Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.7% → 97.6%

Time: 15.3s

Alternatives: 23

Speedup: 0.5×

• 36.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y + \left(t + -2\right)\right) \cdot \frac{b}{z} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* b (- (+ y t) 2.0)))
      INFINITY)
   (+ (+ x (+ (* b (- y 2.0)) (* t (- b a)))) (- a (* (+ y -1.0) z)))
   (* z (- (* (+ y (+ t -2.0)) (/ b z)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0))) <= ((double) INFINITY)) {
		tmp = (x + ((b * (y - 2.0)) + (t * (b - a)))) + (a - ((y + -1.0) * z));
	} else {
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0))) <= Double.POSITIVE_INFINITY) {
		tmp = (x + ((b * (y - 2.0)) + (t * (b - a)))) + (a - ((y + -1.0) * z));
	} else {
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0))) <= math.inf:
		tmp = (x + ((b * (y - 2.0)) + (t * (b - a)))) + (a - ((y + -1.0) * z))
	else:
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(y + t) - 2.0))) <= Inf)
		tmp = Float64(Float64(x + Float64(Float64(b * Float64(y - 2.0)) + Float64(t * Float64(b - a)))) + Float64(a - Float64(Float64(y + -1.0) * z)));
	else
		tmp = Float64(z * Float64(Float64(Float64(y + Float64(t + -2.0)) * Float64(b / z)) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0))) <= Inf)
		tmp = (x + ((b * (y - 2.0)) + (t * (b - a)))) + (a - ((y + -1.0) * z));
	else
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * N[(b / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 50.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. mul-1-neg 50.0%

         \[\leadsto \color{blue}{\left(-y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. *-commutative 50.0%

         \[\leadsto \left(-\color{blue}{z \cdot y}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. distribute-rgt-neg-in 50.0%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Simplified 50.0%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in z around inf 64.3%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot y + \frac{b \cdot \left(\left(t + y\right) - 2\right)}{z}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto z \cdot \color{blue}{\left(\frac{b \cdot \left(\left(t + y\right) - 2\right)}{z} + -1 \cdot y\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto z \cdot \left(\frac{b \cdot \left(\left(t + y\right) - 2\right)}{z} + \color{blue}{\left(-y\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto z \cdot \color{blue}{\left(\frac{b \cdot \left(\left(t + y\right) - 2\right)}{z} - y\right)} \]

      4. *-commutative 64.3%

         \[\leadsto z \cdot \left(\frac{\color{blue}{\left(\left(t + y\right) - 2\right) \cdot b}}{z} - y\right) \]

      5. associate-/l* 71.4%

         \[\leadsto z \cdot \left(\color{blue}{\left(\left(t + y\right) - 2\right) \cdot \frac{b}{z}} - y\right) \]

      6. +-commutative 71.4%

         \[\leadsto z \cdot \left(\left(\color{blue}{\left(y + t\right)} - 2\right) \cdot \frac{b}{z} - y\right) \]

      7. associate-+r- 71.4%

         \[\leadsto z \cdot \left(\color{blue}{\left(y + \left(t - 2\right)\right)} \cdot \frac{b}{z} - y\right) \]

      8. sub-neg 71.4%

         \[\leadsto z \cdot \left(\left(y + \color{blue}{\left(t + \left(-2\right)\right)}\right) \cdot \frac{b}{z} - y\right) \]

      9. metadata-eval 71.4%

         \[\leadsto z \cdot \left(\left(y + \left(t + \color{blue}{-2}\right)\right) \cdot \frac{b}{z} - y\right) \]

   8. Simplified 71.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y + \left(t + -2\right)\right) \cdot \frac{b}{z} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 24.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.0098:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-262}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-281}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+220}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))) (t_2 (* y (- z))))
   (if (<= z -3.5e+169)
     t_2
     (if (<= z -6.6e+71)
       t_1
       (if (<= z -0.0098)
         (* y b)
         (if (<= z -7e-262)
           (* t b)
           (if (<= z 1.22e-281)
             (* y b)
             (if (<= z 1.2e-239)
               t_1
               (if (<= z 7.2e-217)
                 x
                 (if (<= z 7.5e-11)
                   (* t b)
                   (if (<= z 3.2e+61)
                     t_1
                     (if (<= z 1.12e+220) t_2 z))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (z <= -3.5e+169) {
		tmp = t_2;
	} else if (z <= -6.6e+71) {
		tmp = t_1;
	} else if (z <= -0.0098) {
		tmp = y * b;
	} else if (z <= -7e-262) {
		tmp = t * b;
	} else if (z <= 1.22e-281) {
		tmp = y * b;
	} else if (z <= 1.2e-239) {
		tmp = t_1;
	} else if (z <= 7.2e-217) {
		tmp = x;
	} else if (z <= 7.5e-11) {
		tmp = t * b;
	} else if (z <= 3.2e+61) {
		tmp = t_1;
	} else if (z <= 1.12e+220) {
		tmp = t_2;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -a
    t_2 = y * -z
    if (z <= (-3.5d+169)) then
        tmp = t_2
    else if (z <= (-6.6d+71)) then
        tmp = t_1
    else if (z <= (-0.0098d0)) then
        tmp = y * b
    else if (z <= (-7d-262)) then
        tmp = t * b
    else if (z <= 1.22d-281) then
        tmp = y * b
    else if (z <= 1.2d-239) then
        tmp = t_1
    else if (z <= 7.2d-217) then
        tmp = x
    else if (z <= 7.5d-11) then
        tmp = t * b
    else if (z <= 3.2d+61) then
        tmp = t_1
    else if (z <= 1.12d+220) then
        tmp = t_2
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (z <= -3.5e+169) {
		tmp = t_2;
	} else if (z <= -6.6e+71) {
		tmp = t_1;
	} else if (z <= -0.0098) {
		tmp = y * b;
	} else if (z <= -7e-262) {
		tmp = t * b;
	} else if (z <= 1.22e-281) {
		tmp = y * b;
	} else if (z <= 1.2e-239) {
		tmp = t_1;
	} else if (z <= 7.2e-217) {
		tmp = x;
	} else if (z <= 7.5e-11) {
		tmp = t * b;
	} else if (z <= 3.2e+61) {
		tmp = t_1;
	} else if (z <= 1.12e+220) {
		tmp = t_2;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	t_2 = y * -z
	tmp = 0
	if z <= -3.5e+169:
		tmp = t_2
	elif z <= -6.6e+71:
		tmp = t_1
	elif z <= -0.0098:
		tmp = y * b
	elif z <= -7e-262:
		tmp = t * b
	elif z <= 1.22e-281:
		tmp = y * b
	elif z <= 1.2e-239:
		tmp = t_1
	elif z <= 7.2e-217:
		tmp = x
	elif z <= 7.5e-11:
		tmp = t * b
	elif z <= 3.2e+61:
		tmp = t_1
	elif z <= 1.12e+220:
		tmp = t_2
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (z <= -3.5e+169)
		tmp = t_2;
	elseif (z <= -6.6e+71)
		tmp = t_1;
	elseif (z <= -0.0098)
		tmp = Float64(y * b);
	elseif (z <= -7e-262)
		tmp = Float64(t * b);
	elseif (z <= 1.22e-281)
		tmp = Float64(y * b);
	elseif (z <= 1.2e-239)
		tmp = t_1;
	elseif (z <= 7.2e-217)
		tmp = x;
	elseif (z <= 7.5e-11)
		tmp = Float64(t * b);
	elseif (z <= 3.2e+61)
		tmp = t_1;
	elseif (z <= 1.12e+220)
		tmp = t_2;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	t_2 = y * -z;
	tmp = 0.0;
	if (z <= -3.5e+169)
		tmp = t_2;
	elseif (z <= -6.6e+71)
		tmp = t_1;
	elseif (z <= -0.0098)
		tmp = y * b;
	elseif (z <= -7e-262)
		tmp = t * b;
	elseif (z <= 1.22e-281)
		tmp = y * b;
	elseif (z <= 1.2e-239)
		tmp = t_1;
	elseif (z <= 7.2e-217)
		tmp = x;
	elseif (z <= 7.5e-11)
		tmp = t * b;
	elseif (z <= 3.2e+61)
		tmp = t_1;
	elseif (z <= 1.12e+220)
		tmp = t_2;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[z, -3.5e+169], t$95$2, If[LessEqual[z, -6.6e+71], t$95$1, If[LessEqual[z, -0.0098], N[(y * b), $MachinePrecision], If[LessEqual[z, -7e-262], N[(t * b), $MachinePrecision], If[LessEqual[z, 1.22e-281], N[(y * b), $MachinePrecision], If[LessEqual[z, 1.2e-239], t$95$1, If[LessEqual[z, 7.2e-217], x, If[LessEqual[z, 7.5e-11], N[(t * b), $MachinePrecision], If[LessEqual[z, 3.2e+61], t$95$1, If[LessEqual[z, 1.12e+220], t$95$2, z]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.50000000000000019e169 or 3.1999999999999998e61 < z < 1.12000000000000006e220

   1. Initial program 88.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.7%

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

   4. Taylor expanded in y around inf 44.6%

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

      1. associate-*r* 44.6%

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

      2. mul-1-neg 44.6%

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

   6. Simplified 44.6%

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

   if -3.50000000000000019e169 < z < -6.5999999999999996e71 or 1.21999999999999996e-281 < z < 1.19999999999999996e-239 or 7.5e-11 < z < 3.1999999999999998e61

   1. Initial program 93.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 53.7%

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

   4. Taylor expanded in t around inf 38.9%

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

      1. mul-1-neg 38.9%

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

      2. distribute-rgt-neg-out 38.9%

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

   6. Simplified 38.9%

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

   if -6.5999999999999996e71 < z < -0.0097999999999999997 or -7.00000000000000023e-262 < z < 1.21999999999999996e-281

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 64.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in y around inf 51.3%

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

   if -0.0097999999999999997 < z < -7.00000000000000023e-262 or 7.19999999999999962e-217 < z < 7.5e-11

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.4%

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

   4. Taylor expanded in b around inf 35.7%

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

   if 1.19999999999999996e-239 < z < 7.19999999999999962e-217

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.7%

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

   if 1.12000000000000006e220 < z

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 73.4%

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

   4. Taylor expanded in y around 0 51.5%

      \[\leadsto \color{blue}{z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+169}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq -0.0098:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-262}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-281}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+220}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y + \left(t + -2\right)\right) \cdot \frac{b}{z} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* b (- (+ y t) 2.0)))))
   (if (<= t_1 INFINITY) t_1 (* z (- (* (+ y (+ t -2.0)) (/ b z)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(Float64(y + Float64(t + -2.0)) * Float64(b / z)) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = z * (((y + (t + -2.0)) * (b / z)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * N[(b / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 50.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. mul-1-neg 50.0%

         \[\leadsto \color{blue}{\left(-y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. *-commutative 50.0%

         \[\leadsto \left(-\color{blue}{z \cdot y}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. distribute-rgt-neg-in 50.0%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Simplified 50.0%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in z around inf 64.3%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot y + \frac{b \cdot \left(\left(t + y\right) - 2\right)}{z}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 64.3%

         \[\leadsto z \cdot \color{blue}{\left(\frac{b \cdot \left(\left(t + y\right) - 2\right)}{z} + -1 \cdot y\right)} \]

      2. mul-1-neg 64.3%

         \[\leadsto z \cdot \left(\frac{b \cdot \left(\left(t + y\right) - 2\right)}{z} + \color{blue}{\left(-y\right)}\right) \]

      3. unsub-neg 64.3%

         \[\leadsto z \cdot \color{blue}{\left(\frac{b \cdot \left(\left(t + y\right) - 2\right)}{z} - y\right)} \]

      4. *-commutative 64.3%

         \[\leadsto z \cdot \left(\frac{\color{blue}{\left(\left(t + y\right) - 2\right) \cdot b}}{z} - y\right) \]

      5. associate-/l* 71.4%

         \[\leadsto z \cdot \left(\color{blue}{\left(\left(t + y\right) - 2\right) \cdot \frac{b}{z}} - y\right) \]

      6. +-commutative 71.4%

         \[\leadsto z \cdot \left(\left(\color{blue}{\left(y + t\right)} - 2\right) \cdot \frac{b}{z} - y\right) \]

      7. associate-+r- 71.4%

         \[\leadsto z \cdot \left(\color{blue}{\left(y + \left(t - 2\right)\right)} \cdot \frac{b}{z} - y\right) \]

      8. sub-neg 71.4%

         \[\leadsto z \cdot \left(\left(y + \color{blue}{\left(t + \left(-2\right)\right)}\right) \cdot \frac{b}{z} - y\right) \]

      9. metadata-eval 71.4%

         \[\leadsto z \cdot \left(\left(y + \left(t + \color{blue}{-2}\right)\right) \cdot \frac{b}{z} - y\right) \]

   8. Simplified 71.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y + \left(t + -2\right)\right) \cdot \frac{b}{z} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-166}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-275}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -4.8e+63)
     t_2
     (if (<= t -2.8e-113)
       t_1
       (if (<= t -5.4e-166)
         z
         (if (<= t -1.05e-307)
           t_1
           (if (<= t 2.65e-275) a (if (<= t 5.2e+22) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.8e+63) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -5.4e-166) {
		tmp = z;
	} else if (t <= -1.05e-307) {
		tmp = t_1;
	} else if (t <= 2.65e-275) {
		tmp = a;
	} else if (t <= 5.2e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-4.8d+63)) then
        tmp = t_2
    else if (t <= (-2.8d-113)) then
        tmp = t_1
    else if (t <= (-5.4d-166)) then
        tmp = z
    else if (t <= (-1.05d-307)) then
        tmp = t_1
    else if (t <= 2.65d-275) then
        tmp = a
    else if (t <= 5.2d+22) 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 a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -4.8e+63) {
		tmp = t_2;
	} else if (t <= -2.8e-113) {
		tmp = t_1;
	} else if (t <= -5.4e-166) {
		tmp = z;
	} else if (t <= -1.05e-307) {
		tmp = t_1;
	} else if (t <= 2.65e-275) {
		tmp = a;
	} else if (t <= 5.2e+22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -4.8e+63:
		tmp = t_2
	elif t <= -2.8e-113:
		tmp = t_1
	elif t <= -5.4e-166:
		tmp = z
	elif t <= -1.05e-307:
		tmp = t_1
	elif t <= 2.65e-275:
		tmp = a
	elif t <= 5.2e+22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.8e+63)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -5.4e-166)
		tmp = z;
	elseif (t <= -1.05e-307)
		tmp = t_1;
	elseif (t <= 2.65e-275)
		tmp = a;
	elseif (t <= 5.2e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.8e+63)
		tmp = t_2;
	elseif (t <= -2.8e-113)
		tmp = t_1;
	elseif (t <= -5.4e-166)
		tmp = z;
	elseif (t <= -1.05e-307)
		tmp = t_1;
	elseif (t <= 2.65e-275)
		tmp = a;
	elseif (t <= 5.2e+22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+63], t$95$2, If[LessEqual[t, -2.8e-113], t$95$1, If[LessEqual[t, -5.4e-166], z, If[LessEqual[t, -1.05e-307], t$95$1, If[LessEqual[t, 2.65e-275], a, If[LessEqual[t, 5.2e+22], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.8e63 or 5.2e22 < t

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.2%

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

   if -4.8e63 < t < -2.8e-113 or -5.40000000000000013e-166 < t < -1.0500000000000001e-307 or 2.64999999999999993e-275 < t < 5.2e22

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 40.4%

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

   if -2.8e-113 < t < -5.40000000000000013e-166

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 42.4%

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

   4. Taylor expanded in y around 0 42.4%

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

   if -1.0500000000000001e-307 < t < 2.64999999999999993e-275

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 63.8%

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

   4. Taylor expanded in t around 0 63.8%

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

Alternative 5: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-255}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -1.35e+103)
     t_2
     (if (<= b -2.65e-273)
       t_1
       (if (<= b 4.5e-255)
         t_3
         (if (<= b 4.6e-162) t_1 (if (<= b 8.5e+14) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -1.35e+103) {
		tmp = t_2;
	} else if (b <= -2.65e-273) {
		tmp = t_1;
	} else if (b <= 4.5e-255) {
		tmp = t_3;
	} else if (b <= 4.6e-162) {
		tmp = t_1;
	} else if (b <= 8.5e+14) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-1.35d+103)) then
        tmp = t_2
    else if (b <= (-2.65d-273)) then
        tmp = t_1
    else if (b <= 4.5d-255) then
        tmp = t_3
    else if (b <= 4.6d-162) then
        tmp = t_1
    else if (b <= 8.5d+14) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -1.35e+103) {
		tmp = t_2;
	} else if (b <= -2.65e-273) {
		tmp = t_1;
	} else if (b <= 4.5e-255) {
		tmp = t_3;
	} else if (b <= 4.6e-162) {
		tmp = t_1;
	} else if (b <= 8.5e+14) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -1.35e+103:
		tmp = t_2
	elif b <= -2.65e-273:
		tmp = t_1
	elif b <= 4.5e-255:
		tmp = t_3
	elif b <= 4.6e-162:
		tmp = t_1
	elif b <= 8.5e+14:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -1.35e+103)
		tmp = t_2;
	elseif (b <= -2.65e-273)
		tmp = t_1;
	elseif (b <= 4.5e-255)
		tmp = t_3;
	elseif (b <= 4.6e-162)
		tmp = t_1;
	elseif (b <= 8.5e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -1.35e+103)
		tmp = t_2;
	elseif (b <= -2.65e-273)
		tmp = t_1;
	elseif (b <= 4.5e-255)
		tmp = t_3;
	elseif (b <= 4.6e-162)
		tmp = t_1;
	elseif (b <= 8.5e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e+103], t$95$2, If[LessEqual[b, -2.65e-273], t$95$1, If[LessEqual[b, 4.5e-255], t$95$3, If[LessEqual[b, 4.6e-162], t$95$1, If[LessEqual[b, 8.5e+14], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.34999999999999996e103 or 8.5e14 < b

   1. Initial program 93.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 76.9%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -1.34999999999999996e103 < b < -2.64999999999999984e-273 or 4.49999999999999979e-255 < b < 4.5999999999999996e-162

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 73.3%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]

   4. Taylor expanded in b around 0 61.8%

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

   if -2.64999999999999984e-273 < b < 4.49999999999999979e-255 or 4.5999999999999996e-162 < b < 8.5e14

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.0%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   4. Taylor expanded in b around 0 77.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+103}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-273}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-255}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-162}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+14}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8200000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -2.4e+101)
     t_2
     (if (<= b -8200000000000.0)
       t_1
       (if (<= b -9e-13)
         t_2
         (if (<= b -6e-50) (* z (- 1.0 y)) (if (<= b 1.12e+14) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.4e+101) {
		tmp = t_2;
	} else if (b <= -8200000000000.0) {
		tmp = t_1;
	} else if (b <= -9e-13) {
		tmp = t_2;
	} else if (b <= -6e-50) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.12e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-2.4d+101)) then
        tmp = t_2
    else if (b <= (-8200000000000.0d0)) then
        tmp = t_1
    else if (b <= (-9d-13)) then
        tmp = t_2
    else if (b <= (-6d-50)) then
        tmp = z * (1.0d0 - y)
    else if (b <= 1.12d+14) 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 a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.4e+101) {
		tmp = t_2;
	} else if (b <= -8200000000000.0) {
		tmp = t_1;
	} else if (b <= -9e-13) {
		tmp = t_2;
	} else if (b <= -6e-50) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.12e+14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.4e+101:
		tmp = t_2
	elif b <= -8200000000000.0:
		tmp = t_1
	elif b <= -9e-13:
		tmp = t_2
	elif b <= -6e-50:
		tmp = z * (1.0 - y)
	elif b <= 1.12e+14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.4e+101)
		tmp = t_2;
	elseif (b <= -8200000000000.0)
		tmp = t_1;
	elseif (b <= -9e-13)
		tmp = t_2;
	elseif (b <= -6e-50)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 1.12e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.4e+101)
		tmp = t_2;
	elseif (b <= -8200000000000.0)
		tmp = t_1;
	elseif (b <= -9e-13)
		tmp = t_2;
	elseif (b <= -6e-50)
		tmp = z * (1.0 - y);
	elseif (b <= 1.12e+14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+101], t$95$2, If[LessEqual[b, -8200000000000.0], t$95$1, If[LessEqual[b, -9e-13], t$95$2, If[LessEqual[b, -6e-50], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.12e+14], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.39999999999999988e101 or -8.2e12 < b < -9e-13 or 1.12e14 < b

   1. Initial program 94.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 75.5%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if -2.39999999999999988e101 < b < -8.2e12 or -5.99999999999999981e-50 < b < 1.12e14

   1. Initial program 94.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 66.4%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   4. Taylor expanded in b around 0 58.8%

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

   if -9e-13 < b < -5.99999999999999981e-50

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.5%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -8200000000000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-13}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+14}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -3.1e+64)
     t_2
     (if (<= t -4.3e-166)
       t_1
       (if (<= t -5.8e-280)
         (* y (- b z))
         (if (<= t 1.35e-244) t_1 (if (<= t 6.2e+19) (* b (- y 2.0)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3.1e+64) {
		tmp = t_2;
	} else if (t <= -4.3e-166) {
		tmp = t_1;
	} else if (t <= -5.8e-280) {
		tmp = y * (b - z);
	} else if (t <= 1.35e-244) {
		tmp = t_1;
	} else if (t <= 6.2e+19) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = t * (b - a)
    if (t <= (-3.1d+64)) then
        tmp = t_2
    else if (t <= (-4.3d-166)) then
        tmp = t_1
    else if (t <= (-5.8d-280)) then
        tmp = y * (b - z)
    else if (t <= 1.35d-244) then
        tmp = t_1
    else if (t <= 6.2d+19) then
        tmp = b * (y - 2.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -3.1e+64) {
		tmp = t_2;
	} else if (t <= -4.3e-166) {
		tmp = t_1;
	} else if (t <= -5.8e-280) {
		tmp = y * (b - z);
	} else if (t <= 1.35e-244) {
		tmp = t_1;
	} else if (t <= 6.2e+19) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -3.1e+64:
		tmp = t_2
	elif t <= -4.3e-166:
		tmp = t_1
	elif t <= -5.8e-280:
		tmp = y * (b - z)
	elif t <= 1.35e-244:
		tmp = t_1
	elif t <= 6.2e+19:
		tmp = b * (y - 2.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.1e+64)
		tmp = t_2;
	elseif (t <= -4.3e-166)
		tmp = t_1;
	elseif (t <= -5.8e-280)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 1.35e-244)
		tmp = t_1;
	elseif (t <= 6.2e+19)
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.1e+64)
		tmp = t_2;
	elseif (t <= -4.3e-166)
		tmp = t_1;
	elseif (t <= -5.8e-280)
		tmp = y * (b - z);
	elseif (t <= 1.35e-244)
		tmp = t_1;
	elseif (t <= 6.2e+19)
		tmp = b * (y - 2.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+64], t$95$2, If[LessEqual[t, -4.3e-166], t$95$1, If[LessEqual[t, -5.8e-280], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-244], t$95$1, If[LessEqual[t, 6.2e+19], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.0999999999999999e64 or 6.2e19 < t

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.2%

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

   if -3.0999999999999999e64 < t < -4.3000000000000001e-166 or -5.8e-280 < t < 1.35e-244

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 40.7%

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

   if -4.3000000000000001e-166 < t < -5.8e-280

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 49.5%

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

   if 1.35e-244 < t < 6.2e19

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around 0 47.8%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 33.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-236}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -2.8e+130)
     t_1
     (if (<= a -6e-111)
       x
       (if (<= a -1.55e-236)
         z
         (if (<= a 1.8e-294) x (if (<= a 2.6e+63) (* t b) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.8e+130) {
		tmp = t_1;
	} else if (a <= -6e-111) {
		tmp = x;
	} else if (a <= -1.55e-236) {
		tmp = z;
	} else if (a <= 1.8e-294) {
		tmp = x;
	} else if (a <= 2.6e+63) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-2.8d+130)) then
        tmp = t_1
    else if (a <= (-6d-111)) then
        tmp = x
    else if (a <= (-1.55d-236)) then
        tmp = z
    else if (a <= 1.8d-294) then
        tmp = x
    else if (a <= 2.6d+63) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -2.8e+130) {
		tmp = t_1;
	} else if (a <= -6e-111) {
		tmp = x;
	} else if (a <= -1.55e-236) {
		tmp = z;
	} else if (a <= 1.8e-294) {
		tmp = x;
	} else if (a <= 2.6e+63) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -2.8e+130:
		tmp = t_1
	elif a <= -6e-111:
		tmp = x
	elif a <= -1.55e-236:
		tmp = z
	elif a <= 1.8e-294:
		tmp = x
	elif a <= 2.6e+63:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.8e+130)
		tmp = t_1;
	elseif (a <= -6e-111)
		tmp = x;
	elseif (a <= -1.55e-236)
		tmp = z;
	elseif (a <= 1.8e-294)
		tmp = x;
	elseif (a <= 2.6e+63)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.8e+130)
		tmp = t_1;
	elseif (a <= -6e-111)
		tmp = x;
	elseif (a <= -1.55e-236)
		tmp = z;
	elseif (a <= 1.8e-294)
		tmp = x;
	elseif (a <= 2.6e+63)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+130], t$95$1, If[LessEqual[a, -6e-111], x, If[LessEqual[a, -1.55e-236], z, If[LessEqual[a, 1.8e-294], x, If[LessEqual[a, 2.6e+63], N[(t * b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.7999999999999999e130 or 2.6000000000000001e63 < a

   1. Initial program 86.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 56.1%

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

   if -2.7999999999999999e130 < a < -6.00000000000000016e-111 or -1.5499999999999999e-236 < a < 1.8000000000000001e-294

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 31.2%

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

   if -6.00000000000000016e-111 < a < -1.5499999999999999e-236

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.1%

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

   4. Taylor expanded in y around 0 29.3%

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

   if 1.8000000000000001e-294 < a < 2.6000000000000001e63

   1. Initial program 98.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 35.3%

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

   4. Taylor expanded in b around inf 34.0%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-236}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+63}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 700000:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (+ x (* z (- 1.0 y)))))
   (if (<= z -1.3e+174)
     t_2
     (if (<= z -3.8e+80)
       t_1
       (if (<= z 700000.0)
         (+ x (* b (- (+ y t) 2.0)))
         (if (<= z 1.4e+64) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -1.3e+174) {
		tmp = t_2;
	} else if (z <= -3.8e+80) {
		tmp = t_1;
	} else if (z <= 700000.0) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (z <= 1.4e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (z * (1.0d0 - y))
    if (z <= (-1.3d+174)) then
        tmp = t_2
    else if (z <= (-3.8d+80)) then
        tmp = t_1
    else if (z <= 700000.0d0) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (z <= 1.4d+64) 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 a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -1.3e+174) {
		tmp = t_2;
	} else if (z <= -3.8e+80) {
		tmp = t_1;
	} else if (z <= 700000.0) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (z <= 1.4e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (z * (1.0 - y))
	tmp = 0
	if z <= -1.3e+174:
		tmp = t_2
	elif z <= -3.8e+80:
		tmp = t_1
	elif z <= 700000.0:
		tmp = x + (b * ((y + t) - 2.0))
	elif z <= 1.4e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (z <= -1.3e+174)
		tmp = t_2;
	elseif (z <= -3.8e+80)
		tmp = t_1;
	elseif (z <= 700000.0)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (z <= 1.4e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (z <= -1.3e+174)
		tmp = t_2;
	elseif (z <= -3.8e+80)
		tmp = t_1;
	elseif (z <= 700000.0)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (z <= 1.4e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+174], t$95$2, If[LessEqual[z, -3.8e+80], t$95$1, If[LessEqual[z, 700000.0], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2999999999999999e174 or 1.40000000000000012e64 < z

   1. Initial program 90.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 85.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]

   4. Taylor expanded in b around 0 70.8%

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

   if -1.2999999999999999e174 < z < -3.79999999999999997e80 or 7e5 < z < 1.40000000000000012e64

   1. Initial program 94.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 84.1%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   4. Taylor expanded in b around 0 71.9%

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

   if -3.79999999999999997e80 < z < 7e5

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 80.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]

   4. Taylor expanded in z around 0 76.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+174}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+80}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 700000:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+64}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z - y \cdot z\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+75}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;z \leq 5400000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- z (* y z))))
   (if (<= z -1.3e+174)
     t_1
     (if (<= z -9e+75)
       (- a (* t a))
       (if (<= z 5400000.0)
         (* b (- (+ y t) 2.0))
         (if (<= z 2.4e+64) (* a (- 1.0 t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z - (y * z);
	double tmp;
	if (z <= -1.3e+174) {
		tmp = t_1;
	} else if (z <= -9e+75) {
		tmp = a - (t * a);
	} else if (z <= 5400000.0) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 2.4e+64) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z - (y * z)
    if (z <= (-1.3d+174)) then
        tmp = t_1
    else if (z <= (-9d+75)) then
        tmp = a - (t * a)
    else if (z <= 5400000.0d0) then
        tmp = b * ((y + t) - 2.0d0)
    else if (z <= 2.4d+64) then
        tmp = a * (1.0d0 - 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 a, double b) {
	double t_1 = z - (y * z);
	double tmp;
	if (z <= -1.3e+174) {
		tmp = t_1;
	} else if (z <= -9e+75) {
		tmp = a - (t * a);
	} else if (z <= 5400000.0) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 2.4e+64) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z - (y * z)
	tmp = 0
	if z <= -1.3e+174:
		tmp = t_1
	elif z <= -9e+75:
		tmp = a - (t * a)
	elif z <= 5400000.0:
		tmp = b * ((y + t) - 2.0)
	elif z <= 2.4e+64:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z - Float64(y * z))
	tmp = 0.0
	if (z <= -1.3e+174)
		tmp = t_1;
	elseif (z <= -9e+75)
		tmp = Float64(a - Float64(t * a));
	elseif (z <= 5400000.0)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (z <= 2.4e+64)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z - (y * z);
	tmp = 0.0;
	if (z <= -1.3e+174)
		tmp = t_1;
	elseif (z <= -9e+75)
		tmp = a - (t * a);
	elseif (z <= 5400000.0)
		tmp = b * ((y + t) - 2.0);
	elseif (z <= 2.4e+64)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+174], t$95$1, If[LessEqual[z, -9e+75], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5400000.0], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+64], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2999999999999999e174 or 2.39999999999999999e64 < z

   1. Initial program 90.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.8%

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

   4. Taylor expanded in y around 0 67.8%

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

   if -1.2999999999999999e174 < z < -9.0000000000000007e75

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.9%

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

      1. sub-neg 46.9%

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

      2. distribute-rgt-in 46.9%

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

      3. *-un-lft-identity 46.9%

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

   5. Applied egg-rr 46.9%

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

      1. distribute-lft-neg-out 46.9%

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

      2. unsub-neg 46.9%

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

      3. *-commutative 46.9%

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

   7. Applied egg-rr 46.9%

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

   if -9.0000000000000007e75 < z < 5.4e6

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 58.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if 5.4e6 < z < 2.39999999999999999e64

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 60.8%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+174}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+75}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;z \leq 5400000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;z \leq 3300000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -1.3e+174)
     t_1
     (if (<= z -7.5e+80)
       (- a (* t a))
       (if (<= z 3300000.0)
         (* b (- (+ y t) 2.0))
         (if (<= z 1.2e+64) (* a (- 1.0 t)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.3e+174) {
		tmp = t_1;
	} else if (z <= -7.5e+80) {
		tmp = a - (t * a);
	} else if (z <= 3300000.0) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 1.2e+64) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (z <= (-1.3d+174)) then
        tmp = t_1
    else if (z <= (-7.5d+80)) then
        tmp = a - (t * a)
    else if (z <= 3300000.0d0) then
        tmp = b * ((y + t) - 2.0d0)
    else if (z <= 1.2d+64) then
        tmp = a * (1.0d0 - 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 a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.3e+174) {
		tmp = t_1;
	} else if (z <= -7.5e+80) {
		tmp = a - (t * a);
	} else if (z <= 3300000.0) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 1.2e+64) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if z <= -1.3e+174:
		tmp = t_1
	elif z <= -7.5e+80:
		tmp = a - (t * a)
	elif z <= 3300000.0:
		tmp = b * ((y + t) - 2.0)
	elif z <= 1.2e+64:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.3e+174)
		tmp = t_1;
	elseif (z <= -7.5e+80)
		tmp = Float64(a - Float64(t * a));
	elseif (z <= 3300000.0)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (z <= 1.2e+64)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.3e+174)
		tmp = t_1;
	elseif (z <= -7.5e+80)
		tmp = a - (t * a);
	elseif (z <= 3300000.0)
		tmp = b * ((y + t) - 2.0);
	elseif (z <= 1.2e+64)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+174], t$95$1, If[LessEqual[z, -7.5e+80], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3300000.0], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+64], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2999999999999999e174 or 1.2e64 < z

   1. Initial program 90.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 67.8%

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

   if -1.2999999999999999e174 < z < -7.49999999999999994e80

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.9%

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

      1. sub-neg 46.9%

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

      2. distribute-rgt-in 46.9%

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

      3. *-un-lft-identity 46.9%

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

   5. Applied egg-rr 46.9%

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

      1. distribute-lft-neg-out 46.9%

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

      2. unsub-neg 46.9%

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

      3. *-commutative 46.9%

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

   7. Applied egg-rr 46.9%

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

   if -7.49999999999999994e80 < z < 3.3e6

   1. Initial program 97.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 58.1%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   if 3.3e6 < z < 1.2e64

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 60.8%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;z \leq 3300000:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -32000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-252}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 470000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -32000000.0)
     t_2
     (if (<= t -1.05e-307)
       t_1
       (if (<= t 1.6e-252) a (if (<= t 470000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -32000000.0) {
		tmp = t_2;
	} else if (t <= -1.05e-307) {
		tmp = t_1;
	} else if (t <= 1.6e-252) {
		tmp = a;
	} else if (t <= 470000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-32000000.0d0)) then
        tmp = t_2
    else if (t <= (-1.05d-307)) then
        tmp = t_1
    else if (t <= 1.6d-252) then
        tmp = a
    else if (t <= 470000.0d0) 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 a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -32000000.0) {
		tmp = t_2;
	} else if (t <= -1.05e-307) {
		tmp = t_1;
	} else if (t <= 1.6e-252) {
		tmp = a;
	} else if (t <= 470000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -32000000.0:
		tmp = t_2
	elif t <= -1.05e-307:
		tmp = t_1
	elif t <= 1.6e-252:
		tmp = a
	elif t <= 470000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -32000000.0)
		tmp = t_2;
	elseif (t <= -1.05e-307)
		tmp = t_1;
	elseif (t <= 1.6e-252)
		tmp = a;
	elseif (t <= 470000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -32000000.0)
		tmp = t_2;
	elseif (t <= -1.05e-307)
		tmp = t_1;
	elseif (t <= 1.6e-252)
		tmp = a;
	elseif (t <= 470000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -32000000.0], t$95$2, If[LessEqual[t, -1.05e-307], t$95$1, If[LessEqual[t, 1.6e-252], a, If[LessEqual[t, 470000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2e7 or 4.7e5 < t

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.4%

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

   if -3.2e7 < t < -1.0500000000000001e-307 or 1.6000000000000001e-252 < t < 4.7e5

   1. Initial program 99.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 39.0%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in t around 0 38.0%

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right)} \]

   if -1.0500000000000001e-307 < t < 1.6000000000000001e-252

   1. Initial program 93.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 39.5%

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

   4. Taylor expanded in t around 0 39.5%

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

Alternative 13: 39.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -265000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- t 2.0))))
   (if (<= b -3.1e+101)
     t_2
     (if (<= b -265000000000.0)
       t_1
       (if (<= b -2.6e-46) (* y (- z)) (if (<= b 5.5e+60) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -3.1e+101) {
		tmp = t_2;
	} else if (b <= -265000000000.0) {
		tmp = t_1;
	} else if (b <= -2.6e-46) {
		tmp = y * -z;
	} else if (b <= 5.5e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (t - 2.0d0)
    if (b <= (-3.1d+101)) then
        tmp = t_2
    else if (b <= (-265000000000.0d0)) then
        tmp = t_1
    else if (b <= (-2.6d-46)) then
        tmp = y * -z
    else if (b <= 5.5d+60) 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 a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -3.1e+101) {
		tmp = t_2;
	} else if (b <= -265000000000.0) {
		tmp = t_1;
	} else if (b <= -2.6e-46) {
		tmp = y * -z;
	} else if (b <= 5.5e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (t - 2.0)
	tmp = 0
	if b <= -3.1e+101:
		tmp = t_2
	elif b <= -265000000000.0:
		tmp = t_1
	elif b <= -2.6e-46:
		tmp = y * -z
	elif b <= 5.5e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -3.1e+101)
		tmp = t_2;
	elseif (b <= -265000000000.0)
		tmp = t_1;
	elseif (b <= -2.6e-46)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 5.5e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -3.1e+101)
		tmp = t_2;
	elseif (b <= -265000000000.0)
		tmp = t_1;
	elseif (b <= -2.6e-46)
		tmp = y * -z;
	elseif (b <= 5.5e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+101], t$95$2, If[LessEqual[b, -265000000000.0], t$95$1, If[LessEqual[b, -2.6e-46], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 5.5e+60], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.09999999999999999e101 or 5.5000000000000001e60 < b

   1. Initial program 93.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   4. Step-by-step derivation

      1. mul-1-neg 81.2%

         \[\leadsto \color{blue}{\left(-y \cdot z\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. *-commutative 81.2%

         \[\leadsto \left(-\color{blue}{z \cdot y}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. distribute-rgt-neg-in 81.2%

         \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{z \cdot \left(-y\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Taylor expanded in y around 0 56.7%

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]

   if -3.09999999999999999e101 < b < -2.65e11 or -2.6000000000000002e-46 < b < 5.5000000000000001e60

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 36.8%

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

   if -2.65e11 < b < -2.6000000000000002e-46

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 46.4%

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

   4. Taylor expanded in y around inf 39.4%

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

      1. associate-*r* 39.4%

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

      2. mul-1-neg 39.4%

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

   6. Simplified 39.4%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+101}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -265000000000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-46}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+66}:\\ \;\;\;\;\left(x + t\_1\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= a -1.9e+134)
     (+ (- x (* t a)) (- a (* (+ y -1.0) z)))
     (if (<= a 1.3e+66)
       (+ (+ x t_1) (* z (- 1.0 y)))
       (+ t_1 (+ x (* a (- 1.0 t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (a <= -1.9e+134) {
		tmp = (x - (t * a)) + (a - ((y + -1.0) * z));
	} else if (a <= 1.3e+66) {
		tmp = (x + t_1) + (z * (1.0 - y));
	} else {
		tmp = t_1 + (x + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (a <= (-1.9d+134)) then
        tmp = (x - (t * a)) + (a - ((y + (-1.0d0)) * z))
    else if (a <= 1.3d+66) then
        tmp = (x + t_1) + (z * (1.0d0 - y))
    else
        tmp = t_1 + (x + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (a <= -1.9e+134) {
		tmp = (x - (t * a)) + (a - ((y + -1.0) * z));
	} else if (a <= 1.3e+66) {
		tmp = (x + t_1) + (z * (1.0 - y));
	} else {
		tmp = t_1 + (x + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if a <= -1.9e+134:
		tmp = (x - (t * a)) + (a - ((y + -1.0) * z))
	elif a <= 1.3e+66:
		tmp = (x + t_1) + (z * (1.0 - y))
	else:
		tmp = t_1 + (x + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (a <= -1.9e+134)
		tmp = Float64(Float64(x - Float64(t * a)) + Float64(a - Float64(Float64(y + -1.0) * z)));
	elseif (a <= 1.3e+66)
		tmp = Float64(Float64(x + t_1) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(t_1 + Float64(x + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (a <= -1.9e+134)
		tmp = (x - (t * a)) + (a - ((y + -1.0) * z));
	elseif (a <= 1.3e+66)
		tmp = (x + t_1) + (z * (1.0 - y));
	else
		tmp = t_1 + (x + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.9e+134], N[(N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(a - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+66], N[(N[(x + t$95$1), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.89999999999999999e134

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 97.1%

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]

   4. Taylor expanded in b around 0 81.5%

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

      1. associate-*r* 81.5%

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

      2. mul-1-neg 81.5%

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

   6. Simplified 81.5%

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

   if -1.89999999999999999e134 < a < 1.30000000000000006e66

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 94.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]

   if 1.30000000000000006e66 < a

   1. Initial program 83.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+66}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;x + \left(t\_2 - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;\left(x + t\_1\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -3.1e+134)
     (+ x (- t_2 (* (+ y -1.0) z)))
     (if (<= a 2.3e+68) (+ (+ x t_1) (* z (- 1.0 y))) (+ t_1 (+ x t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -3.1e+134) {
		tmp = x + (t_2 - ((y + -1.0) * z));
	} else if (a <= 2.3e+68) {
		tmp = (x + t_1) + (z * (1.0 - y));
	} else {
		tmp = t_1 + (x + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (a <= (-3.1d+134)) then
        tmp = x + (t_2 - ((y + (-1.0d0)) * z))
    else if (a <= 2.3d+68) then
        tmp = (x + t_1) + (z * (1.0d0 - y))
    else
        tmp = t_1 + (x + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -3.1e+134) {
		tmp = x + (t_2 - ((y + -1.0) * z));
	} else if (a <= 2.3e+68) {
		tmp = (x + t_1) + (z * (1.0 - y));
	} else {
		tmp = t_1 + (x + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -3.1e+134:
		tmp = x + (t_2 - ((y + -1.0) * z))
	elif a <= 2.3e+68:
		tmp = (x + t_1) + (z * (1.0 - y))
	else:
		tmp = t_1 + (x + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -3.1e+134)
		tmp = Float64(x + Float64(t_2 - Float64(Float64(y + -1.0) * z)));
	elseif (a <= 2.3e+68)
		tmp = Float64(Float64(x + t_1) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(t_1 + Float64(x + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -3.1e+134)
		tmp = x + (t_2 - ((y + -1.0) * z));
	elseif (a <= 2.3e+68)
		tmp = (x + t_1) + (z * (1.0 - y));
	else
		tmp = t_1 + (x + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.1e+134], N[(x + N[(t$95$2 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+68], N[(N[(x + t$95$1), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(x + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.09999999999999982e134

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 81.4%

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

   if -3.09999999999999982e134 < a < 2.3e68

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 94.4%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]

   if 2.3e68 < a

   1. Initial program 83.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+134}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+68}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + a \cdot \left(1 - t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= z -2.3e+214)
     (+ x (* z (- 1.0 y)))
     (if (<= z 1.65e-27)
       (+ (* b (- (+ y t) 2.0)) (+ x t_1))
       (+ x (- t_1 (* (+ y -1.0) z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (z <= -2.3e+214) {
		tmp = x + (z * (1.0 - y));
	} else if (z <= 1.65e-27) {
		tmp = (b * ((y + t) - 2.0)) + (x + t_1);
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (z <= (-2.3d+214)) then
        tmp = x + (z * (1.0d0 - y))
    else if (z <= 1.65d-27) then
        tmp = (b * ((y + t) - 2.0d0)) + (x + t_1)
    else
        tmp = x + (t_1 - ((y + (-1.0d0)) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (z <= -2.3e+214) {
		tmp = x + (z * (1.0 - y));
	} else if (z <= 1.65e-27) {
		tmp = (b * ((y + t) - 2.0)) + (x + t_1);
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if z <= -2.3e+214:
		tmp = x + (z * (1.0 - y))
	elif z <= 1.65e-27:
		tmp = (b * ((y + t) - 2.0)) + (x + t_1)
	else:
		tmp = x + (t_1 - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (z <= -2.3e+214)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (z <= 1.65e-27)
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(x + t_1));
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (z <= -2.3e+214)
		tmp = x + (z * (1.0 - y));
	elseif (z <= 1.65e-27)
		tmp = (b * ((y + t) - 2.0)) + (x + t_1);
	else
		tmp = x + (t_1 - ((y + -1.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+214], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-27], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999999e214

   1. Initial program 85.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 90.0%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]

   4. Taylor expanded in b around 0 95.1%

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

   if -2.2999999999999999e214 < z < 1.64999999999999999e-27

   1. Initial program 96.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.7%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if 1.64999999999999999e-27 < z

   1. Initial program 93.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 78.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-143}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-251}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+61}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.5e+63)
   (* t b)
   (if (<= t -5.5e-143)
     z
     (if (<= t 2.6e-251) a (if (<= t 7e+61) (* y b) (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.5e+63) {
		tmp = t * b;
	} else if (t <= -5.5e-143) {
		tmp = z;
	} else if (t <= 2.6e-251) {
		tmp = a;
	} else if (t <= 7e+61) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.5d+63)) then
        tmp = t * b
    else if (t <= (-5.5d-143)) then
        tmp = z
    else if (t <= 2.6d-251) then
        tmp = a
    else if (t <= 7d+61) then
        tmp = y * b
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.5e+63) {
		tmp = t * b;
	} else if (t <= -5.5e-143) {
		tmp = z;
	} else if (t <= 2.6e-251) {
		tmp = a;
	} else if (t <= 7e+61) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.5e+63:
		tmp = t * b
	elif t <= -5.5e-143:
		tmp = z
	elif t <= 2.6e-251:
		tmp = a
	elif t <= 7e+61:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.5e+63)
		tmp = Float64(t * b);
	elseif (t <= -5.5e-143)
		tmp = z;
	elseif (t <= 2.6e-251)
		tmp = a;
	elseif (t <= 7e+61)
		tmp = Float64(y * b);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.5e+63)
		tmp = t * b;
	elseif (t <= -5.5e-143)
		tmp = z;
	elseif (t <= 2.6e-251)
		tmp = a;
	elseif (t <= 7e+61)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.5e+63], N[(t * b), $MachinePrecision], If[LessEqual[t, -5.5e-143], z, If[LessEqual[t, 2.6e-251], a, If[LessEqual[t, 7e+61], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.50000000000000005e63 or 7.00000000000000036e61 < t

   1. Initial program 89.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 76.7%

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

   4. Taylor expanded in b around inf 50.0%

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

   if -2.50000000000000005e63 < t < -5.50000000000000041e-143

   1. Initial program 94.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 39.8%

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

   4. Taylor expanded in y around 0 22.4%

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

   if -5.50000000000000041e-143 < t < 2.5999999999999999e-251

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 31.2%

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

   4. Taylor expanded in t around 0 31.2%

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

   if 2.5999999999999999e-251 < t < 7.00000000000000036e61

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

   4. Taylor expanded in y around inf 26.5%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+63}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-143}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-251}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+61}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+64}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-143}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-275}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 0.19:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+64)
   (* t b)
   (if (<= t -2.1e-143) z (if (<= t 4.8e-275) a (if (<= t 0.19) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+64) {
		tmp = t * b;
	} else if (t <= -2.1e-143) {
		tmp = z;
	} else if (t <= 4.8e-275) {
		tmp = a;
	} else if (t <= 0.19) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.75d+64)) then
        tmp = t * b
    else if (t <= (-2.1d-143)) then
        tmp = z
    else if (t <= 4.8d-275) then
        tmp = a
    else if (t <= 0.19d0) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+64) {
		tmp = t * b;
	} else if (t <= -2.1e-143) {
		tmp = z;
	} else if (t <= 4.8e-275) {
		tmp = a;
	} else if (t <= 0.19) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+64:
		tmp = t * b
	elif t <= -2.1e-143:
		tmp = z
	elif t <= 4.8e-275:
		tmp = a
	elif t <= 0.19:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+64)
		tmp = Float64(t * b);
	elseif (t <= -2.1e-143)
		tmp = z;
	elseif (t <= 4.8e-275)
		tmp = a;
	elseif (t <= 0.19)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.75e+64)
		tmp = t * b;
	elseif (t <= -2.1e-143)
		tmp = z;
	elseif (t <= 4.8e-275)
		tmp = a;
	elseif (t <= 0.19)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+64], N[(t * b), $MachinePrecision], If[LessEqual[t, -2.1e-143], z, If[LessEqual[t, 4.8e-275], a, If[LessEqual[t, 0.19], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7499999999999999e64 or 0.19 < t

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.5%

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

   4. Taylor expanded in b around inf 46.8%

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

   if -1.7499999999999999e64 < t < -2.1000000000000001e-143

   1. Initial program 94.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 39.8%

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

   4. Taylor expanded in y around 0 22.4%

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

   if -2.1000000000000001e-143 < t < 4.79999999999999981e-275

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 35.3%

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

   4. Taylor expanded in t around 0 35.3%

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

   if 4.79999999999999981e-275 < t < 0.19

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 19.4%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+64}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-143}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-275}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 0.19:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 85.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+101} \lor \neg \left(b \leq 2.5 \cdot 10^{+66}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.6e+101) (not (<= b 2.5e+66)))
   (+ (* b (- (+ y t) 2.0)) (+ x a))
   (+ x (- (* a (- 1.0 t)) (* (+ y -1.0) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.6e+101) || !(b <= 2.5e+66)) {
		tmp = (b * ((y + t) - 2.0)) + (x + a);
	} else {
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7.6d+101)) .or. (.not. (b <= 2.5d+66))) then
        tmp = (b * ((y + t) - 2.0d0)) + (x + a)
    else
        tmp = x + ((a * (1.0d0 - t)) - ((y + (-1.0d0)) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.6e+101) || !(b <= 2.5e+66)) {
		tmp = (b * ((y + t) - 2.0)) + (x + a);
	} else {
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.6e+101) or not (b <= 2.5e+66):
		tmp = (b * ((y + t) - 2.0)) + (x + a)
	else:
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.6e+101) || !(b <= 2.5e+66))
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(x + a));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.6e+101) || ~((b <= 2.5e+66)))
		tmp = (b * ((y + t) - 2.0)) + (x + a);
	else
		tmp = x + ((a * (1.0 - t)) - ((y + -1.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.6e+101], N[Not[LessEqual[b, 2.5e+66]], $MachinePrecision]], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.5999999999999996e101 or 2.49999999999999996e66 < b

   1. Initial program 93.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 84.6%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   4. Taylor expanded in t around 0 86.5%

      \[\leadsto \color{blue}{\left(x - -1 \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 86.5%

         \[\leadsto \color{blue}{\left(x + \left(--1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. metadata-eval 86.5%

         \[\leadsto \left(x + \color{blue}{1} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. *-lft-identity 86.5%

         \[\leadsto \left(x + \color{blue}{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. +-commutative 86.5%

         \[\leadsto \color{blue}{\left(a + x\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Simplified 86.5%

      \[\leadsto \color{blue}{\left(a + x\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if -7.5999999999999996e101 < b < 2.49999999999999996e66

   1. Initial program 95.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 84.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{+101} \lor \neg \left(b \leq 2.5 \cdot 10^{+66}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+210}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.4e+210)
   (+ x (* z (- 1.0 y)))
   (if (<= z 7.2e+138) (+ (* b (- (+ y t) 2.0)) (+ x a)) (- z (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.4e+210) {
		tmp = x + (z * (1.0 - y));
	} else if (z <= 7.2e+138) {
		tmp = (b * ((y + t) - 2.0)) + (x + a);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.4d+210)) then
        tmp = x + (z * (1.0d0 - y))
    else if (z <= 7.2d+138) then
        tmp = (b * ((y + t) - 2.0d0)) + (x + a)
    else
        tmp = z - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.4e+210) {
		tmp = x + (z * (1.0 - y));
	} else if (z <= 7.2e+138) {
		tmp = (b * ((y + t) - 2.0)) + (x + a);
	} else {
		tmp = z - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.4e+210:
		tmp = x + (z * (1.0 - y))
	elif z <= 7.2e+138:
		tmp = (b * ((y + t) - 2.0)) + (x + a)
	else:
		tmp = z - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.4e+210)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (z <= 7.2e+138)
		tmp = Float64(Float64(b * Float64(Float64(y + t) - 2.0)) + Float64(x + a));
	else
		tmp = Float64(z - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.4e+210)
		tmp = x + (z * (1.0 - y));
	elseif (z <= 7.2e+138)
		tmp = (b * ((y + t) - 2.0)) + (x + a);
	else
		tmp = z - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.4e+210], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+138], N[(N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e210

   1. Initial program 85.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 90.5%

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - z \cdot \left(y - 1\right)} \]

   4. Taylor expanded in b around 0 95.4%

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

   if -1.4000000000000001e210 < z < 7.2000000000000002e138

   1. Initial program 95.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.5%

      \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   4. Taylor expanded in t around 0 76.7%

      \[\leadsto \color{blue}{\left(x - -1 \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 76.7%

         \[\leadsto \color{blue}{\left(x + \left(--1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. metadata-eval 76.7%

         \[\leadsto \left(x + \color{blue}{1} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. *-lft-identity 76.7%

         \[\leadsto \left(x + \color{blue}{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      4. +-commutative 76.7%

         \[\leadsto \color{blue}{\left(a + x\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   6. Simplified 76.7%

      \[\leadsto \color{blue}{\left(a + x\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   if 7.2000000000000002e138 < z

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 73.1%

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

   4. Taylor expanded in y around 0 73.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+210}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;z - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+98}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+52}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.6e+98) x (if (<= x 4.3e+52) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e+98) {
		tmp = x;
	} else if (x <= 4.3e+52) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-9.6d+98)) then
        tmp = x
    else if (x <= 4.3d+52) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e+98) {
		tmp = x;
	} else if (x <= 4.3e+52) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.6e+98:
		tmp = x
	elif x <= 4.3e+52:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.6e+98)
		tmp = x;
	elseif (x <= 4.3e+52)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.6e+98)
		tmp = x;
	elseif (x <= 4.3e+52)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.6e+98], x, If[LessEqual[x, 4.3e+52], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5999999999999995e98 or 4.3e52 < x

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 33.6%

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

   if -9.5999999999999995e98 < x < 4.3e52

   1. Initial program 94.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 31.5%

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

   4. Taylor expanded in y around 0 16.1%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 20.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+58}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.3e+99) x (if (<= x 4e+58) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+99) {
		tmp = x;
	} else if (x <= 4e+58) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.3d+99)) then
        tmp = x
    else if (x <= 4d+58) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+99) {
		tmp = x;
	} else if (x <= 4e+58) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.3e+99:
		tmp = x
	elif x <= 4e+58:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.3e+99)
		tmp = x;
	elseif (x <= 4e+58)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.3e+99)
		tmp = x;
	elseif (x <= 4e+58)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.3e+99], x, If[LessEqual[x, 4e+58], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2999999999999999e99 or 3.99999999999999978e58 < x

   1. Initial program 94.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 34.8%

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

   if -3.2999999999999999e99 < x < 3.99999999999999978e58

   1. Initial program 94.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 29.5%

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

   4. Taylor expanded in t around 0 14.0%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 11.1% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 94.5%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in a around inf 24.1%

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

4. Taylor expanded in t around 0 10.7%

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

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))