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

Percentage Accurate: 94.9% → 97.9%

Time: 13.3s

Alternatives: 23

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: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 79.2%

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

4. Final simplification 98.9%

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

Alternative 2: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 79.2%

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

4. Final simplification 98.9%

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

Alternative 3: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y \cdot z - z\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -45000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (* y z) z)))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (* a (- 1.0 t))))
   (if (<= b -45000.0)
     t_2
     (if (<= b -6.8e-285)
       t_1
       (if (<= b 1.5e-290)
         t_3
         (if (<= b 9.8e-193)
           t_1
           (if (<= b 2.9e-134)
             t_3
             (if (<= b 4.5e-118)
               t_1
               (if (<= b 2.6e-82) t_3 (if (<= b 2.9e+36) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y * z) - z);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -45000.0) {
		tmp = t_2;
	} else if (b <= -6.8e-285) {
		tmp = t_1;
	} else if (b <= 1.5e-290) {
		tmp = t_3;
	} else if (b <= 9.8e-193) {
		tmp = t_1;
	} else if (b <= 2.9e-134) {
		tmp = t_3;
	} else if (b <= 4.5e-118) {
		tmp = t_1;
	} else if (b <= 2.6e-82) {
		tmp = t_3;
	} else if (b <= 2.9e+36) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x - ((y * z) - z)
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = a * (1.0d0 - t)
    if (b <= (-45000.0d0)) then
        tmp = t_2
    else if (b <= (-6.8d-285)) then
        tmp = t_1
    else if (b <= 1.5d-290) then
        tmp = t_3
    else if (b <= 9.8d-193) then
        tmp = t_1
    else if (b <= 2.9d-134) then
        tmp = t_3
    else if (b <= 4.5d-118) then
        tmp = t_1
    else if (b <= 2.6d-82) then
        tmp = t_3
    else if (b <= 2.9d+36) 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 - ((y * z) - z);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -45000.0) {
		tmp = t_2;
	} else if (b <= -6.8e-285) {
		tmp = t_1;
	} else if (b <= 1.5e-290) {
		tmp = t_3;
	} else if (b <= 9.8e-193) {
		tmp = t_1;
	} else if (b <= 2.9e-134) {
		tmp = t_3;
	} else if (b <= 4.5e-118) {
		tmp = t_1;
	} else if (b <= 2.6e-82) {
		tmp = t_3;
	} else if (b <= 2.9e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y * z) - z)
	t_2 = ((y + t) - 2.0) * b
	t_3 = a * (1.0 - t)
	tmp = 0
	if b <= -45000.0:
		tmp = t_2
	elif b <= -6.8e-285:
		tmp = t_1
	elif b <= 1.5e-290:
		tmp = t_3
	elif b <= 9.8e-193:
		tmp = t_1
	elif b <= 2.9e-134:
		tmp = t_3
	elif b <= 4.5e-118:
		tmp = t_1
	elif b <= 2.6e-82:
		tmp = t_3
	elif b <= 2.9e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y * z) - z))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -45000.0)
		tmp = t_2;
	elseif (b <= -6.8e-285)
		tmp = t_1;
	elseif (b <= 1.5e-290)
		tmp = t_3;
	elseif (b <= 9.8e-193)
		tmp = t_1;
	elseif (b <= 2.9e-134)
		tmp = t_3;
	elseif (b <= 4.5e-118)
		tmp = t_1;
	elseif (b <= 2.6e-82)
		tmp = t_3;
	elseif (b <= 2.9e+36)
		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 - ((y * z) - z);
	t_2 = ((y + t) - 2.0) * b;
	t_3 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -45000.0)
		tmp = t_2;
	elseif (b <= -6.8e-285)
		tmp = t_1;
	elseif (b <= 1.5e-290)
		tmp = t_3;
	elseif (b <= 9.8e-193)
		tmp = t_1;
	elseif (b <= 2.9e-134)
		tmp = t_3;
	elseif (b <= 4.5e-118)
		tmp = t_1;
	elseif (b <= 2.6e-82)
		tmp = t_3;
	elseif (b <= 2.9e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -45000.0], t$95$2, If[LessEqual[b, -6.8e-285], t$95$1, If[LessEqual[b, 1.5e-290], t$95$3, If[LessEqual[b, 9.8e-193], t$95$1, If[LessEqual[b, 2.9e-134], t$95$3, If[LessEqual[b, 4.5e-118], t$95$1, If[LessEqual[b, 2.6e-82], t$95$3, If[LessEqual[b, 2.9e+36], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -45000 or 2.9e36 < 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. Taylor expanded in b around inf 73.7%

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

   if -45000 < b < -6.7999999999999998e-285 or 1.49999999999999996e-290 < b < 9.80000000000000032e-193 or 2.89999999999999993e-134 < b < 4.5e-118 or 2.6e-82 < b < 2.9e36

   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. Taylor expanded in b around 0 90.1%

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

   3. Taylor expanded in a around 0 69.8%

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

      1. sub-neg 69.8%

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

      2. metadata-eval 69.8%

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

      3. distribute-rgt-in 69.8%

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

      4. neg-mul-1 69.8%

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

      5. unsub-neg 69.8%

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

   5. Simplified 69.8%

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

   if -6.7999999999999998e-285 < b < 1.49999999999999996e-290 or 9.80000000000000032e-193 < b < 2.89999999999999993e-134 or 4.5e-118 < b < 2.6e-82

   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. Taylor expanded in a around inf 80.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -45000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-285}:\\ \;\;\;\;x - \left(y \cdot z - z\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-290}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-193}:\\ \;\;\;\;x - \left(y \cdot z - z\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-134}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-118}:\\ \;\;\;\;x - \left(y \cdot z - z\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+36}:\\ \;\;\;\;x - \left(y \cdot z - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 4: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.7 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -480000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (+ (* (+ y -1.0) z) (* t a)))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -6.7e+87)
     t_2
     (if (<= b -5.8e+18)
       t_1
       (if (<= b -480000.0)
         t_2
         (if (<= b -5.8e-285)
           t_1
           (if (<= b 5.4e-295)
             (* a (- 1.0 t))
             (if (<= b 6.5e+36) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y + -1.0) * z) + (t * a));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -6.7e+87) {
		tmp = t_2;
	} else if (b <= -5.8e+18) {
		tmp = t_1;
	} else if (b <= -480000.0) {
		tmp = t_2;
	} else if (b <= -5.8e-285) {
		tmp = t_1;
	} else if (b <= 5.4e-295) {
		tmp = a * (1.0 - t);
	} else if (b <= 6.5e+36) {
		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 - (((y + (-1.0d0)) * z) + (t * a))
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-6.7d+87)) then
        tmp = t_2
    else if (b <= (-5.8d+18)) then
        tmp = t_1
    else if (b <= (-480000.0d0)) then
        tmp = t_2
    else if (b <= (-5.8d-285)) then
        tmp = t_1
    else if (b <= 5.4d-295) then
        tmp = a * (1.0d0 - t)
    else if (b <= 6.5d+36) 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 - (((y + -1.0) * z) + (t * a));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -6.7e+87) {
		tmp = t_2;
	} else if (b <= -5.8e+18) {
		tmp = t_1;
	} else if (b <= -480000.0) {
		tmp = t_2;
	} else if (b <= -5.8e-285) {
		tmp = t_1;
	} else if (b <= 5.4e-295) {
		tmp = a * (1.0 - t);
	} else if (b <= 6.5e+36) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y + -1.0) * z) + (t * a))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -6.7e+87:
		tmp = t_2
	elif b <= -5.8e+18:
		tmp = t_1
	elif b <= -480000.0:
		tmp = t_2
	elif b <= -5.8e-285:
		tmp = t_1
	elif b <= 5.4e-295:
		tmp = a * (1.0 - t)
	elif b <= 6.5e+36:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(t * a)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -6.7e+87)
		tmp = t_2;
	elseif (b <= -5.8e+18)
		tmp = t_1;
	elseif (b <= -480000.0)
		tmp = t_2;
	elseif (b <= -5.8e-285)
		tmp = t_1;
	elseif (b <= 5.4e-295)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 6.5e+36)
		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 - (((y + -1.0) * z) + (t * a));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -6.7e+87)
		tmp = t_2;
	elseif (b <= -5.8e+18)
		tmp = t_1;
	elseif (b <= -480000.0)
		tmp = t_2;
	elseif (b <= -5.8e-285)
		tmp = t_1;
	elseif (b <= 5.4e-295)
		tmp = a * (1.0 - t);
	elseif (b <= 6.5e+36)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -6.7e+87], t$95$2, If[LessEqual[b, -5.8e+18], t$95$1, If[LessEqual[b, -480000.0], t$95$2, If[LessEqual[b, -5.8e-285], t$95$1, If[LessEqual[b, 5.4e-295], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+36], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.7000000000000003e87 or -5.8e18 < b < -4.8e5 or 6.4999999999999998e36 < b

   1. Initial program 88.8%

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

   2. Taylor expanded in b around inf 81.2%

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

   if -6.7000000000000003e87 < b < -5.8e18 or -4.8e5 < b < -5.7999999999999999e-285 or 5.4000000000000002e-295 < b < 6.4999999999999998e36

   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. Taylor expanded in b around 0 87.8%

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

   3. Taylor expanded in t around inf 82.3%

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

      1. *-commutative 82.3%

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

   5. Simplified 82.3%

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

   if -5.7999999999999999e-285 < b < 5.4000000000000002e-295

   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. Taylor expanded in a around inf 88.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+87}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \mathbf{elif}\;b \leq -480000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-285}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+36}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 5: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-45}:\\ \;\;\;\;t_2 - y \cdot z\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (+ (* (+ y -1.0) z) (* t a)))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -5e+89)
     t_2
     (if (<= b -8.5e+19)
       t_1
       (if (<= b -5e-45)
         (- t_2 (* y z))
         (if (<= b -5.8e-285)
           t_1
           (if (<= b 5.4e-295)
             (* a (- 1.0 t))
             (if (<= b 4.4e+37) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y + -1.0) * z) + (t * a));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5e+89) {
		tmp = t_2;
	} else if (b <= -8.5e+19) {
		tmp = t_1;
	} else if (b <= -5e-45) {
		tmp = t_2 - (y * z);
	} else if (b <= -5.8e-285) {
		tmp = t_1;
	} else if (b <= 5.4e-295) {
		tmp = a * (1.0 - t);
	} else if (b <= 4.4e+37) {
		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 - (((y + (-1.0d0)) * z) + (t * a))
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-5d+89)) then
        tmp = t_2
    else if (b <= (-8.5d+19)) then
        tmp = t_1
    else if (b <= (-5d-45)) then
        tmp = t_2 - (y * z)
    else if (b <= (-5.8d-285)) then
        tmp = t_1
    else if (b <= 5.4d-295) then
        tmp = a * (1.0d0 - t)
    else if (b <= 4.4d+37) 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 - (((y + -1.0) * z) + (t * a));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -5e+89) {
		tmp = t_2;
	} else if (b <= -8.5e+19) {
		tmp = t_1;
	} else if (b <= -5e-45) {
		tmp = t_2 - (y * z);
	} else if (b <= -5.8e-285) {
		tmp = t_1;
	} else if (b <= 5.4e-295) {
		tmp = a * (1.0 - t);
	} else if (b <= 4.4e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y + -1.0) * z) + (t * a))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -5e+89:
		tmp = t_2
	elif b <= -8.5e+19:
		tmp = t_1
	elif b <= -5e-45:
		tmp = t_2 - (y * z)
	elif b <= -5.8e-285:
		tmp = t_1
	elif b <= 5.4e-295:
		tmp = a * (1.0 - t)
	elif b <= 4.4e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y + -1.0) * z) + Float64(t * a)))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -5e+89)
		tmp = t_2;
	elseif (b <= -8.5e+19)
		tmp = t_1;
	elseif (b <= -5e-45)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= -5.8e-285)
		tmp = t_1;
	elseif (b <= 5.4e-295)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 4.4e+37)
		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 - (((y + -1.0) * z) + (t * a));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -5e+89)
		tmp = t_2;
	elseif (b <= -8.5e+19)
		tmp = t_1;
	elseif (b <= -5e-45)
		tmp = t_2 - (y * z);
	elseif (b <= -5.8e-285)
		tmp = t_1;
	elseif (b <= 5.4e-295)
		tmp = a * (1.0 - t);
	elseif (b <= 4.4e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -5e+89], t$95$2, If[LessEqual[b, -8.5e+19], t$95$1, If[LessEqual[b, -5e-45], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-285], t$95$1, If[LessEqual[b, 5.4e-295], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e+37], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.99999999999999983e89 or 4.4000000000000001e37 < b

   1. Initial program 88.1%

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

   2. Taylor expanded in b around inf 81.3%

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

   if -4.99999999999999983e89 < b < -8.5e19 or -4.99999999999999976e-45 < b < -5.7999999999999999e-285 or 5.4000000000000002e-295 < b < 4.4000000000000001e37

   1. Initial program 98.5%

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

   2. Taylor expanded in b around 0 88.5%

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

   3. Taylor expanded in t around inf 83.5%

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

      1. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   if -8.5e19 < b < -4.99999999999999976e-45

   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. Taylor expanded in y around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. *-commutative 82.5%

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

      3. distribute-rgt-neg-in 82.5%

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

   4. Simplified 82.5%

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

   if -5.7999999999999999e-285 < b < 5.4000000000000002e-295

   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. Taylor expanded in a around inf 88.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+19}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-45}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-285}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+37}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 6: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + -1\right) \cdot z\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+20}:\\ \;\;\;\;x - \left(t_1 + t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-9}:\\ \;\;\;\;t_2 - y \cdot z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ y -1.0) z)) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= b -2.3e+84)
     t_2
     (if (<= b -1.75e+20)
       (- x (+ t_1 (* t a)))
       (if (<= b -1.8e-9)
         (- t_2 (* y z))
         (if (<= b 3.7e+37) (+ x (- (* a (- 1.0 t)) t_1)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + -1.0) * z;
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.3e+84) {
		tmp = t_2;
	} else if (b <= -1.75e+20) {
		tmp = x - (t_1 + (t * a));
	} else if (b <= -1.8e-9) {
		tmp = t_2 - (y * z);
	} else if (b <= 3.7e+37) {
		tmp = x + ((a * (1.0 - t)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + (-1.0d0)) * z
    t_2 = ((y + t) - 2.0d0) * b
    if (b <= (-2.3d+84)) then
        tmp = t_2
    else if (b <= (-1.75d+20)) then
        tmp = x - (t_1 + (t * a))
    else if (b <= (-1.8d-9)) then
        tmp = t_2 - (y * z)
    else if (b <= 3.7d+37) then
        tmp = x + ((a * (1.0d0 - t)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + -1.0) * z;
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -2.3e+84) {
		tmp = t_2;
	} else if (b <= -1.75e+20) {
		tmp = x - (t_1 + (t * a));
	} else if (b <= -1.8e-9) {
		tmp = t_2 - (y * z);
	} else if (b <= 3.7e+37) {
		tmp = x + ((a * (1.0 - t)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y + -1.0) * z
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -2.3e+84:
		tmp = t_2
	elif b <= -1.75e+20:
		tmp = x - (t_1 + (t * a))
	elif b <= -1.8e-9:
		tmp = t_2 - (y * z)
	elif b <= 3.7e+37:
		tmp = x + ((a * (1.0 - t)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + -1.0) * z)
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.3e+84)
		tmp = t_2;
	elseif (b <= -1.75e+20)
		tmp = Float64(x - Float64(t_1 + Float64(t * a)));
	elseif (b <= -1.8e-9)
		tmp = Float64(t_2 - Float64(y * z));
	elseif (b <= 3.7e+37)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y + -1.0) * z;
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.3e+84)
		tmp = t_2;
	elseif (b <= -1.75e+20)
		tmp = x - (t_1 + (t * a));
	elseif (b <= -1.8e-9)
		tmp = t_2 - (y * z);
	elseif (b <= 3.7e+37)
		tmp = x + ((a * (1.0 - t)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.3e+84], t$95$2, If[LessEqual[b, -1.75e+20], N[(x - N[(t$95$1 + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.8e-9], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+37], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.2999999999999999e84 or 3.6999999999999999e37 < b

   1. Initial program 88.1%

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

   2. Taylor expanded in b around inf 81.3%

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

   if -2.2999999999999999e84 < b < -1.75e20

   1. Initial program 94.9%

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

   2. Taylor expanded in b around 0 67.5%

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

   3. Taylor expanded in t around inf 67.5%

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

      1. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -1.75e20 < b < -1.8e-9

   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. Taylor expanded in y around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. *-commutative 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

   4. Simplified 87.2%

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

   if -1.8e-9 < b < 3.6999999999999999e37

   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. Taylor expanded in b around 0 92.2%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+84}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{+20}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z + t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-9}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 7: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -110000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-289}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 900000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* (- (+ y t) 2.0) b)) (t_3 (* a (- 1.0 t))))
   (if (<= b -110000.0)
     t_2
     (if (<= b -1.02e-284)
       t_1
       (if (<= b 1.95e-289)
         t_3
         (if (<= b 1.75e-193)
           t_1
           (if (<= b 2.5e-82) t_3 (if (<= b 900000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -110000.0) {
		tmp = t_2;
	} else if (b <= -1.02e-284) {
		tmp = t_1;
	} else if (b <= 1.95e-289) {
		tmp = t_3;
	} else if (b <= 1.75e-193) {
		tmp = t_1;
	} else if (b <= 2.5e-82) {
		tmp = t_3;
	} else if (b <= 900000000.0) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = a * (1.0d0 - t)
    if (b <= (-110000.0d0)) then
        tmp = t_2
    else if (b <= (-1.02d-284)) then
        tmp = t_1
    else if (b <= 1.95d-289) then
        tmp = t_3
    else if (b <= 1.75d-193) then
        tmp = t_1
    else if (b <= 2.5d-82) then
        tmp = t_3
    else if (b <= 900000000.0d0) 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 - (y * z);
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = a * (1.0 - t);
	double tmp;
	if (b <= -110000.0) {
		tmp = t_2;
	} else if (b <= -1.02e-284) {
		tmp = t_1;
	} else if (b <= 1.95e-289) {
		tmp = t_3;
	} else if (b <= 1.75e-193) {
		tmp = t_1;
	} else if (b <= 2.5e-82) {
		tmp = t_3;
	} else if (b <= 900000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = ((y + t) - 2.0) * b
	t_3 = a * (1.0 - t)
	tmp = 0
	if b <= -110000.0:
		tmp = t_2
	elif b <= -1.02e-284:
		tmp = t_1
	elif b <= 1.95e-289:
		tmp = t_3
	elif b <= 1.75e-193:
		tmp = t_1
	elif b <= 2.5e-82:
		tmp = t_3
	elif b <= 900000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -110000.0)
		tmp = t_2;
	elseif (b <= -1.02e-284)
		tmp = t_1;
	elseif (b <= 1.95e-289)
		tmp = t_3;
	elseif (b <= 1.75e-193)
		tmp = t_1;
	elseif (b <= 2.5e-82)
		tmp = t_3;
	elseif (b <= 900000000.0)
		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 - (y * z);
	t_2 = ((y + t) - 2.0) * b;
	t_3 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -110000.0)
		tmp = t_2;
	elseif (b <= -1.02e-284)
		tmp = t_1;
	elseif (b <= 1.95e-289)
		tmp = t_3;
	elseif (b <= 1.75e-193)
		tmp = t_1;
	elseif (b <= 2.5e-82)
		tmp = t_3;
	elseif (b <= 900000000.0)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -110000.0], t$95$2, If[LessEqual[b, -1.02e-284], t$95$1, If[LessEqual[b, 1.95e-289], t$95$3, If[LessEqual[b, 1.75e-193], t$95$1, If[LessEqual[b, 2.5e-82], t$95$3, If[LessEqual[b, 900000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e5 or 9e8 < b

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf 70.7%

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

   if -1.1e5 < b < -1.02e-284 or 1.9499999999999999e-289 < b < 1.75000000000000002e-193 or 2.4999999999999999e-82 < b < 9e8

   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. Taylor expanded in b around 0 90.5%

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

   3. Taylor expanded in y around inf 63.9%

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

   if -1.02e-284 < b < 1.9499999999999999e-289 or 1.75000000000000002e-193 < b < 2.4999999999999999e-82

   1. Initial program 97.4%

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

   2. Taylor expanded in a around inf 69.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -110000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-284}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-289}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-193}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 900000000:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 8: 87.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -15000 \lor \neg \left(b \leq 1020000000\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 - \left(y + -1\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -15000.0) (not (<= b 1020000000.0)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ x (- t_1 (* (+ y -1.0) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -15000.0) || !(b <= 1020000000.0)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-15000.0d0)) .or. (.not. (b <= 1020000000.0d0))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = x + (t_1 - ((y + (-1.0d0)) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -15000.0) || !(b <= 1020000000.0)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 - ((y + -1.0) * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -15000.0) or not (b <= 1020000000.0):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = x + (t_1 - ((y + -1.0) * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -15000.0) || !(b <= 1020000000.0))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(x + Float64(t_1 - Float64(Float64(y + -1.0) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((b <= -15000.0) || ~((b <= 1020000000.0)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = x + (t_1 - ((y + -1.0) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -15000.0], N[Not[LessEqual[b, 1020000000.0]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -15000 or 1.02e9 < b

   1. Initial program 90.4%

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

   2. Taylor expanded in z around 0 85.3%

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

   if -15000 < b < 1.02e9

   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. Taylor expanded in b around 0 92.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -15000 \lor \neg \left(b \leq 1020000000\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \end{array} \]

Alternative 9: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.56 \cdot 10^{-9}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1360000000:\\ \;\;\;\;x + \left(t_2 - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))) (t_2 (* a (- 1.0 t))))
   (if (<= b -1.56e-9)
     (+ t_1 (* z (- 1.0 y)))
     (if (<= b 1360000000.0) (+ x (- t_2 (* (+ y -1.0) z))) (+ t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -1.56e-9) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (b <= 1360000000.0) {
		tmp = x + (t_2 - ((y + -1.0) * z));
	} else {
		tmp = t_1 + 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 + (((y + t) - 2.0d0) * b)
    t_2 = a * (1.0d0 - t)
    if (b <= (-1.56d-9)) then
        tmp = t_1 + (z * (1.0d0 - y))
    else if (b <= 1360000000.0d0) then
        tmp = x + (t_2 - ((y + (-1.0d0)) * z))
    else
        tmp = t_1 + 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 + (((y + t) - 2.0) * b);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -1.56e-9) {
		tmp = t_1 + (z * (1.0 - y));
	} else if (b <= 1360000000.0) {
		tmp = x + (t_2 - ((y + -1.0) * z));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((y + t) - 2.0) * b)
	t_2 = a * (1.0 - t)
	tmp = 0
	if b <= -1.56e-9:
		tmp = t_1 + (z * (1.0 - y))
	elif b <= 1360000000.0:
		tmp = x + (t_2 - ((y + -1.0) * z))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -1.56e-9)
		tmp = Float64(t_1 + Float64(z * Float64(1.0 - y)));
	elseif (b <= 1360000000.0)
		tmp = Float64(x + Float64(t_2 - Float64(Float64(y + -1.0) * z)));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((y + t) - 2.0) * b);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -1.56e-9)
		tmp = t_1 + (z * (1.0 - y));
	elseif (b <= 1360000000.0)
		tmp = x + (t_2 - ((y + -1.0) * z));
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.56e-9], N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1360000000.0], N[(x + N[(t$95$2 - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.56e-9

   1. Initial program 91.0%

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

   2. Taylor expanded in a around 0 83.9%

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

   if -1.56e-9 < b < 1.36e9

   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. Taylor expanded in b around 0 93.3%

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

   if 1.36e9 < b

   1. Initial program 90.2%

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

   2. Taylor expanded in z around 0 87.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{-9}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1360000000:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 10: 37.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+54}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))))
   (if (<= b -9.5e+119)
     t_1
     (if (<= b -1.15e+54)
       (* y b)
       (if (<= b -6.5e-48)
         t_1
         (if (<= b -6.2e-167) x (if (<= b 1.05e+36) (* 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 * (t - 2.0);
	double tmp;
	if (b <= -9.5e+119) {
		tmp = t_1;
	} else if (b <= -1.15e+54) {
		tmp = y * b;
	} else if (b <= -6.5e-48) {
		tmp = t_1;
	} else if (b <= -6.2e-167) {
		tmp = x;
	} else if (b <= 1.05e+36) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    if (b <= (-9.5d+119)) then
        tmp = t_1
    else if (b <= (-1.15d+54)) then
        tmp = y * b
    else if (b <= (-6.5d-48)) then
        tmp = t_1
    else if (b <= (-6.2d-167)) then
        tmp = x
    else if (b <= 1.05d+36) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double tmp;
	if (b <= -9.5e+119) {
		tmp = t_1;
	} else if (b <= -1.15e+54) {
		tmp = y * b;
	} else if (b <= -6.5e-48) {
		tmp = t_1;
	} else if (b <= -6.2e-167) {
		tmp = x;
	} else if (b <= 1.05e+36) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	tmp = 0
	if b <= -9.5e+119:
		tmp = t_1
	elif b <= -1.15e+54:
		tmp = y * b
	elif b <= -6.5e-48:
		tmp = t_1
	elif b <= -6.2e-167:
		tmp = x
	elif b <= 1.05e+36:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -9.5e+119)
		tmp = t_1;
	elseif (b <= -1.15e+54)
		tmp = Float64(y * b);
	elseif (b <= -6.5e-48)
		tmp = t_1;
	elseif (b <= -6.2e-167)
		tmp = x;
	elseif (b <= 1.05e+36)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -9.5e+119)
		tmp = t_1;
	elseif (b <= -1.15e+54)
		tmp = y * b;
	elseif (b <= -6.5e-48)
		tmp = t_1;
	elseif (b <= -6.2e-167)
		tmp = x;
	elseif (b <= 1.05e+36)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.5e+119], t$95$1, If[LessEqual[b, -1.15e+54], N[(y * b), $MachinePrecision], If[LessEqual[b, -6.5e-48], t$95$1, If[LessEqual[b, -6.2e-167], x, If[LessEqual[b, 1.05e+36], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.4999999999999994e119 or -1.14999999999999997e54 < b < -6.5e-48 or 1.05000000000000002e36 < b

   1. Initial program 89.9%

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

   2. Taylor expanded in b around inf 73.7%

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

   3. Taylor expanded in y around 0 50.4%

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

   if -9.4999999999999994e119 < b < -1.14999999999999997e54

   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. Taylor expanded in z around 0 71.6%

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

   3. Taylor expanded in y around inf 42.2%

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

   if -6.5e-48 < b < -6.2e-167

   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. Taylor expanded in x around inf 40.7%

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

   if -6.2e-167 < b < 1.05000000000000002e36

   1. Initial program 99.0%

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

   2. Taylor expanded in a around inf 44.0%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{+54}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+36}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 11: 49.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 25000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* t (- b a))))
   (if (<= t -1.1e+84)
     t_2
     (if (<= t -3.3e-164)
       t_1
       (if (<= t 9.5e-302)
         (* y (- b z))
         (if (<= t 4.6e-276)
           t_1
           (if (<= t 25000000.0) (* b (- y 2.0)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.1e+84) {
		tmp = t_2;
	} else if (t <= -3.3e-164) {
		tmp = t_1;
	} else if (t <= 9.5e-302) {
		tmp = y * (b - z);
	} else if (t <= 4.6e-276) {
		tmp = t_1;
	} else if (t <= 25000000.0) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * z)
    t_2 = t * (b - a)
    if (t <= (-1.1d+84)) then
        tmp = t_2
    else if (t <= (-3.3d-164)) then
        tmp = t_1
    else if (t <= 9.5d-302) then
        tmp = y * (b - z)
    else if (t <= 4.6d-276) then
        tmp = t_1
    else if (t <= 25000000.0d0) then
        tmp = b * (y - 2.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.1e+84) {
		tmp = t_2;
	} else if (t <= -3.3e-164) {
		tmp = t_1;
	} else if (t <= 9.5e-302) {
		tmp = y * (b - z);
	} else if (t <= 4.6e-276) {
		tmp = t_1;
	} else if (t <= 25000000.0) {
		tmp = b * (y - 2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.1e+84:
		tmp = t_2
	elif t <= -3.3e-164:
		tmp = t_1
	elif t <= 9.5e-302:
		tmp = y * (b - z)
	elif t <= 4.6e-276:
		tmp = t_1
	elif t <= 25000000.0:
		tmp = b * (y - 2.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.1e+84)
		tmp = t_2;
	elseif (t <= -3.3e-164)
		tmp = t_1;
	elseif (t <= 9.5e-302)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 4.6e-276)
		tmp = t_1;
	elseif (t <= 25000000.0)
		tmp = Float64(b * Float64(y - 2.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.1e+84)
		tmp = t_2;
	elseif (t <= -3.3e-164)
		tmp = t_1;
	elseif (t <= 9.5e-302)
		tmp = y * (b - z);
	elseif (t <= 4.6e-276)
		tmp = t_1;
	elseif (t <= 25000000.0)
		tmp = b * (y - 2.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+84], t$95$2, If[LessEqual[t, -3.3e-164], t$95$1, If[LessEqual[t, 9.5e-302], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-276], t$95$1, If[LessEqual[t, 25000000.0], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.0999999999999999e84 or 2.5e7 < 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. Taylor expanded in t around inf 71.2%

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

   if -1.0999999999999999e84 < t < -3.3e-164 or 9.49999999999999991e-302 < t < 4.59999999999999963e-276

   1. Initial program 96.3%

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

   2. Taylor expanded in b around 0 67.6%

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

   3. Taylor expanded in y around inf 53.2%

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

   if -3.3e-164 < t < 9.49999999999999991e-302

   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. Taylor expanded in y around inf 43.5%

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

   if 4.59999999999999963e-276 < t < 2.5e7

   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. Taylor expanded in b around inf 47.8%

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

   3. Taylor expanded in t around 0 47.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-164}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-302}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-276}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 25000000:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 12: 26.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+89}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-253}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-26}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+38}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.2e+89)
   (* t b)
   (if (<= t -3.5e-165)
     x
     (if (<= t 6.2e-253)
       (* y b)
       (if (<= t 4e-26) (* b -2.0) (if (<= t 4.2e+38) (* y b) (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+89) {
		tmp = t * b;
	} else if (t <= -3.5e-165) {
		tmp = x;
	} else if (t <= 6.2e-253) {
		tmp = y * b;
	} else if (t <= 4e-26) {
		tmp = b * -2.0;
	} else if (t <= 4.2e+38) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.2d+89)) then
        tmp = t * b
    else if (t <= (-3.5d-165)) then
        tmp = x
    else if (t <= 6.2d-253) then
        tmp = y * b
    else if (t <= 4d-26) then
        tmp = b * (-2.0d0)
    else if (t <= 4.2d+38) then
        tmp = y * b
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.2e+89) {
		tmp = t * b;
	} else if (t <= -3.5e-165) {
		tmp = x;
	} else if (t <= 6.2e-253) {
		tmp = y * b;
	} else if (t <= 4e-26) {
		tmp = b * -2.0;
	} else if (t <= 4.2e+38) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.2e+89:
		tmp = t * b
	elif t <= -3.5e-165:
		tmp = x
	elif t <= 6.2e-253:
		tmp = y * b
	elif t <= 4e-26:
		tmp = b * -2.0
	elif t <= 4.2e+38:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.2e+89)
		tmp = Float64(t * b);
	elseif (t <= -3.5e-165)
		tmp = x;
	elseif (t <= 6.2e-253)
		tmp = Float64(y * b);
	elseif (t <= 4e-26)
		tmp = Float64(b * -2.0);
	elseif (t <= 4.2e+38)
		tmp = Float64(y * b);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.2e+89)
		tmp = t * b;
	elseif (t <= -3.5e-165)
		tmp = x;
	elseif (t <= 6.2e-253)
		tmp = y * b;
	elseif (t <= 4e-26)
		tmp = b * -2.0;
	elseif (t <= 4.2e+38)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.2e+89], N[(t * b), $MachinePrecision], If[LessEqual[t, -3.5e-165], x, If[LessEqual[t, 6.2e-253], N[(y * b), $MachinePrecision], If[LessEqual[t, 4e-26], N[(b * -2.0), $MachinePrecision], If[LessEqual[t, 4.2e+38], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.19999999999999972e89 or 4.2e38 < t

   1. Initial program 89.4%

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

   2. Taylor expanded in b around inf 43.7%

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

   3. Taylor expanded in t around inf 36.7%

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

   if -4.19999999999999972e89 < t < -3.5000000000000002e-165

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf 34.9%

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

   if -3.5000000000000002e-165 < t < 6.19999999999999991e-253 or 4.0000000000000002e-26 < t < 4.2e38

   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. Taylor expanded in z around 0 73.7%

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

   3. Taylor expanded in y around inf 37.4%

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

   if 6.19999999999999991e-253 < t < 4.0000000000000002e-26

   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. Taylor expanded in b around inf 43.7%

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

   3. Taylor expanded in y around 0 32.4%

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

   4. Taylor expanded in t around 0 32.4%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+89}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-253}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-26}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+38}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 13: 66.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+84} \lor \neg \left(t \leq 260000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e+84) (not (<= t 260000000.0)))
   (* t (- b a))
   (+ a (+ x (* b (+ y -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e+84) || !(t <= 260000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = a + (x + (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 <= (-1.05d+84)) .or. (.not. (t <= 260000000.0d0))) then
        tmp = t * (b - a)
    else
        tmp = a + (x + (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 <= -1.05e+84) || !(t <= 260000000.0)) {
		tmp = t * (b - a);
	} else {
		tmp = a + (x + (b * (y + -2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e+84) or not (t <= 260000000.0):
		tmp = t * (b - a)
	else:
		tmp = a + (x + (b * (y + -2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e+84) || !(t <= 260000000.0))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(a + Float64(x + 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 <= -1.05e+84) || ~((t <= 260000000.0)))
		tmp = t * (b - a);
	else
		tmp = a + (x + (b * (y + -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.05e+84], N[Not[LessEqual[t, 260000000.0]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05000000000000009e84 or 2.6e8 < 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. Taylor expanded in t around inf 71.2%

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

   if -1.05000000000000009e84 < t < 2.6e8

   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. Taylor expanded in z around 0 77.1%

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

   3. Taylor expanded in t around 0 75.8%

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

      1. sub-neg 75.8%

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

      2. sub-neg 75.8%

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

      3. metadata-eval 75.8%

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

      4. neg-mul-1 75.8%

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

      5. remove-double-neg 75.8%

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

   5. Simplified 75.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+84} \lor \neg \left(t \leq 260000000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \end{array} \]

Alternative 14: 65.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-38}:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.2e+39)
     t_1
     (if (<= y 6e-38)
       (+ x (- z (* b (- 2.0 t))))
       (if (<= y 1.1e+15) (* a (- 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.2e+39) {
		tmp = t_1;
	} else if (y <= 6e-38) {
		tmp = x + (z - (b * (2.0 - t)));
	} else if (y <= 1.1e+15) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.2d+39)) then
        tmp = t_1
    else if (y <= 6d-38) then
        tmp = x + (z - (b * (2.0d0 - t)))
    else if (y <= 1.1d+15) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.2e+39) {
		tmp = t_1;
	} else if (y <= 6e-38) {
		tmp = x + (z - (b * (2.0 - t)));
	} else if (y <= 1.1e+15) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.2e+39:
		tmp = t_1
	elif y <= 6e-38:
		tmp = x + (z - (b * (2.0 - t)))
	elif y <= 1.1e+15:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.2e+39)
		tmp = t_1;
	elseif (y <= 6e-38)
		tmp = Float64(x + Float64(z - Float64(b * Float64(2.0 - t))));
	elseif (y <= 1.1e+15)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.2e+39)
		tmp = t_1;
	elseif (y <= 6e-38)
		tmp = x + (z - (b * (2.0 - t)));
	elseif (y <= 1.1e+15)
		tmp = a * (1.0 - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+39], t$95$1, If[LessEqual[y, 6e-38], N[(x + N[(z - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+15], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e39 or 1.1e15 < y

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 60.7%

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

   if -1.2e39 < y < 5.99999999999999977e-38

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0 77.5%

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

      1. associate--l+ 77.5%

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

      2. sub-neg 77.5%

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

      3. +-commutative 77.5%

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

      4. metadata-eval 77.5%

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

      5. associate-+r+ 77.5%

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

      6. sub-neg 77.5%

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

      7. metadata-eval 77.5%

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

      8. fma-neg 77.5%

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

      9. associate-+r+ 77.5%

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

      10. +-commutative 77.5%

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

      11. associate-+r+ 77.5%

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

      12. distribute-rgt-neg-in 77.5%

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

      13. distribute-neg-in 77.5%

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

      14. neg-mul-1 77.5%

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

      15. metadata-eval 77.5%

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

      16. distribute-rgt-in 77.5%

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

      17. *-lft-identity 77.5%

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

      18. fma-udef 77.5%

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

      19. neg-mul-1 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in y around 0 76.7%

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

   if 5.99999999999999977e-38 < y < 1.1e15

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf 64.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-38}:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 15: 25.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-79}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 0.00025:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.06e+117)
   x
   (if (<= x -5.2e-79)
     (* t b)
     (if (<= x 0.00025) (* t (- a)) (if (<= x 7.2e+162) (* y (- z)) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.06e+117) {
		tmp = x;
	} else if (x <= -5.2e-79) {
		tmp = t * b;
	} else if (x <= 0.00025) {
		tmp = t * -a;
	} else if (x <= 7.2e+162) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.06d+117)) then
        tmp = x
    else if (x <= (-5.2d-79)) then
        tmp = t * b
    else if (x <= 0.00025d0) then
        tmp = t * -a
    else if (x <= 7.2d+162) then
        tmp = y * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.06e+117) {
		tmp = x;
	} else if (x <= -5.2e-79) {
		tmp = t * b;
	} else if (x <= 0.00025) {
		tmp = t * -a;
	} else if (x <= 7.2e+162) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.06e+117:
		tmp = x
	elif x <= -5.2e-79:
		tmp = t * b
	elif x <= 0.00025:
		tmp = t * -a
	elif x <= 7.2e+162:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.06e+117)
		tmp = x;
	elseif (x <= -5.2e-79)
		tmp = Float64(t * b);
	elseif (x <= 0.00025)
		tmp = Float64(t * Float64(-a));
	elseif (x <= 7.2e+162)
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.06e+117)
		tmp = x;
	elseif (x <= -5.2e-79)
		tmp = t * b;
	elseif (x <= 0.00025)
		tmp = t * -a;
	elseif (x <= 7.2e+162)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.06e+117], x, If[LessEqual[x, -5.2e-79], N[(t * b), $MachinePrecision], If[LessEqual[x, 0.00025], N[(t * (-a)), $MachinePrecision], If[LessEqual[x, 7.2e+162], N[(y * (-z)), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.06e117 or 7.19999999999999987e162 < x

   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. Taylor expanded in x around inf 45.8%

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

   if -1.06e117 < x < -5.19999999999999987e-79

   1. Initial program 87.8%

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

   2. Taylor expanded in b around inf 56.8%

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

   3. Taylor expanded in t around inf 39.4%

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

   if -5.19999999999999987e-79 < x < 2.5000000000000001e-4

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf 38.4%

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

   3. Taylor expanded in t around inf 28.7%

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

      1. associate-*r* 28.7%

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

      2. *-commutative 28.7%

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

      3. neg-mul-1 28.7%

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

   5. Simplified 28.7%

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

   if 2.5000000000000001e-4 < x < 7.19999999999999987e162

   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. Taylor expanded in y around inf 50.5%

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

   3. Taylor expanded in b around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. distribute-rgt-neg-out 36.3%

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

   5. Simplified 36.3%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-79}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 0.00025:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 31.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-50}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 0.81:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.5e+113)
   x
   (if (<= x -5.3e-50)
     (* t b)
     (if (<= x 0.81) (* a (- 1.0 t)) (if (<= x 8e+162) (* y (- z)) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.5e+113) {
		tmp = x;
	} else if (x <= -5.3e-50) {
		tmp = t * b;
	} else if (x <= 0.81) {
		tmp = a * (1.0 - t);
	} else if (x <= 8e+162) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5.5d+113)) then
        tmp = x
    else if (x <= (-5.3d-50)) then
        tmp = t * b
    else if (x <= 0.81d0) then
        tmp = a * (1.0d0 - t)
    else if (x <= 8d+162) then
        tmp = y * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.5e+113) {
		tmp = x;
	} else if (x <= -5.3e-50) {
		tmp = t * b;
	} else if (x <= 0.81) {
		tmp = a * (1.0 - t);
	} else if (x <= 8e+162) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.5e+113:
		tmp = x
	elif x <= -5.3e-50:
		tmp = t * b
	elif x <= 0.81:
		tmp = a * (1.0 - t)
	elif x <= 8e+162:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.5e+113)
		tmp = x;
	elseif (x <= -5.3e-50)
		tmp = Float64(t * b);
	elseif (x <= 0.81)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (x <= 8e+162)
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5.5e+113)
		tmp = x;
	elseif (x <= -5.3e-50)
		tmp = t * b;
	elseif (x <= 0.81)
		tmp = a * (1.0 - t);
	elseif (x <= 8e+162)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.5e+113], x, If[LessEqual[x, -5.3e-50], N[(t * b), $MachinePrecision], If[LessEqual[x, 0.81], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+162], N[(y * (-z)), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.5000000000000001e113 or 7.9999999999999995e162 < x

   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. Taylor expanded in x around inf 45.8%

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

   if -5.5000000000000001e113 < x < -5.3000000000000001e-50

   1. Initial program 88.8%

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

   2. Taylor expanded in b around inf 61.9%

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

   3. Taylor expanded in t around inf 40.5%

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

   if -5.3000000000000001e-50 < x < 0.81000000000000005

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 39.0%

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

   if 0.81000000000000005 < x < 7.9999999999999995e162

   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. Taylor expanded in y around inf 50.5%

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

   3. Taylor expanded in b around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. distribute-rgt-neg-out 36.3%

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

   5. Simplified 36.3%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-50}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 0.81:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+162}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 25.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.36e+108)
   x
   (if (<= x -5.5e-78) (* t b) (if (<= x 2e+17) (* t (- a)) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.36e+108) {
		tmp = x;
	} else if (x <= -5.5e-78) {
		tmp = t * b;
	} else if (x <= 2e+17) {
		tmp = t * -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.36d+108)) then
        tmp = x
    else if (x <= (-5.5d-78)) then
        tmp = t * b
    else if (x <= 2d+17) then
        tmp = t * -a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.36e+108) {
		tmp = x;
	} else if (x <= -5.5e-78) {
		tmp = t * b;
	} else if (x <= 2e+17) {
		tmp = t * -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.36e+108:
		tmp = x
	elif x <= -5.5e-78:
		tmp = t * b
	elif x <= 2e+17:
		tmp = t * -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.36e+108)
		tmp = x;
	elseif (x <= -5.5e-78)
		tmp = Float64(t * b);
	elseif (x <= 2e+17)
		tmp = Float64(t * Float64(-a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.36e+108)
		tmp = x;
	elseif (x <= -5.5e-78)
		tmp = t * b;
	elseif (x <= 2e+17)
		tmp = t * -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.36e+108], x, If[LessEqual[x, -5.5e-78], N[(t * b), $MachinePrecision], If[LessEqual[x, 2e+17], N[(t * (-a)), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3599999999999999e108 or 2e17 < x

   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. Taylor expanded in x around inf 39.2%

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

   if -1.3599999999999999e108 < x < -5.50000000000000017e-78

   1. Initial program 87.8%

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

   2. Taylor expanded in b around inf 56.8%

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

   3. Taylor expanded in t around inf 39.4%

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

   if -5.50000000000000017e-78 < x < 2e17

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf 38.1%

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

   3. Taylor expanded in t around inf 28.5%

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

      1. associate-*r* 28.5%

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

      2. *-commutative 28.5%

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

      3. neg-mul-1 28.5%

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

   5. Simplified 28.5%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-78}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 19.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-178}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-6}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.5e+153) x (if (<= x -4.2e-178) a (if (<= x 6e-6) (* b -2.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.5e+153) {
		tmp = x;
	} else if (x <= -4.2e-178) {
		tmp = a;
	} else if (x <= 6e-6) {
		tmp = b * -2.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.5d+153)) then
        tmp = x
    else if (x <= (-4.2d-178)) then
        tmp = a
    else if (x <= 6d-6) then
        tmp = b * (-2.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.5e+153) {
		tmp = x;
	} else if (x <= -4.2e-178) {
		tmp = a;
	} else if (x <= 6e-6) {
		tmp = b * -2.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.5e+153:
		tmp = x
	elif x <= -4.2e-178:
		tmp = a
	elif x <= 6e-6:
		tmp = b * -2.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.5e+153)
		tmp = x;
	elseif (x <= -4.2e-178)
		tmp = a;
	elseif (x <= 6e-6)
		tmp = Float64(b * -2.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.5e+153)
		tmp = x;
	elseif (x <= -4.2e-178)
		tmp = a;
	elseif (x <= 6e-6)
		tmp = b * -2.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.5e+153], x, If[LessEqual[x, -4.2e-178], a, If[LessEqual[x, 6e-6], N[(b * -2.0), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4999999999999999e153 or 6.0000000000000002e-6 < x

   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. Taylor expanded in x around inf 40.6%

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

   if -3.4999999999999999e153 < x < -4.2e-178

   1. Initial program 90.5%

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

   2. Taylor expanded in a around inf 31.9%

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

   3. Taylor expanded in t around 0 15.2%

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

   if -4.2e-178 < x < 6.0000000000000002e-6

   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. Taylor expanded in b around inf 45.2%

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

   3. Taylor expanded in y around 0 32.3%

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

   4. Taylor expanded in t around 0 19.4%

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

4. Final simplification 26.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-178}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-6}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 25.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{-18}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.5e+84)
   (* t b)
   (if (<= t 7.6e-246) x (if (<= t 1e-18) (* b -2.0) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+84) {
		tmp = t * b;
	} else if (t <= 7.6e-246) {
		tmp = x;
	} else if (t <= 1e-18) {
		tmp = b * -2.0;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-9.5d+84)) then
        tmp = t * b
    else if (t <= 7.6d-246) then
        tmp = x
    else if (t <= 1d-18) then
        tmp = b * (-2.0d0)
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.5e+84) {
		tmp = t * b;
	} else if (t <= 7.6e-246) {
		tmp = x;
	} else if (t <= 1e-18) {
		tmp = b * -2.0;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.5e+84:
		tmp = t * b
	elif t <= 7.6e-246:
		tmp = x
	elif t <= 1e-18:
		tmp = b * -2.0
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.5e+84)
		tmp = Float64(t * b);
	elseif (t <= 7.6e-246)
		tmp = x;
	elseif (t <= 1e-18)
		tmp = Float64(b * -2.0);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -9.5e+84)
		tmp = t * b;
	elseif (t <= 7.6e-246)
		tmp = x;
	elseif (t <= 1e-18)
		tmp = b * -2.0;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.5e+84], N[(t * b), $MachinePrecision], If[LessEqual[t, 7.6e-246], x, If[LessEqual[t, 1e-18], N[(b * -2.0), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.49999999999999979e84 or 1.0000000000000001e-18 < t

   1. Initial program 90.3%

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

   2. Taylor expanded in b around inf 44.0%

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

   3. Taylor expanded in t around inf 33.7%

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

   if -9.49999999999999979e84 < t < 7.59999999999999951e-246

   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. Taylor expanded in x around inf 28.1%

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

   if 7.59999999999999951e-246 < t < 1.0000000000000001e-18

   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. Taylor expanded in b around inf 45.7%

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

   3. Taylor expanded in y around 0 32.3%

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

   4. Taylor expanded in t around 0 32.3%

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

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{-18}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 20: 47.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+84} \lor \neg \left(t \leq 5600000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e+84) (not (<= t 5600000.0)))
   (* 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 <= -1.05e+84) || !(t <= 5600000.0)) {
		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 <= (-1.05d+84)) .or. (.not. (t <= 5600000.0d0))) 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 <= -1.05e+84) || !(t <= 5600000.0)) {
		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 <= -1.05e+84) or not (t <= 5600000.0):
		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 <= -1.05e+84) || !(t <= 5600000.0))
		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 <= -1.05e+84) || ~((t <= 5600000.0)))
		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, -1.05e+84], N[Not[LessEqual[t, 5600000.0]], $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 < -1.05000000000000009e84 or 5.6e6 < 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. Taylor expanded in t around inf 71.2%

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

   if -1.05000000000000009e84 < t < 5.6e6

   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. Taylor expanded in b around inf 40.5%

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

   3. Taylor expanded in t around 0 39.1%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+84} \lor \neg \left(t \leq 5600000\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \end{array} \]

Alternative 21: 40.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.7e-10)
   (* b (- y 2.0))
   (if (<= b 7e+35) (* a (- 1.0 t)) (* b (- t 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.7e-10) {
		tmp = b * (y - 2.0);
	} else if (b <= 7e+35) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 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 (b <= (-2.7d-10)) then
        tmp = b * (y - 2.0d0)
    else if (b <= 7d+35) then
        tmp = a * (1.0d0 - t)
    else
        tmp = b * (t - 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 (b <= -2.7e-10) {
		tmp = b * (y - 2.0);
	} else if (b <= 7e+35) {
		tmp = a * (1.0 - t);
	} else {
		tmp = b * (t - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.7e-10:
		tmp = b * (y - 2.0)
	elif b <= 7e+35:
		tmp = a * (1.0 - t)
	else:
		tmp = b * (t - 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.7e-10)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (b <= 7e+35)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = Float64(b * Float64(t - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.7e-10)
		tmp = b * (y - 2.0);
	elseif (b <= 7e+35)
		tmp = a * (1.0 - t);
	else
		tmp = b * (t - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.7e-10], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+35], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.7e-10

   1. Initial program 91.0%

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

   2. Taylor expanded in b around inf 66.8%

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

   3. Taylor expanded in t around 0 49.4%

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

   if -2.7e-10 < b < 7.0000000000000001e35

   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. Taylor expanded in a around inf 39.6%

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

   if 7.0000000000000001e35 < b

   1. Initial program 88.9%

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

   2. Taylor expanded in b around inf 79.2%

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

   3. Taylor expanded in y around 0 54.1%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 22: 20.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-11}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5e+153) x (if (<= x 2.76e-11) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5e+153) {
		tmp = x;
	} else if (x <= 2.76e-11) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-5d+153)) then
        tmp = x
    else if (x <= 2.76d-11) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5e+153) {
		tmp = x;
	} else if (x <= 2.76e-11) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5e+153:
		tmp = x
	elif x <= 2.76e-11:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5e+153)
		tmp = x;
	elseif (x <= 2.76e-11)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -5e+153)
		tmp = x;
	elseif (x <= 2.76e-11)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5e+153], x, If[LessEqual[x, 2.76e-11], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000018e153 or 2.76e-11 < x

   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. Taylor expanded in x around inf 39.7%

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

   if -5.00000000000000018e153 < x < 2.76e-11

   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. Taylor expanded in a around inf 34.2%

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

   3. Taylor expanded in t around 0 13.6%

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

4. Final simplification 23.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.76 \cdot 10^{-11}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 11.0% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

2. Taylor expanded in a around inf 27.3%

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

3. Taylor expanded in t around 0 9.8%

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

4. Final simplification 9.8%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023271 
(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)))