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

Percentage Accurate: 94.9% → 95.5%

Time: 22.0s

Alternatives: 24

Speedup: 0.8×

• 36.3% 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: 95.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+210}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(t \cdot \left(b - a\right) - b \cdot \left(2 - y\right)\right)\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.2e+210)
   (fma (+ y (+ t -2.0)) b (- x (* y z)))
   (+ (+ x (- (* t (- b a)) (* b (- 2.0 y)))) (- a (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+210) {
		tmp = fma((y + (t + -2.0)), b, (x - (y * z)));
	} else {
		tmp = (x + ((t * (b - a)) - (b * (2.0 - y)))) + (a - (z * (y + -1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.2e+210)
		tmp = fma(Float64(y + Float64(t + -2.0)), b, Float64(x - Float64(y * z)));
	else
		tmp = Float64(Float64(x + Float64(Float64(t * Float64(b - a)) - Float64(b * Float64(2.0 - y)))) + Float64(a - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.2e+210], N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision] - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.1999999999999995e210

   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. Step-by-step derivation

      1. +-commutative 88.9%

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

      2. fma-def 94.4%

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

      3. associate--l+ 94.4%

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

      4. sub-neg 94.4%

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

      5. metadata-eval 94.4%

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

      6. sub-neg 94.4%

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

      7. associate-+l- 94.4%

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

      8. fma-neg 94.4%

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

      9. sub-neg 94.4%

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

      10. metadata-eval 94.4%

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

      11. remove-double-neg 94.4%

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

      12. sub-neg 94.4%

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

      13. metadata-eval 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around inf 89.3%

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

   if -9.1999999999999995e210 < b

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 99.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+210}:\\ \;\;\;\;\mathsf{fma}\left(y + \left(t + -2\right), b, x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(t \cdot \left(b - a\right) - b \cdot \left(2 - y\right)\right)\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-def 98.4%

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

   3. associate--l+ 98.4%

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

   4. sub-neg 98.4%

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

   5. metadata-eval 98.4%

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

   6. sub-neg 98.4%

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

   7. associate-+l- 98.4%

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

   8. fma-neg 98.4%

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

   9. sub-neg 98.4%

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

   10. metadata-eval 98.4%

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

   11. remove-double-neg 98.4%

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

   12. sub-neg 98.4%

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

   13. metadata-eval 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 97.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ y t) 2.0)) (+ (- x (* z (+ y -1.0))) (* a (- 1.0 t))))))
   (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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)));
	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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)));
	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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)))
	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(b * Float64(Float64(y + t) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y + -1.0))) + Float64(a * Float64(1.0 - t))))
	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 = (b * ((y + t) - 2.0)) + ((x - (z * (y + -1.0))) + (a * (1.0 - t)));
	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[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 67.5%

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

4. Final simplification 98.8%

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

Alternative 4: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \left(y + -1\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := \left(x + a\right) - t \cdot a\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-215}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 0.0074:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+56} \lor \neg \left(b \leq 7.5 \cdot 10^{+120}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z (+ y -1.0))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (- (+ x a) (* t a))))
   (if (<= b -1.75e+59)
     t_2
     (if (<= b -4.6e-110)
       t_1
       (if (<= b 2.6e-215)
         t_3
         (if (<= b 0.0074)
           t_1
           (if (or (<= b 9.8e+56) (not (<= b 7.5e+120))) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (y + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = (x + a) - (t * a);
	double tmp;
	if (b <= -1.75e+59) {
		tmp = t_2;
	} else if (b <= -4.6e-110) {
		tmp = t_1;
	} else if (b <= 2.6e-215) {
		tmp = t_3;
	} else if (b <= 0.0074) {
		tmp = t_1;
	} else if ((b <= 9.8e+56) || !(b <= 7.5e+120)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - (z * (y + (-1.0d0)))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = (x + a) - (t * a)
    if (b <= (-1.75d+59)) then
        tmp = t_2
    else if (b <= (-4.6d-110)) then
        tmp = t_1
    else if (b <= 2.6d-215) then
        tmp = t_3
    else if (b <= 0.0074d0) then
        tmp = t_1
    else if ((b <= 9.8d+56) .or. (.not. (b <= 7.5d+120))) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (y + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = (x + a) - (t * a);
	double tmp;
	if (b <= -1.75e+59) {
		tmp = t_2;
	} else if (b <= -4.6e-110) {
		tmp = t_1;
	} else if (b <= 2.6e-215) {
		tmp = t_3;
	} else if (b <= 0.0074) {
		tmp = t_1;
	} else if ((b <= 9.8e+56) || !(b <= 7.5e+120)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * (y + -1.0))
	t_2 = b * ((y + t) - 2.0)
	t_3 = (x + a) - (t * a)
	tmp = 0
	if b <= -1.75e+59:
		tmp = t_2
	elif b <= -4.6e-110:
		tmp = t_1
	elif b <= 2.6e-215:
		tmp = t_3
	elif b <= 0.0074:
		tmp = t_1
	elif (b <= 9.8e+56) or not (b <= 7.5e+120):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * Float64(y + -1.0)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(Float64(x + a) - Float64(t * a))
	tmp = 0.0
	if (b <= -1.75e+59)
		tmp = t_2;
	elseif (b <= -4.6e-110)
		tmp = t_1;
	elseif (b <= 2.6e-215)
		tmp = t_3;
	elseif (b <= 0.0074)
		tmp = t_1;
	elseif ((b <= 9.8e+56) || !(b <= 7.5e+120))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * (y + -1.0));
	t_2 = b * ((y + t) - 2.0);
	t_3 = (x + a) - (t * a);
	tmp = 0.0;
	if (b <= -1.75e+59)
		tmp = t_2;
	elseif (b <= -4.6e-110)
		tmp = t_1;
	elseif (b <= 2.6e-215)
		tmp = t_3;
	elseif (b <= 0.0074)
		tmp = t_1;
	elseif ((b <= 9.8e+56) || ~((b <= 7.5e+120)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + a), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e+59], t$95$2, If[LessEqual[b, -4.6e-110], t$95$1, If[LessEqual[b, 2.6e-215], t$95$3, If[LessEqual[b, 0.0074], t$95$1, If[Or[LessEqual[b, 9.8e+56], N[Not[LessEqual[b, 7.5e+120]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.75e59 or 0.0074000000000000003 < b < 9.8000000000000005e56 or 7.5000000000000006e120 < b

   1. Initial program 93.5%

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

   3. Taylor expanded in b around inf 77.5%

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

   if -1.75e59 < b < -4.6000000000000003e-110 or 2.6e-215 < b < 0.0074000000000000003

   1. Initial program 98.7%

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

   3. Taylor expanded in a around 0 79.7%

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

   4. Taylor expanded in b around 0 61.9%

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

   if -4.6000000000000003e-110 < b < 2.6e-215 or 9.8000000000000005e56 < b < 7.5000000000000006e120

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in b around 0 92.0%

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

      1. sub-neg 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

      4. sub-neg 92.0%

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

      5. metadata-eval 92.0%

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

      6. distribute-neg-in 92.0%

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

      7. neg-mul-1 92.0%

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

      8. remove-double-neg 92.0%

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

      9. distribute-rgt-neg-in 92.0%

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

      10. neg-sub0 92.0%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 92.0%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 92.0%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in z around 0 65.5%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-110}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-215}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;b \leq 0.0074:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+56} \lor \neg \left(b \leq 7.5 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 10^{-308}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+109}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= a -2.2e+77)
     t_2
     (if (<= a -2.2e-66)
       t_1
       (if (<= a -2.2e-155)
         (* y (- z))
         (if (<= a 1e-308)
           (+ x z)
           (if (<= a 1.16e-126) t_1 (if (<= a 6.5e+109) (+ x z) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.2e+77) {
		tmp = t_2;
	} else if (a <= -2.2e-66) {
		tmp = t_1;
	} else if (a <= -2.2e-155) {
		tmp = y * -z;
	} else if (a <= 1e-308) {
		tmp = x + z;
	} else if (a <= 1.16e-126) {
		tmp = t_1;
	} else if (a <= 6.5e+109) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (a <= (-2.2d+77)) then
        tmp = t_2
    else if (a <= (-2.2d-66)) then
        tmp = t_1
    else if (a <= (-2.2d-155)) then
        tmp = y * -z
    else if (a <= 1d-308) then
        tmp = x + z
    else if (a <= 1.16d-126) then
        tmp = t_1
    else if (a <= 6.5d+109) then
        tmp = x + z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -2.2e+77) {
		tmp = t_2;
	} else if (a <= -2.2e-66) {
		tmp = t_1;
	} else if (a <= -2.2e-155) {
		tmp = y * -z;
	} else if (a <= 1e-308) {
		tmp = x + z;
	} else if (a <= 1.16e-126) {
		tmp = t_1;
	} else if (a <= 6.5e+109) {
		tmp = x + z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -2.2e+77:
		tmp = t_2
	elif a <= -2.2e-66:
		tmp = t_1
	elif a <= -2.2e-155:
		tmp = y * -z
	elif a <= 1e-308:
		tmp = x + z
	elif a <= 1.16e-126:
		tmp = t_1
	elif a <= 6.5e+109:
		tmp = x + z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -2.2e+77)
		tmp = t_2;
	elseif (a <= -2.2e-66)
		tmp = t_1;
	elseif (a <= -2.2e-155)
		tmp = Float64(y * Float64(-z));
	elseif (a <= 1e-308)
		tmp = Float64(x + z);
	elseif (a <= 1.16e-126)
		tmp = t_1;
	elseif (a <= 6.5e+109)
		tmp = Float64(x + z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -2.2e+77)
		tmp = t_2;
	elseif (a <= -2.2e-66)
		tmp = t_1;
	elseif (a <= -2.2e-155)
		tmp = y * -z;
	elseif (a <= 1e-308)
		tmp = x + z;
	elseif (a <= 1.16e-126)
		tmp = t_1;
	elseif (a <= 6.5e+109)
		tmp = x + z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+77], t$95$2, If[LessEqual[a, -2.2e-66], t$95$1, If[LessEqual[a, -2.2e-155], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, 1e-308], N[(x + z), $MachinePrecision], If[LessEqual[a, 1.16e-126], t$95$1, If[LessEqual[a, 6.5e+109], N[(x + z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.2e77 or 6.5e109 < a

   1. Initial program 94.9%

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

   3. Taylor expanded in a around inf 58.6%

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

   if -2.2e77 < a < -2.2000000000000001e-66 or 9.9999999999999991e-309 < a < 1.16e-126

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-rgt-neg-in 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in y around 0 42.5%

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

   if -2.2000000000000001e-66 < a < -2.1999999999999999e-155

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 58.4%

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

   4. Taylor expanded in b around 0 43.5%

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

      1. mul-1-neg 43.5%

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

      2. distribute-rgt-neg-out 43.5%

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

   6. Simplified 43.5%

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

   if -2.1999999999999999e-155 < a < 9.9999999999999991e-309 or 1.16e-126 < a < 6.5e109

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0 94.7%

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

   4. Taylor expanded in y around 0 66.7%

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

      1. neg-mul-1 66.7%

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

      2. associate--l+ 66.7%

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

      3. sub-neg 66.7%

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

      4. metadata-eval 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in b around 0 47.3%

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

      1. +-commutative 47.3%

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

   9. Simplified 47.3%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+77}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 10^{-308}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-126}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+109}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{+69}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;b \leq 0.0074 \lor \neg \left(b \leq 3.1 \cdot 10^{+55}\right) \land b \leq 1.45 \cdot 10^{+173}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -1.42e+69)
     (+ x t_1)
     (if (or (<= b 0.0074) (and (not (<= b 3.1e+55)) (<= b 1.45e+173)))
       (+ (- x (* t a)) (- a (* z (+ y -1.0))))
       (- t_1 (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.42e+69) {
		tmp = x + t_1;
	} else if ((b <= 0.0074) || (!(b <= 3.1e+55) && (b <= 1.45e+173))) {
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-1.42d+69)) then
        tmp = x + t_1
    else if ((b <= 0.0074d0) .or. (.not. (b <= 3.1d+55)) .and. (b <= 1.45d+173)) then
        tmp = (x - (t * a)) + (a - (z * (y + (-1.0d0))))
    else
        tmp = t_1 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.42e+69) {
		tmp = x + t_1;
	} else if ((b <= 0.0074) || (!(b <= 3.1e+55) && (b <= 1.45e+173))) {
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)));
	} else {
		tmp = t_1 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.42e+69:
		tmp = x + t_1
	elif (b <= 0.0074) or (not (b <= 3.1e+55) and (b <= 1.45e+173)):
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)))
	else:
		tmp = t_1 - (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.42e+69)
		tmp = Float64(x + t_1);
	elseif ((b <= 0.0074) || (!(b <= 3.1e+55) && (b <= 1.45e+173)))
		tmp = Float64(Float64(x - Float64(t * a)) + Float64(a - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(t_1 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.42e+69)
		tmp = x + t_1;
	elseif ((b <= 0.0074) || (~((b <= 3.1e+55)) && (b <= 1.45e+173)))
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)));
	else
		tmp = t_1 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.42e+69], N[(x + t$95$1), $MachinePrecision], If[Or[LessEqual[b, 0.0074], And[N[Not[LessEqual[b, 3.1e+55]], $MachinePrecision], LessEqual[b, 1.45e+173]]], N[(N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.42e69

   1. Initial program 93.3%

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

   3. Taylor expanded in a around 0 84.4%

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

   4. Taylor expanded in z around 0 78.6%

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

   if -1.42e69 < b < 0.0074000000000000003 or 3.09999999999999994e55 < b < 1.45000000000000003e173

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0 99.4%

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

   4. Taylor expanded in b around 0 86.4%

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

      1. sub-neg 86.4%

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

      2. mul-1-neg 86.4%

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

      3. unsub-neg 86.4%

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

      4. sub-neg 86.4%

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

      5. metadata-eval 86.4%

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

      6. distribute-neg-in 86.4%

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

      7. neg-mul-1 86.4%

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

      8. remove-double-neg 86.4%

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

      9. distribute-rgt-neg-in 86.4%

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

      10. neg-sub0 86.4%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 86.4%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 86.4%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 86.4%

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

   6. Simplified 86.4%

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

   if 0.0074000000000000003 < b < 3.09999999999999994e55 or 1.45000000000000003e173 < b

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf 94.7%

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

      1. mul-1-neg 94.7%

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

      2. distribute-rgt-neg-in 94.7%

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

   5. Simplified 94.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+69}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 0.0074 \lor \neg \left(b \leq 3.1 \cdot 10^{+55}\right) \land b \leq 1.45 \cdot 10^{+173}:\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + b \cdot \left(t - 2\right)\\ t_2 := \left(x + z\right) + -2 \cdot b\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3000000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.059:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ z (* b (- t 2.0))))
        (t_2 (+ (+ x z) (* -2.0 b)))
        (t_3 (* y (- b z))))
   (if (<= y -3000000000000.0)
     t_3
     (if (<= y -2.1e-151)
       t_1
       (if (<= y -2.7e-272)
         t_2
         (if (<= y 6.5e-266) t_1 (if (<= y 0.059) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (b * (t - 2.0));
	double t_2 = (x + z) + (-2.0 * b);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -3000000000000.0) {
		tmp = t_3;
	} else if (y <= -2.1e-151) {
		tmp = t_1;
	} else if (y <= -2.7e-272) {
		tmp = t_2;
	} else if (y <= 6.5e-266) {
		tmp = t_1;
	} else if (y <= 0.059) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z + (b * (t - 2.0d0))
    t_2 = (x + z) + ((-2.0d0) * b)
    t_3 = y * (b - z)
    if (y <= (-3000000000000.0d0)) then
        tmp = t_3
    else if (y <= (-2.1d-151)) then
        tmp = t_1
    else if (y <= (-2.7d-272)) then
        tmp = t_2
    else if (y <= 6.5d-266) then
        tmp = t_1
    else if (y <= 0.059d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z + (b * (t - 2.0));
	double t_2 = (x + z) + (-2.0 * b);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -3000000000000.0) {
		tmp = t_3;
	} else if (y <= -2.1e-151) {
		tmp = t_1;
	} else if (y <= -2.7e-272) {
		tmp = t_2;
	} else if (y <= 6.5e-266) {
		tmp = t_1;
	} else if (y <= 0.059) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z + (b * (t - 2.0))
	t_2 = (x + z) + (-2.0 * b)
	t_3 = y * (b - z)
	tmp = 0
	if y <= -3000000000000.0:
		tmp = t_3
	elif y <= -2.1e-151:
		tmp = t_1
	elif y <= -2.7e-272:
		tmp = t_2
	elif y <= 6.5e-266:
		tmp = t_1
	elif y <= 0.059:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z + Float64(b * Float64(t - 2.0)))
	t_2 = Float64(Float64(x + z) + Float64(-2.0 * b))
	t_3 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3000000000000.0)
		tmp = t_3;
	elseif (y <= -2.1e-151)
		tmp = t_1;
	elseif (y <= -2.7e-272)
		tmp = t_2;
	elseif (y <= 6.5e-266)
		tmp = t_1;
	elseif (y <= 0.059)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z + (b * (t - 2.0));
	t_2 = (x + z) + (-2.0 * b);
	t_3 = y * (b - z);
	tmp = 0.0;
	if (y <= -3000000000000.0)
		tmp = t_3;
	elseif (y <= -2.1e-151)
		tmp = t_1;
	elseif (y <= -2.7e-272)
		tmp = t_2;
	elseif (y <= 6.5e-266)
		tmp = t_1;
	elseif (y <= 0.059)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + z), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3000000000000.0], t$95$3, If[LessEqual[y, -2.1e-151], t$95$1, If[LessEqual[y, -2.7e-272], t$95$2, If[LessEqual[y, 6.5e-266], t$95$1, If[LessEqual[y, 0.059], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e12 or 0.058999999999999997 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 68.4%

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

   if -3e12 < y < -2.0999999999999999e-151 or -2.69999999999999993e-272 < y < 6.50000000000000024e-266

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 76.3%

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

   4. Taylor expanded in y around 0 71.1%

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

      1. neg-mul-1 71.1%

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

      2. associate--l+ 71.1%

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

      3. sub-neg 71.1%

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

      4. metadata-eval 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in x around 0 58.9%

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

   if -2.0999999999999999e-151 < y < -2.69999999999999993e-272 or 6.50000000000000024e-266 < y < 0.058999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 73.9%

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

   4. Taylor expanded in y around 0 73.9%

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

      1. neg-mul-1 73.9%

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

      2. associate--l+ 73.9%

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

      3. sub-neg 73.9%

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

      4. metadata-eval 73.9%

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

   6. Simplified 73.9%

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

   7. Taylor expanded in t around 0 59.6%

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

      1. associate-+r+ 59.6%

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

      2. +-commutative 59.6%

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

      3. *-commutative 59.6%

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

   9. Simplified 59.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3000000000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-151}:\\ \;\;\;\;z + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-272}:\\ \;\;\;\;\left(x + z\right) + -2 \cdot b\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-266}:\\ \;\;\;\;z + b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 0.059:\\ \;\;\;\;\left(x + z\right) + -2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -3800:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-309}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-275}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+109}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -3800.0)
     t_1
     (if (<= a -4e-159)
       (* y (- z))
       (if (<= a -8e-309)
         (+ x z)
         (if (<= a 1.4e-275) (* t b) (if (<= a 7e+109) (+ x z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -3800.0) {
		tmp = t_1;
	} else if (a <= -4e-159) {
		tmp = y * -z;
	} else if (a <= -8e-309) {
		tmp = x + z;
	} else if (a <= 1.4e-275) {
		tmp = t * b;
	} else if (a <= 7e+109) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-3800.0d0)) then
        tmp = t_1
    else if (a <= (-4d-159)) then
        tmp = y * -z
    else if (a <= (-8d-309)) then
        tmp = x + z
    else if (a <= 1.4d-275) then
        tmp = t * b
    else if (a <= 7d+109) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -3800.0) {
		tmp = t_1;
	} else if (a <= -4e-159) {
		tmp = y * -z;
	} else if (a <= -8e-309) {
		tmp = x + z;
	} else if (a <= 1.4e-275) {
		tmp = t * b;
	} else if (a <= 7e+109) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -3800.0:
		tmp = t_1
	elif a <= -4e-159:
		tmp = y * -z
	elif a <= -8e-309:
		tmp = x + z
	elif a <= 1.4e-275:
		tmp = t * b
	elif a <= 7e+109:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -3800.0)
		tmp = t_1;
	elseif (a <= -4e-159)
		tmp = Float64(y * Float64(-z));
	elseif (a <= -8e-309)
		tmp = Float64(x + z);
	elseif (a <= 1.4e-275)
		tmp = Float64(t * b);
	elseif (a <= 7e+109)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -3800.0)
		tmp = t_1;
	elseif (a <= -4e-159)
		tmp = y * -z;
	elseif (a <= -8e-309)
		tmp = x + z;
	elseif (a <= 1.4e-275)
		tmp = t * b;
	elseif (a <= 7e+109)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3800.0], t$95$1, If[LessEqual[a, -4e-159], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, -8e-309], N[(x + z), $MachinePrecision], If[LessEqual[a, 1.4e-275], N[(t * b), $MachinePrecision], If[LessEqual[a, 7e+109], N[(x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3800 or 6.99999999999999966e109 < a

   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. Add Preprocessing

   3. Taylor expanded in a around inf 54.2%

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

   if -3800 < a < -3.99999999999999995e-159

   1. Initial program 97.5%

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

   3. Taylor expanded in y around inf 49.1%

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

   4. Taylor expanded in b around 0 33.9%

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

      1. mul-1-neg 33.9%

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

      2. distribute-rgt-neg-out 33.9%

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

   6. Simplified 33.9%

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

   if -3.99999999999999995e-159 < a < -8.0000000000000003e-309 or 1.39999999999999997e-275 < a < 6.99999999999999966e109

   1. Initial program 96.6%

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

   3. Taylor expanded in a around 0 95.6%

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

   4. Taylor expanded in y around 0 66.8%

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

      1. neg-mul-1 66.8%

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

      2. associate--l+ 66.8%

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

      3. sub-neg 66.8%

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

      4. metadata-eval 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in b around 0 45.0%

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

      1. +-commutative 45.0%

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

   9. Simplified 45.0%

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

   if -8.0000000000000003e-309 < a < 1.39999999999999997e-275

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 47.5%

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

   4. Taylor expanded in b around inf 47.5%

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

      1. *-commutative 47.5%

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

   6. Simplified 47.5%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3800:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-309}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-275}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+109}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-275}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 0.059:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -5500000000000.0)
     t_1
     (if (<= y -2e-210)
       (* t (- b a))
       (if (<= y -3.5e-275)
         (+ x z)
         (if (<= y 1.15e-276)
           (* b (- t 2.0))
           (if (<= y 0.059) (+ x z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5500000000000.0) {
		tmp = t_1;
	} else if (y <= -2e-210) {
		tmp = t * (b - a);
	} else if (y <= -3.5e-275) {
		tmp = x + z;
	} else if (y <= 1.15e-276) {
		tmp = b * (t - 2.0);
	} else if (y <= 0.059) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-5500000000000.0d0)) then
        tmp = t_1
    else if (y <= (-2d-210)) then
        tmp = t * (b - a)
    else if (y <= (-3.5d-275)) then
        tmp = x + z
    else if (y <= 1.15d-276) then
        tmp = b * (t - 2.0d0)
    else if (y <= 0.059d0) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -5500000000000.0) {
		tmp = t_1;
	} else if (y <= -2e-210) {
		tmp = t * (b - a);
	} else if (y <= -3.5e-275) {
		tmp = x + z;
	} else if (y <= 1.15e-276) {
		tmp = b * (t - 2.0);
	} else if (y <= 0.059) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -5500000000000.0:
		tmp = t_1
	elif y <= -2e-210:
		tmp = t * (b - a)
	elif y <= -3.5e-275:
		tmp = x + z
	elif y <= 1.15e-276:
		tmp = b * (t - 2.0)
	elif y <= 0.059:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -5500000000000.0)
		tmp = t_1;
	elseif (y <= -2e-210)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= -3.5e-275)
		tmp = Float64(x + z);
	elseif (y <= 1.15e-276)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= 0.059)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -5500000000000.0)
		tmp = t_1;
	elseif (y <= -2e-210)
		tmp = t * (b - a);
	elseif (y <= -3.5e-275)
		tmp = x + z;
	elseif (y <= 1.15e-276)
		tmp = b * (t - 2.0);
	elseif (y <= 0.059)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5500000000000.0], t$95$1, If[LessEqual[y, -2e-210], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-275], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.15e-276], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.059], N[(x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5e12 or 0.058999999999999997 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 68.4%

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

   if -5.5e12 < y < -2.0000000000000001e-210

   1. Initial program 95.9%

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

   3. Taylor expanded in t around inf 46.9%

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

   if -2.0000000000000001e-210 < y < -3.49999999999999969e-275 or 1.14999999999999991e-276 < y < 0.058999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 75.7%

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

   4. Taylor expanded in y around 0 75.7%

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

      1. neg-mul-1 75.7%

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

      2. associate--l+ 75.7%

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

      3. sub-neg 75.7%

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

      4. metadata-eval 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in b around 0 55.9%

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

      1. +-commutative 55.9%

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

   9. Simplified 55.9%

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

   if -3.49999999999999969e-275 < y < 1.14999999999999991e-276

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-rgt-neg-in 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in y around 0 68.5%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5500000000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-275}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq 0.059:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.06 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 0.0014:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+55} \lor \neg \left(b \leq 7.5 \cdot 10^{+120}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -1.06e+69)
     t_1
     (if (<= b 0.0014)
       (+ a (- x (* z (+ y -1.0))))
       (if (or (<= b 2.5e+55) (not (<= b 7.5e+120)))
         t_1
         (- (+ x a) (* t a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.06e+69) {
		tmp = t_1;
	} else if (b <= 0.0014) {
		tmp = a + (x - (z * (y + -1.0)));
	} else if ((b <= 2.5e+55) || !(b <= 7.5e+120)) {
		tmp = t_1;
	} else {
		tmp = (x + a) - (t * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-1.06d+69)) then
        tmp = t_1
    else if (b <= 0.0014d0) then
        tmp = a + (x - (z * (y + (-1.0d0))))
    else if ((b <= 2.5d+55) .or. (.not. (b <= 7.5d+120))) then
        tmp = t_1
    else
        tmp = (x + a) - (t * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.06e+69) {
		tmp = t_1;
	} else if (b <= 0.0014) {
		tmp = a + (x - (z * (y + -1.0)));
	} else if ((b <= 2.5e+55) || !(b <= 7.5e+120)) {
		tmp = t_1;
	} else {
		tmp = (x + a) - (t * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.06e+69:
		tmp = t_1
	elif b <= 0.0014:
		tmp = a + (x - (z * (y + -1.0)))
	elif (b <= 2.5e+55) or not (b <= 7.5e+120):
		tmp = t_1
	else:
		tmp = (x + a) - (t * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.06e+69)
		tmp = t_1;
	elseif (b <= 0.0014)
		tmp = Float64(a + Float64(x - Float64(z * Float64(y + -1.0))));
	elseif ((b <= 2.5e+55) || !(b <= 7.5e+120))
		tmp = t_1;
	else
		tmp = Float64(Float64(x + a) - Float64(t * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.06e+69)
		tmp = t_1;
	elseif (b <= 0.0014)
		tmp = a + (x - (z * (y + -1.0)));
	elseif ((b <= 2.5e+55) || ~((b <= 7.5e+120)))
		tmp = t_1;
	else
		tmp = (x + a) - (t * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.06e+69], t$95$1, If[LessEqual[b, 0.0014], N[(a + N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 2.5e+55], N[Not[LessEqual[b, 7.5e+120]], $MachinePrecision]], t$95$1, N[(N[(x + a), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.06000000000000004e69 or 0.00139999999999999999 < b < 2.50000000000000023e55 or 7.5000000000000006e120 < b

   1. Initial program 93.2%

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

   3. Taylor expanded in b around inf 78.7%

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

   if -1.06000000000000004e69 < b < 0.00139999999999999999

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0 99.3%

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

   4. Taylor expanded in b around 0 88.6%

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

      1. sub-neg 88.6%

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

      2. mul-1-neg 88.6%

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

      3. unsub-neg 88.6%

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

      4. sub-neg 88.6%

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

      5. metadata-eval 88.6%

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

      6. distribute-neg-in 88.6%

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

      7. neg-mul-1 88.6%

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

      8. remove-double-neg 88.6%

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

      9. distribute-rgt-neg-in 88.6%

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

      10. neg-sub0 88.6%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 88.6%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 88.6%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 88.6%

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

   6. Simplified 88.6%

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

   7. Taylor expanded in t around 0 69.2%

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

      1. +-commutative 69.2%

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

   9. Simplified 69.2%

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

   if 2.50000000000000023e55 < b < 7.5000000000000006e120

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in b around 0 71.5%

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

      1. sub-neg 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. sub-neg 71.5%

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

      5. metadata-eval 71.5%

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

      6. distribute-neg-in 71.5%

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

      7. neg-mul-1 71.5%

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

      8. remove-double-neg 71.5%

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

      9. distribute-rgt-neg-in 71.5%

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

      10. neg-sub0 71.5%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 71.5%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 71.5%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in z around 0 57.2%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 0.0014:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+55} \lor \neg \left(b \leq 7.5 \cdot 10^{+120}\right):\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-270}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 0.00042:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -3.6e-28)
     t_1
     (if (<= b -5.7e-270)
       (+ x z)
       (if (<= b 2.3e-216)
         (* a (- 1.0 t))
         (if (<= b 0.00042) (- x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.6e-28) {
		tmp = t_1;
	} else if (b <= -5.7e-270) {
		tmp = x + z;
	} else if (b <= 2.3e-216) {
		tmp = a * (1.0 - t);
	} else if (b <= 0.00042) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-3.6d-28)) then
        tmp = t_1
    else if (b <= (-5.7d-270)) then
        tmp = x + z
    else if (b <= 2.3d-216) then
        tmp = a * (1.0d0 - t)
    else if (b <= 0.00042d0) then
        tmp = x - (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.6e-28) {
		tmp = t_1;
	} else if (b <= -5.7e-270) {
		tmp = x + z;
	} else if (b <= 2.3e-216) {
		tmp = a * (1.0 - t);
	} else if (b <= 0.00042) {
		tmp = x - (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -3.6e-28:
		tmp = t_1
	elif b <= -5.7e-270:
		tmp = x + z
	elif b <= 2.3e-216:
		tmp = a * (1.0 - t)
	elif b <= 0.00042:
		tmp = x - (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -3.6e-28)
		tmp = t_1;
	elseif (b <= -5.7e-270)
		tmp = Float64(x + z);
	elseif (b <= 2.3e-216)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 0.00042)
		tmp = Float64(x - Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -3.6e-28)
		tmp = t_1;
	elseif (b <= -5.7e-270)
		tmp = x + z;
	elseif (b <= 2.3e-216)
		tmp = a * (1.0 - t);
	elseif (b <= 0.00042)
		tmp = x - (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.6e-28], t$95$1, If[LessEqual[b, -5.7e-270], N[(x + z), $MachinePrecision], If[LessEqual[b, 2.3e-216], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.00042], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.5999999999999999e-28 or 4.2000000000000002e-4 < b

   1. Initial program 93.8%

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

   3. Taylor expanded in b around inf 66.5%

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

   if -3.5999999999999999e-28 < b < -5.7000000000000002e-270

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0 71.1%

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

   4. Taylor expanded in y around 0 56.1%

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

      1. neg-mul-1 56.1%

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

      2. associate--l+ 56.1%

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

      3. sub-neg 56.1%

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

      4. metadata-eval 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in b around 0 52.9%

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

      1. +-commutative 52.9%

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

   9. Simplified 52.9%

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

   if -5.7000000000000002e-270 < b < 2.29999999999999997e-216

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 55.9%

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

   if 2.29999999999999997e-216 < b < 4.2000000000000002e-4

   1. Initial program 97.4%

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

   3. Taylor expanded in a around 0 79.1%

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

   4. Taylor expanded in b around 0 65.6%

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

   5. Taylor expanded in y around inf 54.0%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{-28}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{-270}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-216}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 0.00042:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \left(y + -1\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 0.007:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* z (+ y -1.0)))) (t_2 (* b (- (+ y t) 2.0))))
   (if (<= b -1.15e+59)
     t_2
     (if (<= b 7e-280)
       t_1
       (if (<= b 6.8e-217) (* a (- 1.0 t)) (if (<= b 0.007) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (y + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.15e+59) {
		tmp = t_2;
	} else if (b <= 7e-280) {
		tmp = t_1;
	} else if (b <= 6.8e-217) {
		tmp = a * (1.0 - t);
	} else if (b <= 0.007) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (z * (y + (-1.0d0)))
    t_2 = b * ((y + t) - 2.0d0)
    if (b <= (-1.15d+59)) then
        tmp = t_2
    else if (b <= 7d-280) then
        tmp = t_1
    else if (b <= 6.8d-217) then
        tmp = a * (1.0d0 - t)
    else if (b <= 0.007d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (z * (y + -1.0));
	double t_2 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.15e+59) {
		tmp = t_2;
	} else if (b <= 7e-280) {
		tmp = t_1;
	} else if (b <= 6.8e-217) {
		tmp = a * (1.0 - t);
	} else if (b <= 0.007) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z * (y + -1.0))
	t_2 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.15e+59:
		tmp = t_2
	elif b <= 7e-280:
		tmp = t_1
	elif b <= 6.8e-217:
		tmp = a * (1.0 - t)
	elif b <= 0.007:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(z * Float64(y + -1.0)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.15e+59)
		tmp = t_2;
	elseif (b <= 7e-280)
		tmp = t_1;
	elseif (b <= 6.8e-217)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 0.007)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (z * (y + -1.0));
	t_2 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.15e+59)
		tmp = t_2;
	elseif (b <= 7e-280)
		tmp = t_1;
	elseif (b <= 6.8e-217)
		tmp = a * (1.0 - t);
	elseif (b <= 0.007)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+59], t$95$2, If[LessEqual[b, 7e-280], t$95$1, If[LessEqual[b, 6.8e-217], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.007], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15000000000000004e59 or 0.00700000000000000015 < b

   1. Initial program 92.9%

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

   3. Taylor expanded in b around inf 69.7%

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

   if -1.15000000000000004e59 < b < 7.0000000000000002e-280 or 6.80000000000000032e-217 < b < 0.00700000000000000015

   1. Initial program 99.2%

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

   3. Taylor expanded in a around 0 73.6%

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

   4. Taylor expanded in b around 0 62.6%

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

   if 7.0000000000000002e-280 < b < 6.80000000000000032e-217

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 62.1%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-280}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 0.007:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 95.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+236}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(t \cdot \left(b - a\right) - b \cdot \left(2 - y\right)\right)\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.6e+236)
   (+ x (* b (- (+ y t) 2.0)))
   (+ (+ x (- (* t (- b a)) (* b (- 2.0 y)))) (- a (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.6e+236) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + ((t * (b - a)) - (b * (2.0 - y)))) + (a - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.6d+236)) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = (x + ((t * (b - a)) - (b * (2.0d0 - y)))) + (a - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.6e+236) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = (x + ((t * (b - a)) - (b * (2.0 - y)))) + (a - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.6e+236:
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = (x + ((t * (b - a)) - (b * (2.0 - y)))) + (a - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.6e+236)
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(Float64(x + Float64(Float64(t * Float64(b - a)) - Float64(b * Float64(2.0 - y)))) + Float64(a - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.6e+236)
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = (x + ((t * (b - a)) - (b * (2.0 - y)))) + (a - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.6e+236], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision] - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5999999999999998e236

   1. Initial program 91.7%

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

   3. Taylor expanded in a around 0 84.0%

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

   4. Taylor expanded in z around 0 92.3%

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

   if -6.5999999999999998e236 < b

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0 99.2%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+236}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(t \cdot \left(b - a\right) - b \cdot \left(2 - y\right)\right)\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.5e+82)
     t_1
     (if (<= t -7.5e-239)
       (+ x z)
       (if (<= t 9.5e-277)
         (* a (- 1.0 t))
         (if (<= t 2.25e+18) (+ x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.5e+82) {
		tmp = t_1;
	} else if (t <= -7.5e-239) {
		tmp = x + z;
	} else if (t <= 9.5e-277) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.25e+18) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2.5d+82)) then
        tmp = t_1
    else if (t <= (-7.5d-239)) then
        tmp = x + z
    else if (t <= 9.5d-277) then
        tmp = a * (1.0d0 - t)
    else if (t <= 2.25d+18) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2.5e+82) {
		tmp = t_1;
	} else if (t <= -7.5e-239) {
		tmp = x + z;
	} else if (t <= 9.5e-277) {
		tmp = a * (1.0 - t);
	} else if (t <= 2.25e+18) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.5e+82:
		tmp = t_1
	elif t <= -7.5e-239:
		tmp = x + z
	elif t <= 9.5e-277:
		tmp = a * (1.0 - t)
	elif t <= 2.25e+18:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.5e+82)
		tmp = t_1;
	elseif (t <= -7.5e-239)
		tmp = Float64(x + z);
	elseif (t <= 9.5e-277)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 2.25e+18)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.5e+82)
		tmp = t_1;
	elseif (t <= -7.5e-239)
		tmp = x + z;
	elseif (t <= 9.5e-277)
		tmp = a * (1.0 - t);
	elseif (t <= 2.25e+18)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+82], t$95$1, If[LessEqual[t, -7.5e-239], N[(x + z), $MachinePrecision], If[LessEqual[t, 9.5e-277], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+18], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.50000000000000008e82 or 2.25e18 < t

   1. Initial program 93.3%

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

   3. Taylor expanded in t around inf 70.2%

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

   if -2.50000000000000008e82 < t < -7.4999999999999999e-239 or 9.5e-277 < t < 2.25e18

   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. Add Preprocessing

   3. Taylor expanded in a around 0 85.9%

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

   4. Taylor expanded in y around 0 43.9%

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

      1. neg-mul-1 43.9%

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

      2. associate--l+ 43.9%

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

      3. sub-neg 43.9%

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

      4. metadata-eval 43.9%

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

   6. Simplified 43.9%

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

   7. Taylor expanded in b around 0 34.5%

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

      1. +-commutative 34.5%

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

   9. Simplified 34.5%

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

   if -7.4999999999999999e-239 < t < 9.5e-277

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 58.4%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+81} \lor \neg \left(a \leq 2.5 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.3e+81) (not (<= a 2.5e+111)))
   (+ (- x (* t a)) (- a (* z (+ y -1.0))))
   (+ (+ x (* b (- (+ y t) 2.0))) (* z (- 1.0 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.3e+81) || !(a <= 2.5e+111)) {
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.3d+81)) .or. (.not. (a <= 2.5d+111))) then
        tmp = (x - (t * a)) + (a - (z * (y + (-1.0d0))))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + (z * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.3e+81) || !(a <= 2.5e+111)) {
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.3e+81) or not (a <= 2.5e+111):
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.3e+81) || !(a <= 2.5e+111))
		tmp = Float64(Float64(x - Float64(t * a)) + Float64(a - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + Float64(z * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.3e+81) || ~((a <= 2.5e+111)))
		tmp = (x - (t * a)) + (a - (z * (y + -1.0)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + (z * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.3e+81], N[Not[LessEqual[a, 2.5e+111]], $MachinePrecision]], N[(N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(a - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2999999999999999e81 or 2.4999999999999998e111 < a

   1. Initial program 94.9%

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

   3. Taylor expanded in t around 0 97.9%

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

   4. Taylor expanded in b around 0 87.4%

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

      1. sub-neg 87.4%

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

      2. mul-1-neg 87.4%

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

      3. unsub-neg 87.4%

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

      4. sub-neg 87.4%

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

      5. metadata-eval 87.4%

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

      6. distribute-neg-in 87.4%

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

      7. neg-mul-1 87.4%

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

      8. remove-double-neg 87.4%

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

      9. distribute-rgt-neg-in 87.4%

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

      10. neg-sub0 87.4%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 87.4%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 87.4%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 87.4%

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

   6. Simplified 87.4%

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

   if -2.2999999999999999e81 < a < 2.4999999999999998e111

   1. Initial program 97.4%

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

   3. Taylor expanded in a around 0 94.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+81} \lor \neg \left(a \leq 2.5 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x - t \cdot a\right) + \left(a - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 36.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -30500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-276}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-277}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+55}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))))
   (if (<= y -30500000.0)
     t_1
     (if (<= y -4.6e-276)
       (+ x z)
       (if (<= y 4.6e-277) (* t b) (if (<= y 4.4e+55) (+ x z) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -30500000.0) {
		tmp = t_1;
	} else if (y <= -4.6e-276) {
		tmp = x + z;
	} else if (y <= 4.6e-277) {
		tmp = t * b;
	} else if (y <= 4.4e+55) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -z
    if (y <= (-30500000.0d0)) then
        tmp = t_1
    else if (y <= (-4.6d-276)) then
        tmp = x + z
    else if (y <= 4.6d-277) then
        tmp = t * b
    else if (y <= 4.4d+55) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double tmp;
	if (y <= -30500000.0) {
		tmp = t_1;
	} else if (y <= -4.6e-276) {
		tmp = x + z;
	} else if (y <= 4.6e-277) {
		tmp = t * b;
	} else if (y <= 4.4e+55) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	tmp = 0
	if y <= -30500000.0:
		tmp = t_1
	elif y <= -4.6e-276:
		tmp = x + z
	elif y <= 4.6e-277:
		tmp = t * b
	elif y <= 4.4e+55:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -30500000.0)
		tmp = t_1;
	elseif (y <= -4.6e-276)
		tmp = Float64(x + z);
	elseif (y <= 4.6e-277)
		tmp = Float64(t * b);
	elseif (y <= 4.4e+55)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	tmp = 0.0;
	if (y <= -30500000.0)
		tmp = t_1;
	elseif (y <= -4.6e-276)
		tmp = x + z;
	elseif (y <= 4.6e-277)
		tmp = t * b;
	elseif (y <= 4.4e+55)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -30500000.0], t$95$1, If[LessEqual[y, -4.6e-276], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.6e-277], N[(t * b), $MachinePrecision], If[LessEqual[y, 4.4e+55], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.05e7 or 4.40000000000000021e55 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf 71.3%

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

   4. Taylor expanded in b around 0 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-out 42.3%

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

   6. Simplified 42.3%

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

   if -3.05e7 < y < -4.59999999999999963e-276 or 4.6e-277 < y < 4.40000000000000021e55

   1. Initial program 99.2%

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

   3. Taylor expanded in a around 0 72.9%

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

   4. Taylor expanded in y around 0 67.5%

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

      1. neg-mul-1 67.5%

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

      2. associate--l+ 67.5%

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

      3. sub-neg 67.5%

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

      4. metadata-eval 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in b around 0 43.2%

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

      1. +-commutative 43.2%

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

   9. Simplified 43.2%

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

   if -4.59999999999999963e-276 < y < 4.6e-277

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 65.9%

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

   4. Taylor expanded in b around inf 48.4%

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

      1. *-commutative 48.4%

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

   6. Simplified 48.4%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30500000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-276}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-277}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+55}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 71.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -0.82:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-239}:\\ \;\;\;\;\left(a + \left(x + z\right)\right) - t \cdot a\\ \mathbf{elif}\;b \leq 0.0072:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= b -0.82)
     t_1
     (if (<= b 1.3e-239)
       (- (+ a (+ x z)) (* t a))
       (if (<= b 0.0072) (+ a (- x (* z (+ y -1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -0.82) {
		tmp = t_1;
	} else if (b <= 1.3e-239) {
		tmp = (a + (x + z)) - (t * a);
	} else if (b <= 0.0072) {
		tmp = a + (x - (z * (y + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((y + t) - 2.0d0))
    if (b <= (-0.82d0)) then
        tmp = t_1
    else if (b <= 1.3d-239) then
        tmp = (a + (x + z)) - (t * a)
    else if (b <= 0.0072d0) then
        tmp = a + (x - (z * (y + (-1.0d0))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (b <= -0.82) {
		tmp = t_1;
	} else if (b <= 1.3e-239) {
		tmp = (a + (x + z)) - (t * a);
	} else if (b <= 0.0072) {
		tmp = a + (x - (z * (y + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if b <= -0.82:
		tmp = t_1
	elif b <= 1.3e-239:
		tmp = (a + (x + z)) - (t * a)
	elif b <= 0.0072:
		tmp = a + (x - (z * (y + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (b <= -0.82)
		tmp = t_1;
	elseif (b <= 1.3e-239)
		tmp = Float64(Float64(a + Float64(x + z)) - Float64(t * a));
	elseif (b <= 0.0072)
		tmp = Float64(a + Float64(x - Float64(z * Float64(y + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (b <= -0.82)
		tmp = t_1;
	elseif (b <= 1.3e-239)
		tmp = (a + (x + z)) - (t * a);
	elseif (b <= 0.0072)
		tmp = a + (x - (z * (y + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.82], t$95$1, If[LessEqual[b, 1.3e-239], N[(N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0072], N[(a + N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.819999999999999951 or 0.0071999999999999998 < b

   1. Initial program 93.6%

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

   3. Taylor expanded in a around 0 85.2%

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

   4. Taylor expanded in z around 0 74.5%

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

   if -0.819999999999999951 < b < 1.30000000000000001e-239

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in b around 0 94.5%

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

      1. sub-neg 94.5%

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

      2. mul-1-neg 94.5%

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

      3. unsub-neg 94.5%

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

      4. sub-neg 94.5%

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

      5. metadata-eval 94.5%

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

      6. distribute-neg-in 94.5%

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

      7. neg-mul-1 94.5%

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

      8. remove-double-neg 94.5%

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

      9. distribute-rgt-neg-in 94.5%

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

      10. neg-sub0 94.5%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 94.5%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 94.5%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 94.5%

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

   6. Simplified 94.5%

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

   7. Taylor expanded in y around 0 79.5%

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

   if 1.30000000000000001e-239 < b < 0.0071999999999999998

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 97.8%

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

   4. Taylor expanded in b around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. mul-1-neg 84.3%

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

      3. unsub-neg 84.3%

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

      4. sub-neg 84.3%

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

      5. metadata-eval 84.3%

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

      6. distribute-neg-in 84.3%

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

      7. neg-mul-1 84.3%

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

      8. remove-double-neg 84.3%

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

      9. distribute-rgt-neg-in 84.3%

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

      10. neg-sub0 84.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 84.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 84.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in t around 0 75.0%

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

      1. +-commutative 75.0%

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

   9. Simplified 75.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.82:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-239}:\\ \;\;\;\;\left(a + \left(x + z\right)\right) - t \cdot a\\ \mathbf{elif}\;b \leq 0.0072:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 69.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -3.15 \cdot 10^{-46}:\\ \;\;\;\;t\_1 - y \cdot z\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-239}:\\ \;\;\;\;\left(a + \left(x + z\right)\right) - t \cdot a\\ \mathbf{elif}\;b \leq 0.0039:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -3.15e-46)
     (- t_1 (* y z))
     (if (<= b 5.5e-239)
       (- (+ a (+ x z)) (* t a))
       (if (<= b 0.0039) (+ a (- x (* z (+ y -1.0)))) (+ x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.15e-46) {
		tmp = t_1 - (y * z);
	} else if (b <= 5.5e-239) {
		tmp = (a + (x + z)) - (t * a);
	} else if (b <= 0.0039) {
		tmp = a + (x - (z * (y + -1.0)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-3.15d-46)) then
        tmp = t_1 - (y * z)
    else if (b <= 5.5d-239) then
        tmp = (a + (x + z)) - (t * a)
    else if (b <= 0.0039d0) then
        tmp = a + (x - (z * (y + (-1.0d0))))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -3.15e-46) {
		tmp = t_1 - (y * z);
	} else if (b <= 5.5e-239) {
		tmp = (a + (x + z)) - (t * a);
	} else if (b <= 0.0039) {
		tmp = a + (x - (z * (y + -1.0)));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -3.15e-46:
		tmp = t_1 - (y * z)
	elif b <= 5.5e-239:
		tmp = (a + (x + z)) - (t * a)
	elif b <= 0.0039:
		tmp = a + (x - (z * (y + -1.0)))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -3.15e-46)
		tmp = Float64(t_1 - Float64(y * z));
	elseif (b <= 5.5e-239)
		tmp = Float64(Float64(a + Float64(x + z)) - Float64(t * a));
	elseif (b <= 0.0039)
		tmp = Float64(a + Float64(x - Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -3.15e-46)
		tmp = t_1 - (y * z);
	elseif (b <= 5.5e-239)
		tmp = (a + (x + z)) - (t * a);
	elseif (b <= 0.0039)
		tmp = a + (x - (z * (y + -1.0)));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.15e-46], N[(t$95$1 - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-239], N[(N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0039], N[(a + N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.15e-46

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. distribute-rgt-neg-in 72.0%

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

   5. Simplified 72.0%

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

   if -3.15e-46 < b < 5.49999999999999978e-239

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

   4. Taylor expanded in b around 0 95.3%

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

      1. sub-neg 95.3%

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

      2. mul-1-neg 95.3%

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

      3. unsub-neg 95.3%

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

      4. sub-neg 95.3%

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

      5. metadata-eval 95.3%

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

      6. distribute-neg-in 95.3%

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

      7. neg-mul-1 95.3%

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

      8. remove-double-neg 95.3%

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

      9. distribute-rgt-neg-in 95.3%

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

      10. neg-sub0 95.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 95.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 95.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 95.3%

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

   6. Simplified 95.3%

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

   7. Taylor expanded in y around 0 82.8%

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

   if 5.49999999999999978e-239 < b < 0.0038999999999999998

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 97.8%

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

   4. Taylor expanded in b around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. mul-1-neg 84.3%

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

      3. unsub-neg 84.3%

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

      4. sub-neg 84.3%

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

      5. metadata-eval 84.3%

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

      6. distribute-neg-in 84.3%

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

      7. neg-mul-1 84.3%

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

      8. remove-double-neg 84.3%

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

      9. distribute-rgt-neg-in 84.3%

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

      10. neg-sub0 84.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 84.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 84.3%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in t around 0 75.0%

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

      1. +-commutative 75.0%

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

   9. Simplified 75.0%

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

   if 0.0038999999999999998 < b

   1. Initial program 92.2%

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

   3. Taylor expanded in a around 0 87.9%

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

   4. Taylor expanded in z around 0 75.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.15 \cdot 10^{-46}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right) - y \cdot z\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-239}:\\ \;\;\;\;\left(a + \left(x + z\right)\right) - t \cdot a\\ \mathbf{elif}\;b \leq 0.0039:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 71.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.36 \lor \neg \left(b \leq 0.0074\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -0.36) (not (<= b 0.0074)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ a (- x (* z (+ y -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.36) || !(b <= 0.0074)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = a + (x - (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-0.36d0)) .or. (.not. (b <= 0.0074d0))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = a + (x - (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -0.36) || !(b <= 0.0074)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = a + (x - (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -0.36) or not (b <= 0.0074):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = a + (x - (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -0.36) || !(b <= 0.0074))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(a + Float64(x - Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -0.36) || ~((b <= 0.0074)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = a + (x - (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -0.36], N[Not[LessEqual[b, 0.0074]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(x - N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.35999999999999999 or 0.0074000000000000003 < b

   1. Initial program 93.6%

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

   3. Taylor expanded in a around 0 85.2%

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

   4. Taylor expanded in z around 0 74.5%

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

   if -0.35999999999999999 < b < 0.0074000000000000003

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0 99.2%

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

   4. Taylor expanded in b around 0 90.9%

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

      1. sub-neg 90.9%

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

      2. mul-1-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. sub-neg 90.9%

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

      5. metadata-eval 90.9%

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

      6. distribute-neg-in 90.9%

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

      7. neg-mul-1 90.9%

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

      8. remove-double-neg 90.9%

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

      9. distribute-rgt-neg-in 90.9%

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

      10. neg-sub0 90.9%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 90.9%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 90.9%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in t around 0 71.1%

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

      1. +-commutative 71.1%

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

   9. Simplified 71.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.36 \lor \neg \left(b \leq 0.0074\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x - z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+127}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-210}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.1e+127)
   (* t b)
   (if (<= t -3.1e-210) z (if (<= t 3.3e-16) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.1e+127) {
		tmp = t * b;
	} else if (t <= -3.1e-210) {
		tmp = z;
	} else if (t <= 3.3e-16) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.1d+127)) then
        tmp = t * b
    else if (t <= (-3.1d-210)) then
        tmp = z
    else if (t <= 3.3d-16) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.1e+127) {
		tmp = t * b;
	} else if (t <= -3.1e-210) {
		tmp = z;
	} else if (t <= 3.3e-16) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.1e+127:
		tmp = t * b
	elif t <= -3.1e-210:
		tmp = z
	elif t <= 3.3e-16:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.1e+127)
		tmp = Float64(t * b);
	elseif (t <= -3.1e-210)
		tmp = z;
	elseif (t <= 3.3e-16)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.1e+127)
		tmp = t * b;
	elseif (t <= -3.1e-210)
		tmp = z;
	elseif (t <= 3.3e-16)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.1e+127], N[(t * b), $MachinePrecision], If[LessEqual[t, -3.1e-210], z, If[LessEqual[t, 3.3e-16], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.10000000000000046e127 or 3.29999999999999988e-16 < t

   1. Initial program 93.1%

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

   3. Taylor expanded in t around inf 68.6%

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

   4. Taylor expanded in b around inf 37.5%

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

      1. *-commutative 37.5%

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

   6. Simplified 37.5%

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

   if -6.10000000000000046e127 < t < -3.09999999999999987e-210

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0 82.3%

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

   4. Taylor expanded in y around 0 41.6%

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

      1. neg-mul-1 41.6%

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

      2. associate--l+ 41.6%

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

      3. sub-neg 41.6%

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

      4. metadata-eval 41.6%

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

   6. Simplified 41.6%

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

   7. Taylor expanded in z around inf 20.6%

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

   if -3.09999999999999987e-210 < t < 3.29999999999999988e-16

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 25.2%

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

4. Final simplification 28.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+127}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-210}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 32.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+127} \lor \neg \left(t \leq 3.5 \cdot 10^{+211}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9e+127) (not (<= t 3.5e+211))) (* t b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+127) || !(t <= 3.5e+211)) {
		tmp = t * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-9d+127)) .or. (.not. (t <= 3.5d+211))) then
        tmp = t * b
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9e+127) || !(t <= 3.5e+211)) {
		tmp = t * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9e+127) or not (t <= 3.5e+211):
		tmp = t * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9e+127) || !(t <= 3.5e+211))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9e+127) || ~((t <= 3.5e+211)))
		tmp = t * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9e+127], N[Not[LessEqual[t, 3.5e+211]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000068e127 or 3.49999999999999996e211 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf 80.8%

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

   4. Taylor expanded in b around inf 47.0%

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

      1. *-commutative 47.0%

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

   6. Simplified 47.0%

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

   if -9.00000000000000068e127 < t < 3.49999999999999996e211

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0 79.6%

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

   4. Taylor expanded in y around 0 42.9%

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

      1. neg-mul-1 42.9%

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

      2. associate--l+ 42.9%

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

      3. sub-neg 42.9%

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

      4. metadata-eval 42.9%

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

   6. Simplified 42.9%

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

   7. Taylor expanded in b around 0 31.5%

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

      1. +-commutative 31.5%

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

   9. Simplified 31.5%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+127} \lor \neg \left(t \leq 3.5 \cdot 10^{+211}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 32.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+211}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.22e+86) (* a (- t)) (if (<= t 3.5e+211) (+ x z) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.22e+86) {
		tmp = a * -t;
	} else if (t <= 3.5e+211) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.22d+86)) then
        tmp = a * -t
    else if (t <= 3.5d+211) then
        tmp = x + z
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.22e+86) {
		tmp = a * -t;
	} else if (t <= 3.5e+211) {
		tmp = x + z;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.22e+86:
		tmp = a * -t
	elif t <= 3.5e+211:
		tmp = x + z
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.22e+86)
		tmp = Float64(a * Float64(-t));
	elseif (t <= 3.5e+211)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.22e+86)
		tmp = a * -t;
	elseif (t <= 3.5e+211)
		tmp = x + z;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.22e+86], N[(a * (-t)), $MachinePrecision], If[LessEqual[t, 3.5e+211], N[(x + z), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.21999999999999996e86

   1. Initial program 93.8%

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

   3. Taylor expanded in t around 0 97.9%

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

   4. Taylor expanded in b around 0 64.8%

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

      1. sub-neg 64.8%

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

      2. mul-1-neg 64.8%

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

      3. unsub-neg 64.8%

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

      4. sub-neg 64.8%

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

      5. metadata-eval 64.8%

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

      6. distribute-neg-in 64.8%

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

      7. neg-mul-1 64.8%

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

      8. remove-double-neg 64.8%

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

      9. distribute-rgt-neg-in 64.8%

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

      10. neg-sub0 64.8%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)}\right) \]

      11. +-commutative 64.8%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \left(0 - \color{blue}{\left(-1 + y\right)}\right)\right) \]

      12. associate--r+ 64.8%

          \[\leadsto \left(x - a \cdot t\right) + \left(a + z \cdot \color{blue}{\left(\left(0 - -1\right) - y\right)}\right) \]

      13. metadata-eval 64.8%

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

   6. Simplified 64.8%

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

   7. Taylor expanded in t around inf 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-rgt-neg-out 45.4%

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

   9. Simplified 45.4%

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

   if -1.21999999999999996e86 < t < 3.49999999999999996e211

   1. Initial program 98.4%

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

   3. Taylor expanded in a around 0 80.6%

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

   4. Taylor expanded in y around 0 43.4%

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

      1. neg-mul-1 43.4%

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

      2. associate--l+ 43.4%

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

      3. sub-neg 43.4%

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

      4. metadata-eval 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in b around 0 31.7%

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

      1. +-commutative 31.7%

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

   9. Simplified 31.7%

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

   if 3.49999999999999996e211 < t

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf 80.1%

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

   4. Taylor expanded in b around inf 60.3%

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

      1. *-commutative 60.3%

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

   6. Simplified 60.3%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+211}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 20.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 13000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.6e+83) x (if (<= x 13000000000.0) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.6e+83) {
		tmp = x;
	} else if (x <= 13000000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8.6d+83)) then
        tmp = x
    else if (x <= 13000000000.0d0) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.6e+83) {
		tmp = x;
	} else if (x <= 13000000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8.6e+83:
		tmp = x
	elif x <= 13000000000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.6e+83)
		tmp = x;
	elseif (x <= 13000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8.6e+83)
		tmp = x;
	elseif (x <= 13000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.6e+83], x, If[LessEqual[x, 13000000000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.6e83 or 1.3e10 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 38.8%

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

   if -8.6e83 < x < 1.3e10

   1. Initial program 95.3%

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

   3. Taylor expanded in a around 0 70.8%

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

   4. Taylor expanded in y around 0 37.3%

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

      1. neg-mul-1 37.3%

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

      2. associate--l+ 37.3%

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

      3. sub-neg 37.3%

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

      4. metadata-eval 37.3%

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

   6. Simplified 37.3%

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

   7. Taylor expanded in z around inf 15.2%

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

4. Final simplification 25.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 13000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 15.6% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in x around inf 17.5%

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

4. Final simplification 17.5%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(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)))