Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.5s

Alternatives: 12

Speedup: 1.0×

• 34.5% 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: 53.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := x - z \cdot t\\ t_3 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-225}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (- x (* z t))) (t_3 (* x (- y))))
   (if (<= y -1.6e+119)
     t_1
     (if (<= y -6e+16)
       t_3
       (if (<= y -2.2e-86)
         (* x (+ z 1.0))
         (if (<= y -6e-174)
           t_2
           (if (<= y -1.16e-225)
             (+ x (* x z))
             (if (<= y 3400.0) t_2 (if (<= y 1.15e+203) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x - (z * t);
	double t_3 = x * -y;
	double tmp;
	if (y <= -1.6e+119) {
		tmp = t_1;
	} else if (y <= -6e+16) {
		tmp = t_3;
	} else if (y <= -2.2e-86) {
		tmp = x * (z + 1.0);
	} else if (y <= -6e-174) {
		tmp = t_2;
	} else if (y <= -1.16e-225) {
		tmp = x + (x * z);
	} else if (y <= 3400.0) {
		tmp = t_2;
	} else if (y <= 1.15e+203) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = x - (z * t)
    t_3 = x * -y
    if (y <= (-1.6d+119)) then
        tmp = t_1
    else if (y <= (-6d+16)) then
        tmp = t_3
    else if (y <= (-2.2d-86)) then
        tmp = x * (z + 1.0d0)
    else if (y <= (-6d-174)) then
        tmp = t_2
    else if (y <= (-1.16d-225)) then
        tmp = x + (x * z)
    else if (y <= 3400.0d0) then
        tmp = t_2
    else if (y <= 1.15d+203) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x - (z * t);
	double t_3 = x * -y;
	double tmp;
	if (y <= -1.6e+119) {
		tmp = t_1;
	} else if (y <= -6e+16) {
		tmp = t_3;
	} else if (y <= -2.2e-86) {
		tmp = x * (z + 1.0);
	} else if (y <= -6e-174) {
		tmp = t_2;
	} else if (y <= -1.16e-225) {
		tmp = x + (x * z);
	} else if (y <= 3400.0) {
		tmp = t_2;
	} else if (y <= 1.15e+203) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = x - (z * t)
	t_3 = x * -y
	tmp = 0
	if y <= -1.6e+119:
		tmp = t_1
	elif y <= -6e+16:
		tmp = t_3
	elif y <= -2.2e-86:
		tmp = x * (z + 1.0)
	elif y <= -6e-174:
		tmp = t_2
	elif y <= -1.16e-225:
		tmp = x + (x * z)
	elif y <= 3400.0:
		tmp = t_2
	elif y <= 1.15e+203:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(x - Float64(z * t))
	t_3 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.6e+119)
		tmp = t_1;
	elseif (y <= -6e+16)
		tmp = t_3;
	elseif (y <= -2.2e-86)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= -6e-174)
		tmp = t_2;
	elseif (y <= -1.16e-225)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 3400.0)
		tmp = t_2;
	elseif (y <= 1.15e+203)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = x - (z * t);
	t_3 = x * -y;
	tmp = 0.0;
	if (y <= -1.6e+119)
		tmp = t_1;
	elseif (y <= -6e+16)
		tmp = t_3;
	elseif (y <= -2.2e-86)
		tmp = x * (z + 1.0);
	elseif (y <= -6e-174)
		tmp = t_2;
	elseif (y <= -1.16e-225)
		tmp = x + (x * z);
	elseif (y <= 3400.0)
		tmp = t_2;
	elseif (y <= 1.15e+203)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.6e+119], t$95$1, If[LessEqual[y, -6e+16], t$95$3, If[LessEqual[y, -2.2e-86], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-174], t$95$2, If[LessEqual[y, -1.16e-225], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3400.0], t$95$2, If[LessEqual[y, 1.15e+203], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.59999999999999995e119 or 3400 < y < 1.15e203

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-/l* 88.5%

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

      4. distribute-lft-out 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in t around inf 58.3%

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

   7. Taylor expanded in z around 0 57.3%

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

      1. *-commutative 57.3%

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

   9. Simplified 57.3%

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

   if -1.59999999999999995e119 < y < -6e16 or 1.15e203 < 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 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in y around inf 65.5%

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

       1. mul-1-neg 65.5%

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

       2. distribute-rgt-neg-out 65.5%

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

   11. Simplified 65.5%

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

   if -6e16 < y < -2.2000000000000002e-86

   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 75.3%

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

      1. mul-1-neg 75.3%

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

      2. distribute-rgt-neg-in 75.3%

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

      3. sub-neg 75.3%

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

      4. +-commutative 75.3%

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

      5. distribute-neg-in 75.3%

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

      6. remove-double-neg 75.3%

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

      7. sub-neg 75.3%

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

   5. Simplified 75.3%

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

      1. sub-neg 75.3%

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

      2. distribute-lft-in 75.3%

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

   7. Applied egg-rr 75.3%

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

   8. Taylor expanded in x around inf 57.3%

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

      1. *-commutative 57.3%

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

      2. distribute-rgt1-in 57.3%

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

   10. Applied egg-rr 57.3%

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

   if -2.2000000000000002e-86 < y < -6.00000000000000042e-174 or -1.16000000000000001e-225 < y < 3400

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.0%

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

      1. *-commutative 98.0%

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

      2. *-commutative 98.0%

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

      3. associate-/l* 98.0%

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

      4. distribute-lft-out 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in t around inf 84.0%

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

   7. Taylor expanded in y around 0 81.8%

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

      1. mul-1-neg 81.8%

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

   9. Simplified 81.8%

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

   if -6.00000000000000042e-174 < y < -1.16000000000000001e-225

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. remove-double-neg 100.0%

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

      7. sub-neg 100.0%

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

   5. Simplified 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around inf 89.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-174}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-225}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+203}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -5.3 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+204}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -5.3e+119)
     (* y t)
     (if (<= y -5.6e+16)
       t_1
       (if (<= y -6.6e-26)
         (* y t)
         (if (<= y 3400.0) x (if (<= y 4.9e+204) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -5.3e+119) {
		tmp = y * t;
	} else if (y <= -5.6e+16) {
		tmp = t_1;
	} else if (y <= -6.6e-26) {
		tmp = y * t;
	} else if (y <= 3400.0) {
		tmp = x;
	} else if (y <= 4.9e+204) {
		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 <= (-5.3d+119)) then
        tmp = y * t
    else if (y <= (-5.6d+16)) then
        tmp = t_1
    else if (y <= (-6.6d-26)) then
        tmp = y * t
    else if (y <= 3400.0d0) then
        tmp = x
    else if (y <= 4.9d+204) 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 <= -5.3e+119) {
		tmp = y * t;
	} else if (y <= -5.6e+16) {
		tmp = t_1;
	} else if (y <= -6.6e-26) {
		tmp = y * t;
	} else if (y <= 3400.0) {
		tmp = x;
	} else if (y <= 4.9e+204) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -5.3e+119:
		tmp = y * t
	elif y <= -5.6e+16:
		tmp = t_1
	elif y <= -6.6e-26:
		tmp = y * t
	elif y <= 3400.0:
		tmp = x
	elif y <= 4.9e+204:
		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 <= -5.3e+119)
		tmp = Float64(y * t);
	elseif (y <= -5.6e+16)
		tmp = t_1;
	elseif (y <= -6.6e-26)
		tmp = Float64(y * t);
	elseif (y <= 3400.0)
		tmp = x;
	elseif (y <= 4.9e+204)
		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 <= -5.3e+119)
		tmp = y * t;
	elseif (y <= -5.6e+16)
		tmp = t_1;
	elseif (y <= -6.6e-26)
		tmp = y * t;
	elseif (y <= 3400.0)
		tmp = x;
	elseif (y <= 4.9e+204)
		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, -5.3e+119], N[(y * t), $MachinePrecision], If[LessEqual[y, -5.6e+16], t$95$1, If[LessEqual[y, -6.6e-26], N[(y * t), $MachinePrecision], If[LessEqual[y, 3400.0], x, If[LessEqual[y, 4.9e+204], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.29999999999999972e119 or -5.6e16 < y < -6.5999999999999997e-26 or 3400 < y < 4.8999999999999997e204

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-/l* 86.8%

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

      4. distribute-lft-out 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in t around inf 55.9%

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

   7. Taylor expanded in z around 0 56.2%

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

      1. *-commutative 56.2%

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

   9. Simplified 56.2%

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

   10. Taylor expanded in x around 0 55.9%

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

   if -5.29999999999999972e119 < y < -5.6e16 or 4.8999999999999997e204 < 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 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in y around inf 65.5%

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

       1. mul-1-neg 65.5%

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

       2. distribute-rgt-neg-out 65.5%

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

   11. Simplified 65.5%

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

   if -6.5999999999999997e-26 < y < 3400

   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 31.9%

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

      1. *-commutative 31.9%

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

   5. Simplified 31.9%

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

   6. Taylor expanded in y around 0 29.6%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-26}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+204}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ t_2 := x + z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))) (t_2 (+ x (* z (- x t)))))
   (if (<= z -2e-8)
     t_2
     (if (<= z 4.05e-35)
       t_1
       (if (<= z 1.95e-19) (* x (- 1.0 y)) (if (<= z 3.25e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double t_2 = x + (z * (x - t));
	double tmp;
	if (z <= -2e-8) {
		tmp = t_2;
	} else if (z <= 4.05e-35) {
		tmp = t_1;
	} else if (z <= 1.95e-19) {
		tmp = x * (1.0 - y);
	} else if (z <= 3.25e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * t)
    t_2 = x + (z * (x - t))
    if (z <= (-2d-8)) then
        tmp = t_2
    else if (z <= 4.05d-35) then
        tmp = t_1
    else if (z <= 1.95d-19) then
        tmp = x * (1.0d0 - y)
    else if (z <= 3.25d+27) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = x + (z * (x - t));
	double tmp;
	if (z <= -2e-8) {
		tmp = t_2;
	} else if (z <= 4.05e-35) {
		tmp = t_1;
	} else if (z <= 1.95e-19) {
		tmp = x * (1.0 - y);
	} else if (z <= 3.25e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	t_2 = x + (z * (x - t))
	tmp = 0
	if z <= -2e-8:
		tmp = t_2
	elif z <= 4.05e-35:
		tmp = t_1
	elif z <= 1.95e-19:
		tmp = x * (1.0 - y)
	elif z <= 3.25e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	t_2 = Float64(x + Float64(z * Float64(x - t)))
	tmp = 0.0
	if (z <= -2e-8)
		tmp = t_2;
	elseif (z <= 4.05e-35)
		tmp = t_1;
	elseif (z <= 1.95e-19)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 3.25e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	t_2 = x + (z * (x - t));
	tmp = 0.0;
	if (z <= -2e-8)
		tmp = t_2;
	elseif (z <= 4.05e-35)
		tmp = t_1;
	elseif (z <= 1.95e-19)
		tmp = x * (1.0 - y);
	elseif (z <= 3.25e+27)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-8], t$95$2, If[LessEqual[z, 4.05e-35], t$95$1, If[LessEqual[z, 1.95e-19], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e-8 or 3.2500000000000002e27 < 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 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-rgt-neg-in 82.6%

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

      3. sub-neg 82.6%

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

      4. +-commutative 82.6%

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

      5. distribute-neg-in 82.6%

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

      6. remove-double-neg 82.6%

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

      7. sub-neg 82.6%

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

   5. Simplified 82.6%

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

   if -2e-8 < z < 4.05000000000000015e-35 or 1.94999999999999998e-19 < z < 3.2500000000000002e27

   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 79.2%

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

   if 4.05000000000000015e-35 < z < 1.94999999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-8}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-35}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+27}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (* x (- y))))
   (if (<= y -7.4e+118)
     t_1
     (if (<= y -2.9e+16)
       t_2
       (if (<= y 3400.0) (+ x (* x z)) (if (<= y 1.02e+204) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x * -y;
	double tmp;
	if (y <= -7.4e+118) {
		tmp = t_1;
	} else if (y <= -2.9e+16) {
		tmp = t_2;
	} else if (y <= 3400.0) {
		tmp = x + (x * z);
	} else if (y <= 1.02e+204) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = x * -y
    if (y <= (-7.4d+118)) then
        tmp = t_1
    else if (y <= (-2.9d+16)) then
        tmp = t_2
    else if (y <= 3400.0d0) then
        tmp = x + (x * z)
    else if (y <= 1.02d+204) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x * -y;
	double tmp;
	if (y <= -7.4e+118) {
		tmp = t_1;
	} else if (y <= -2.9e+16) {
		tmp = t_2;
	} else if (y <= 3400.0) {
		tmp = x + (x * z);
	} else if (y <= 1.02e+204) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = x * -y
	tmp = 0
	if y <= -7.4e+118:
		tmp = t_1
	elif y <= -2.9e+16:
		tmp = t_2
	elif y <= 3400.0:
		tmp = x + (x * z)
	elif y <= 1.02e+204:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -7.4e+118)
		tmp = t_1;
	elseif (y <= -2.9e+16)
		tmp = t_2;
	elseif (y <= 3400.0)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 1.02e+204)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = x * -y;
	tmp = 0.0;
	if (y <= -7.4e+118)
		tmp = t_1;
	elseif (y <= -2.9e+16)
		tmp = t_2;
	elseif (y <= 3400.0)
		tmp = x + (x * z);
	elseif (y <= 1.02e+204)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -7.4e+118], t$95$1, If[LessEqual[y, -2.9e+16], t$95$2, If[LessEqual[y, 3400.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+204], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999973e118 or 3400 < y < 1.02e204

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-/l* 88.5%

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

      4. distribute-lft-out 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in t around inf 58.3%

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

   7. Taylor expanded in z around 0 57.3%

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

      1. *-commutative 57.3%

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

   9. Simplified 57.3%

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

   if -7.39999999999999973e118 < y < -2.9e16 or 1.02e204 < 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 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in y around inf 65.5%

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

       1. mul-1-neg 65.5%

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

       2. distribute-rgt-neg-out 65.5%

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

   11. Simplified 65.5%

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

   if -2.9e16 < y < 3400

   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 93.1%

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

      1. mul-1-neg 93.1%

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

      2. distribute-rgt-neg-in 93.1%

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

      3. sub-neg 93.1%

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

      4. +-commutative 93.1%

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

      5. distribute-neg-in 93.1%

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

      6. remove-double-neg 93.1%

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

      7. sub-neg 93.1%

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

   5. Simplified 93.1%

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

      1. sub-neg 93.1%

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

      2. distribute-lft-in 89.4%

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

   7. Applied egg-rr 89.4%

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

   8. Taylor expanded in x around inf 52.8%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+118}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+204}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+205}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -2e+120)
     (* y t)
     (if (<= y -2.6e+17)
       t_1
       (if (<= y 3400.0) (* x (+ z 1.0)) (if (<= y 3.6e+205) (* y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -2e+120) {
		tmp = y * t;
	} else if (y <= -2.6e+17) {
		tmp = t_1;
	} else if (y <= 3400.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 3.6e+205) {
		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 <= (-2d+120)) then
        tmp = y * t
    else if (y <= (-2.6d+17)) then
        tmp = t_1
    else if (y <= 3400.0d0) then
        tmp = x * (z + 1.0d0)
    else if (y <= 3.6d+205) 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 <= -2e+120) {
		tmp = y * t;
	} else if (y <= -2.6e+17) {
		tmp = t_1;
	} else if (y <= 3400.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 3.6e+205) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -2e+120:
		tmp = y * t
	elif y <= -2.6e+17:
		tmp = t_1
	elif y <= 3400.0:
		tmp = x * (z + 1.0)
	elif y <= 3.6e+205:
		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 <= -2e+120)
		tmp = Float64(y * t);
	elseif (y <= -2.6e+17)
		tmp = t_1;
	elseif (y <= 3400.0)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 3.6e+205)
		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 <= -2e+120)
		tmp = y * t;
	elseif (y <= -2.6e+17)
		tmp = t_1;
	elseif (y <= 3400.0)
		tmp = x * (z + 1.0);
	elseif (y <= 3.6e+205)
		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, -2e+120], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.6e+17], t$95$1, If[LessEqual[y, 3400.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+205], N[(y * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e120 or 3400 < y < 3.60000000000000002e205

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-/l* 88.5%

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

      4. distribute-lft-out 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in t around inf 58.3%

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

   7. Taylor expanded in z around 0 57.3%

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

      1. *-commutative 57.3%

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

   9. Simplified 57.3%

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

   10. Taylor expanded in x around 0 56.9%

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

   if -2e120 < y < -2.6e17 or 3.60000000000000002e205 < 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 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in y around inf 65.5%

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

       1. mul-1-neg 65.5%

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

       2. distribute-rgt-neg-out 65.5%

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

   11. Simplified 65.5%

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

   if -2.6e17 < y < 3400

   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 93.1%

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

      1. mul-1-neg 93.1%

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

      2. distribute-rgt-neg-in 93.1%

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

      3. sub-neg 93.1%

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

      4. +-commutative 93.1%

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

      5. distribute-neg-in 93.1%

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

      6. remove-double-neg 93.1%

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

      7. sub-neg 93.1%

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

   5. Simplified 93.1%

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

      1. sub-neg 93.1%

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

      2. distribute-lft-in 89.4%

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

   7. Applied egg-rr 89.4%

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

   8. Taylor expanded in x around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. distribute-rgt1-in 52.8%

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

   10. Applied egg-rr 52.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+120}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+205}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+201}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1.7e+119)
     (* y t)
     (if (<= y -2.15e+17)
       t_1
       (if (<= y 3400.0) (+ x (* x z)) (if (<= y 4.6e+201) (* y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.7e+119) {
		tmp = y * t;
	} else if (y <= -2.15e+17) {
		tmp = t_1;
	} else if (y <= 3400.0) {
		tmp = x + (x * z);
	} else if (y <= 4.6e+201) {
		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 <= (-1.7d+119)) then
        tmp = y * t
    else if (y <= (-2.15d+17)) then
        tmp = t_1
    else if (y <= 3400.0d0) then
        tmp = x + (x * z)
    else if (y <= 4.6d+201) 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 <= -1.7e+119) {
		tmp = y * t;
	} else if (y <= -2.15e+17) {
		tmp = t_1;
	} else if (y <= 3400.0) {
		tmp = x + (x * z);
	} else if (y <= 4.6e+201) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -1.7e+119:
		tmp = y * t
	elif y <= -2.15e+17:
		tmp = t_1
	elif y <= 3400.0:
		tmp = x + (x * z)
	elif y <= 4.6e+201:
		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 <= -1.7e+119)
		tmp = Float64(y * t);
	elseif (y <= -2.15e+17)
		tmp = t_1;
	elseif (y <= 3400.0)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 4.6e+201)
		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 <= -1.7e+119)
		tmp = y * t;
	elseif (y <= -2.15e+17)
		tmp = t_1;
	elseif (y <= 3400.0)
		tmp = x + (x * z);
	elseif (y <= 4.6e+201)
		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, -1.7e+119], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.15e+17], t$95$1, If[LessEqual[y, 3400.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+201], N[(y * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000007e119 or 3400 < y < 4.6000000000000002e201

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-/l* 88.5%

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

      4. distribute-lft-out 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in t around inf 58.3%

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

   7. Taylor expanded in z around 0 57.3%

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

      1. *-commutative 57.3%

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

   9. Simplified 57.3%

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

   10. Taylor expanded in x around 0 56.9%

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

   if -1.70000000000000007e119 < y < -2.15e17 or 4.6000000000000002e201 < 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 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in x around inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in y around inf 65.5%

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

       1. mul-1-neg 65.5%

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

       2. distribute-rgt-neg-out 65.5%

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

   11. Simplified 65.5%

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

   if -2.15e17 < y < 3400

   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 93.1%

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

      1. mul-1-neg 93.1%

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

      2. distribute-rgt-neg-in 93.1%

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

      3. sub-neg 93.1%

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

      4. +-commutative 93.1%

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

      5. distribute-neg-in 93.1%

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

      6. remove-double-neg 93.1%

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

      7. sub-neg 93.1%

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

   5. Simplified 93.1%

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

      1. sub-neg 93.1%

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

      2. distribute-lft-in 89.4%

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

   7. Applied egg-rr 89.4%

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

   8. Taylor expanded in x around inf 52.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 3400:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+201}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-20} \lor \neg \left(z \leq 2.05 \cdot 10^{+36}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.08e-20) (not (<= z 2.05e+36)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.08e-20) || !(z <= 2.05e+36)) {
		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 <= (-1.08d-20)) .or. (.not. (z <= 2.05d+36))) 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 <= -1.08e-20) || !(z <= 2.05e+36)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.08e-20) or not (z <= 2.05e+36):
		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 <= -1.08e-20) || !(z <= 2.05e+36))
		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 <= -1.08e-20) || ~((z <= 2.05e+36)))
		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, -1.08e-20], N[Not[LessEqual[z, 2.05e+36]], $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 < -1.08e-20 or 2.05000000000000006e36 < 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 83.2%

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

      1. mul-1-neg 83.2%

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

      2. distribute-rgt-neg-in 83.2%

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

      3. sub-neg 83.2%

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

      4. +-commutative 83.2%

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

      5. distribute-neg-in 83.2%

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

      6. remove-double-neg 83.2%

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

      7. sub-neg 83.2%

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

   5. Simplified 83.2%

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

   if -1.08e-20 < z < 2.05000000000000006e36

   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 91.3%

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

      1. *-commutative 91.3%

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

   5. Simplified 91.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-20} \lor \neg \left(z \leq 2.05 \cdot 10^{+36}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.16 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+126}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.16e+189)
   (* x (- 1.0 y))
   (if (<= x 3.5e+126) (+ x (* (- y z) t)) (* x (+ z 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.16e+189) {
		tmp = x * (1.0 - y);
	} else if (x <= 3.5e+126) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.16d+189)) then
        tmp = x * (1.0d0 - y)
    else if (x <= 3.5d+126) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.16e+189) {
		tmp = x * (1.0 - y);
	} else if (x <= 3.5e+126) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.16e+189:
		tmp = x * (1.0 - y)
	elif x <= 3.5e+126:
		tmp = x + ((y - z) * t)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.16e+189)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= 3.5e+126)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.16e+189)
		tmp = x * (1.0 - y);
	elseif (x <= 3.5e+126)
		tmp = x + ((y - z) * t);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.16e+189], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+126], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.16e189

   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 79.2%

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

      1. *-commutative 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in x around inf 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

   8. Simplified 79.2%

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

   if -2.16e189 < x < 3.5000000000000003e126

   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 75.8%

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

   if 3.5000000000000003e126 < 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 69.4%

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

      1. mul-1-neg 69.4%

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

      2. distribute-rgt-neg-in 69.4%

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

      3. sub-neg 69.4%

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

      4. +-commutative 69.4%

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

      5. distribute-neg-in 69.4%

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

      6. remove-double-neg 69.4%

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

      7. sub-neg 69.4%

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

   5. Simplified 69.4%

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

      1. sub-neg 69.4%

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

      2. distribute-lft-in 62.7%

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

   7. Applied egg-rr 62.7%

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

   8. Taylor expanded in x around inf 60.0%

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

      1. *-commutative 60.0%

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

      2. distribute-rgt1-in 60.0%

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

   10. Applied egg-rr 60.0%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.16 \cdot 10^{+189}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+126}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-141} \lor \neg \left(x \leq 2.2 \cdot 10^{-108}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.02e-141) (not (<= x 2.2e-108))) (* x (- 1.0 y)) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-141) || !(x <= 2.2e-108)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.02d-141)) .or. (.not. (x <= 2.2d-108))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-141) || !(x <= 2.2e-108)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.02e-141) or not (x <= 2.2e-108):
		tmp = x * (1.0 - y)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.02e-141) || !(x <= 2.2e-108))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.02e-141) || ~((x <= 2.2e-108)))
		tmp = x * (1.0 - y);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.02e-141], N[Not[LessEqual[x, 2.2e-108]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e-141 or 2.2000000000000001e-108 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 58.2%

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

      1. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in x around inf 45.7%

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

      1. mul-1-neg 45.7%

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

      2. unsub-neg 45.7%

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

   8. Simplified 45.7%

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

   if -1.02e-141 < x < 2.2000000000000001e-108

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. *-commutative 88.7%

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

      3. associate-/l* 86.5%

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

      4. distribute-lft-out 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in t around inf 78.7%

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

   7. Taylor expanded in z around 0 54.2%

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

      1. *-commutative 54.2%

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

   9. Simplified 54.2%

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

   10. Taylor expanded in x around 0 47.4%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-141} \lor \neg \left(x \leq 2.2 \cdot 10^{-108}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-25} \lor \neg \left(y \leq 3400\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.7e-25) (not (<= y 3400.0))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.7e-25) || !(y <= 3400.0)) {
		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 <= (-1.7d-25)) .or. (.not. (y <= 3400.0d0))) 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 <= -1.7e-25) || !(y <= 3400.0)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.7e-25) or not (y <= 3400.0):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.7e-25) || !(y <= 3400.0))
		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 <= -1.7e-25) || ~((y <= 3400.0)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.7e-25], N[Not[LessEqual[y, 3400.0]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000001e-25 or 3400 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-/l* 83.0%

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

      4. distribute-lft-out 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in t around inf 47.4%

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

   7. Taylor expanded in z around 0 49.0%

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

      1. *-commutative 49.0%

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

   9. Simplified 49.0%

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

   10. Taylor expanded in x around 0 48.7%

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

   if -1.70000000000000001e-25 < y < 3400

   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 31.9%

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

      1. *-commutative 31.9%

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

   5. Simplified 31.9%

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

   6. Taylor expanded in y around 0 29.6%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-25} \lor \neg \left(y \leq 3400\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 18.0% 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 y around inf 57.6%

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

   1. *-commutative 57.6%

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

5. Simplified 57.6%

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

6. Taylor expanded in y around 0 15.6%

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

7. Final simplification 15.6%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.7% 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 2024060 
(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))))