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

Percentage Accurate: 95.3% → 98.0%

Time: 16.8s

Alternatives: 26

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: 95.3% 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: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) 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 t around inf 77.0%

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

4. Final simplification 98.8%

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

Alternative 2: 97.4% 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 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.9%

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

   3. associate--l+ 96.9%

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

   4. sub-neg 96.9%

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

   5. metadata-eval 96.9%

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

   6. sub-neg 96.9%

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

   7. associate-+l- 96.9%

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

   8. fma-neg 97.6%

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

   9. sub-neg 97.6%

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

   10. metadata-eval 97.6%

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

   11. remove-double-neg 97.6%

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

   12. sub-neg 97.6%

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

   13. metadata-eval 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 3: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-136}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* y (- z))))
   (if (<= y -6e+140)
     t_2
     (if (<= y -9.2e+94)
       (* y b)
       (if (<= y -3.9e+26)
         t_2
         (if (<= y -2e-20)
           t_1
           (if (<= y 9.5e-136)
             (+ x z)
             (if (<= y 7.8e-83)
               t_1
               (if (<= y 1.85e+20)
                 (+ x z)
                 (if (<= y 1.05e+128)
                   t_2
                   (if (<= y 2.2e+165)
                     t_1
                     (if (<= y 1e+212) t_2 (* y b)))))))))))))

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 = y * -z;
	double tmp;
	if (y <= -6e+140) {
		tmp = t_2;
	} else if (y <= -9.2e+94) {
		tmp = y * b;
	} else if (y <= -3.9e+26) {
		tmp = t_2;
	} else if (y <= -2e-20) {
		tmp = t_1;
	} else if (y <= 9.5e-136) {
		tmp = x + z;
	} else if (y <= 7.8e-83) {
		tmp = t_1;
	} else if (y <= 1.85e+20) {
		tmp = x + z;
	} else if (y <= 1.05e+128) {
		tmp = t_2;
	} else if (y <= 2.2e+165) {
		tmp = t_1;
	} else if (y <= 1e+212) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = y * -z
    if (y <= (-6d+140)) then
        tmp = t_2
    else if (y <= (-9.2d+94)) then
        tmp = y * b
    else if (y <= (-3.9d+26)) then
        tmp = t_2
    else if (y <= (-2d-20)) then
        tmp = t_1
    else if (y <= 9.5d-136) then
        tmp = x + z
    else if (y <= 7.8d-83) then
        tmp = t_1
    else if (y <= 1.85d+20) then
        tmp = x + z
    else if (y <= 1.05d+128) then
        tmp = t_2
    else if (y <= 2.2d+165) then
        tmp = t_1
    else if (y <= 1d+212) then
        tmp = t_2
    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 t_1 = a * (1.0 - t);
	double t_2 = y * -z;
	double tmp;
	if (y <= -6e+140) {
		tmp = t_2;
	} else if (y <= -9.2e+94) {
		tmp = y * b;
	} else if (y <= -3.9e+26) {
		tmp = t_2;
	} else if (y <= -2e-20) {
		tmp = t_1;
	} else if (y <= 9.5e-136) {
		tmp = x + z;
	} else if (y <= 7.8e-83) {
		tmp = t_1;
	} else if (y <= 1.85e+20) {
		tmp = x + z;
	} else if (y <= 1.05e+128) {
		tmp = t_2;
	} else if (y <= 2.2e+165) {
		tmp = t_1;
	} else if (y <= 1e+212) {
		tmp = t_2;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = y * -z
	tmp = 0
	if y <= -6e+140:
		tmp = t_2
	elif y <= -9.2e+94:
		tmp = y * b
	elif y <= -3.9e+26:
		tmp = t_2
	elif y <= -2e-20:
		tmp = t_1
	elif y <= 9.5e-136:
		tmp = x + z
	elif y <= 7.8e-83:
		tmp = t_1
	elif y <= 1.85e+20:
		tmp = x + z
	elif y <= 1.05e+128:
		tmp = t_2
	elif y <= 2.2e+165:
		tmp = t_1
	elif y <= 1e+212:
		tmp = t_2
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -6e+140)
		tmp = t_2;
	elseif (y <= -9.2e+94)
		tmp = Float64(y * b);
	elseif (y <= -3.9e+26)
		tmp = t_2;
	elseif (y <= -2e-20)
		tmp = t_1;
	elseif (y <= 9.5e-136)
		tmp = Float64(x + z);
	elseif (y <= 7.8e-83)
		tmp = t_1;
	elseif (y <= 1.85e+20)
		tmp = Float64(x + z);
	elseif (y <= 1.05e+128)
		tmp = t_2;
	elseif (y <= 2.2e+165)
		tmp = t_1;
	elseif (y <= 1e+212)
		tmp = t_2;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = y * -z;
	tmp = 0.0;
	if (y <= -6e+140)
		tmp = t_2;
	elseif (y <= -9.2e+94)
		tmp = y * b;
	elseif (y <= -3.9e+26)
		tmp = t_2;
	elseif (y <= -2e-20)
		tmp = t_1;
	elseif (y <= 9.5e-136)
		tmp = x + z;
	elseif (y <= 7.8e-83)
		tmp = t_1;
	elseif (y <= 1.85e+20)
		tmp = x + z;
	elseif (y <= 1.05e+128)
		tmp = t_2;
	elseif (y <= 2.2e+165)
		tmp = t_1;
	elseif (y <= 1e+212)
		tmp = t_2;
	else
		tmp = y * b;
	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[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -6e+140], t$95$2, If[LessEqual[y, -9.2e+94], N[(y * b), $MachinePrecision], If[LessEqual[y, -3.9e+26], t$95$2, If[LessEqual[y, -2e-20], t$95$1, If[LessEqual[y, 9.5e-136], N[(x + z), $MachinePrecision], If[LessEqual[y, 7.8e-83], t$95$1, If[LessEqual[y, 1.85e+20], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.05e+128], t$95$2, If[LessEqual[y, 2.2e+165], t$95$1, If[LessEqual[y, 1e+212], t$95$2, N[(y * b), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.99999999999999993e140 or -9.1999999999999999e94 < y < -3.9e26 or 1.85e20 < y < 1.05e128 or 2.1999999999999999e165 < y < 9.9999999999999991e211

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 73.3%

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

   4. Taylor expanded in b around 0 52.2%

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

      1. mul-1-neg 52.2%

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

      2. *-commutative 52.2%

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

      3. distribute-rgt-neg-in 52.2%

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

   6. Simplified 52.2%

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

   if -5.99999999999999993e140 < y < -9.1999999999999999e94 or 9.9999999999999991e211 < y

   1. Initial program 90.0%

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

   3. Taylor expanded in b around inf 71.1%

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

   4. Taylor expanded in y around inf 62.2%

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

   if -3.9e26 < y < -1.99999999999999989e-20 or 9.5000000000000007e-136 < y < 7.800000000000001e-83 or 1.05e128 < y < 2.1999999999999999e165

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf 56.1%

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

   if -1.99999999999999989e-20 < y < 9.5000000000000007e-136 or 7.800000000000001e-83 < y < 1.85e20

   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 66.7%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate--r+ 65.9%

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

      2. sub-neg 65.9%

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

      3. metadata-eval 65.9%

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

      4. sub-neg 65.9%

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

      5. sub-neg 65.9%

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

      6. mul-1-neg 65.9%

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

      7. remove-double-neg 65.9%

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

      8. distribute-lft-in 65.9%

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

      9. *-commutative 65.9%

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

      10. distribute-neg-in 65.9%

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

      11. distribute-rgt-neg-in 65.9%

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

      12. mul-1-neg 65.9%

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

      13. neg-mul-1 65.9%

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

      14. remove-double-neg 65.9%

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

      15. *-rgt-identity 65.9%

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

      16. distribute-lft-in 65.9%

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

      17. +-commutative 65.9%

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

      18. mul-1-neg 65.9%

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

      19. sub-neg 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in a around 0 49.5%

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

      1. +-commutative 49.5%

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

   9. Simplified 49.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+94}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-136}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+20}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+165}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 10^{+212}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;b \leq -190000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+92}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+127} \lor \neg \left(b \leq 7.5 \cdot 10^{+177}\right):\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))))
   (if (<= b -190000000.0)
     t_1
     (if (<= b 1.15e-291)
       (* a (- 1.0 t))
       (if (<= b 9.0)
         (+ x z)
         (if (<= b 1.25e+75)
           t_1
           (if (<= b 3e+92)
             (+ x z)
             (if (or (<= b 6.6e+127) (not (<= b 7.5e+177)))
               (* b (- t 2.0))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double tmp;
	if (b <= -190000000.0) {
		tmp = t_1;
	} else if (b <= 1.15e-291) {
		tmp = a * (1.0 - t);
	} else if (b <= 9.0) {
		tmp = x + z;
	} else if (b <= 1.25e+75) {
		tmp = t_1;
	} else if (b <= 3e+92) {
		tmp = x + z;
	} else if ((b <= 6.6e+127) || !(b <= 7.5e+177)) {
		tmp = b * (t - 2.0);
	} 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 - 2.0d0)
    if (b <= (-190000000.0d0)) then
        tmp = t_1
    else if (b <= 1.15d-291) then
        tmp = a * (1.0d0 - t)
    else if (b <= 9.0d0) then
        tmp = x + z
    else if (b <= 1.25d+75) then
        tmp = t_1
    else if (b <= 3d+92) then
        tmp = x + z
    else if ((b <= 6.6d+127) .or. (.not. (b <= 7.5d+177))) then
        tmp = b * (t - 2.0d0)
    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 - 2.0);
	double tmp;
	if (b <= -190000000.0) {
		tmp = t_1;
	} else if (b <= 1.15e-291) {
		tmp = a * (1.0 - t);
	} else if (b <= 9.0) {
		tmp = x + z;
	} else if (b <= 1.25e+75) {
		tmp = t_1;
	} else if (b <= 3e+92) {
		tmp = x + z;
	} else if ((b <= 6.6e+127) || !(b <= 7.5e+177)) {
		tmp = b * (t - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	tmp = 0
	if b <= -190000000.0:
		tmp = t_1
	elif b <= 1.15e-291:
		tmp = a * (1.0 - t)
	elif b <= 9.0:
		tmp = x + z
	elif b <= 1.25e+75:
		tmp = t_1
	elif b <= 3e+92:
		tmp = x + z
	elif (b <= 6.6e+127) or not (b <= 7.5e+177):
		tmp = b * (t - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	tmp = 0.0
	if (b <= -190000000.0)
		tmp = t_1;
	elseif (b <= 1.15e-291)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 9.0)
		tmp = Float64(x + z);
	elseif (b <= 1.25e+75)
		tmp = t_1;
	elseif (b <= 3e+92)
		tmp = Float64(x + z);
	elseif ((b <= 6.6e+127) || !(b <= 7.5e+177))
		tmp = Float64(b * Float64(t - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	tmp = 0.0;
	if (b <= -190000000.0)
		tmp = t_1;
	elseif (b <= 1.15e-291)
		tmp = a * (1.0 - t);
	elseif (b <= 9.0)
		tmp = x + z;
	elseif (b <= 1.25e+75)
		tmp = t_1;
	elseif (b <= 3e+92)
		tmp = x + z;
	elseif ((b <= 6.6e+127) || ~((b <= 7.5e+177)))
		tmp = b * (t - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -190000000.0], t$95$1, If[LessEqual[b, 1.15e-291], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.0], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.25e+75], t$95$1, If[LessEqual[b, 3e+92], N[(x + z), $MachinePrecision], If[Or[LessEqual[b, 6.6e+127], N[Not[LessEqual[b, 7.5e+177]], $MachinePrecision]], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9e8 or 9 < b < 1.2500000000000001e75 or 6.59999999999999953e127 < b < 7.50000000000000039e177

   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 67.3%

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

   4. Taylor expanded in t around 0 53.5%

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

   if -1.9e8 < b < 1.15e-291

   1. Initial program 98.8%

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

   3. Taylor expanded in a around inf 38.7%

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

   if 1.15e-291 < b < 9 or 1.2500000000000001e75 < b < 3.00000000000000013e92

   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 87.9%

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

   4. Taylor expanded in y around 0 69.5%

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

      1. associate--r+ 69.5%

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

      2. sub-neg 69.5%

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

      3. metadata-eval 69.5%

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

      4. sub-neg 69.5%

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

      5. sub-neg 69.5%

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

      6. mul-1-neg 69.5%

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

      7. remove-double-neg 69.5%

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

      8. distribute-lft-in 69.5%

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

      9. *-commutative 69.5%

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

      10. distribute-neg-in 69.5%

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

      11. distribute-rgt-neg-in 69.5%

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

      12. mul-1-neg 69.5%

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

      13. neg-mul-1 69.5%

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

      14. remove-double-neg 69.5%

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

      15. *-rgt-identity 69.5%

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

      16. distribute-lft-in 69.5%

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

      17. +-commutative 69.5%

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

      18. mul-1-neg 69.5%

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

      19. sub-neg 69.5%

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

   6. Simplified 69.5%

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

   7. Taylor expanded in a around 0 47.9%

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

      1. +-commutative 47.9%

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

   9. Simplified 47.9%

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

   if 3.00000000000000013e92 < b < 6.59999999999999953e127 or 7.50000000000000039e177 < b

   1. Initial program 85.2%

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

   3. Taylor expanded in b around inf 80.0%

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

   4. Taylor expanded in y around 0 70.9%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -190000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+75}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+92}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+127} \lor \neg \left(b \leq 7.5 \cdot 10^{+177}\right):\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-14}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+115} \lor \neg \left(y \leq 1.5 \cdot 10^{+166}\right) \land y \leq 4.5 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -6.4e+157)
     t_1
     (if (<= y -4.5e+90)
       (* y b)
       (if (<= y -1.14e-14)
         (* t b)
         (if (<= y 1.5e+25)
           (+ x z)
           (if (or (<= y 3.4e+115) (and (not (<= y 1.5e+166)) (<= y 4.5e+213)))
             t_1
             (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -6.4e+157) {
		tmp = t_1;
	} else if (y <= -4.5e+90) {
		tmp = y * b;
	} else if (y <= -1.14e-14) {
		tmp = t * b;
	} else if (y <= 1.5e+25) {
		tmp = x + z;
	} else if ((y <= 3.4e+115) || (!(y <= 1.5e+166) && (y <= 4.5e+213))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-6.4d+157)) then
        tmp = t_1
    else if (y <= (-4.5d+90)) then
        tmp = y * b
    else if (y <= (-1.14d-14)) then
        tmp = t * b
    else if (y <= 1.5d+25) then
        tmp = x + z
    else if ((y <= 3.4d+115) .or. (.not. (y <= 1.5d+166)) .and. (y <= 4.5d+213)) then
        tmp = t_1
    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 t_1 = y * -z;
	double tmp;
	if (y <= -6.4e+157) {
		tmp = t_1;
	} else if (y <= -4.5e+90) {
		tmp = y * b;
	} else if (y <= -1.14e-14) {
		tmp = t * b;
	} else if (y <= 1.5e+25) {
		tmp = x + z;
	} else if ((y <= 3.4e+115) || (!(y <= 1.5e+166) && (y <= 4.5e+213))) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -6.4e+157:
		tmp = t_1
	elif y <= -4.5e+90:
		tmp = y * b
	elif y <= -1.14e-14:
		tmp = t * b
	elif y <= 1.5e+25:
		tmp = x + z
	elif (y <= 3.4e+115) or (not (y <= 1.5e+166) and (y <= 4.5e+213)):
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -6.4e+157)
		tmp = t_1;
	elseif (y <= -4.5e+90)
		tmp = Float64(y * b);
	elseif (y <= -1.14e-14)
		tmp = Float64(t * b);
	elseif (y <= 1.5e+25)
		tmp = Float64(x + z);
	elseif ((y <= 3.4e+115) || (!(y <= 1.5e+166) && (y <= 4.5e+213)))
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -6.4e+157)
		tmp = t_1;
	elseif (y <= -4.5e+90)
		tmp = y * b;
	elseif (y <= -1.14e-14)
		tmp = t * b;
	elseif (y <= 1.5e+25)
		tmp = x + z;
	elseif ((y <= 3.4e+115) || (~((y <= 1.5e+166)) && (y <= 4.5e+213)))
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -6.4e+157], t$95$1, If[LessEqual[y, -4.5e+90], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.14e-14], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.5e+25], N[(x + z), $MachinePrecision], If[Or[LessEqual[y, 3.4e+115], And[N[Not[LessEqual[y, 1.5e+166]], $MachinePrecision], LessEqual[y, 4.5e+213]]], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.3999999999999999e157 or 1.50000000000000003e25 < y < 3.4000000000000001e115 or 1.49999999999999999e166 < y < 4.5000000000000002e213

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 80.3%

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

   4. Taylor expanded in b around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. *-commutative 57.3%

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

      3. distribute-rgt-neg-in 57.3%

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

   6. Simplified 57.3%

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

   if -6.3999999999999999e157 < y < -4.5e90 or 3.4000000000000001e115 < y < 1.49999999999999999e166 or 4.5000000000000002e213 < y

   1. Initial program 92.3%

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

   3. Taylor expanded in b around inf 57.3%

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

   4. Taylor expanded in y around inf 52.3%

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

   if -4.5e90 < y < -1.1400000000000001e-14

   1. Initial program 94.9%

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

   3. Taylor expanded in b around inf 36.5%

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

   4. Taylor expanded in t around inf 36.1%

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

   if -1.1400000000000001e-14 < y < 1.50000000000000003e25

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0 67.3%

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

   4. Taylor expanded in y around 0 66.6%

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

      1. associate--r+ 66.6%

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

      2. sub-neg 66.6%

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

      3. metadata-eval 66.6%

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

      4. sub-neg 66.6%

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

      5. sub-neg 66.6%

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

      6. mul-1-neg 66.6%

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

      7. remove-double-neg 66.6%

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

      8. distribute-lft-in 66.6%

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

      9. *-commutative 66.6%

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

      10. distribute-neg-in 66.6%

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

      11. distribute-rgt-neg-in 66.6%

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

      12. mul-1-neg 66.6%

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

      13. neg-mul-1 66.6%

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

      14. remove-double-neg 66.6%

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

      15. *-rgt-identity 66.6%

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

      16. distribute-lft-in 66.6%

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

      17. +-commutative 66.6%

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

      18. mul-1-neg 66.6%

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

      19. sub-neg 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in a around 0 45.9%

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

      1. +-commutative 45.9%

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

   9. Simplified 45.9%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+90}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.14 \cdot 10^{-14}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+25}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+115} \lor \neg \left(y \leq 1.5 \cdot 10^{+166}\right) \land y \leq 4.5 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(b \cdot \left(2 - t\right) - z\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+70}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+27}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-305}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (* b (- 2.0 t)) z))) (t_2 (* y (- b z))))
   (if (<= y -1.5e+136)
     t_2
     (if (<= y -2.3e+70)
       (+ x (* b (- (+ y t) 2.0)))
       (if (<= y -8.8e+27)
         (+ x (* z (- 1.0 y)))
         (if (<= y -1.5e-229)
           t_1
           (if (<= y 3.4e-305)
             (+ (+ x z) (* a (- 1.0 t)))
             (if (<= y 2.15e+21) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((b * (2.0 - t)) - z);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.5e+136) {
		tmp = t_2;
	} else if (y <= -2.3e+70) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= -8.8e+27) {
		tmp = x + (z * (1.0 - y));
	} else if (y <= -1.5e-229) {
		tmp = t_1;
	} else if (y <= 3.4e-305) {
		tmp = (x + z) + (a * (1.0 - t));
	} else if (y <= 2.15e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((b * (2.0d0 - t)) - z)
    t_2 = y * (b - z)
    if (y <= (-1.5d+136)) then
        tmp = t_2
    else if (y <= (-2.3d+70)) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (y <= (-8.8d+27)) then
        tmp = x + (z * (1.0d0 - y))
    else if (y <= (-1.5d-229)) then
        tmp = t_1
    else if (y <= 3.4d-305) then
        tmp = (x + z) + (a * (1.0d0 - t))
    else if (y <= 2.15d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((b * (2.0 - t)) - z);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.5e+136) {
		tmp = t_2;
	} else if (y <= -2.3e+70) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= -8.8e+27) {
		tmp = x + (z * (1.0 - y));
	} else if (y <= -1.5e-229) {
		tmp = t_1;
	} else if (y <= 3.4e-305) {
		tmp = (x + z) + (a * (1.0 - t));
	} else if (y <= 2.15e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((b * (2.0 - t)) - z)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.5e+136:
		tmp = t_2
	elif y <= -2.3e+70:
		tmp = x + (b * ((y + t) - 2.0))
	elif y <= -8.8e+27:
		tmp = x + (z * (1.0 - y))
	elif y <= -1.5e-229:
		tmp = t_1
	elif y <= 3.4e-305:
		tmp = (x + z) + (a * (1.0 - t))
	elif y <= 2.15e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(b * Float64(2.0 - t)) - z))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.5e+136)
		tmp = t_2;
	elseif (y <= -2.3e+70)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (y <= -8.8e+27)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (y <= -1.5e-229)
		tmp = t_1;
	elseif (y <= 3.4e-305)
		tmp = Float64(Float64(x + z) + Float64(a * Float64(1.0 - t)));
	elseif (y <= 2.15e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((b * (2.0 - t)) - z);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.5e+136)
		tmp = t_2;
	elseif (y <= -2.3e+70)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (y <= -8.8e+27)
		tmp = x + (z * (1.0 - y));
	elseif (y <= -1.5e-229)
		tmp = t_1;
	elseif (y <= 3.4e-305)
		tmp = (x + z) + (a * (1.0 - t));
	elseif (y <= 2.15e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+136], t$95$2, If[LessEqual[y, -2.3e+70], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.8e+27], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-229], t$95$1, If[LessEqual[y, 3.4e-305], N[(N[(x + z), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+21], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.49999999999999989e136 or 2.15e21 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 77.9%

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

   if -1.49999999999999989e136 < y < -2.29999999999999994e70

   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 a around 0 80.2%

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

   4. Taylor expanded in z around 0 71.0%

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

   if -2.29999999999999994e70 < y < -8.7999999999999995e27

   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 0 100.0%

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

   4. Taylor expanded in a around 0 87.6%

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

   if -8.7999999999999995e27 < y < -1.50000000000000001e-229 or 3.4000000000000001e-305 < y < 2.15e21

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 81.5%

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

   4. Taylor expanded in t around 0 81.5%

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

      1. sub-neg 81.5%

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

      2. metadata-eval 81.5%

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

      3. cancel-sign-sub-inv 81.5%

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

      4. sub-neg 81.5%

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

      5. metadata-eval 81.5%

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

      6. distribute-lft-in 81.5%

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

      7. +-commutative 81.5%

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

      8. fma-udef 81.5%

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

      9. +-commutative 81.5%

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

      10. distribute-lft-neg-in 81.5%

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

      11. distribute-rgt-neg-in 81.5%

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

      12. fma-def 81.5%

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

      13. +-commutative 81.5%

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

      14. distribute-neg-in 81.5%

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

      15. metadata-eval 81.5%

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

      16. sub-neg 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in y around 0 79.8%

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

   if -1.50000000000000001e-229 < y < 3.4000000000000001e-305

   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 92.5%

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

   4. Taylor expanded in y around 0 92.5%

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

      1. associate--r+ 92.5%

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

      2. sub-neg 92.5%

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

      3. metadata-eval 92.5%

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

      4. sub-neg 92.5%

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

      5. sub-neg 92.5%

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

      6. mul-1-neg 92.5%

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

      7. remove-double-neg 92.5%

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

      8. distribute-lft-in 92.5%

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

      9. *-commutative 92.5%

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

      10. distribute-neg-in 92.5%

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

      11. distribute-rgt-neg-in 92.5%

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

      12. mul-1-neg 92.5%

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

      13. neg-mul-1 92.5%

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

      14. remove-double-neg 92.5%

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

      15. *-rgt-identity 92.5%

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

      16. distribute-lft-in 92.5%

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

      17. +-commutative 92.5%

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

      18. mul-1-neg 92.5%

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

      19. sub-neg 92.5%

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

   6. Simplified 92.5%

      \[\leadsto \color{blue}{\left(x + z\right) + a \cdot \left(1 - t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+70}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+27}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-229}:\\ \;\;\;\;x - \left(b \cdot \left(2 - t\right) - z\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-305}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+21}:\\ \;\;\;\;x - \left(b \cdot \left(2 - t\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+264}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+156}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -126000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+93}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -1.55e+264)
     (* y b)
     (if (<= b -7.5e+186)
       t_1
       (if (<= b -3.2e+156)
         (* y b)
         (if (<= b -126000000.0)
           t_1
           (if (<= b 1.26e-291)
             (* a (- 1.0 t))
             (if (<= b 1.95e+93) (+ x z) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -1.55e+264) {
		tmp = y * b;
	} else if (b <= -7.5e+186) {
		tmp = t_1;
	} else if (b <= -3.2e+156) {
		tmp = y * b;
	} else if (b <= -126000000.0) {
		tmp = t_1;
	} else if (b <= 1.26e-291) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.95e+93) {
		tmp = x + 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 * (t - 2.0d0)
    if (b <= (-1.55d+264)) then
        tmp = y * b
    else if (b <= (-7.5d+186)) then
        tmp = t_1
    else if (b <= (-3.2d+156)) then
        tmp = y * b
    else if (b <= (-126000000.0d0)) then
        tmp = t_1
    else if (b <= 1.26d-291) then
        tmp = a * (1.0d0 - t)
    else if (b <= 1.95d+93) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -1.55e+264) {
		tmp = y * b;
	} else if (b <= -7.5e+186) {
		tmp = t_1;
	} else if (b <= -3.2e+156) {
		tmp = y * b;
	} else if (b <= -126000000.0) {
		tmp = t_1;
	} else if (b <= 1.26e-291) {
		tmp = a * (1.0 - t);
	} else if (b <= 1.95e+93) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -1.55e+264:
		tmp = y * b
	elif b <= -7.5e+186:
		tmp = t_1
	elif b <= -3.2e+156:
		tmp = y * b
	elif b <= -126000000.0:
		tmp = t_1
	elif b <= 1.26e-291:
		tmp = a * (1.0 - t)
	elif b <= 1.95e+93:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -1.55e+264)
		tmp = Float64(y * b);
	elseif (b <= -7.5e+186)
		tmp = t_1;
	elseif (b <= -3.2e+156)
		tmp = Float64(y * b);
	elseif (b <= -126000000.0)
		tmp = t_1;
	elseif (b <= 1.26e-291)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 1.95e+93)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -1.55e+264)
		tmp = y * b;
	elseif (b <= -7.5e+186)
		tmp = t_1;
	elseif (b <= -3.2e+156)
		tmp = y * b;
	elseif (b <= -126000000.0)
		tmp = t_1;
	elseif (b <= 1.26e-291)
		tmp = a * (1.0 - t);
	elseif (b <= 1.95e+93)
		tmp = x + 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[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+264], N[(y * b), $MachinePrecision], If[LessEqual[b, -7.5e+186], t$95$1, If[LessEqual[b, -3.2e+156], N[(y * b), $MachinePrecision], If[LessEqual[b, -126000000.0], t$95$1, If[LessEqual[b, 1.26e-291], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e+93], N[(x + z), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.54999999999999991e264 or -7.4999999999999998e186 < b < -3.20000000000000002e156

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf 90.2%

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

   4. Taylor expanded in y around inf 73.8%

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

   if -1.54999999999999991e264 < b < -7.4999999999999998e186 or -3.20000000000000002e156 < b < -1.26e8 or 1.9500000000000001e93 < b

   1. Initial program 89.6%

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

   3. Taylor expanded in b around inf 67.8%

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

   4. Taylor expanded in y around 0 51.9%

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

   if -1.26e8 < b < 1.26000000000000002e-291

   1. Initial program 98.8%

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

   3. Taylor expanded in a around inf 39.1%

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

   if 1.26000000000000002e-291 < b < 1.9500000000000001e93

   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 b around 0 80.7%

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

   4. Taylor expanded in y around 0 66.2%

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

      1. associate--r+ 66.2%

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

      2. sub-neg 66.2%

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

      3. metadata-eval 66.2%

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

      4. sub-neg 66.2%

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

      5. sub-neg 66.2%

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

      6. mul-1-neg 66.2%

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

      7. remove-double-neg 66.2%

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

      8. distribute-lft-in 66.2%

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

      9. *-commutative 66.2%

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

      10. distribute-neg-in 66.2%

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

      11. distribute-rgt-neg-in 66.2%

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

      12. mul-1-neg 66.2%

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

      13. neg-mul-1 66.2%

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

      14. remove-double-neg 66.2%

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

      15. *-rgt-identity 66.2%

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

      16. distribute-lft-in 66.2%

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

      17. +-commutative 66.2%

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

      18. mul-1-neg 66.2%

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

      19. sub-neg 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in a around 0 43.0%

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

      1. +-commutative 43.0%

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

   9. Simplified 43.0%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+264}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+186}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+156}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -126000000:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-291}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+93}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-186}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-112}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+66}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- y 2.0))) (t_2 (* t (- b a))))
   (if (<= t -1.35e+57)
     t_2
     (if (<= t -4.8e-186)
       (+ x z)
       (if (<= t -1.2e-299)
         t_1
         (if (<= t 5.2e-112)
           (+ x z)
           (if (<= t 4.8e-51) t_1 (if (<= t 4e+66) (+ x z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.35e+57) {
		tmp = t_2;
	} else if (t <= -4.8e-186) {
		tmp = x + z;
	} else if (t <= -1.2e-299) {
		tmp = t_1;
	} else if (t <= 5.2e-112) {
		tmp = x + z;
	} else if (t <= 4.8e-51) {
		tmp = t_1;
	} else if (t <= 4e+66) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (y - 2.0d0)
    t_2 = t * (b - a)
    if (t <= (-1.35d+57)) then
        tmp = t_2
    else if (t <= (-4.8d-186)) then
        tmp = x + z
    else if (t <= (-1.2d-299)) then
        tmp = t_1
    else if (t <= 5.2d-112) then
        tmp = x + z
    else if (t <= 4.8d-51) then
        tmp = t_1
    else if (t <= 4d+66) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y - 2.0);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.35e+57) {
		tmp = t_2;
	} else if (t <= -4.8e-186) {
		tmp = x + z;
	} else if (t <= -1.2e-299) {
		tmp = t_1;
	} else if (t <= 5.2e-112) {
		tmp = x + z;
	} else if (t <= 4.8e-51) {
		tmp = t_1;
	} else if (t <= 4e+66) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y - 2.0)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.35e+57:
		tmp = t_2
	elif t <= -4.8e-186:
		tmp = x + z
	elif t <= -1.2e-299:
		tmp = t_1
	elif t <= 5.2e-112:
		tmp = x + z
	elif t <= 4.8e-51:
		tmp = t_1
	elif t <= 4e+66:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y - 2.0))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.35e+57)
		tmp = t_2;
	elseif (t <= -4.8e-186)
		tmp = Float64(x + z);
	elseif (t <= -1.2e-299)
		tmp = t_1;
	elseif (t <= 5.2e-112)
		tmp = Float64(x + z);
	elseif (t <= 4.8e-51)
		tmp = t_1;
	elseif (t <= 4e+66)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y - 2.0);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.35e+57)
		tmp = t_2;
	elseif (t <= -4.8e-186)
		tmp = x + z;
	elseif (t <= -1.2e-299)
		tmp = t_1;
	elseif (t <= 5.2e-112)
		tmp = x + z;
	elseif (t <= 4.8e-51)
		tmp = t_1;
	elseif (t <= 4e+66)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+57], t$95$2, If[LessEqual[t, -4.8e-186], N[(x + z), $MachinePrecision], If[LessEqual[t, -1.2e-299], t$95$1, If[LessEqual[t, 5.2e-112], N[(x + z), $MachinePrecision], If[LessEqual[t, 4.8e-51], t$95$1, If[LessEqual[t, 4e+66], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3499999999999999e57 or 3.99999999999999978e66 < t

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf 75.1%

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

   if -1.3499999999999999e57 < t < -4.80000000000000006e-186 or -1.2000000000000001e-299 < t < 5.19999999999999983e-112 or 4.8e-51 < t < 3.99999999999999978e66

   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 73.7%

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

   4. Taylor expanded in y around 0 57.3%

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

      1. associate--r+ 57.3%

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

      2. sub-neg 57.3%

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

      3. metadata-eval 57.3%

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

      4. sub-neg 57.3%

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

      5. sub-neg 57.3%

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

      6. mul-1-neg 57.3%

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

      7. remove-double-neg 57.3%

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

      8. distribute-lft-in 57.3%

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

      9. *-commutative 57.3%

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

      10. distribute-neg-in 57.3%

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

      11. distribute-rgt-neg-in 57.3%

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

      12. mul-1-neg 57.3%

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

      13. neg-mul-1 57.3%

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

      14. remove-double-neg 57.3%

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

      15. *-rgt-identity 57.3%

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

      16. distribute-lft-in 57.3%

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

      17. +-commutative 57.3%

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

      18. mul-1-neg 57.3%

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

      19. sub-neg 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in a around 0 42.2%

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

      1. +-commutative 42.2%

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

   9. Simplified 42.2%

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

   if -4.80000000000000006e-186 < t < -1.2000000000000001e-299 or 5.19999999999999983e-112 < t < 4.8e-51

   1. Initial program 95.9%

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

   3. Taylor expanded in b around inf 48.6%

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

   4. Taylor expanded in t around 0 48.6%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-186}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-112}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+66}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-136}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.5e+26)
     t_1
     (if (<= y -2e-20)
       (* a (- 1.0 t))
       (if (<= y 3.7e-136)
         (+ x z)
         (if (<= y 4.6e-82) (* t (- b a)) (if (<= y 1.2e+20) (+ x z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.5e+26) {
		tmp = t_1;
	} else if (y <= -2e-20) {
		tmp = a * (1.0 - t);
	} else if (y <= 3.7e-136) {
		tmp = x + z;
	} else if (y <= 4.6e-82) {
		tmp = t * (b - a);
	} else if (y <= 1.2e+20) {
		tmp = x + 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 = y * (b - z)
    if (y <= (-2.5d+26)) then
        tmp = t_1
    else if (y <= (-2d-20)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 3.7d-136) then
        tmp = x + z
    else if (y <= 4.6d-82) then
        tmp = t * (b - a)
    else if (y <= 1.2d+20) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.5e+26) {
		tmp = t_1;
	} else if (y <= -2e-20) {
		tmp = a * (1.0 - t);
	} else if (y <= 3.7e-136) {
		tmp = x + z;
	} else if (y <= 4.6e-82) {
		tmp = t * (b - a);
	} else if (y <= 1.2e+20) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -2.5e+26:
		tmp = t_1
	elif y <= -2e-20:
		tmp = a * (1.0 - t)
	elif y <= 3.7e-136:
		tmp = x + z
	elif y <= 4.6e-82:
		tmp = t * (b - a)
	elif y <= 1.2e+20:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.5e+26)
		tmp = t_1;
	elseif (y <= -2e-20)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 3.7e-136)
		tmp = Float64(x + z);
	elseif (y <= 4.6e-82)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 1.2e+20)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.5e+26)
		tmp = t_1;
	elseif (y <= -2e-20)
		tmp = a * (1.0 - t);
	elseif (y <= 3.7e-136)
		tmp = x + z;
	elseif (y <= 4.6e-82)
		tmp = t * (b - a);
	elseif (y <= 1.2e+20)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+26], t$95$1, If[LessEqual[y, -2e-20], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-136], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.6e-82], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+20], N[(x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.5e26 or 1.2e20 < y

   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 y around inf 70.9%

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

   if -2.5e26 < y < -1.99999999999999989e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 68.1%

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

   if -1.99999999999999989e-20 < y < 3.7e-136 or 4.59999999999999994e-82 < y < 1.2e20

   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 66.7%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate--r+ 65.9%

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

      2. sub-neg 65.9%

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

      3. metadata-eval 65.9%

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

      4. sub-neg 65.9%

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

      5. sub-neg 65.9%

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

      6. mul-1-neg 65.9%

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

      7. remove-double-neg 65.9%

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

      8. distribute-lft-in 65.9%

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

      9. *-commutative 65.9%

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

      10. distribute-neg-in 65.9%

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

      11. distribute-rgt-neg-in 65.9%

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

      12. mul-1-neg 65.9%

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

      13. neg-mul-1 65.9%

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

      14. remove-double-neg 65.9%

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

      15. *-rgt-identity 65.9%

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

      16. distribute-lft-in 65.9%

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

      17. +-commutative 65.9%

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

      18. mul-1-neg 65.9%

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

      19. sub-neg 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in a around 0 49.5%

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

      1. +-commutative 49.5%

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

   9. Simplified 49.5%

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

   if 3.7e-136 < y < 4.59999999999999994e-82

   1. Initial program 90.9%

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

   3. Taylor expanded in t around inf 65.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-136}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -118000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-291}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -118000000.0)
     t_2
     (if (<= b -1.35e-267)
       t_1
       (if (<= b 2.9e-291)
         (+ z (* a (- 1.0 t)))
         (if (<= b 6.5e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -118000000.0) {
		tmp = t_2;
	} else if (b <= -1.35e-267) {
		tmp = t_1;
	} else if (b <= 2.9e-291) {
		tmp = z + (a * (1.0 - t));
	} else if (b <= 6.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-118000000.0d0)) then
        tmp = t_2
    else if (b <= (-1.35d-267)) then
        tmp = t_1
    else if (b <= 2.9d-291) then
        tmp = z + (a * (1.0d0 - t))
    else if (b <= 6.5d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -118000000.0) {
		tmp = t_2;
	} else if (b <= -1.35e-267) {
		tmp = t_1;
	} else if (b <= 2.9e-291) {
		tmp = z + (a * (1.0 - t));
	} else if (b <= 6.5e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -118000000.0:
		tmp = t_2
	elif b <= -1.35e-267:
		tmp = t_1
	elif b <= 2.9e-291:
		tmp = z + (a * (1.0 - t))
	elif b <= 6.5e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -118000000.0)
		tmp = t_2;
	elseif (b <= -1.35e-267)
		tmp = t_1;
	elseif (b <= 2.9e-291)
		tmp = Float64(z + Float64(a * Float64(1.0 - t)));
	elseif (b <= 6.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -118000000.0)
		tmp = t_2;
	elseif (b <= -1.35e-267)
		tmp = t_1;
	elseif (b <= 2.9e-291)
		tmp = z + (a * (1.0 - t));
	elseif (b <= 6.5e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -118000000.0], t$95$2, If[LessEqual[b, -1.35e-267], t$95$1, If[LessEqual[b, 2.9e-291], N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.18e8 or 6.50000000000000011e-16 < b

   1. Initial program 90.0%

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

   3. Taylor expanded in a around 0 87.5%

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

   4. Taylor expanded in z around 0 79.5%

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

   if -1.18e8 < b < -1.34999999999999994e-267 or 2.90000000000000002e-291 < b < 6.50000000000000011e-16

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0 90.3%

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

   4. Taylor expanded in a around 0 65.1%

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

   if -1.34999999999999994e-267 < b < 2.90000000000000002e-291

   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 0 100.0%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. associate--r+ 75.5%

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

      2. sub-neg 75.5%

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

      3. metadata-eval 75.5%

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

      4. sub-neg 75.5%

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

      5. sub-neg 75.5%

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

      6. mul-1-neg 75.5%

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

      7. remove-double-neg 75.5%

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

      8. distribute-lft-in 75.5%

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

      9. *-commutative 75.5%

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

      10. distribute-neg-in 75.5%

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

      11. distribute-rgt-neg-in 75.5%

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

      12. mul-1-neg 75.5%

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

      13. neg-mul-1 75.5%

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

      14. remove-double-neg 75.5%

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

      15. *-rgt-identity 75.5%

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

      16. distribute-lft-in 75.5%

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

      17. +-commutative 75.5%

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

      18. mul-1-neg 75.5%

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

      19. sub-neg 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in x around 0 68.9%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -118000000:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-267}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-291}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+70}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+24}:\\ \;\;\;\;x - \left(b \cdot \left(2 - t\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.52e+137)
     t_1
     (if (<= y -1.35e+70)
       (+ x (* b (- (+ y t) 2.0)))
       (if (<= y -5.8e+28)
         (+ x (* z (- 1.0 y)))
         (if (<= y 2.15e+24) (- x (- (* b (- 2.0 t)) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.52e+137) {
		tmp = t_1;
	} else if (y <= -1.35e+70) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= -5.8e+28) {
		tmp = x + (z * (1.0 - y));
	} else if (y <= 2.15e+24) {
		tmp = x - ((b * (2.0 - t)) - 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 = y * (b - z)
    if (y <= (-1.52d+137)) then
        tmp = t_1
    else if (y <= (-1.35d+70)) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else if (y <= (-5.8d+28)) then
        tmp = x + (z * (1.0d0 - y))
    else if (y <= 2.15d+24) then
        tmp = x - ((b * (2.0d0 - t)) - 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 = y * (b - z);
	double tmp;
	if (y <= -1.52e+137) {
		tmp = t_1;
	} else if (y <= -1.35e+70) {
		tmp = x + (b * ((y + t) - 2.0));
	} else if (y <= -5.8e+28) {
		tmp = x + (z * (1.0 - y));
	} else if (y <= 2.15e+24) {
		tmp = x - ((b * (2.0 - t)) - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.52e+137:
		tmp = t_1
	elif y <= -1.35e+70:
		tmp = x + (b * ((y + t) - 2.0))
	elif y <= -5.8e+28:
		tmp = x + (z * (1.0 - y))
	elif y <= 2.15e+24:
		tmp = x - ((b * (2.0 - t)) - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.52e+137)
		tmp = t_1;
	elseif (y <= -1.35e+70)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	elseif (y <= -5.8e+28)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (y <= 2.15e+24)
		tmp = Float64(x - Float64(Float64(b * Float64(2.0 - t)) - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.52e+137)
		tmp = t_1;
	elseif (y <= -1.35e+70)
		tmp = x + (b * ((y + t) - 2.0));
	elseif (y <= -5.8e+28)
		tmp = x + (z * (1.0 - y));
	elseif (y <= 2.15e+24)
		tmp = x - ((b * (2.0 - t)) - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.52e+137], t$95$1, If[LessEqual[y, -1.35e+70], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e+28], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+24], N[(x - N[(N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.52000000000000006e137 or 2.14999999999999994e24 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 77.9%

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

   if -1.52000000000000006e137 < y < -1.35e70

   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 a around 0 80.2%

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

   4. Taylor expanded in z around 0 71.0%

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

   if -1.35e70 < y < -5.8000000000000002e28

   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 0 100.0%

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

   4. Taylor expanded in a around 0 87.6%

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

   if -5.8000000000000002e28 < y < 2.14999999999999994e24

   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 a around 0 78.7%

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

   4. Taylor expanded in t around 0 78.7%

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

      1. sub-neg 78.7%

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

      2. metadata-eval 78.7%

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

      3. cancel-sign-sub-inv 78.7%

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

      4. sub-neg 78.7%

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

      5. metadata-eval 78.7%

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

      6. distribute-lft-in 78.7%

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

      7. +-commutative 78.7%

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

      8. fma-udef 78.7%

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

      9. +-commutative 78.7%

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

      10. distribute-lft-neg-in 78.7%

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

      11. distribute-rgt-neg-in 78.7%

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

      12. fma-def 78.7%

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

      13. +-commutative 78.7%

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

      14. distribute-neg-in 78.7%

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

      15. metadata-eval 78.7%

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

      16. sub-neg 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{x + \left(z + b \cdot \left(t - 2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+137}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+70}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+24}:\\ \;\;\;\;x - \left(b \cdot \left(2 - t\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-263}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-135}:\\ \;\;\;\;a + \left(x + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+19}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.4e+35)
     t_1
     (if (<= y 5.3e-263)
       (+ a (+ x z))
       (if (<= y 1.8e-135)
         (+ a (+ x (* -2.0 b)))
         (if (<= y 9.2e+19) (+ z (* a (- 1.0 t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.4e+35) {
		tmp = t_1;
	} else if (y <= 5.3e-263) {
		tmp = a + (x + z);
	} else if (y <= 1.8e-135) {
		tmp = a + (x + (-2.0 * b));
	} else if (y <= 9.2e+19) {
		tmp = z + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.4d+35)) then
        tmp = t_1
    else if (y <= 5.3d-263) then
        tmp = a + (x + z)
    else if (y <= 1.8d-135) then
        tmp = a + (x + ((-2.0d0) * b))
    else if (y <= 9.2d+19) then
        tmp = z + (a * (1.0d0 - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.4e+35) {
		tmp = t_1;
	} else if (y <= 5.3e-263) {
		tmp = a + (x + z);
	} else if (y <= 1.8e-135) {
		tmp = a + (x + (-2.0 * b));
	} else if (y <= 9.2e+19) {
		tmp = z + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.4e+35:
		tmp = t_1
	elif y <= 5.3e-263:
		tmp = a + (x + z)
	elif y <= 1.8e-135:
		tmp = a + (x + (-2.0 * b))
	elif y <= 9.2e+19:
		tmp = z + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.4e+35)
		tmp = t_1;
	elseif (y <= 5.3e-263)
		tmp = Float64(a + Float64(x + z));
	elseif (y <= 1.8e-135)
		tmp = Float64(a + Float64(x + Float64(-2.0 * b)));
	elseif (y <= 9.2e+19)
		tmp = Float64(z + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.4e+35)
		tmp = t_1;
	elseif (y <= 5.3e-263)
		tmp = a + (x + z);
	elseif (y <= 1.8e-135)
		tmp = a + (x + (-2.0 * b));
	elseif (y <= 9.2e+19)
		tmp = z + (a * (1.0 - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+35], t$95$1, If[LessEqual[y, 5.3e-263], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-135], N[(a + N[(x + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+19], N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.39999999999999999e35 or 9.2e19 < y

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -1.39999999999999999e35 < y < 5.2999999999999997e-263

   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 72.0%

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

   4. Taylor expanded in y around 0 70.7%

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

      1. associate--r+ 70.7%

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

      2. sub-neg 70.7%

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

      3. metadata-eval 70.7%

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

      4. sub-neg 70.7%

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

      5. sub-neg 70.7%

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

      6. mul-1-neg 70.7%

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

      7. remove-double-neg 70.7%

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

      8. distribute-lft-in 70.7%

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

      9. *-commutative 70.7%

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

      10. distribute-neg-in 70.7%

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

      11. distribute-rgt-neg-in 70.7%

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

      12. mul-1-neg 70.7%

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

      13. neg-mul-1 70.7%

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

      14. remove-double-neg 70.7%

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

      15. *-rgt-identity 70.7%

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

      16. distribute-lft-in 70.7%

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

      17. +-commutative 70.7%

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

      18. mul-1-neg 70.7%

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

      19. sub-neg 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in t around 0 59.3%

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

   if 5.2999999999999997e-263 < y < 1.79999999999999989e-135

   1. Initial program 93.9%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in z around 0 88.6%

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

   5. Taylor expanded in t around 0 68.5%

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

      1. sub-neg 68.5%

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

      2. sub-neg 68.5%

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

      3. metadata-eval 68.5%

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

      4. mul-1-neg 68.5%

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

      5. remove-double-neg 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in y around 0 68.5%

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

      1. *-commutative 68.5%

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

   10. Simplified 68.5%

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

   if 1.79999999999999989e-135 < y < 9.2e19

   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 b around 0 62.7%

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

   4. Taylor expanded in y around 0 59.7%

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

      1. associate--r+ 59.7%

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

      2. sub-neg 59.7%

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

      3. metadata-eval 59.7%

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

      4. sub-neg 59.7%

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

      5. sub-neg 59.7%

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

      6. mul-1-neg 59.7%

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

      7. remove-double-neg 59.7%

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

      8. distribute-lft-in 59.7%

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

      9. *-commutative 59.7%

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

      10. distribute-neg-in 59.7%

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

      11. distribute-rgt-neg-in 59.7%

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

      12. mul-1-neg 59.7%

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

      13. neg-mul-1 59.7%

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

      14. remove-double-neg 59.7%

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

      15. *-rgt-identity 59.7%

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

      16. distribute-lft-in 59.7%

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

      17. +-commutative 59.7%

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

      18. mul-1-neg 59.7%

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

      19. sub-neg 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in x around 0 49.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-263}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-135}:\\ \;\;\;\;a + \left(x + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+19}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x + y \cdot b\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-52}:\\ \;\;\;\;a + \left(x + -2 \cdot b\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ x (* y b)))) (t_2 (* t (- b a))))
   (if (<= t -2.05e+60)
     t_2
     (if (<= t 5.8e-102)
       t_1
       (if (<= t 2.45e-52)
         (+ a (+ x (* -2.0 b)))
         (if (<= t 9.5e+65) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (y * b));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.05e+60) {
		tmp = t_2;
	} else if (t <= 5.8e-102) {
		tmp = t_1;
	} else if (t <= 2.45e-52) {
		tmp = a + (x + (-2.0 * b));
	} else if (t <= 9.5e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (x + (y * b))
    t_2 = t * (b - a)
    if (t <= (-2.05d+60)) then
        tmp = t_2
    else if (t <= 5.8d-102) then
        tmp = t_1
    else if (t <= 2.45d-52) then
        tmp = a + (x + ((-2.0d0) * b))
    else if (t <= 9.5d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (y * b));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.05e+60) {
		tmp = t_2;
	} else if (t <= 5.8e-102) {
		tmp = t_1;
	} else if (t <= 2.45e-52) {
		tmp = a + (x + (-2.0 * b));
	} else if (t <= 9.5e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x + (y * b))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.05e+60:
		tmp = t_2
	elif t <= 5.8e-102:
		tmp = t_1
	elif t <= 2.45e-52:
		tmp = a + (x + (-2.0 * b))
	elif t <= 9.5e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x + Float64(y * b)))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.05e+60)
		tmp = t_2;
	elseif (t <= 5.8e-102)
		tmp = t_1;
	elseif (t <= 2.45e-52)
		tmp = Float64(a + Float64(x + Float64(-2.0 * b)));
	elseif (t <= 9.5e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (x + (y * b));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.05e+60)
		tmp = t_2;
	elseif (t <= 5.8e-102)
		tmp = t_1;
	elseif (t <= 2.45e-52)
		tmp = a + (x + (-2.0 * b));
	elseif (t <= 9.5e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(x + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+60], t$95$2, If[LessEqual[t, 5.8e-102], t$95$1, If[LessEqual[t, 2.45e-52], N[(a + N[(x + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.05e60 or 9.5000000000000005e65 < t

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf 75.1%

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

   if -2.05e60 < t < 5.79999999999999973e-102 or 2.45000000000000009e-52 < t < 9.5000000000000005e65

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 98.6%

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

   4. Taylor expanded in z around 0 68.9%

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

   5. Taylor expanded in t around 0 67.0%

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

      1. sub-neg 67.0%

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

      2. sub-neg 67.0%

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

      3. metadata-eval 67.0%

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

      4. mul-1-neg 67.0%

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

      5. remove-double-neg 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in y around inf 58.6%

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

   if 5.79999999999999973e-102 < t < 2.45000000000000009e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in z around 0 76.5%

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

   5. Taylor expanded in t around 0 76.5%

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

      1. sub-neg 76.5%

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

      2. sub-neg 76.5%

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

      3. metadata-eval 76.5%

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

      4. mul-1-neg 76.5%

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

      5. remove-double-neg 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in y around 0 64.6%

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

      1. *-commutative 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;a + \left(x + y \cdot b\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-52}:\\ \;\;\;\;a + \left(x + -2 \cdot b\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+65}:\\ \;\;\;\;a + \left(x + y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-292}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.65e+124)
     t_2
     (if (<= b -1.45e-267)
       t_1
       (if (<= b 5.8e-292) (+ z (* a (- 1.0 t))) (if (<= b 1.6) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.65e+124) {
		tmp = t_2;
	} else if (b <= -1.45e-267) {
		tmp = t_1;
	} else if (b <= 5.8e-292) {
		tmp = z + (a * (1.0 - t));
	} else if (b <= 1.6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.65d+124)) then
        tmp = t_2
    else if (b <= (-1.45d-267)) then
        tmp = t_1
    else if (b <= 5.8d-292) then
        tmp = z + (a * (1.0d0 - t))
    else if (b <= 1.6d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.65e+124) {
		tmp = t_2;
	} else if (b <= -1.45e-267) {
		tmp = t_1;
	} else if (b <= 5.8e-292) {
		tmp = z + (a * (1.0 - t));
	} else if (b <= 1.6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.65e+124:
		tmp = t_2
	elif b <= -1.45e-267:
		tmp = t_1
	elif b <= 5.8e-292:
		tmp = z + (a * (1.0 - t))
	elif b <= 1.6:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.65e+124)
		tmp = t_2;
	elseif (b <= -1.45e-267)
		tmp = t_1;
	elseif (b <= 5.8e-292)
		tmp = Float64(z + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1.6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.65e+124)
		tmp = t_2;
	elseif (b <= -1.45e-267)
		tmp = t_1;
	elseif (b <= 5.8e-292)
		tmp = z + (a * (1.0 - t));
	elseif (b <= 1.6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+124], t$95$2, If[LessEqual[b, -1.45e-267], t$95$1, If[LessEqual[b, 5.8e-292], N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.65000000000000007e124 or 1.6000000000000001 < b

   1. Initial program 87.9%

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

   3. Taylor expanded in b around inf 75.1%

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

   if -1.65000000000000007e124 < b < -1.45000000000000011e-267 or 5.79999999999999985e-292 < b < 1.6000000000000001

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 86.2%

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

   4. Taylor expanded in a around 0 62.6%

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

   if -1.45000000000000011e-267 < b < 5.79999999999999985e-292

   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 0 100.0%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. associate--r+ 75.5%

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

      2. sub-neg 75.5%

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

      3. metadata-eval 75.5%

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

      4. sub-neg 75.5%

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

      5. sub-neg 75.5%

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

      6. mul-1-neg 75.5%

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

      7. remove-double-neg 75.5%

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

      8. distribute-lft-in 75.5%

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

      9. *-commutative 75.5%

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

      10. distribute-neg-in 75.5%

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

      11. distribute-rgt-neg-in 75.5%

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

      12. mul-1-neg 75.5%

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

      13. neg-mul-1 75.5%

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

      14. remove-double-neg 75.5%

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

      15. *-rgt-identity 75.5%

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

      16. distribute-lft-in 75.5%

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

      17. +-commutative 75.5%

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

      18. mul-1-neg 75.5%

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

      19. sub-neg 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in x around 0 68.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-267}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-292}:\\ \;\;\;\;z + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.6:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-16} \lor \neg \left(z \leq 2 \cdot 10^{+81}\right):\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= z -5.8e-16) (not (<= z 2e+81)))
     (+ x (+ t_1 (* z (- 1.0 y))))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((z <= -5.8e-16) || !(z <= 2e+81)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((z <= (-5.8d-16)) .or. (.not. (z <= 2d+81))) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((z <= -5.8e-16) || !(z <= 2e+81)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (z <= -5.8e-16) or not (z <= 2e+81):
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((z <= -5.8e-16) || !(z <= 2e+81))
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((z <= -5.8e-16) || ~((z <= 2e+81)))
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5.8e-16], N[Not[LessEqual[z, 2e+81]], $MachinePrecision]], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999996e-16 or 1.99999999999999984e81 < z

   1. Initial program 93.1%

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

   3. Taylor expanded in b around 0 79.8%

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

   if -5.7999999999999996e-16 < z < 1.99999999999999984e81

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 92.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-16} \lor \neg \left(z \leq 2 \cdot 10^{+81}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-13} \lor \neg \left(z \leq 9.5 \cdot 10^{+78}\right):\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (or (<= z -1.6e-13) (not (<= z 9.5e+78)))
     (+ t_1 (* z (- 1.0 y)))
     (+ t_1 (* a (- 1.0 t))))))

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 ((z <= -1.6e-13) || !(z <= 9.5e+78)) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if ((z <= (-1.6d-13)) .or. (.not. (z <= 9.5d+78))) then
        tmp = t_1 + (z * (1.0d0 - y))
    else
        tmp = t_1 + (a * (1.0d0 - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if ((z <= -1.6e-13) || !(z <= 9.5e+78)) {
		tmp = t_1 + (z * (1.0 - y));
	} else {
		tmp = t_1 + (a * (1.0 - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if (z <= -1.6e-13) or not (z <= 9.5e+78):
		tmp = t_1 + (z * (1.0 - y))
	else:
		tmp = t_1 + (a * (1.0 - t))
	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 ((z <= -1.6e-13) || !(z <= 9.5e+78))
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(t_1 + Float64(a * Float64(1.0 - t)));
	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 ((z <= -1.6e-13) || ~((z <= 9.5e+78)))
		tmp = t_1 + (z * (1.0 - y));
	else
		tmp = t_1 + (a * (1.0 - t));
	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[Or[LessEqual[z, -1.6e-13], N[Not[LessEqual[z, 9.5e+78]], $MachinePrecision]], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e-13 or 9.5000000000000006e78 < z

   1. Initial program 93.1%

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

   3. Taylor expanded in a around 0 89.7%

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

   if -1.6e-13 < z < 9.5000000000000006e78

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 92.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-13} \lor \neg \left(z \leq 9.5 \cdot 10^{+78}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-14} \lor \neg \left(z \leq 7.2 \cdot 10^{+76}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x - \left(t \cdot \left(a - b\right) + b \cdot \left(2 - y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.15e-14) (not (<= z 7.2e+76)))
   (+ (+ x (* b (- (+ y t) 2.0))) (* z (- 1.0 y)))
   (+ a (- x (+ (* t (- a b)) (* b (- 2.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.15e-14) || !(z <= 7.2e+76)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = a + (x - ((t * (a - b)) + (b * (2.0 - 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 ((z <= (-2.15d-14)) .or. (.not. (z <= 7.2d+76))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + (z * (1.0d0 - y))
    else
        tmp = a + (x - ((t * (a - b)) + (b * (2.0d0 - 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 ((z <= -2.15e-14) || !(z <= 7.2e+76)) {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	} else {
		tmp = a + (x - ((t * (a - b)) + (b * (2.0 - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.15e-14) or not (z <= 7.2e+76):
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y))
	else:
		tmp = a + (x - ((t * (a - b)) + (b * (2.0 - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.15e-14) || !(z <= 7.2e+76))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(z * Float64(1.0 - y)));
	else
		tmp = Float64(a + Float64(x - Float64(Float64(t * Float64(a - b)) + Float64(b * Float64(2.0 - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.15e-14) || ~((z <= 7.2e+76)))
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	else
		tmp = a + (x - ((t * (a - b)) + (b * (2.0 - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.15e-14], N[Not[LessEqual[z, 7.2e+76]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(x - N[(N[(t * N[(a - b), $MachinePrecision]), $MachinePrecision] + N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.14999999999999999e-14 or 7.2000000000000006e76 < z

   1. Initial program 93.1%

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

   3. Taylor expanded in a around 0 89.7%

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

   if -2.14999999999999999e-14 < z < 7.2000000000000006e76

   1. Initial program 96.1%

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

   3. Taylor expanded in t around 0 96.7%

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

   4. Taylor expanded in z around 0 93.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-14} \lor \neg \left(z \leq 7.2 \cdot 10^{+76}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x - \left(t \cdot \left(a - b\right) + b \cdot \left(2 - y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 27.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+57}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-52}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.5e+57)
   (* t b)
   (if (<= t 4.3e-107)
     x
     (if (<= t 3.05e-52) (* -2.0 b) (if (<= t 1.6e+65) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.5e+57) {
		tmp = t * b;
	} else if (t <= 4.3e-107) {
		tmp = x;
	} else if (t <= 3.05e-52) {
		tmp = -2.0 * b;
	} else if (t <= 1.6e+65) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.5d+57)) then
        tmp = t * b
    else if (t <= 4.3d-107) then
        tmp = x
    else if (t <= 3.05d-52) then
        tmp = (-2.0d0) * b
    else if (t <= 1.6d+65) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.5e+57) {
		tmp = t * b;
	} else if (t <= 4.3e-107) {
		tmp = x;
	} else if (t <= 3.05e-52) {
		tmp = -2.0 * b;
	} else if (t <= 1.6e+65) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.5e+57:
		tmp = t * b
	elif t <= 4.3e-107:
		tmp = x
	elif t <= 3.05e-52:
		tmp = -2.0 * b
	elif t <= 1.6e+65:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.5e+57)
		tmp = Float64(t * b);
	elseif (t <= 4.3e-107)
		tmp = x;
	elseif (t <= 3.05e-52)
		tmp = Float64(-2.0 * b);
	elseif (t <= 1.6e+65)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.5e+57)
		tmp = t * b;
	elseif (t <= 4.3e-107)
		tmp = x;
	elseif (t <= 3.05e-52)
		tmp = -2.0 * b;
	elseif (t <= 1.6e+65)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.5e+57], N[(t * b), $MachinePrecision], If[LessEqual[t, 4.3e-107], x, If[LessEqual[t, 3.05e-52], N[(-2.0 * b), $MachinePrecision], If[LessEqual[t, 1.6e+65], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999996e57 or 1.60000000000000003e65 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in b around inf 45.6%

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

   4. Taylor expanded in t around inf 42.4%

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

   if -4.49999999999999996e57 < t < 4.2999999999999997e-107 or 3.04999999999999995e-52 < t < 1.60000000000000003e65

   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 x around inf 25.5%

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

   if 4.2999999999999997e-107 < t < 3.04999999999999995e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 53.8%

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

   4. Taylor expanded in t around 0 53.8%

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

   5. Taylor expanded in y around 0 42.9%

      \[\leadsto \color{blue}{-2 \cdot b} \]
   6. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto \color{blue}{b \cdot -2} \]

   7. Simplified 42.9%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+57}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-52}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+57}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-134}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.5e+57)
   (* t b)
   (if (<= t -2.95e-192)
     x
     (if (<= t 4e-134) (* y b) (if (<= t 4.7e+64) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+57) {
		tmp = t * b;
	} else if (t <= -2.95e-192) {
		tmp = x;
	} else if (t <= 4e-134) {
		tmp = y * b;
	} else if (t <= 4.7e+64) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.5d+57)) then
        tmp = t * b
    else if (t <= (-2.95d-192)) then
        tmp = x
    else if (t <= 4d-134) then
        tmp = y * b
    else if (t <= 4.7d+64) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e+57) {
		tmp = t * b;
	} else if (t <= -2.95e-192) {
		tmp = x;
	} else if (t <= 4e-134) {
		tmp = y * b;
	} else if (t <= 4.7e+64) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.5e+57:
		tmp = t * b
	elif t <= -2.95e-192:
		tmp = x
	elif t <= 4e-134:
		tmp = y * b
	elif t <= 4.7e+64:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.5e+57)
		tmp = Float64(t * b);
	elseif (t <= -2.95e-192)
		tmp = x;
	elseif (t <= 4e-134)
		tmp = Float64(y * b);
	elseif (t <= 4.7e+64)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.5e+57)
		tmp = t * b;
	elseif (t <= -2.95e-192)
		tmp = x;
	elseif (t <= 4e-134)
		tmp = y * b;
	elseif (t <= 4.7e+64)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.5e+57], N[(t * b), $MachinePrecision], If[LessEqual[t, -2.95e-192], x, If[LessEqual[t, 4e-134], N[(y * b), $MachinePrecision], If[LessEqual[t, 4.7e+64], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5e57 or 4.70000000000000029e64 < t

   1. Initial program 87.8%

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

   3. Taylor expanded in b around inf 45.6%

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

   4. Taylor expanded in t around inf 42.4%

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

   if -1.5e57 < t < -2.9499999999999998e-192 or 4.00000000000000016e-134 < t < 4.70000000000000029e64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 27.5%

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

   if -2.9499999999999998e-192 < t < 4.00000000000000016e-134

   1. Initial program 96.6%

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

   3. Taylor expanded in b around inf 34.7%

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

   4. Taylor expanded in y around inf 27.5%

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

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+57}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-192}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-134}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -125000000 \lor \neg \left(b \leq 92000000000000\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -125000000.0) (not (<= b 92000000000000.0)))
   (+ 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 <= -125000000.0) || !(b <= 92000000000000.0)) {
		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 <= (-125000000.0d0)) .or. (.not. (b <= 92000000000000.0d0))) 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 <= -125000000.0) || !(b <= 92000000000000.0)) {
		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 <= -125000000.0) or not (b <= 92000000000000.0):
		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 <= -125000000.0) || !(b <= 92000000000000.0))
		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 <= -125000000.0) || ~((b <= 92000000000000.0)))
		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, -125000000.0], N[Not[LessEqual[b, 92000000000000.0]], $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 < -1.25e8 or 9.2e13 < b

   1. Initial program 89.8%

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

   3. Taylor expanded in a around 0 88.0%

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

   4. Taylor expanded in z around 0 79.9%

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

   if -1.25e8 < b < 9.2e13

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 91.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -125000000 \lor \neg \left(b \leq 92000000000000\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -126000000 \lor \neg \left(b \leq 10^{+14}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -126000000.0) (not (<= b 1e+14)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (- (* a (- 1.0 t)) (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -126000000.0) || !(b <= 1e+14)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-126000000.0d0)) .or. (.not. (b <= 1d+14))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -126000000.0) || !(b <= 1e+14)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -126000000.0) or not (b <= 1e+14):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) - (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -126000000.0) || !(b <= 1e+14))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -126000000.0) || ~((b <= 1e+14)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -126000000.0], N[Not[LessEqual[b, 1e+14]], $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[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.26e8 or 1e14 < b

   1. Initial program 89.8%

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

   3. Taylor expanded in a around 0 88.0%

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

   4. Taylor expanded in z around 0 79.9%

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

   if -1.26e8 < b < 1e14

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 91.0%

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

   4. Taylor expanded in y around inf 78.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -126000000 \lor \neg \left(b \leq 10^{+14}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 56.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+38} \lor \neg \left(y \leq 7.4 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4e+38) (not (<= y 7.4e+22))) (* y (- b z)) (+ a (+ x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4e+38) || !(y <= 7.4e+22)) {
		tmp = y * (b - z);
	} else {
		tmp = a + (x + 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 ((y <= (-1.4d+38)) .or. (.not. (y <= 7.4d+22))) then
        tmp = y * (b - z)
    else
        tmp = a + (x + 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 ((y <= -1.4e+38) || !(y <= 7.4e+22)) {
		tmp = y * (b - z);
	} else {
		tmp = a + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.4e+38) or not (y <= 7.4e+22):
		tmp = y * (b - z)
	else:
		tmp = a + (x + z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.4e+38) || !(y <= 7.4e+22))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(a + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.4e+38) || ~((y <= 7.4e+22)))
		tmp = y * (b - z);
	else
		tmp = a + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.4e+38], N[Not[LessEqual[y, 7.4e+22]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e38 or 7.3999999999999996e22 < y

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -1.4e38 < y < 7.3999999999999996e22

   1. Initial program 97.0%

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

   3. Taylor expanded in b around 0 67.6%

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

   4. Taylor expanded in y around 0 66.3%

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

      1. associate--r+ 66.3%

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

      2. sub-neg 66.3%

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

      3. metadata-eval 66.3%

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

      4. sub-neg 66.3%

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

      5. sub-neg 66.3%

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

      6. mul-1-neg 66.3%

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

      7. remove-double-neg 66.3%

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

      8. distribute-lft-in 66.3%

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

      9. *-commutative 66.3%

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

      10. distribute-neg-in 66.3%

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

      11. distribute-rgt-neg-in 66.3%

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

      12. mul-1-neg 66.3%

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

      13. neg-mul-1 66.3%

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

      14. remove-double-neg 66.3%

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

      15. *-rgt-identity 66.3%

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

      16. distribute-lft-in 66.3%

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

      17. +-commutative 66.3%

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

      18. mul-1-neg 66.3%

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

      19. sub-neg 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in t around 0 54.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+38} \lor \neg \left(y \leq 7.4 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 35.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+93} \lor \neg \left(y \leq 2.9 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.6e+93) (not (<= y 2.9e+81))) (* y b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.6e+93) || !(y <= 2.9e+81)) {
		tmp = y * b;
	} else {
		tmp = x + 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 ((y <= (-6.6d+93)) .or. (.not. (y <= 2.9d+81))) then
        tmp = y * b
    else
        tmp = x + 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 ((y <= -6.6e+93) || !(y <= 2.9e+81)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.6e+93) or not (y <= 2.9e+81):
		tmp = y * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.6e+93) || !(y <= 2.9e+81))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.6e+93) || ~((y <= 2.9e+81)))
		tmp = y * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.6e+93], N[Not[LessEqual[y, 2.9e+81]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.60000000000000017e93 or 2.9e81 < y

   1. Initial program 91.0%

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

   3. Taylor expanded in b around inf 44.9%

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

   4. Taylor expanded in y around inf 41.2%

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

   if -6.60000000000000017e93 < y < 2.9e81

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0 69.4%

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

   4. Taylor expanded in y around 0 61.7%

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

      1. associate--r+ 61.7%

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

      2. sub-neg 61.7%

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

      3. metadata-eval 61.7%

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

      4. sub-neg 61.7%

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

      5. sub-neg 61.7%

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

      6. mul-1-neg 61.7%

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

      7. remove-double-neg 61.7%

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

      8. distribute-lft-in 61.7%

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

      9. *-commutative 61.7%

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

      10. distribute-neg-in 61.7%

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

      11. distribute-rgt-neg-in 61.7%

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

      12. mul-1-neg 61.7%

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

      13. neg-mul-1 61.7%

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

      14. remove-double-neg 61.7%

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

      15. *-rgt-identity 61.7%

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

      16. distribute-lft-in 61.7%

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

      17. +-commutative 61.7%

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

      18. mul-1-neg 61.7%

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

      19. sub-neg 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in a around 0 39.7%

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

      1. +-commutative 39.7%

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

   9. Simplified 39.7%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+93} \lor \neg \left(y \leq 2.9 \cdot 10^{+81}\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6e+121) x (if (<= x 1.65e+38) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+121) {
		tmp = x;
	} else if (x <= 1.65e+38) {
		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 <= (-6d+121)) then
        tmp = x
    else if (x <= 1.65d+38) 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 <= -6e+121) {
		tmp = x;
	} else if (x <= 1.65e+38) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6e+121:
		tmp = x
	elif x <= 1.65e+38:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6e+121)
		tmp = x;
	elseif (x <= 1.65e+38)
		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 <= -6e+121)
		tmp = x;
	elseif (x <= 1.65e+38)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6e+121], x, If[LessEqual[x, 1.65e+38], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000005e121 or 1.65e38 < x

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 39.0%

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

   if -6.0000000000000005e121 < x < 1.65e38

   1. Initial program 94.3%

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

   3. Taylor expanded in a around inf 28.9%

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

   4. Taylor expanded in t around 0 12.8%

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

4. Final simplification 22.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 20.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.35 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.35e-16) x (if (<= x 3.8e-8) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.35e-16) {
		tmp = x;
	} else if (x <= 3.8e-8) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-4.35d-16)) then
        tmp = x
    else if (x <= 3.8d-8) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.35e-16) {
		tmp = x;
	} else if (x <= 3.8e-8) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.35e-16:
		tmp = x
	elif x <= 3.8e-8:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.35e-16)
		tmp = x;
	elseif (x <= 3.8e-8)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.35e-16)
		tmp = x;
	elseif (x <= 3.8e-8)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.35e-16], x, If[LessEqual[x, 3.8e-8], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.35000000000000018e-16 or 3.80000000000000028e-8 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 29.9%

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

   if -4.35000000000000018e-16 < x < 3.80000000000000028e-8

   1. Initial program 94.8%

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

   3. Taylor expanded in b around 0 59.9%

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

   4. Taylor expanded in y around 0 43.1%

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

      1. associate--r+ 43.1%

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

      2. sub-neg 43.1%

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

      3. metadata-eval 43.1%

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

      4. sub-neg 43.1%

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

      5. sub-neg 43.1%

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

      6. mul-1-neg 43.1%

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

      7. remove-double-neg 43.1%

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

      8. distribute-lft-in 43.1%

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

      9. *-commutative 43.1%

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

      10. distribute-neg-in 43.1%

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

      11. distribute-rgt-neg-in 43.1%

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

      12. mul-1-neg 43.1%

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

      13. neg-mul-1 43.1%

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

      14. remove-double-neg 43.1%

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

      15. *-rgt-identity 43.1%

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

      16. distribute-lft-in 43.1%

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

      17. +-commutative 43.1%

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

      18. mul-1-neg 43.1%

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

      19. sub-neg 43.1%

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

   6. Simplified 43.1%

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

   7. Taylor expanded in z around inf 16.5%

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

4. Final simplification 23.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.35 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 10.7% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

3. Taylor expanded in a around inf 24.2%

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

4. Taylor expanded in t around 0 10.4%

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

5. Final simplification 10.4%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(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)))