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

Percentage Accurate: 95.2% → 97.5%

Time: 12.1s

Alternatives: 25

Speedup: 0.5×

• 35.8% 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: 95.2% 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: 97.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0)))
        (t_2 (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) t_1)))
   (if (<= t_2 INFINITY) t_2 t_1)))

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 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1;
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1;
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	t_2 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	t_2 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + t_1;
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	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[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

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 b around inf 63.6%

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

4. Final simplification 98.4%

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

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 95.7%

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

   2. fma-define 97.2%

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

   3. associate--l+ 97.2%

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

   4. sub-neg 97.2%

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

   5. metadata-eval 97.2%

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

   6. sub-neg 97.2%

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

   7. associate-+l- 97.2%

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

   8. fma-neg 97.3%

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

   9. sub-neg 97.3%

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

   10. metadata-eval 97.3%

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

   11. remove-double-neg 97.3%

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

   12. sub-neg 97.3%

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

   13. metadata-eval 97.3%

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

3. Simplified 97.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)} \]
4. Add Preprocessing

5. Final simplification 97.3%

   \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \]
6. Add Preprocessing

Alternative 3: 53.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := x + \left(z + a\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (+ x (+ z a))) (t_3 (* t (- b a))))
   (if (<= t -2.8e+78)
     t_3
     (if (<= t -5e+25)
       t_1
       (if (<= t -1.35e-209)
         t_2
         (if (<= t 2.2e-82) t_1 (if (<= t 1.2e+45) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = x + (z + a);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -2.8e+78) {
		tmp = t_3;
	} else if (t <= -5e+25) {
		tmp = t_1;
	} else if (t <= -1.35e-209) {
		tmp = t_2;
	} else if (t <= 2.2e-82) {
		tmp = t_1;
	} else if (t <= 1.2e+45) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = y * (b - z)
    t_2 = x + (z + a)
    t_3 = t * (b - a)
    if (t <= (-2.8d+78)) then
        tmp = t_3
    else if (t <= (-5d+25)) then
        tmp = t_1
    else if (t <= (-1.35d-209)) then
        tmp = t_2
    else if (t <= 2.2d-82) then
        tmp = t_1
    else if (t <= 1.2d+45) then
        tmp = t_2
    else
        tmp = t_3
    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 = x + (z + a);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -2.8e+78) {
		tmp = t_3;
	} else if (t <= -5e+25) {
		tmp = t_1;
	} else if (t <= -1.35e-209) {
		tmp = t_2;
	} else if (t <= 2.2e-82) {
		tmp = t_1;
	} else if (t <= 1.2e+45) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = x + (z + a)
	t_3 = t * (b - a)
	tmp = 0
	if t <= -2.8e+78:
		tmp = t_3
	elif t <= -5e+25:
		tmp = t_1
	elif t <= -1.35e-209:
		tmp = t_2
	elif t <= 2.2e-82:
		tmp = t_1
	elif t <= 1.2e+45:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(x + Float64(z + a))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.8e+78)
		tmp = t_3;
	elseif (t <= -5e+25)
		tmp = t_1;
	elseif (t <= -1.35e-209)
		tmp = t_2;
	elseif (t <= 2.2e-82)
		tmp = t_1;
	elseif (t <= 1.2e+45)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = x + (z + a);
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.8e+78)
		tmp = t_3;
	elseif (t <= -5e+25)
		tmp = t_1;
	elseif (t <= -1.35e-209)
		tmp = t_2;
	elseif (t <= 2.2e-82)
		tmp = t_1;
	elseif (t <= 1.2e+45)
		tmp = t_2;
	else
		tmp = t_3;
	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[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+78], t$95$3, If[LessEqual[t, -5e+25], t$95$1, If[LessEqual[t, -1.35e-209], t$95$2, If[LessEqual[t, 2.2e-82], t$95$1, If[LessEqual[t, 1.2e+45], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8000000000000001e78 or 1.19999999999999995e45 < t

   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 t around inf 76.6%

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

   if -2.8000000000000001e78 < t < -5.00000000000000024e25 or -1.34999999999999999e-209 < t < 2.19999999999999986e-82

   1. Initial program 95.1%

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

   3. Taylor expanded in y around inf 55.9%

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

   if -5.00000000000000024e25 < t < -1.34999999999999999e-209 or 2.19999999999999986e-82 < t < 1.19999999999999995e45

   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 0 73.9%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. associate--r+ 70.6%

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

      2. sub-neg 70.6%

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

      3. neg-mul-1 70.6%

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

      4. remove-double-neg 70.6%

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

      5. sub-neg 70.6%

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

      6. metadata-eval 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in y around 0 56.3%

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

      1. sub-neg 56.3%

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

      2. +-commutative 56.3%

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

      3. neg-mul-1 56.3%

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

      4. remove-double-neg 56.3%

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

      5. associate-+l+ 56.3%

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

   9. Simplified 56.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-209}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+59}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-301}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.4e+182)
   (* t (- a))
   (if (<= t -4e+78)
     (* t b)
     (if (<= t -1e+59)
       (* y b)
       (if (<= t 1.25e-301) (+ x z) (if (<= t 6.5e+43) (+ x a) (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.4e+182) {
		tmp = t * -a;
	} else if (t <= -4e+78) {
		tmp = t * b;
	} else if (t <= -1e+59) {
		tmp = y * b;
	} else if (t <= 1.25e-301) {
		tmp = x + z;
	} else if (t <= 6.5e+43) {
		tmp = x + a;
	} 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 <= (-9.4d+182)) then
        tmp = t * -a
    else if (t <= (-4d+78)) then
        tmp = t * b
    else if (t <= (-1d+59)) then
        tmp = y * b
    else if (t <= 1.25d-301) then
        tmp = x + z
    else if (t <= 6.5d+43) then
        tmp = x + a
    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 <= -9.4e+182) {
		tmp = t * -a;
	} else if (t <= -4e+78) {
		tmp = t * b;
	} else if (t <= -1e+59) {
		tmp = y * b;
	} else if (t <= 1.25e-301) {
		tmp = x + z;
	} else if (t <= 6.5e+43) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.4e+182:
		tmp = t * -a
	elif t <= -4e+78:
		tmp = t * b
	elif t <= -1e+59:
		tmp = y * b
	elif t <= 1.25e-301:
		tmp = x + z
	elif t <= 6.5e+43:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.4e+182)
		tmp = Float64(t * Float64(-a));
	elseif (t <= -4e+78)
		tmp = Float64(t * b);
	elseif (t <= -1e+59)
		tmp = Float64(y * b);
	elseif (t <= 1.25e-301)
		tmp = Float64(x + z);
	elseif (t <= 6.5e+43)
		tmp = Float64(x + a);
	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 <= -9.4e+182)
		tmp = t * -a;
	elseif (t <= -4e+78)
		tmp = t * b;
	elseif (t <= -1e+59)
		tmp = y * b;
	elseif (t <= 1.25e-301)
		tmp = x + z;
	elseif (t <= 6.5e+43)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.4e+182], N[(t * (-a)), $MachinePrecision], If[LessEqual[t, -4e+78], N[(t * b), $MachinePrecision], If[LessEqual[t, -1e+59], N[(y * b), $MachinePrecision], If[LessEqual[t, 1.25e-301], N[(x + z), $MachinePrecision], If[LessEqual[t, 6.5e+43], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.39999999999999966e182

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf 80.3%

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

   4. Taylor expanded in b around 0 61.1%

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

      1. associate-*r* 61.1%

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

      2. neg-mul-1 61.1%

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

   6. Simplified 61.1%

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

   if -9.39999999999999966e182 < t < -4.00000000000000003e78 or 6.4999999999999998e43 < t

   1. Initial program 92.2%

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

   3. Taylor expanded in t around inf 75.1%

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

   4. Taylor expanded in b around inf 51.4%

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

   if -4.00000000000000003e78 < t < -9.99999999999999972e58

   1. Initial program 71.4%

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

   3. Taylor expanded in b around inf 71.6%

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

   4. Taylor expanded in y around inf 71.6%

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

   if -9.99999999999999972e58 < t < 1.25000000000000003e-301

   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 0 69.6%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. associate--r+ 65.3%

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

      2. sub-neg 65.3%

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

      3. neg-mul-1 65.3%

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

      4. remove-double-neg 65.3%

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

      5. sub-neg 65.3%

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

      6. metadata-eval 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 41.7%

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

      1. sub-neg 41.7%

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

      2. +-commutative 41.7%

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

      3. neg-mul-1 41.7%

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

      4. remove-double-neg 41.7%

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

      5. associate-+l+ 41.7%

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

   9. Simplified 41.7%

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

   10. Taylor expanded in a around 0 35.0%

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

       1. +-commutative 35.0%

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

   12. Simplified 35.0%

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

   if 1.25000000000000003e-301 < t < 6.4999999999999998e43

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 72.1%

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

   4. Taylor expanded in t around 0 72.1%

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

      1. associate--r+ 72.1%

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

      2. sub-neg 72.1%

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

      3. neg-mul-1 72.1%

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

      4. remove-double-neg 72.1%

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

      5. sub-neg 72.1%

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

      6. metadata-eval 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in y around 0 48.1%

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

      1. sub-neg 48.1%

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

      2. +-commutative 48.1%

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

      3. neg-mul-1 48.1%

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

      4. remove-double-neg 48.1%

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

      5. associate-+l+ 48.1%

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

   9. Simplified 48.1%

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

   10. Taylor expanded in z around 0 40.0%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+59}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-301}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-208}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -4e+78)
     t_2
     (if (<= t -4.5e+24)
       t_1
       (if (<= t -1.65e-208) (+ x z) (if (<= t 8.5e+43) 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 <= -4e+78) {
		tmp = t_2;
	} else if (t <= -4.5e+24) {
		tmp = t_1;
	} else if (t <= -1.65e-208) {
		tmp = x + z;
	} else if (t <= 8.5e+43) {
		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 <= (-4d+78)) then
        tmp = t_2
    else if (t <= (-4.5d+24)) then
        tmp = t_1
    else if (t <= (-1.65d-208)) then
        tmp = x + z
    else if (t <= 8.5d+43) 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 <= -4e+78) {
		tmp = t_2;
	} else if (t <= -4.5e+24) {
		tmp = t_1;
	} else if (t <= -1.65e-208) {
		tmp = x + z;
	} else if (t <= 8.5e+43) {
		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 <= -4e+78:
		tmp = t_2
	elif t <= -4.5e+24:
		tmp = t_1
	elif t <= -1.65e-208:
		tmp = x + z
	elif t <= 8.5e+43:
		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 <= -4e+78)
		tmp = t_2;
	elseif (t <= -4.5e+24)
		tmp = t_1;
	elseif (t <= -1.65e-208)
		tmp = Float64(x + z);
	elseif (t <= 8.5e+43)
		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 <= -4e+78)
		tmp = t_2;
	elseif (t <= -4.5e+24)
		tmp = t_1;
	elseif (t <= -1.65e-208)
		tmp = x + z;
	elseif (t <= 8.5e+43)
		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, -4e+78], t$95$2, If[LessEqual[t, -4.5e+24], t$95$1, If[LessEqual[t, -1.65e-208], N[(x + z), $MachinePrecision], If[LessEqual[t, 8.5e+43], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000003e78 or 8.5e43 < t

   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 t around inf 76.6%

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

   if -4.00000000000000003e78 < t < -4.50000000000000019e24 or -1.65000000000000003e-208 < t < 8.5e43

   1. Initial program 96.3%

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

   3. Taylor expanded in y around inf 51.1%

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

   if -4.50000000000000019e24 < t < -1.65000000000000003e-208

   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 0 71.6%

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

   4. Taylor expanded in t around 0 66.2%

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

      1. associate--r+ 66.2%

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

      2. sub-neg 66.2%

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

      3. neg-mul-1 66.2%

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

      4. remove-double-neg 66.2%

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

      5. sub-neg 66.2%

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

      6. metadata-eval 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in y around 0 54.7%

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

      1. sub-neg 54.7%

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

      2. +-commutative 54.7%

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

      3. neg-mul-1 54.7%

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

      4. remove-double-neg 54.7%

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

      5. associate-+l+ 54.7%

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

   9. Simplified 54.7%

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

   10. Taylor expanded in a around 0 43.2%

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

       1. +-commutative 43.2%

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

   12. Simplified 43.2%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+78}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-208}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-209}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.15e+60)
     t_1
     (if (<= t -1.35e-209)
       (+ x z)
       (if (<= t 1.46e-301) (* y (- z)) (if (<= t 3.65e+43) (+ x a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1.15e+60) {
		tmp = t_1;
	} else if (t <= -1.35e-209) {
		tmp = x + z;
	} else if (t <= 1.46e-301) {
		tmp = y * -z;
	} else if (t <= 3.65e+43) {
		tmp = x + a;
	} 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 = t * (b - a)
    if (t <= (-1.15d+60)) then
        tmp = t_1
    else if (t <= (-1.35d-209)) then
        tmp = x + z
    else if (t <= 1.46d-301) then
        tmp = y * -z
    else if (t <= 3.65d+43) then
        tmp = x + a
    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 = t * (b - a);
	double tmp;
	if (t <= -1.15e+60) {
		tmp = t_1;
	} else if (t <= -1.35e-209) {
		tmp = x + z;
	} else if (t <= 1.46e-301) {
		tmp = y * -z;
	} else if (t <= 3.65e+43) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.15e+60:
		tmp = t_1
	elif t <= -1.35e-209:
		tmp = x + z
	elif t <= 1.46e-301:
		tmp = y * -z
	elif t <= 3.65e+43:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.15e+60)
		tmp = t_1;
	elseif (t <= -1.35e-209)
		tmp = Float64(x + z);
	elseif (t <= 1.46e-301)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 3.65e+43)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.15e+60)
		tmp = t_1;
	elseif (t <= -1.35e-209)
		tmp = x + z;
	elseif (t <= 1.46e-301)
		tmp = y * -z;
	elseif (t <= 3.65e+43)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+60], t$95$1, If[LessEqual[t, -1.35e-209], N[(x + z), $MachinePrecision], If[LessEqual[t, 1.46e-301], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 3.65e+43], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.15000000000000008e60 or 3.6499999999999998e43 < t

   1. Initial program 92.0%

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

   3. Taylor expanded in t around inf 73.6%

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

   if -1.15000000000000008e60 < t < -1.34999999999999999e-209

   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 0 73.8%

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

   4. Taylor expanded in t around 0 67.4%

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

      1. associate--r+ 67.4%

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

      2. sub-neg 67.4%

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

      3. neg-mul-1 67.4%

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

      4. remove-double-neg 67.4%

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

      5. sub-neg 67.4%

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

      6. metadata-eval 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in y around 0 51.5%

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

      1. sub-neg 51.5%

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

      2. +-commutative 51.5%

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

      3. neg-mul-1 51.5%

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

      4. remove-double-neg 51.5%

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

      5. associate-+l+ 51.5%

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

   9. Simplified 51.5%

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

   10. Taylor expanded in a around 0 41.6%

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

       1. +-commutative 41.6%

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

   12. Simplified 41.6%

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

   if -1.34999999999999999e-209 < t < 1.46000000000000002e-301

   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 48.9%

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

   4. Taylor expanded in y around inf 37.5%

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

      1. associate-*r* 37.5%

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

      2. neg-mul-1 37.5%

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

   6. Simplified 37.5%

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

   if 1.46000000000000002e-301 < t < 3.6499999999999998e43

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 72.1%

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

   4. Taylor expanded in t around 0 72.1%

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

      1. associate--r+ 72.1%

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

      2. sub-neg 72.1%

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

      3. neg-mul-1 72.1%

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

      4. remove-double-neg 72.1%

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

      5. sub-neg 72.1%

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

      6. metadata-eval 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in y around 0 48.1%

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

      1. sub-neg 48.1%

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

      2. +-commutative 48.1%

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

      3. neg-mul-1 48.1%

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

      4. remove-double-neg 48.1%

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

      5. associate-+l+ 48.1%

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

   9. Simplified 48.1%

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

   10. Taylor expanded in z around 0 40.0%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-209}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-195}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.9e+38)
   (* y (- z))
   (if (<= y -5.2e-165)
     (* b (- t 2.0))
     (if (<= y 5.6e-195)
       (+ x z)
       (if (<= y 4.5e+83) (* a (- 1.0 t)) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.9e+38) {
		tmp = y * -z;
	} else if (y <= -5.2e-165) {
		tmp = b * (t - 2.0);
	} else if (y <= 5.6e-195) {
		tmp = x + z;
	} else if (y <= 4.5e+83) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * 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 (y <= (-2.9d+38)) then
        tmp = y * -z
    else if (y <= (-5.2d-165)) then
        tmp = b * (t - 2.0d0)
    else if (y <= 5.6d-195) then
        tmp = x + z
    else if (y <= 4.5d+83) then
        tmp = a * (1.0d0 - t)
    else
        tmp = y * 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 (y <= -2.9e+38) {
		tmp = y * -z;
	} else if (y <= -5.2e-165) {
		tmp = b * (t - 2.0);
	} else if (y <= 5.6e-195) {
		tmp = x + z;
	} else if (y <= 4.5e+83) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.9e+38:
		tmp = y * -z
	elif y <= -5.2e-165:
		tmp = b * (t - 2.0)
	elif y <= 5.6e-195:
		tmp = x + z
	elif y <= 4.5e+83:
		tmp = a * (1.0 - t)
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.9e+38)
		tmp = Float64(y * Float64(-z));
	elseif (y <= -5.2e-165)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 5.6e-195)
		tmp = Float64(x + z);
	elseif (y <= 4.5e+83)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.9e+38)
		tmp = y * -z;
	elseif (y <= -5.2e-165)
		tmp = b * (t - 2.0);
	elseif (y <= 5.6e-195)
		tmp = x + z;
	elseif (y <= 4.5e+83)
		tmp = a * (1.0 - t);
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.9e+38], N[(y * (-z)), $MachinePrecision], If[LessEqual[y, -5.2e-165], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-195], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.5e+83], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.90000000000000007e38

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf 45.8%

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

   4. Taylor expanded in y around inf 45.8%

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

      1. associate-*r* 45.8%

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

      2. neg-mul-1 45.8%

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

   6. Simplified 45.8%

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

   if -2.90000000000000007e38 < y < -5.20000000000000015e-165

   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 inf 56.8%

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

   4. Taylor expanded in y around 0 54.6%

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

   if -5.20000000000000015e-165 < y < 5.60000000000000007e-195

   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 b around 0 71.8%

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

   4. Taylor expanded in t around 0 55.0%

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

      1. associate--r+ 55.0%

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

      2. sub-neg 55.0%

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

      3. neg-mul-1 55.0%

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

      4. remove-double-neg 55.0%

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

      5. sub-neg 55.0%

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

      6. metadata-eval 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in y around 0 55.0%

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

      1. sub-neg 55.0%

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

      2. +-commutative 55.0%

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

      3. neg-mul-1 55.0%

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

      4. remove-double-neg 55.0%

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

      5. associate-+l+ 55.0%

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

   9. Simplified 55.0%

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

   10. Taylor expanded in a around 0 49.9%

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

       1. +-commutative 49.9%

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

   12. Simplified 49.9%

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

   if 5.60000000000000007e-195 < y < 4.4999999999999999e83

   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 a around inf 47.2%

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

   if 4.4999999999999999e83 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in b around inf 57.4%

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

   4. Taylor expanded in y around inf 53.2%

      \[\leadsto \color{blue}{b \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-195}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1700000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-195}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1700000000.0)
   (* y (- z))
   (if (<= y -1.6e-100)
     (* t b)
     (if (<= y 3.2e-195)
       (+ x z)
       (if (<= y 5.9e+88) (* a (- 1.0 t)) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1700000000.0) {
		tmp = y * -z;
	} else if (y <= -1.6e-100) {
		tmp = t * b;
	} else if (y <= 3.2e-195) {
		tmp = x + z;
	} else if (y <= 5.9e+88) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * 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 (y <= (-1700000000.0d0)) then
        tmp = y * -z
    else if (y <= (-1.6d-100)) then
        tmp = t * b
    else if (y <= 3.2d-195) then
        tmp = x + z
    else if (y <= 5.9d+88) then
        tmp = a * (1.0d0 - t)
    else
        tmp = y * 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 (y <= -1700000000.0) {
		tmp = y * -z;
	} else if (y <= -1.6e-100) {
		tmp = t * b;
	} else if (y <= 3.2e-195) {
		tmp = x + z;
	} else if (y <= 5.9e+88) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1700000000.0:
		tmp = y * -z
	elif y <= -1.6e-100:
		tmp = t * b
	elif y <= 3.2e-195:
		tmp = x + z
	elif y <= 5.9e+88:
		tmp = a * (1.0 - t)
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1700000000.0)
		tmp = Float64(y * Float64(-z));
	elseif (y <= -1.6e-100)
		tmp = Float64(t * b);
	elseif (y <= 3.2e-195)
		tmp = Float64(x + z);
	elseif (y <= 5.9e+88)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1700000000.0)
		tmp = y * -z;
	elseif (y <= -1.6e-100)
		tmp = t * b;
	elseif (y <= 3.2e-195)
		tmp = x + z;
	elseif (y <= 5.9e+88)
		tmp = a * (1.0 - t);
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1700000000.0], N[(y * (-z)), $MachinePrecision], If[LessEqual[y, -1.6e-100], N[(t * b), $MachinePrecision], If[LessEqual[y, 3.2e-195], N[(x + z), $MachinePrecision], If[LessEqual[y, 5.9e+88], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.7e9

   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 z around inf 44.1%

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

   4. Taylor expanded in y around inf 44.1%

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

      1. associate-*r* 44.1%

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

      2. neg-mul-1 44.1%

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

   6. Simplified 44.1%

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

   if -1.7e9 < y < -1.60000000000000008e-100

   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 inf 65.6%

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

   4. Taylor expanded in b around inf 55.8%

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

   if -1.60000000000000008e-100 < y < 3.2000000000000001e-195

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 67.3%

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

   4. Taylor expanded in t around 0 52.8%

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

      1. associate--r+ 52.8%

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

      2. sub-neg 52.8%

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

      3. neg-mul-1 52.8%

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

      4. remove-double-neg 52.8%

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

      5. sub-neg 52.8%

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

      6. metadata-eval 52.8%

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

   6. Simplified 52.8%

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

   7. Taylor expanded in y around 0 52.8%

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

      1. sub-neg 52.8%

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

      2. +-commutative 52.8%

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

      3. neg-mul-1 52.8%

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

      4. remove-double-neg 52.8%

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

      5. associate-+l+ 52.8%

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

   9. Simplified 52.8%

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

   10. Taylor expanded in a around 0 44.9%

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

       1. +-commutative 44.9%

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

   12. Simplified 44.9%

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

   if 3.2000000000000001e-195 < y < 5.89999999999999967e88

   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 a around inf 47.2%

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

   if 5.89999999999999967e88 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in b around inf 57.4%

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

   4. Taylor expanded in y around inf 53.2%

      \[\leadsto \color{blue}{b \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1700000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-195}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -6.3 \cdot 10^{-44} \lor \neg \left(b \leq 6.8 \cdot 10^{+26}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= b -6.3e-44) (not (<= b 6.8e+26)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (+ (* 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 ((b <= -6.3e-44) || !(b <= 6.8e+26)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + 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 ((b <= (-6.3d-44)) .or. (.not. (b <= 6.8d+26))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + ((a * (1.0d0 - t)) + 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 ((b <= -6.3e-44) || !(b <= 6.8e+26)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + ((a * (1.0 - t)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (b <= -6.3e-44) or not (b <= 6.8e+26):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + ((a * (1.0 - t)) + 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 ((b <= -6.3e-44) || !(b <= 6.8e+26))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + 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 ((b <= -6.3e-44) || ~((b <= 6.8e+26)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + ((a * (1.0 - t)) + 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[Or[LessEqual[b, -6.3e-44], N[Not[LessEqual[b, 6.8e+26]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.2999999999999998e-44 or 6.8000000000000005e26 < b

   1. Initial program 91.9%

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

   3. Taylor expanded in a around 0 88.9%

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

   if -6.2999999999999998e-44 < b < 6.8000000000000005e26

   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 0 95.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.3 \cdot 10^{-44} \lor \neg \left(b \leq 6.8 \cdot 10^{+26}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;x + \left(t\_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -2.3e+33)
     t_2
     (if (<= b 2.4e+25) (+ x (+ t_1 (* z (- 1.0 y)))) (+ t_2 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 t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2.3e+33) {
		tmp = t_2;
	} else if (b <= 2.4e+25) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = t_2 + 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) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-2.3d+33)) then
        tmp = t_2
    else if (b <= 2.4d+25) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = t_2 + 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 t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2.3e+33) {
		tmp = t_2;
	} else if (b <= 2.4e+25) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -2.3e+33:
		tmp = t_2
	elif b <= 2.4e+25:
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -2.3e+33)
		tmp = t_2;
	elseif (b <= 2.4e+25)
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -2.3e+33)
		tmp = t_2;
	elseif (b <= 2.4e+25)
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = t_2 + 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]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+33], t$95$2, If[LessEqual[b, 2.4e+25], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.30000000000000011e33

   1. Initial program 87.7%

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

   3. Taylor expanded in a around 0 89.6%

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

   4. Taylor expanded in z around 0 86.4%

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

   if -2.30000000000000011e33 < b < 2.39999999999999996e25

   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 0 93.6%

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

   if 2.39999999999999996e25 < b

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 85.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-295}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+26}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -8.8e-44)
     t_1
     (if (<= b -5.8e-295)
       (+ x (* a (- 1.0 t)))
       (if (<= b 2.75e+26) (- (+ x a) (* y z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -8.8e-44) {
		tmp = t_1;
	} else if (b <= -5.8e-295) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.75e+26) {
		tmp = (x + a) - (y * z);
	} 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 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-8.8d-44)) then
        tmp = t_1
    else if (b <= (-5.8d-295)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 2.75d+26) then
        tmp = (x + a) - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -8.8e-44) {
		tmp = t_1;
	} else if (b <= -5.8e-295) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.75e+26) {
		tmp = (x + a) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -8.8e-44:
		tmp = t_1
	elif b <= -5.8e-295:
		tmp = x + (a * (1.0 - t))
	elif b <= 2.75e+26:
		tmp = (x + a) - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -8.8e-44)
		tmp = t_1;
	elseif (b <= -5.8e-295)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 2.75e+26)
		tmp = Float64(Float64(x + a) - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -8.8e-44)
		tmp = t_1;
	elseif (b <= -5.8e-295)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 2.75e+26)
		tmp = (x + a) - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e-44], t$95$1, If[LessEqual[b, -5.8e-295], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.75e+26], N[(N[(x + a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.80000000000000048e-44 or 2.7499999999999998e26 < b

   1. Initial program 91.9%

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

   3. Taylor expanded in a around 0 88.9%

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

   4. Taylor expanded in z around 0 80.5%

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

   if -8.80000000000000048e-44 < b < -5.8000000000000003e-295

   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 0 95.8%

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

   4. Taylor expanded in a around inf 74.1%

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

   if -5.8000000000000003e-295 < b < 2.7499999999999998e26

   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 0 95.2%

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

   4. Taylor expanded in t around 0 75.9%

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

      1. associate--r+ 75.9%

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

      2. sub-neg 75.9%

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

      3. neg-mul-1 75.9%

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

      4. remove-double-neg 75.9%

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

      5. sub-neg 75.9%

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

      6. metadata-eval 75.9%

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

   6. Simplified 75.9%

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

   7. Taylor expanded in y around inf 63.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-44}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-295}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+26}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-219}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.2e+18)
   (* y (- z))
   (if (<= y -4.2e-100)
     (* t b)
     (if (<= y 2.5e-219) (+ x z) (if (<= y 2.3e+64) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.2e+18) {
		tmp = y * -z;
	} else if (y <= -4.2e-100) {
		tmp = t * b;
	} else if (y <= 2.5e-219) {
		tmp = x + z;
	} else if (y <= 2.3e+64) {
		tmp = x + a;
	} else {
		tmp = y * 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 (y <= (-3.2d+18)) then
        tmp = y * -z
    else if (y <= (-4.2d-100)) then
        tmp = t * b
    else if (y <= 2.5d-219) then
        tmp = x + z
    else if (y <= 2.3d+64) then
        tmp = x + a
    else
        tmp = y * 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 (y <= -3.2e+18) {
		tmp = y * -z;
	} else if (y <= -4.2e-100) {
		tmp = t * b;
	} else if (y <= 2.5e-219) {
		tmp = x + z;
	} else if (y <= 2.3e+64) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.2e+18:
		tmp = y * -z
	elif y <= -4.2e-100:
		tmp = t * b
	elif y <= 2.5e-219:
		tmp = x + z
	elif y <= 2.3e+64:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.2e+18)
		tmp = Float64(y * Float64(-z));
	elseif (y <= -4.2e-100)
		tmp = Float64(t * b);
	elseif (y <= 2.5e-219)
		tmp = Float64(x + z);
	elseif (y <= 2.3e+64)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.2e+18)
		tmp = y * -z;
	elseif (y <= -4.2e-100)
		tmp = t * b;
	elseif (y <= 2.5e-219)
		tmp = x + z;
	elseif (y <= 2.3e+64)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.2e+18], N[(y * (-z)), $MachinePrecision], If[LessEqual[y, -4.2e-100], N[(t * b), $MachinePrecision], If[LessEqual[y, 2.5e-219], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.3e+64], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.2e18

   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 z around inf 44.1%

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

   4. Taylor expanded in y around inf 44.1%

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

      1. associate-*r* 44.1%

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

      2. neg-mul-1 44.1%

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

   6. Simplified 44.1%

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

   if -3.2e18 < y < -4.20000000000000019e-100

   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 inf 65.6%

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

   4. Taylor expanded in b around inf 55.8%

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

   if -4.20000000000000019e-100 < y < 2.5000000000000001e-219

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 68.6%

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

   4. Taylor expanded in t around 0 53.5%

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

      1. associate--r+ 53.5%

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

      2. sub-neg 53.5%

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

      3. neg-mul-1 53.5%

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

      4. remove-double-neg 53.5%

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

      5. sub-neg 53.5%

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

      6. metadata-eval 53.5%

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

   6. Simplified 53.5%

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

   7. Taylor expanded in y around 0 53.5%

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

      1. sub-neg 53.5%

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

      2. +-commutative 53.5%

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

      3. neg-mul-1 53.5%

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

      4. remove-double-neg 53.5%

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

      5. associate-+l+ 53.5%

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

   9. Simplified 53.5%

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

   10. Taylor expanded in a around 0 45.2%

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

       1. +-commutative 45.2%

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

   12. Simplified 45.2%

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

   if 2.5000000000000001e-219 < y < 2.3e64

   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 b around 0 70.5%

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

   4. Taylor expanded in t around 0 48.0%

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

      1. associate--r+ 48.0%

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

      2. sub-neg 48.0%

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

      3. neg-mul-1 48.0%

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

      4. remove-double-neg 48.0%

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

      5. sub-neg 48.0%

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

      6. metadata-eval 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in y around 0 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. neg-mul-1 40.6%

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

      4. remove-double-neg 40.6%

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

      5. associate-+l+ 40.6%

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

   9. Simplified 40.6%

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

   10. Taylor expanded in z around 0 37.1%

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

   if 2.3e64 < y

   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 b around inf 55.9%

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

   4. Taylor expanded in y around inf 49.8%

      \[\leadsto \color{blue}{b \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-219}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7600000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-218}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7600000000.0)
   (* y b)
   (if (<= y -1.1e-100)
     (* t b)
     (if (<= y 3.4e-218) (+ x z) (if (<= y 2.3e+64) (+ x a) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7600000000.0) {
		tmp = y * b;
	} else if (y <= -1.1e-100) {
		tmp = t * b;
	} else if (y <= 3.4e-218) {
		tmp = x + z;
	} else if (y <= 2.3e+64) {
		tmp = x + a;
	} else {
		tmp = y * 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 (y <= (-7600000000.0d0)) then
        tmp = y * b
    else if (y <= (-1.1d-100)) then
        tmp = t * b
    else if (y <= 3.4d-218) then
        tmp = x + z
    else if (y <= 2.3d+64) then
        tmp = x + a
    else
        tmp = y * 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 (y <= -7600000000.0) {
		tmp = y * b;
	} else if (y <= -1.1e-100) {
		tmp = t * b;
	} else if (y <= 3.4e-218) {
		tmp = x + z;
	} else if (y <= 2.3e+64) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7600000000.0:
		tmp = y * b
	elif y <= -1.1e-100:
		tmp = t * b
	elif y <= 3.4e-218:
		tmp = x + z
	elif y <= 2.3e+64:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7600000000.0)
		tmp = Float64(y * b);
	elseif (y <= -1.1e-100)
		tmp = Float64(t * b);
	elseif (y <= 3.4e-218)
		tmp = Float64(x + z);
	elseif (y <= 2.3e+64)
		tmp = Float64(x + a);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7600000000.0)
		tmp = y * b;
	elseif (y <= -1.1e-100)
		tmp = t * b;
	elseif (y <= 3.4e-218)
		tmp = x + z;
	elseif (y <= 2.3e+64)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7600000000.0], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.1e-100], N[(t * b), $MachinePrecision], If[LessEqual[y, 3.4e-218], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.3e+64], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.6e9 or 2.3e64 < y

   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 b around inf 43.7%

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

   4. Taylor expanded in y around inf 38.9%

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

   if -7.6e9 < y < -1.09999999999999995e-100

   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 inf 65.6%

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

   4. Taylor expanded in b around inf 55.8%

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

   if -1.09999999999999995e-100 < y < 3.39999999999999986e-218

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 68.6%

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

   4. Taylor expanded in t around 0 53.5%

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

      1. associate--r+ 53.5%

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

      2. sub-neg 53.5%

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

      3. neg-mul-1 53.5%

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

      4. remove-double-neg 53.5%

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

      5. sub-neg 53.5%

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

      6. metadata-eval 53.5%

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

   6. Simplified 53.5%

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

   7. Taylor expanded in y around 0 53.5%

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

      1. sub-neg 53.5%

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

      2. +-commutative 53.5%

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

      3. neg-mul-1 53.5%

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

      4. remove-double-neg 53.5%

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

      5. associate-+l+ 53.5%

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

   9. Simplified 53.5%

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

   10. Taylor expanded in a around 0 45.2%

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

       1. +-commutative 45.2%

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

   12. Simplified 45.2%

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

   if 3.39999999999999986e-218 < y < 2.3e64

   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 b around 0 70.5%

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

   4. Taylor expanded in t around 0 48.0%

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

      1. associate--r+ 48.0%

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

      2. sub-neg 48.0%

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

      3. neg-mul-1 48.0%

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

      4. remove-double-neg 48.0%

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

      5. sub-neg 48.0%

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

      6. metadata-eval 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in y around 0 40.6%

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

      1. sub-neg 40.6%

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

      2. +-commutative 40.6%

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

      3. neg-mul-1 40.6%

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

      4. remove-double-neg 40.6%

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

      5. associate-+l+ 40.6%

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

   9. Simplified 40.6%

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

   10. Taylor expanded in z around 0 37.1%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7600000000:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-100}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-218}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+64}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-161}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+75}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.2e+18)
   (* y b)
   (if (<= y -2.7e-161)
     (* t b)
     (if (<= y 1.25e-279) x (if (<= y 3.45e+75) (* t b) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.2e+18) {
		tmp = y * b;
	} else if (y <= -2.7e-161) {
		tmp = t * b;
	} else if (y <= 1.25e-279) {
		tmp = x;
	} else if (y <= 3.45e+75) {
		tmp = t * b;
	} else {
		tmp = y * 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 (y <= (-1.2d+18)) then
        tmp = y * b
    else if (y <= (-2.7d-161)) then
        tmp = t * b
    else if (y <= 1.25d-279) then
        tmp = x
    else if (y <= 3.45d+75) then
        tmp = t * b
    else
        tmp = y * 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 (y <= -1.2e+18) {
		tmp = y * b;
	} else if (y <= -2.7e-161) {
		tmp = t * b;
	} else if (y <= 1.25e-279) {
		tmp = x;
	} else if (y <= 3.45e+75) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.2e+18:
		tmp = y * b
	elif y <= -2.7e-161:
		tmp = t * b
	elif y <= 1.25e-279:
		tmp = x
	elif y <= 3.45e+75:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.2e+18)
		tmp = Float64(y * b);
	elseif (y <= -2.7e-161)
		tmp = Float64(t * b);
	elseif (y <= 1.25e-279)
		tmp = x;
	elseif (y <= 3.45e+75)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.2e+18)
		tmp = y * b;
	elseif (y <= -2.7e-161)
		tmp = t * b;
	elseif (y <= 1.25e-279)
		tmp = x;
	elseif (y <= 3.45e+75)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.2e+18], N[(y * b), $MachinePrecision], If[LessEqual[y, -2.7e-161], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.25e-279], x, If[LessEqual[y, 3.45e+75], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e18 or 3.4500000000000002e75 < y

   1. Initial program 93.6%

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

   3. Taylor expanded in b around inf 44.0%

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

   4. Taylor expanded in y around inf 39.8%

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

   if -1.2e18 < y < -2.6999999999999999e-161 or 1.24999999999999992e-279 < y < 3.4500000000000002e75

   1. Initial program 97.2%

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

   3. Taylor expanded in t around inf 47.7%

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

   4. Taylor expanded in b around inf 32.5%

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

   if -2.6999999999999999e-161 < y < 1.24999999999999992e-279

   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 x around inf 30.5%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+18}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-161}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+75}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 83.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+32} \lor \neg \left(b \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e+32) (not (<= b 2.45e+27)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+32) || !(b <= 2.45e+27)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	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 <= (-1.3d+32)) .or. (.not. (b <= 2.45d+27))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    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 <= -1.3e+32) || !(b <= 2.45e+27)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e+32) or not (b <= 2.45e+27):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e+32) || !(b <= 2.45e+27))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e+32) || ~((b <= 2.45e+27)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e+32], N[Not[LessEqual[b, 2.45e+27]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3000000000000001e32 or 2.45000000000000007e27 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in a around 0 90.2%

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

   4. Taylor expanded in z around 0 84.9%

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

   if -1.3000000000000001e32 < b < 2.45000000000000007e27

   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 0 93.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+32} \lor \neg \left(b \leq 2.45 \cdot 10^{+27}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-293}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -9e+32)
     t_1
     (if (<= b -1.15e-293)
       (+ x (* a (- 1.0 t)))
       (if (<= b 3.4e+59) (- (+ x a) (* y z)) t_1)))))

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 (b <= -9e+32) {
		tmp = t_1;
	} else if (b <= -1.15e-293) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.4e+59) {
		tmp = (x + a) - (y * z);
	} 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 = b * ((y + t) - 2.0d0)
    if (b <= (-9d+32)) then
        tmp = t_1
    else if (b <= (-1.15d-293)) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 3.4d+59) then
        tmp = (x + a) - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9e+32) {
		tmp = t_1;
	} else if (b <= -1.15e-293) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.4e+59) {
		tmp = (x + a) - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9e+32:
		tmp = t_1
	elif b <= -1.15e-293:
		tmp = x + (a * (1.0 - t))
	elif b <= 3.4e+59:
		tmp = (x + a) - (y * z)
	else:
		tmp = t_1
	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 (b <= -9e+32)
		tmp = t_1;
	elseif (b <= -1.15e-293)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 3.4e+59)
		tmp = Float64(Float64(x + a) - Float64(y * z));
	else
		tmp = t_1;
	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 (b <= -9e+32)
		tmp = t_1;
	elseif (b <= -1.15e-293)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 3.4e+59)
		tmp = (x + a) - (y * z);
	else
		tmp = t_1;
	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[b, -9e+32], t$95$1, If[LessEqual[b, -1.15e-293], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+59], N[(N[(x + a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.0000000000000007e32 or 3.40000000000000006e59 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf 80.9%

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

   if -9.0000000000000007e32 < b < -1.14999999999999998e-293

   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 0 91.1%

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

   4. Taylor expanded in a around inf 65.0%

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

   if -1.14999999999999998e-293 < b < 3.40000000000000006e59

   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 0 92.3%

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

   4. Taylor expanded in t around 0 74.4%

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

      1. associate--r+ 74.4%

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

      2. sub-neg 74.4%

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

      3. neg-mul-1 74.4%

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

      4. remove-double-neg 74.4%

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

      5. sub-neg 74.4%

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

      6. metadata-eval 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in y around inf 62.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-293}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;\left(x + a\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-298}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+61}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -7e+32)
     t_1
     (if (<= b 1.45e-298)
       (+ x (* a (- 1.0 t)))
       (if (<= b 2.35e+61) (+ x (* z (- 1.0 y))) t_1)))))

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 (b <= -7e+32) {
		tmp = t_1;
	} else if (b <= 1.45e-298) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.35e+61) {
		tmp = x + (z * (1.0 - y));
	} 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 = b * ((y + t) - 2.0d0)
    if (b <= (-7d+32)) then
        tmp = t_1
    else if (b <= 1.45d-298) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 2.35d+61) then
        tmp = x + (z * (1.0d0 - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7e+32) {
		tmp = t_1;
	} else if (b <= 1.45e-298) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 2.35e+61) {
		tmp = x + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -7e+32:
		tmp = t_1
	elif b <= 1.45e-298:
		tmp = x + (a * (1.0 - t))
	elif b <= 2.35e+61:
		tmp = x + (z * (1.0 - y))
	else:
		tmp = t_1
	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 (b <= -7e+32)
		tmp = t_1;
	elseif (b <= 1.45e-298)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 2.35e+61)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	else
		tmp = t_1;
	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 (b <= -7e+32)
		tmp = t_1;
	elseif (b <= 1.45e-298)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 2.35e+61)
		tmp = x + (z * (1.0 - y));
	else
		tmp = t_1;
	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[b, -7e+32], t$95$1, If[LessEqual[b, 1.45e-298], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.35e+61], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.0000000000000002e32 or 2.3499999999999999e61 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf 80.9%

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

   if -7.0000000000000002e32 < b < 1.45000000000000007e-298

   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 0 92.3%

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

   4. Taylor expanded in a around inf 63.3%

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

   if 1.45000000000000007e-298 < b < 2.3499999999999999e61

   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 0 91.5%

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

   4. Taylor expanded in a around 0 61.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-298}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{+61}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 55.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-120}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+59}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -7e+30)
     t_1
     (if (<= b -9.8e-120)
       (- a (* t a))
       (if (<= b 4.5e+59) (+ x (+ z a)) t_1)))))

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 (b <= -7e+30) {
		tmp = t_1;
	} else if (b <= -9.8e-120) {
		tmp = a - (t * a);
	} else if (b <= 4.5e+59) {
		tmp = x + (z + a);
	} 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 = b * ((y + t) - 2.0d0)
    if (b <= (-7d+30)) then
        tmp = t_1
    else if (b <= (-9.8d-120)) then
        tmp = a - (t * a)
    else if (b <= 4.5d+59) then
        tmp = x + (z + a)
    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 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -7e+30) {
		tmp = t_1;
	} else if (b <= -9.8e-120) {
		tmp = a - (t * a);
	} else if (b <= 4.5e+59) {
		tmp = x + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -7e+30:
		tmp = t_1
	elif b <= -9.8e-120:
		tmp = a - (t * a)
	elif b <= 4.5e+59:
		tmp = x + (z + a)
	else:
		tmp = t_1
	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 (b <= -7e+30)
		tmp = t_1;
	elseif (b <= -9.8e-120)
		tmp = Float64(a - Float64(t * a));
	elseif (b <= 4.5e+59)
		tmp = Float64(x + Float64(z + a));
	else
		tmp = t_1;
	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 (b <= -7e+30)
		tmp = t_1;
	elseif (b <= -9.8e-120)
		tmp = a - (t * a);
	elseif (b <= 4.5e+59)
		tmp = x + (z + a);
	else
		tmp = t_1;
	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[b, -7e+30], t$95$1, If[LessEqual[b, -9.8e-120], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+59], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.00000000000000042e30 or 4.49999999999999959e59 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in b around inf 80.9%

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

   if -7.00000000000000042e30 < b < -9.8000000000000007e-120

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 45.9%

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

      1. sub-neg 45.9%

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

      2. distribute-rgt-in 46.0%

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

      3. *-un-lft-identity 46.0%

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

   5. Applied egg-rr 46.0%

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

   if -9.8000000000000007e-120 < b < 4.49999999999999959e59

   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 0 93.4%

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

   4. Taylor expanded in t around 0 73.3%

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

      1. associate--r+ 73.3%

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

      2. sub-neg 73.3%

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

      3. neg-mul-1 73.3%

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

      4. remove-double-neg 73.3%

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

      5. sub-neg 73.3%

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

      6. metadata-eval 73.3%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in y around 0 49.5%

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

      1. sub-neg 49.5%

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

      2. +-commutative 49.5%

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

      3. neg-mul-1 49.5%

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

      4. remove-double-neg 49.5%

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

      5. associate-+l+ 49.5%

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

   9. Simplified 49.5%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-120}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+59}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+31} \lor \neg \left(b \leq 1.08 \cdot 10^{+27}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.7e+31) (not (<= b 1.08e+27)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ (+ x a) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.7e+31) || !(b <= 1.08e+27)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) + (z * (1.0 - y));
	}
	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 <= (-3.7d+31)) .or. (.not. (b <= 1.08d+27))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x + a) + (z * (1.0d0 - y))
    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 <= -3.7e+31) || !(b <= 1.08e+27)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.7e+31) or not (b <= 1.08e+27):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x + a) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.7e+31) || !(b <= 1.08e+27))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x + a) + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.7e+31) || ~((b <= 1.08e+27)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x + a) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.7e+31], N[Not[LessEqual[b, 1.08e+27]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6999999999999998e31 or 1.08e27 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in a around 0 90.2%

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

   4. Taylor expanded in z around 0 84.9%

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

   if -3.6999999999999998e31 < b < 1.08e27

   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 0 93.6%

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

   4. Taylor expanded in t around 0 69.3%

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

      1. associate--r+ 69.3%

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

      2. sub-neg 69.3%

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

      3. neg-mul-1 69.3%

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

      4. remove-double-neg 69.3%

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

      5. sub-neg 69.3%

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

      6. metadata-eval 69.3%

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

   6. Simplified 69.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+31} \lor \neg \left(b \leq 1.08 \cdot 10^{+27}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+46}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.5e+78)
   (* t b)
   (if (<= t -4e+54) (* y b) (if (<= t 5.1e+46) (+ x a) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.5e+78) {
		tmp = t * b;
	} else if (t <= -4e+54) {
		tmp = y * b;
	} else if (t <= 5.1e+46) {
		tmp = x + a;
	} 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 <= (-4.5d+78)) then
        tmp = t * b
    else if (t <= (-4d+54)) then
        tmp = y * b
    else if (t <= 5.1d+46) then
        tmp = x + a
    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 <= -4.5e+78) {
		tmp = t * b;
	} else if (t <= -4e+54) {
		tmp = y * b;
	} else if (t <= 5.1e+46) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.5e+78:
		tmp = t * b
	elif t <= -4e+54:
		tmp = y * b
	elif t <= 5.1e+46:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.5e+78)
		tmp = Float64(t * b);
	elseif (t <= -4e+54)
		tmp = Float64(y * b);
	elseif (t <= 5.1e+46)
		tmp = Float64(x + a);
	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 <= -4.5e+78)
		tmp = t * b;
	elseif (t <= -4e+54)
		tmp = y * b;
	elseif (t <= 5.1e+46)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.5e+78], N[(t * b), $MachinePrecision], If[LessEqual[t, -4e+54], N[(y * b), $MachinePrecision], If[LessEqual[t, 5.1e+46], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4999999999999999e78 or 5.0999999999999997e46 < t

   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 t around inf 76.6%

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

   4. Taylor expanded in b around inf 45.0%

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

   if -4.4999999999999999e78 < t < -4.0000000000000003e54

   1. Initial program 71.4%

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

   3. Taylor expanded in b around inf 71.6%

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

   4. Taylor expanded in y around inf 71.6%

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

   if -4.0000000000000003e54 < t < 5.0999999999999997e46

   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 b around 0 70.8%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. associate--r+ 68.6%

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

      2. sub-neg 68.6%

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

      3. neg-mul-1 68.6%

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

      4. remove-double-neg 68.6%

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

      5. sub-neg 68.6%

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

      6. metadata-eval 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in y around 0 44.8%

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

      1. sub-neg 44.8%

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

      2. +-commutative 44.8%

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

      3. neg-mul-1 44.8%

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

      4. remove-double-neg 44.8%

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

      5. associate-+l+ 44.8%

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

   9. Simplified 44.8%

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

   10. Taylor expanded in z around 0 33.9%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+54}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+46}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 62.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+33} \lor \neg \left(b \leq 5.8 \cdot 10^{+27}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4e+33) (not (<= b 5.8e+27)))
   (* b (- (+ y t) 2.0))
   (+ x (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4e+33) || !(b <= 5.8e+27)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = 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) :: tmp
    if ((b <= (-4d+33)) .or. (.not. (b <= 5.8d+27))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = 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 tmp;
	if ((b <= -4e+33) || !(b <= 5.8e+27)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4e+33) or not (b <= 5.8e+27):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x + (a * (1.0 - t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4e+33) || !(b <= 5.8e+27))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4e+33) || ~((b <= 5.8e+27)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x + (a * (1.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4e+33], N[Not[LessEqual[b, 5.8e+27]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.9999999999999998e33 or 5.8000000000000002e27 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in b around inf 78.8%

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

   if -3.9999999999999998e33 < b < 5.8000000000000002e27

   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 0 93.6%

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

   4. Taylor expanded in a around inf 58.7%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+33} \lor \neg \left(b \leq 5.8 \cdot 10^{+27}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 25.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.14 \cdot 10^{-79} \lor \neg \left(b \leq 4.4 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.14e-79) (not (<= b 4.4e+97))) (* y b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.14e-79) || !(b <= 4.4e+97)) {
		tmp = y * b;
	} 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 ((b <= (-1.14d-79)) .or. (.not. (b <= 4.4d+97))) then
        tmp = y * b
    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 ((b <= -1.14e-79) || !(b <= 4.4e+97)) {
		tmp = y * b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.14e-79) or not (b <= 4.4e+97):
		tmp = y * b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.14e-79) || !(b <= 4.4e+97))
		tmp = Float64(y * b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.14e-79) || ~((b <= 4.4e+97)))
		tmp = y * b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.14e-79], N[Not[LessEqual[b, 4.4e+97]], $MachinePrecision]], N[(y * b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if b < -1.14e-79 or 4.4000000000000002e97 < b

   1. Initial program 92.4%

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

   3. Taylor expanded in b around inf 73.1%

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

   4. Taylor expanded in y around inf 34.7%

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

   if -1.14e-79 < b < 4.4000000000000002e97

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 23.0%

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

4. Final simplification 29.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.14 \cdot 10^{-79} \lor \neg \left(b \leq 4.4 \cdot 10^{+97}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+198}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+198) z (if (<= z 1.6e+103) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+198) {
		tmp = z;
	} else if (z <= 1.6e+103) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-1.05d+198)) then
        tmp = z
    else if (z <= 1.6d+103) then
        tmp = x
    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 tmp;
	if (z <= -1.05e+198) {
		tmp = z;
	} else if (z <= 1.6e+103) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.05e+198:
		tmp = z
	elif z <= 1.6e+103:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+198)
		tmp = z;
	elseif (z <= 1.6e+103)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.05e+198)
		tmp = z;
	elseif (z <= 1.6e+103)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+198], z, If[LessEqual[z, 1.6e+103], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000006e198 or 1.59999999999999996e103 < z

   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 z around inf 64.0%

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

   4. Taylor expanded in y around 0 27.5%

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

   if -1.05000000000000006e198 < z < 1.59999999999999996e103

   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 x around inf 18.2%

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

Alternative 24: 22.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+59}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.2e+80) x (if (<= x 1.75e+59) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.2e+80) {
		tmp = x;
	} else if (x <= 1.75e+59) {
		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 <= (-2.2d+80)) then
        tmp = x
    else if (x <= 1.75d+59) 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 <= -2.2e+80) {
		tmp = x;
	} else if (x <= 1.75e+59) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.2e+80:
		tmp = x
	elif x <= 1.75e+59:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.2e+80)
		tmp = x;
	elseif (x <= 1.75e+59)
		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 <= -2.2e+80)
		tmp = x;
	elseif (x <= 1.75e+59)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.2e+80], x, If[LessEqual[x, 1.75e+59], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000003e80 or 1.75e59 < x

   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 x around inf 30.0%

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

   if -2.20000000000000003e80 < x < 1.75e59

   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 a around inf 32.2%

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

   4. Taylor expanded in t around 0 11.8%

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

Alternative 25: 11.0% 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 95.7%

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

3. Taylor expanded in a around inf 27.1%

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

4. Taylor expanded in t around 0 10.0%

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

Reproduce

herbie shell --seed 2024144 
(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)))