or. (.not. (y <= 1.4d+63))) 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 <= -1.02e-27) || !(y <= 1.4e+63)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-27) or not (y <= 1.4e+63):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-27) || !(y <= 1.4e+63))
		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 <= -1.02e-27) || ~((y <= 1.4e+63)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-27], N[Not[LessEqual[y, 1.4e+63]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000002e-27 or 1.39999999999999993e63 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.0%

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

   4. Applied egg-rr 95.0%

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

   5. Taylor expanded in x around 0 48.0%

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

      1. associate-+r+ 48.0%

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

      2. mul-1-neg 48.0%

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

      3. *-commutative 48.0%

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

      4. sub-neg 48.0%

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

      5. associate-+l- 48.0%

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

      6. *-commutative 48.0%

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

   7. Applied egg-rr 48.0%

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

   8. Taylor expanded in y around inf 42.5%

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

   if -1.02000000000000002e-27 < y < 1.39999999999999993e63

   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 74.3%

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

   4. Taylor expanded in x around inf 35.8%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-27} \lor \neg \left(y \leq 1.4 \cdot 10^{+63}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 16: 17.7% 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 63.5%

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

4. Taylor expanded in x around inf 20.4%

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

5. Final simplification 20.4%

   \[\leadsto x \]
6. 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 2024081 
(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))))