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

Percentage Accurate: 95.6% → 98.2%

Time: 19.2s

Alternatives: 24

Speedup: 0.5×

• 36.7% 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: 95.6% 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: 98.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (- x (* z (+ y -1.0))) (* 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 * (y + -1.0))) + (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 * (y + -1.0))) + (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 * (y + -1.0))) + (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(y + -1.0))) + 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 * (y + -1.0))) + (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[(y + -1.0), $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 #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 61.3%

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

4. Final simplification 97.7%

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

Alternative 2: 97.9% 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 94.1%

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

   1. +-commutative 94.1%

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

   2. fma-define 96.5%

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

   3. associate--l+ 96.5%

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

   4. sub-neg 96.5%

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

   5. metadata-eval 96.5%

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

   6. sub-neg 96.5%

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

   7. associate-+l- 96.5%

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

   8. fma-neg 96.5%

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

   9. sub-neg 96.5%

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

   10. metadata-eval 96.5%

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

   11. remove-double-neg 96.5%

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

   12. sub-neg 96.5%

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

   13. metadata-eval 96.5%

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

3. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 3: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-88}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-64}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+164}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -8e+50)
     t_1
     (if (<= b -9.5e-88)
       (+ x (+ z a))
       (if (<= b 1.55e-64)
         (+ x (* a (- 1.0 t)))
         (if (<= b 3.7e+164) (- x (* z (+ y -1.0))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -8e+50) {
		tmp = t_1;
	} else if (b <= -9.5e-88) {
		tmp = x + (z + a);
	} else if (b <= 1.55e-64) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.7e+164) {
		tmp = x - (z * (y + -1.0));
	} 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 + t) - 2.0d0)
    if (b <= (-8d+50)) then
        tmp = t_1
    else if (b <= (-9.5d-88)) then
        tmp = x + (z + a)
    else if (b <= 1.55d-64) then
        tmp = x + (a * (1.0d0 - t))
    else if (b <= 3.7d+164) then
        tmp = x - (z * (y + (-1.0d0)))
    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 + t) - 2.0);
	double tmp;
	if (b <= -8e+50) {
		tmp = t_1;
	} else if (b <= -9.5e-88) {
		tmp = x + (z + a);
	} else if (b <= 1.55e-64) {
		tmp = x + (a * (1.0 - t));
	} else if (b <= 3.7e+164) {
		tmp = x - (z * (y + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -8e+50:
		tmp = t_1
	elif b <= -9.5e-88:
		tmp = x + (z + a)
	elif b <= 1.55e-64:
		tmp = x + (a * (1.0 - t))
	elif b <= 3.7e+164:
		tmp = x - (z * (y + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -8e+50)
		tmp = t_1;
	elseif (b <= -9.5e-88)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 1.55e-64)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (b <= 3.7e+164)
		tmp = Float64(x - Float64(z * Float64(y + -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -8e+50)
		tmp = t_1;
	elseif (b <= -9.5e-88)
		tmp = x + (z + a);
	elseif (b <= 1.55e-64)
		tmp = x + (a * (1.0 - t));
	elseif (b <= 3.7e+164)
		tmp = x - (z * (y + -1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+50], t$95$1, If[LessEqual[b, -9.5e-88], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-64], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+164], N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.0000000000000006e50 or 3.7000000000000001e164 < b

   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 b around inf 78.3%

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

   if -8.0000000000000006e50 < b < -9.5e-88

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 87.2%

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

   4. Taylor expanded in y around 0 70.6%

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

      1. associate--l+ 70.6%

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

      2. distribute-lft-out 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in b around 0 70.7%

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

      1. cancel-sign-sub-inv 70.7%

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

      2. metadata-eval 70.7%

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

      3. *-lft-identity 70.7%

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

   9. Simplified 70.7%

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

   if -9.5e-88 < b < 1.55000000000000012e-64

   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 97.0%

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

   4. Taylor expanded in z around 0 64.5%

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

   if 1.55000000000000012e-64 < b < 3.7000000000000001e164

   1. Initial program 92.1%

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

   3. Taylor expanded in b around 0 64.6%

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

   4. Taylor expanded in a around 0 57.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-88}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-64}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+164}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-88}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+20}:\\ \;\;\;\;x + \left(t\_1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.6e+18)
     (+ t_2 t_1)
     (if (<= b -1.8e-88)
       (- (+ x a) (* z (+ y -1.0)))
       (if (<= b 5.8e+20) (+ x (- t_1 (* y z))) (+ x t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.6e+18) {
		tmp = t_2 + t_1;
	} else if (b <= -1.8e-88) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 5.8e+20) {
		tmp = x + (t_1 - (y * z));
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.6d+18)) then
        tmp = t_2 + t_1
    else if (b <= (-1.8d-88)) then
        tmp = (x + a) - (z * (y + (-1.0d0)))
    else if (b <= 5.8d+20) then
        tmp = x + (t_1 - (y * z))
    else
        tmp = x + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.6e+18) {
		tmp = t_2 + t_1;
	} else if (b <= -1.8e-88) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 5.8e+20) {
		tmp = x + (t_1 - (y * z));
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.6e+18:
		tmp = t_2 + t_1
	elif b <= -1.8e-88:
		tmp = (x + a) - (z * (y + -1.0))
	elif b <= 5.8e+20:
		tmp = x + (t_1 - (y * z))
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.6e+18)
		tmp = Float64(t_2 + t_1);
	elseif (b <= -1.8e-88)
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	elseif (b <= 5.8e+20)
		tmp = Float64(x + Float64(t_1 - Float64(y * z)));
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.6e+18)
		tmp = t_2 + t_1;
	elseif (b <= -1.8e-88)
		tmp = (x + a) - (z * (y + -1.0));
	elseif (b <= 5.8e+20)
		tmp = x + (t_1 - (y * z));
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+18], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, -1.8e-88], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+20], N[(x + N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6e18

   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 z around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. mul-1-neg 76.3%

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

      3. sub-neg 76.3%

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

      4. mul-1-neg 76.3%

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

      5. sub-neg 76.3%

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

      6. metadata-eval 76.3%

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

      7. +-commutative 76.3%

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

      8. sub-neg 76.3%

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

      9. metadata-eval 76.3%

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

      10. mul-1-neg 76.3%

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

      11. remove-double-neg 76.3%

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

      12. +-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around -inf 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. +-commutative 81.6%

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

      4. neg-mul-1 81.6%

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

      5. distribute-rgt-neg-in 81.6%

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

      6. distribute-neg-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -1.6e18 < b < -1.8e-88

   1. Initial program 96.0%

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

   3. Taylor expanded in b around 0 88.3%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. associate--r+ 84.8%

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

      2. sub-neg 84.8%

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

      3. neg-mul-1 84.8%

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

      4. remove-double-neg 84.8%

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

      5. sub-neg 84.8%

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

      6. metadata-eval 84.8%

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

      7. +-commutative 84.8%

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

   6. Simplified 84.8%

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

   if -1.8e-88 < b < 5.8e20

   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 92.4%

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

   4. Taylor expanded in y around inf 79.7%

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

      1. *-commutative 79.7%

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

   6. Simplified 79.7%

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

   if 5.8e20 < b

   1. Initial program 87.7%

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

   3. Taylor expanded in z around -inf 71.1%

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

      1. associate-*r* 71.1%

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

      2. mul-1-neg 71.1%

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

      3. sub-neg 71.1%

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

      4. mul-1-neg 71.1%

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

      5. sub-neg 71.1%

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

      6. metadata-eval 71.1%

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

      7. +-commutative 71.1%

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

      8. sub-neg 71.1%

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

      9. metadata-eval 71.1%

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

      10. mul-1-neg 71.1%

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

      11. remove-double-neg 71.1%

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

      12. +-commutative 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in x around inf 76.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-88}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+20}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-87}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -1.4e+52)
     t_1
     (if (<= b -1.9e-87)
       (- (+ x a) (* z (+ y -1.0)))
       (if (<= b 2.2e+20) (+ x (- (* a (- 1.0 t)) (* y z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.4e+52) {
		tmp = t_1;
	} else if (b <= -1.9e-87) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 2.2e+20) {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-1.4d+52)) then
        tmp = t_1
    else if (b <= (-1.9d-87)) then
        tmp = (x + a) - (z * (y + (-1.0d0)))
    else if (b <= 2.2d+20) then
        tmp = x + ((a * (1.0d0 - t)) - (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -1.4e+52) {
		tmp = t_1;
	} else if (b <= -1.9e-87) {
		tmp = (x + a) - (z * (y + -1.0));
	} else if (b <= 2.2e+20) {
		tmp = x + ((a * (1.0 - t)) - (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -1.4e+52:
		tmp = t_1
	elif b <= -1.9e-87:
		tmp = (x + a) - (z * (y + -1.0))
	elif b <= 2.2e+20:
		tmp = x + ((a * (1.0 - t)) - (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -1.4e+52)
		tmp = t_1;
	elseif (b <= -1.9e-87)
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	elseif (b <= 2.2e+20)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -1.4e+52)
		tmp = t_1;
	elseif (b <= -1.9e-87)
		tmp = (x + a) - (z * (y + -1.0));
	elseif (b <= 2.2e+20)
		tmp = x + ((a * (1.0 - t)) - (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+52], t$95$1, If[LessEqual[b, -1.9e-87], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+20], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4e52 or 2.2e20 < b

   1. Initial program 87.3%

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

   3. Taylor expanded in z around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. mul-1-neg 72.5%

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

      3. sub-neg 72.5%

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

      4. mul-1-neg 72.5%

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

      5. sub-neg 72.5%

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

      6. metadata-eval 72.5%

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

      7. +-commutative 72.5%

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

      8. sub-neg 72.5%

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

      9. metadata-eval 72.5%

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

      10. mul-1-neg 72.5%

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

      11. remove-double-neg 72.5%

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

      12. +-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in x around inf 79.6%

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

   if -1.4e52 < b < -1.9e-87

   1. Initial program 96.7%

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

   3. Taylor expanded in b around 0 83.6%

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

   4. Taylor expanded in t around 0 80.7%

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

      1. associate--r+ 80.7%

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

      2. sub-neg 80.7%

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

      3. neg-mul-1 80.7%

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

      4. remove-double-neg 80.7%

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

      5. sub-neg 80.7%

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

      6. metadata-eval 80.7%

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

      7. +-commutative 80.7%

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

   6. Simplified 80.7%

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

   if -1.9e-87 < b < 2.2e20

   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 92.4%

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

   4. Taylor expanded in y around inf 79.7%

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

      1. *-commutative 79.7%

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

   6. Simplified 79.7%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+52}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-87}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + a\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-254}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1700000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z a))) (t_2 (* t (- b a))))
   (if (<= t -1.25e+35)
     t_2
     (if (<= t -7e-93)
       t_1
       (if (<= t 4.7e-254)
         (+ a (* b (- y 2.0)))
         (if (<= t 1700000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.25e+35) {
		tmp = t_2;
	} else if (t <= -7e-93) {
		tmp = t_1;
	} else if (t <= 4.7e-254) {
		tmp = a + (b * (y - 2.0));
	} else if (t <= 1700000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z + a)
    t_2 = t * (b - a)
    if (t <= (-1.25d+35)) then
        tmp = t_2
    else if (t <= (-7d-93)) then
        tmp = t_1
    else if (t <= 4.7d-254) then
        tmp = a + (b * (y - 2.0d0))
    else if (t <= 1700000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z + a);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.25e+35) {
		tmp = t_2;
	} else if (t <= -7e-93) {
		tmp = t_1;
	} else if (t <= 4.7e-254) {
		tmp = a + (b * (y - 2.0));
	} else if (t <= 1700000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + a)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.25e+35:
		tmp = t_2
	elif t <= -7e-93:
		tmp = t_1
	elif t <= 4.7e-254:
		tmp = a + (b * (y - 2.0))
	elif t <= 1700000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + a))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.25e+35)
		tmp = t_2;
	elseif (t <= -7e-93)
		tmp = t_1;
	elseif (t <= 4.7e-254)
		tmp = Float64(a + Float64(b * Float64(y - 2.0)));
	elseif (t <= 1700000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z + a);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.25e+35)
		tmp = t_2;
	elseif (t <= -7e-93)
		tmp = t_1;
	elseif (t <= 4.7e-254)
		tmp = a + (b * (y - 2.0));
	elseif (t <= 1700000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+35], t$95$2, If[LessEqual[t, -7e-93], t$95$1, If[LessEqual[t, 4.7e-254], N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1700000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25000000000000005e35 or 1.7e12 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf 62.9%

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

   if -1.25000000000000005e35 < t < -7e-93 or 4.70000000000000027e-254 < t < 1.7e12

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 95.4%

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

   4. Taylor expanded in y around 0 69.0%

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

      1. associate--l+ 69.0%

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

      2. distribute-lft-out 69.0%

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

   6. Simplified 69.0%

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

   7. Taylor expanded in b around 0 62.4%

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

      1. cancel-sign-sub-inv 62.4%

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

      2. metadata-eval 62.4%

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

      3. *-lft-identity 62.4%

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

   9. Simplified 62.4%

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

   if -7e-93 < t < 4.70000000000000027e-254

   1. Initial program 98.4%

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

   3. Taylor expanded in z around -inf 74.5%

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

      1. associate-*r* 74.5%

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

      2. mul-1-neg 74.5%

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

      3. sub-neg 74.5%

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

      4. mul-1-neg 74.5%

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

      5. sub-neg 74.5%

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

      6. metadata-eval 74.5%

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

      7. +-commutative 74.5%

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

      8. sub-neg 74.5%

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

      9. metadata-eval 74.5%

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

      10. mul-1-neg 74.5%

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

      11. remove-double-neg 74.5%

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

      12. +-commutative 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in a around -inf 70.0%

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

      1. sub-neg 70.0%

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

      2. metadata-eval 70.0%

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

      3. +-commutative 70.0%

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

      4. neg-mul-1 70.0%

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

      5. distribute-rgt-neg-in 70.0%

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

      6. distribute-neg-in 70.0%

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

      7. metadata-eval 70.0%

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

      8. sub-neg 70.0%

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

   8. Simplified 70.0%

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

   9. Taylor expanded in t around 0 70.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-93}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-254}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1700000000000:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -31000000 \lor \neg \left(b \leq 68000000000\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -31000000.0) (not (<= b 68000000000.0)))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1)
     (+ x (- t_1 (* z (+ y -1.0)))))))

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 ((b <= -31000000.0) || !(b <= 68000000000.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 - (z * (y + -1.0)));
	}
	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 ((b <= (-31000000.0d0)) .or. (.not. (b <= 68000000000.0d0))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    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 ((b <= -31000000.0) || !(b <= 68000000000.0)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = x + (t_1 - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -31000000.0) or not (b <= 68000000000.0):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = x + (t_1 - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -31000000.0) || !(b <= 68000000000.0))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	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 ((b <= -31000000.0) || ~((b <= 68000000000.0)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = x + (t_1 - (z * (y + -1.0)));
	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[b, -31000000.0], N[Not[LessEqual[b, 68000000000.0]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.1e7 or 6.8e10 < b

   1. Initial program 88.6%

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

   3. Taylor expanded in z around 0 81.8%

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

   if -3.1e7 < b < 6.8e10

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 93.4%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -31000000 \lor \neg \left(b \leq 68000000000\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -160:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -160.0)
     (+ t_2 t_1)
     (if (<= b 2.9e-77)
       (+ x (- t_1 (* z (+ y -1.0))))
       (+ t_2 (* z (- 1.0 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -160.0) {
		tmp = t_2 + t_1;
	} else if (b <= 2.9e-77) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = t_2 + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-160.0d0)) then
        tmp = t_2 + t_1
    else if (b <= 2.9d-77) then
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    else
        tmp = t_2 + (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 t_1 = a * (1.0 - t);
	double t_2 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -160.0) {
		tmp = t_2 + t_1;
	} else if (b <= 2.9e-77) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = t_2 + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -160.0:
		tmp = t_2 + t_1
	elif b <= 2.9e-77:
		tmp = x + (t_1 - (z * (y + -1.0)))
	else:
		tmp = t_2 + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -160.0)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 2.9e-77)
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(t_2 + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -160.0)
		tmp = t_2 + t_1;
	elseif (b <= 2.9e-77)
		tmp = x + (t_1 - (z * (y + -1.0)));
	else
		tmp = t_2 + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -160.0], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 2.9e-77], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -160

   1. Initial program 88.7%

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

   3. Taylor expanded in z around 0 85.9%

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

   if -160 < b < 2.8999999999999999e-77

   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 97.4%

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

   if 2.8999999999999999e-77 < b

   1. Initial program 91.1%

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

   3. Taylor expanded in a around 0 81.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -160:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-85}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-77}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -2e+16)
     t_1
     (if (<= b -1.95e-85)
       (+ x (+ z a))
       (if (<= b 3.6e-77) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2e+16) {
		tmp = t_1;
	} else if (b <= -1.95e-85) {
		tmp = x + (z + a);
	} else if (b <= 3.6e-77) {
		tmp = x + (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 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-2d+16)) then
        tmp = t_1
    else if (b <= (-1.95d-85)) then
        tmp = x + (z + a)
    else if (b <= 3.6d-77) then
        tmp = x + (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 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -2e+16) {
		tmp = t_1;
	} else if (b <= -1.95e-85) {
		tmp = x + (z + a);
	} else if (b <= 3.6e-77) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -2e+16:
		tmp = t_1
	elif b <= -1.95e-85:
		tmp = x + (z + a)
	elif b <= 3.6e-77:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -2e+16)
		tmp = t_1;
	elseif (b <= -1.95e-85)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 3.6e-77)
		tmp = Float64(x + 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 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -2e+16)
		tmp = t_1;
	elseif (b <= -1.95e-85)
		tmp = x + (z + a);
	elseif (b <= 3.6e-77)
		tmp = x + (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[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+16], t$95$1, If[LessEqual[b, -1.95e-85], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-77], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2e16 or 3.6e-77 < 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 z around -inf 76.5%

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

      1. associate-*r* 76.5%

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

      2. mul-1-neg 76.5%

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

      3. sub-neg 76.5%

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

      4. mul-1-neg 76.5%

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

      5. sub-neg 76.5%

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

      6. metadata-eval 76.5%

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

      7. +-commutative 76.5%

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

      8. sub-neg 76.5%

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

      9. metadata-eval 76.5%

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

      10. mul-1-neg 76.5%

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

      11. remove-double-neg 76.5%

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

      12. +-commutative 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in x around inf 70.9%

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

   if -2e16 < b < -1.94999999999999994e-85

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0 88.6%

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

   4. Taylor expanded in y around 0 76.5%

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

      1. associate--l+ 76.5%

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

      2. distribute-lft-out 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in b around 0 76.7%

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

      1. cancel-sign-sub-inv 76.7%

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

      2. metadata-eval 76.7%

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

      3. *-lft-identity 76.7%

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

   9. Simplified 76.7%

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

   if -1.94999999999999994e-85 < b < 3.6e-77

   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 99.0%

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

   4. Taylor expanded in z around 0 65.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+16}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-85}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-77}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 27.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -600:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-108}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+74}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -600.0)
   (* y b)
   (if (<= y -4.5e-108)
     z
     (if (<= y 1.5e-114) x (if (<= y 1.02e+74) (* t b) (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -600.0) {
		tmp = y * b;
	} else if (y <= -4.5e-108) {
		tmp = z;
	} else if (y <= 1.5e-114) {
		tmp = x;
	} else if (y <= 1.02e+74) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-600.0d0)) then
        tmp = y * b
    else if (y <= (-4.5d-108)) then
        tmp = z
    else if (y <= 1.5d-114) then
        tmp = x
    else if (y <= 1.02d+74) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -600.0) {
		tmp = y * b;
	} else if (y <= -4.5e-108) {
		tmp = z;
	} else if (y <= 1.5e-114) {
		tmp = x;
	} else if (y <= 1.02e+74) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -600.0:
		tmp = y * b
	elif y <= -4.5e-108:
		tmp = z
	elif y <= 1.5e-114:
		tmp = x
	elif y <= 1.02e+74:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -600.0)
		tmp = Float64(y * b);
	elseif (y <= -4.5e-108)
		tmp = z;
	elseif (y <= 1.5e-114)
		tmp = x;
	elseif (y <= 1.02e+74)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -600.0)
		tmp = y * b;
	elseif (y <= -4.5e-108)
		tmp = z;
	elseif (y <= 1.5e-114)
		tmp = x;
	elseif (y <= 1.02e+74)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -600.0], N[(y * b), $MachinePrecision], If[LessEqual[y, -4.5e-108], z, If[LessEqual[y, 1.5e-114], x, If[LessEqual[y, 1.02e+74], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -600 or 1.02000000000000005e74 < y

   1. Initial program 90.8%

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

   3. Taylor expanded in z around -inf 72.5%

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

      1. associate-*r* 72.5%

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

      2. mul-1-neg 72.5%

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

      3. sub-neg 72.5%

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

      4. mul-1-neg 72.5%

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

      5. sub-neg 72.5%

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

      6. metadata-eval 72.5%

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

      7. +-commutative 72.5%

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

      8. sub-neg 72.5%

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

      9. metadata-eval 72.5%

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

      10. mul-1-neg 72.5%

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

      11. remove-double-neg 72.5%

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

      12. +-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in a around -inf 63.1%

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

      1. sub-neg 63.1%

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

      2. metadata-eval 63.1%

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

      3. +-commutative 63.1%

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

      4. neg-mul-1 63.1%

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

      5. distribute-rgt-neg-in 63.1%

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

      6. distribute-neg-in 63.1%

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

      7. metadata-eval 63.1%

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

      8. sub-neg 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in t around 0 45.0%

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

   10. Taylor expanded in y around inf 36.0%

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

       1. *-commutative 36.0%

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

   12. Simplified 36.0%

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

   if -600 < y < -4.4999999999999997e-108

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 41.5%

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

   4. Taylor expanded in y around 0 40.5%

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

   if -4.4999999999999997e-108 < y < 1.50000000000000008e-114

   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 x around inf 30.3%

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

   if 1.50000000000000008e-114 < y < 1.02000000000000005e74

   1. Initial program 93.5%

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

   3. Taylor expanded in t around inf 40.5%

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

   4. Taylor expanded in b around inf 33.9%

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

      1. *-commutative 33.9%

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

   6. Simplified 33.9%

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

Alternative 11: 83.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+18}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+170}:\\ \;\;\;\;x + \left(t\_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -9.2e+18)
     (+ t_2 t_1)
     (if (<= b 3.3e+170) (+ x (- t_1 (* z (+ y -1.0)))) (+ x t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.2e+18) {
		tmp = t_2 + t_1;
	} else if (b <= 3.3e+170) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-9.2d+18)) then
        tmp = t_2 + t_1
    else if (b <= 3.3d+170) then
        tmp = x + (t_1 - (z * (y + (-1.0d0))))
    else
        tmp = x + t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -9.2e+18) {
		tmp = t_2 + t_1;
	} else if (b <= 3.3e+170) {
		tmp = x + (t_1 - (z * (y + -1.0)));
	} else {
		tmp = x + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -9.2e+18:
		tmp = t_2 + t_1
	elif b <= 3.3e+170:
		tmp = x + (t_1 - (z * (y + -1.0)))
	else:
		tmp = x + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -9.2e+18)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 3.3e+170)
		tmp = Float64(x + Float64(t_1 - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(x + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -9.2e+18)
		tmp = t_2 + t_1;
	elseif (b <= 3.3e+170)
		tmp = x + (t_1 - (z * (y + -1.0)));
	else
		tmp = x + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+18], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 3.3e+170], N[(x + N[(t$95$1 - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.2e18

   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 z around -inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. mul-1-neg 76.3%

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

      3. sub-neg 76.3%

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

      4. mul-1-neg 76.3%

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

      5. sub-neg 76.3%

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

      6. metadata-eval 76.3%

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

      7. +-commutative 76.3%

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

      8. sub-neg 76.3%

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

      9. metadata-eval 76.3%

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

      10. mul-1-neg 76.3%

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

      11. remove-double-neg 76.3%

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

      12. +-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in a around -inf 81.6%

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

      1. sub-neg 81.6%

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

      2. metadata-eval 81.6%

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

      3. +-commutative 81.6%

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

      4. neg-mul-1 81.6%

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

      5. distribute-rgt-neg-in 81.6%

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

      6. distribute-neg-in 81.6%

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

      7. metadata-eval 81.6%

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

      8. sub-neg 81.6%

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

   8. Simplified 81.6%

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

   if -9.2e18 < b < 3.30000000000000023e170

   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 88.3%

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

   if 3.30000000000000023e170 < 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 z around -inf 73.3%

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

      1. associate-*r* 73.3%

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

      2. mul-1-neg 73.3%

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

      3. sub-neg 73.3%

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

      4. mul-1-neg 73.3%

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

      5. sub-neg 73.3%

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

      6. metadata-eval 73.3%

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

      7. +-commutative 73.3%

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

      8. sub-neg 73.3%

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

      9. metadata-eval 73.3%

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

      10. mul-1-neg 73.3%

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

      11. remove-double-neg 73.3%

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

      12. +-commutative 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in x around inf 85.8%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+170}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-90}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+91}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -2.3e+50)
     t_1
     (if (<= b -3.4e-90)
       (+ x (+ z a))
       (if (<= b 5.6e+91) (+ x (* a (- 1.0 t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.3e+50) {
		tmp = t_1;
	} else if (b <= -3.4e-90) {
		tmp = x + (z + a);
	} else if (b <= 5.6e+91) {
		tmp = x + (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 = b * ((y + t) - 2.0d0)
    if (b <= (-2.3d+50)) then
        tmp = t_1
    else if (b <= (-3.4d-90)) then
        tmp = x + (z + a)
    else if (b <= 5.6d+91) then
        tmp = x + (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 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -2.3e+50) {
		tmp = t_1;
	} else if (b <= -3.4e-90) {
		tmp = x + (z + a);
	} else if (b <= 5.6e+91) {
		tmp = x + (a * (1.0 - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -2.3e+50:
		tmp = t_1
	elif b <= -3.4e-90:
		tmp = x + (z + a)
	elif b <= 5.6e+91:
		tmp = x + (a * (1.0 - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -2.3e+50)
		tmp = t_1;
	elseif (b <= -3.4e-90)
		tmp = Float64(x + Float64(z + a));
	elseif (b <= 5.6e+91)
		tmp = Float64(x + 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 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -2.3e+50)
		tmp = t_1;
	elseif (b <= -3.4e-90)
		tmp = x + (z + a);
	elseif (b <= 5.6e+91)
		tmp = x + (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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+50], t$95$1, If[LessEqual[b, -3.4e-90], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e+91], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.29999999999999997e50 or 5.5999999999999997e91 < b

   1. Initial program 85.9%

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

   3. Taylor expanded in b around inf 74.5%

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

   if -2.29999999999999997e50 < b < -3.39999999999999994e-90

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 87.2%

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

   4. Taylor expanded in y around 0 70.6%

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

      1. associate--l+ 70.6%

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

      2. distribute-lft-out 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in b around 0 70.7%

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

      1. cancel-sign-sub-inv 70.7%

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

      2. metadata-eval 70.7%

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

      3. *-lft-identity 70.7%

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

   9. Simplified 70.7%

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

   if -3.39999999999999994e-90 < b < 5.5999999999999997e91

   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 90.2%

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

   4. Taylor expanded in z around 0 57.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-90}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+91}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+265}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+52} \lor \neg \left(b \leq 330000000\right):\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+265)
   (* t b)
   (if (or (<= b -8.5e+52) (not (<= b 330000000.0)))
     (* b (- y 2.0))
     (* a (- 1.0 t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+265) {
		tmp = t * b;
	} else if ((b <= -8.5e+52) || !(b <= 330000000.0)) {
		tmp = b * (y - 2.0);
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+265)) then
        tmp = t * b
    else if ((b <= (-8.5d+52)) .or. (.not. (b <= 330000000.0d0))) then
        tmp = b * (y - 2.0d0)
    else
        tmp = a * (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+265) {
		tmp = t * b;
	} else if ((b <= -8.5e+52) || !(b <= 330000000.0)) {
		tmp = b * (y - 2.0);
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+265:
		tmp = t * b
	elif (b <= -8.5e+52) or not (b <= 330000000.0):
		tmp = b * (y - 2.0)
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+265)
		tmp = Float64(t * b);
	elseif ((b <= -8.5e+52) || !(b <= 330000000.0))
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = Float64(a * Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+265)
		tmp = t * b;
	elseif ((b <= -8.5e+52) || ~((b <= 330000000.0)))
		tmp = b * (y - 2.0);
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+265], N[(t * b), $MachinePrecision], If[Or[LessEqual[b, -8.5e+52], N[Not[LessEqual[b, 330000000.0]], $MachinePrecision]], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e265

   1. Initial program 81.8%

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

   3. Taylor expanded in t around inf 82.3%

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

   4. Taylor expanded in b around inf 82.3%

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

      1. *-commutative 82.3%

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

   6. Simplified 82.3%

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

   if -1.15e265 < b < -8.49999999999999994e52 or 3.3e8 < b

   1. Initial program 88.6%

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

   3. Taylor expanded in t around 0 68.9%

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

   4. Taylor expanded in b around inf 46.6%

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

   if -8.49999999999999994e52 < b < 3.3e8

   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 a around inf 41.5%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+265}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+52} \lor \neg \left(b \leq 330000000\right):\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.35 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;a + y \cdot b\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.35e+37)
     t_1
     (if (<= t 1.55e-87)
       (+ a (* y b))
       (if (<= t 5.9e+50) (* y (- b z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -3.35e+37) {
		tmp = t_1;
	} else if (t <= 1.55e-87) {
		tmp = a + (y * b);
	} else if (t <= 5.9e+50) {
		tmp = y * (b - 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 = t * (b - a)
    if (t <= (-3.35d+37)) then
        tmp = t_1
    else if (t <= 1.55d-87) then
        tmp = a + (y * b)
    else if (t <= 5.9d+50) then
        tmp = y * (b - 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 = t * (b - a);
	double tmp;
	if (t <= -3.35e+37) {
		tmp = t_1;
	} else if (t <= 1.55e-87) {
		tmp = a + (y * b);
	} else if (t <= 5.9e+50) {
		tmp = y * (b - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3.35e+37:
		tmp = t_1
	elif t <= 1.55e-87:
		tmp = a + (y * b)
	elif t <= 5.9e+50:
		tmp = y * (b - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.35e+37)
		tmp = t_1;
	elseif (t <= 1.55e-87)
		tmp = Float64(a + Float64(y * b));
	elseif (t <= 5.9e+50)
		tmp = Float64(y * Float64(b - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.35e+37)
		tmp = t_1;
	elseif (t <= 1.55e-87)
		tmp = a + (y * b);
	elseif (t <= 5.9e+50)
		tmp = y * (b - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.35e+37], t$95$1, If[LessEqual[t, 1.55e-87], N[(a + N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.9e+50], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.34999999999999984e37 or 5.8999999999999998e50 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 65.5%

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

   if -3.34999999999999984e37 < t < 1.54999999999999999e-87

   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 z around -inf 76.0%

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

      1. associate-*r* 76.0%

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

      2. mul-1-neg 76.0%

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

      3. sub-neg 76.0%

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

      4. mul-1-neg 76.0%

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

      5. sub-neg 76.0%

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

      6. metadata-eval 76.0%

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

      7. +-commutative 76.0%

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

      8. sub-neg 76.0%

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

      9. metadata-eval 76.0%

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

      10. mul-1-neg 76.0%

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

      11. remove-double-neg 76.0%

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

      12. +-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in a around -inf 59.2%

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

      1. sub-neg 59.2%

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

      2. metadata-eval 59.2%

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

      3. +-commutative 59.2%

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

      4. neg-mul-1 59.2%

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

      5. distribute-rgt-neg-in 59.2%

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

      6. distribute-neg-in 59.2%

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

      7. metadata-eval 59.2%

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

      8. sub-neg 59.2%

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

   8. Simplified 59.2%

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

   9. Taylor expanded in t around 0 57.0%

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

   10. Taylor expanded in y around inf 45.7%

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

   if 1.54999999999999999e-87 < t < 5.8999999999999998e50

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf 49.7%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-87}:\\ \;\;\;\;a + y \cdot b\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{+92}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -8.5e+88)
     t_1
     (if (<= a 8.6e-147) x (if (<= a 1e+92) (* t b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -8.5e+88) {
		tmp = t_1;
	} else if (a <= 8.6e-147) {
		tmp = x;
	} else if (a <= 1e+92) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-8.5d+88)) then
        tmp = t_1
    else if (a <= 8.6d-147) then
        tmp = x
    else if (a <= 1d+92) then
        tmp = t * b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -8.5e+88) {
		tmp = t_1;
	} else if (a <= 8.6e-147) {
		tmp = x;
	} else if (a <= 1e+92) {
		tmp = t * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -8.5e+88:
		tmp = t_1
	elif a <= 8.6e-147:
		tmp = x
	elif a <= 1e+92:
		tmp = t * b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -8.5e+88)
		tmp = t_1;
	elseif (a <= 8.6e-147)
		tmp = x;
	elseif (a <= 1e+92)
		tmp = Float64(t * b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -8.5e+88)
		tmp = t_1;
	elseif (a <= 8.6e-147)
		tmp = x;
	elseif (a <= 1e+92)
		tmp = t * b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+88], t$95$1, If[LessEqual[a, 8.6e-147], x, If[LessEqual[a, 1e+92], N[(t * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.5000000000000005e88 or 1e92 < a

   1. Initial program 93.7%

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

   3. Taylor expanded in a around inf 68.8%

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

   if -8.5000000000000005e88 < a < 8.6000000000000002e-147

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 25.8%

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

   if 8.6000000000000002e-147 < a < 1e92

   1. Initial program 88.5%

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

   3. Taylor expanded in t around inf 33.6%

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

   4. Taylor expanded in b around inf 26.9%

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

      1. *-commutative 26.9%

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

   6. Simplified 26.9%

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

Alternative 16: 72.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+48} \lor \neg \left(b \leq 41000000000\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.2e+48) (not (<= b 41000000000.0)))
   (+ x (* b (- (+ y t) 2.0)))
   (- (+ x a) (* z (+ y -1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.2e+48) || !(b <= 41000000000.0)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) - (z * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.2d+48)) .or. (.not. (b <= 41000000000.0d0))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x + a) - (z * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.2e+48) || !(b <= 41000000000.0)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + a) - (z * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.2e+48) or not (b <= 41000000000.0):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x + a) - (z * (y + -1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.2e+48) || !(b <= 41000000000.0))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x + a) - Float64(z * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.2e+48) || ~((b <= 41000000000.0)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x + a) - (z * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.2e+48], N[Not[LessEqual[b, 41000000000.0]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.2000000000000001e48 or 4.1e10 < b

   1. Initial program 87.7%

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

   3. Taylor expanded in z around -inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. mul-1-neg 72.6%

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

      3. sub-neg 72.6%

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

      4. mul-1-neg 72.6%

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

      5. sub-neg 72.6%

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

      6. metadata-eval 72.6%

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

      7. +-commutative 72.6%

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

      8. sub-neg 72.6%

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

      9. metadata-eval 72.6%

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

      10. mul-1-neg 72.6%

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

      11. remove-double-neg 72.6%

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

      12. +-commutative 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in x around inf 78.3%

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

   if -3.2000000000000001e48 < b < 4.1e10

   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 91.7%

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

   4. Taylor expanded in t around 0 72.7%

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

      1. associate--r+ 72.7%

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

      2. sub-neg 72.7%

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

      3. neg-mul-1 72.7%

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

      4. remove-double-neg 72.7%

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

      5. sub-neg 72.7%

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

      6. metadata-eval 72.7%

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

      7. +-commutative 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+48} \lor \neg \left(b \leq 41000000000\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - z \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+261}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 0.056:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.4e+261)
   (* t b)
   (if (<= t -1.3e-29) (* t (- a)) (if (<= t 0.056) a (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.4e+261) {
		tmp = t * b;
	} else if (t <= -1.3e-29) {
		tmp = t * -a;
	} else if (t <= 0.056) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.4d+261)) then
        tmp = t * b
    else if (t <= (-1.3d-29)) then
        tmp = t * -a
    else if (t <= 0.056d0) then
        tmp = a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.4e+261) {
		tmp = t * b;
	} else if (t <= -1.3e-29) {
		tmp = t * -a;
	} else if (t <= 0.056) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.4e+261:
		tmp = t * b
	elif t <= -1.3e-29:
		tmp = t * -a
	elif t <= 0.056:
		tmp = a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.4e+261)
		tmp = Float64(t * b);
	elseif (t <= -1.3e-29)
		tmp = Float64(t * Float64(-a));
	elseif (t <= 0.056)
		tmp = a;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.4e+261)
		tmp = t * b;
	elseif (t <= -1.3e-29)
		tmp = t * -a;
	elseif (t <= 0.056)
		tmp = a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.4e+261], N[(t * b), $MachinePrecision], If[LessEqual[t, -1.3e-29], N[(t * (-a)), $MachinePrecision], If[LessEqual[t, 0.056], a, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3999999999999998e261 or 0.0560000000000000012 < t

   1. Initial program 85.1%

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

   3. Taylor expanded in t around inf 63.3%

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

   4. Taylor expanded in b around inf 42.2%

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

      1. *-commutative 42.2%

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

   6. Simplified 42.2%

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

   if -2.3999999999999998e261 < t < -1.3000000000000001e-29

   1. Initial program 95.4%

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

   3. Taylor expanded in t around inf 46.1%

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

   4. Taylor expanded in b around 0 40.7%

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

      1. associate-*r* 40.7%

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

      2. neg-mul-1 40.7%

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

   6. Simplified 40.7%

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

   if -1.3000000000000001e-29 < t < 0.0560000000000000012

   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 a around inf 27.9%

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

   4. Taylor expanded in t around 0 27.9%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+261}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-29}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 0.056:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 56.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+48} \lor \neg \left(b \leq 3.2 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7e+48) (not (<= b 3.2e+103)))
   (* b (- (+ y t) 2.0))
   (+ x (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7e+48) || !(b <= 3.2e+103)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (z + a);
	}
	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 <= (-7d+48)) .or. (.not. (b <= 3.2d+103))) then
        tmp = b * ((y + t) - 2.0d0)
    else
        tmp = x + (z + a)
    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 <= -7e+48) || !(b <= 3.2e+103)) {
		tmp = b * ((y + t) - 2.0);
	} else {
		tmp = x + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7e+48) or not (b <= 3.2e+103):
		tmp = b * ((y + t) - 2.0)
	else:
		tmp = x + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7e+48) || !(b <= 3.2e+103))
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	else
		tmp = Float64(x + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7e+48) || ~((b <= 3.2e+103)))
		tmp = b * ((y + t) - 2.0);
	else
		tmp = x + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7e+48], N[Not[LessEqual[b, 3.2e+103]], $MachinePrecision]], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.9999999999999995e48 or 3.19999999999999993e103 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf 76.0%

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

   if -6.9999999999999995e48 < b < 3.19999999999999993e103

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 77.4%

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

   4. Taylor expanded in y around 0 52.2%

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

      1. associate--l+ 52.2%

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

      2. distribute-lft-out 52.2%

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

   6. Simplified 52.2%

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

   7. Taylor expanded in b around 0 51.7%

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

      1. cancel-sign-sub-inv 51.7%

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

      2. metadata-eval 51.7%

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

      3. *-lft-identity 51.7%

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

   9. Simplified 51.7%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+48} \lor \neg \left(b \leq 3.2 \cdot 10^{+103}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+35} \lor \neg \left(t \leq 2150000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e+35) (not (<= t 2150000000000.0)))
   (* t (- b a))
   (+ x (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e+35) || !(t <= 2150000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (z + a);
	}
	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 <= (-1d+35)) .or. (.not. (t <= 2150000000000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = x + (z + a)
    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 <= -1e+35) || !(t <= 2150000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e+35) or not (t <= 2150000000000.0):
		tmp = t * (b - a)
	else:
		tmp = x + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e+35) || !(t <= 2150000000000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e+35) || ~((t <= 2150000000000.0)))
		tmp = t * (b - a);
	else
		tmp = x + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e+35], N[Not[LessEqual[t, 2150000000000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999997e34 or 2.15e12 < t

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf 62.9%

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

   if -9.9999999999999997e34 < t < 2.15e12

   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 96.8%

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

   4. Taylor expanded in y around 0 69.9%

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

      1. associate--l+ 69.9%

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

      2. distribute-lft-out 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in b around 0 58.7%

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

      1. cancel-sign-sub-inv 58.7%

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

      2. metadata-eval 58.7%

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

      3. *-lft-identity 58.7%

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

   9. Simplified 58.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+35} \lor \neg \left(t \leq 2150000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+96} \lor \neg \left(a \leq 1.15 \cdot 10^{+113}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.7e+96) (not (<= a 1.15e+113)))
   (* a (- 1.0 t))
   (* y (- b z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.7e+96) || !(a <= 1.15e+113)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * (b - 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 ((a <= (-1.7d+96)) .or. (.not. (a <= 1.15d+113))) then
        tmp = a * (1.0d0 - t)
    else
        tmp = y * (b - 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 ((a <= -1.7e+96) || !(a <= 1.15e+113)) {
		tmp = a * (1.0 - t);
	} else {
		tmp = y * (b - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -1.7e+96) or not (a <= 1.15e+113):
		tmp = a * (1.0 - t)
	else:
		tmp = y * (b - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -1.7e+96) || !(a <= 1.15e+113))
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(y * Float64(b - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -1.7e+96) || ~((a <= 1.15e+113)))
		tmp = a * (1.0 - t);
	else
		tmp = y * (b - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.7e+96], N[Not[LessEqual[a, 1.15e+113]], $MachinePrecision]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.7e96 or 1.14999999999999998e113 < a

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 73.0%

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

   if -1.7e96 < a < 1.14999999999999998e113

   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 y around inf 39.7%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+96} \lor \neg \left(a \leq 1.15 \cdot 10^{+113}\right):\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+37} \lor \neg \left(t \leq 128000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.5e+37) (not (<= t 128000000000.0)))
   (* t (- b a))
   (* b (- y 2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.5e+37) || !(t <= 128000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = b * (y - 2.0);
	}
	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+37)) .or. (.not. (t <= 128000000000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = b * (y - 2.0d0)
    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+37) || !(t <= 128000000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = b * (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.5e+37) or not (t <= 128000000000.0):
		tmp = t * (b - a)
	else:
		tmp = b * (y - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.5e+37) || !(t <= 128000000000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(b * Float64(y - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.5e+37) || ~((t <= 128000000000.0)))
		tmp = t * (b - a);
	else
		tmp = b * (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.5e+37], N[Not[LessEqual[t, 128000000000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999962e37 or 1.28e11 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 62.6%

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

   if -4.49999999999999962e37 < t < 1.28e11

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 95.4%

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

   4. Taylor expanded in b around inf 32.4%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+37} \lor \neg \left(t \leq 128000000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 26.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+67} \lor \neg \left(t \leq 0.056\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.06e+67) (not (<= t 0.056))) (* t b) a))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.06e+67) || !(t <= 0.056)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	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 <= (-1.06d+67)) .or. (.not. (t <= 0.056d0))) then
        tmp = t * b
    else
        tmp = a
    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 <= -1.06e+67) || !(t <= 0.056)) {
		tmp = t * b;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.06e+67) or not (t <= 0.056):
		tmp = t * b
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.06e+67) || !(t <= 0.056))
		tmp = Float64(t * b);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.06e+67) || ~((t <= 0.056)))
		tmp = t * b;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.06e+67], N[Not[LessEqual[t, 0.056]], $MachinePrecision]], N[(t * b), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if t < -1.0599999999999999e67 or 0.0560000000000000012 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf 61.1%

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

   4. Taylor expanded in b around inf 32.7%

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

      1. *-commutative 32.7%

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

   6. Simplified 32.7%

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

   if -1.0599999999999999e67 < t < 0.0560000000000000012

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf 27.4%

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

   4. Taylor expanded in t around 0 24.1%

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

4. Final simplification 28.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+67} \lor \neg \left(t \leq 0.056\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 21.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -6.2e+112) a (if (<= a 2.95e+96) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -6.2e+112) {
		tmp = a;
	} else if (a <= 2.95e+96) {
		tmp = x;
	} else {
		tmp = a;
	}
	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 (a <= (-6.2d+112)) then
        tmp = a
    else if (a <= 2.95d+96) then
        tmp = x
    else
        tmp = a
    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 (a <= -6.2e+112) {
		tmp = a;
	} else if (a <= 2.95e+96) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -6.2e+112:
		tmp = a
	elif a <= 2.95e+96:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -6.2e+112)
		tmp = a;
	elseif (a <= 2.95e+96)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -6.2e+112)
		tmp = a;
	elseif (a <= 2.95e+96)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -6.2e+112], a, If[LessEqual[a, 2.95e+96], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -6.19999999999999965e112 or 2.95000000000000014e96 < a

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf 72.3%

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

   4. Taylor expanded in t around 0 34.6%

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

   if -6.19999999999999965e112 < a < 2.95000000000000014e96

   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 x around inf 21.9%

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

Alternative 24: 11.3% 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 94.1%

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

3. Taylor expanded in a around inf 30.7%

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

4. Taylor expanded in t around 0 14.3%

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

Reproduce

herbie shell --seed 2024137 
(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)))