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

Percentage Accurate: 95.3% → 97.9%

Time: 17.9s

Alternatives: 22

Speedup: 0.5×

• 36.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-define 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-+l- 100.0%

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

      8. fma-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. remove-double-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   6. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 87.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(y + t\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(x - \mathsf{fma}\left(z, y + -1, a \cdot \left(t + -1\right)\right)\right) + \left(y + \left(t + -2\right)\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
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 96.8%

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

   1. +-commutative 96.8%

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

   2. fma-define 98.8%

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

   3. associate--l+ 98.8%

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

   4. sub-neg 98.8%

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

   5. metadata-eval 98.8%

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

   6. sub-neg 98.8%

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

   7. associate-+l- 98.8%

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

   8. fma-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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

   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 87.5%

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

4. Final simplification 99.6%

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

Alternative 4: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := a + \left(x + z\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.7 \cdot 10^{+47}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4600000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (+ a (+ x z))) (t_3 (* t (- b a))))
   (if (<= t -6.7e+47)
     t_3
     (if (<= t -4600000000.0)
       t_1
       (if (<= t -4.5e-209)
         t_2
         (if (<= t -1.92e-268)
           t_1
           (if (<= t 8e-39)
             t_2
             (if (<= t 4.2e-10) t_1 (if (<= t 3.2e+31) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = a + (x + z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -6.7e+47) {
		tmp = t_3;
	} else if (t <= -4600000000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-209) {
		tmp = t_2;
	} else if (t <= -1.92e-268) {
		tmp = t_1;
	} else if (t <= 8e-39) {
		tmp = t_2;
	} else if (t <= 4.2e-10) {
		tmp = t_1;
	} else if (t <= 3.2e+31) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = a + (x + z)
    t_3 = t * (b - a)
    if (t <= (-6.7d+47)) then
        tmp = t_3
    else if (t <= (-4600000000.0d0)) then
        tmp = t_1
    else if (t <= (-4.5d-209)) then
        tmp = t_2
    else if (t <= (-1.92d-268)) then
        tmp = t_1
    else if (t <= 8d-39) then
        tmp = t_2
    else if (t <= 4.2d-10) then
        tmp = t_1
    else if (t <= 3.2d+31) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = a + (x + z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -6.7e+47) {
		tmp = t_3;
	} else if (t <= -4600000000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-209) {
		tmp = t_2;
	} else if (t <= -1.92e-268) {
		tmp = t_1;
	} else if (t <= 8e-39) {
		tmp = t_2;
	} else if (t <= 4.2e-10) {
		tmp = t_1;
	} else if (t <= 3.2e+31) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = a + (x + z)
	t_3 = t * (b - a)
	tmp = 0
	if t <= -6.7e+47:
		tmp = t_3
	elif t <= -4600000000.0:
		tmp = t_1
	elif t <= -4.5e-209:
		tmp = t_2
	elif t <= -1.92e-268:
		tmp = t_1
	elif t <= 8e-39:
		tmp = t_2
	elif t <= 4.2e-10:
		tmp = t_1
	elif t <= 3.2e+31:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(a + Float64(x + z))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.7e+47)
		tmp = t_3;
	elseif (t <= -4600000000.0)
		tmp = t_1;
	elseif (t <= -4.5e-209)
		tmp = t_2;
	elseif (t <= -1.92e-268)
		tmp = t_1;
	elseif (t <= 8e-39)
		tmp = t_2;
	elseif (t <= 4.2e-10)
		tmp = t_1;
	elseif (t <= 3.2e+31)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = a + (x + z);
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.7e+47)
		tmp = t_3;
	elseif (t <= -4600000000.0)
		tmp = t_1;
	elseif (t <= -4.5e-209)
		tmp = t_2;
	elseif (t <= -1.92e-268)
		tmp = t_1;
	elseif (t <= 8e-39)
		tmp = t_2;
	elseif (t <= 4.2e-10)
		tmp = t_1;
	elseif (t <= 3.2e+31)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.7e+47], t$95$3, If[LessEqual[t, -4600000000.0], t$95$1, If[LessEqual[t, -4.5e-209], t$95$2, If[LessEqual[t, -1.92e-268], t$95$1, If[LessEqual[t, 8e-39], t$95$2, If[LessEqual[t, 4.2e-10], t$95$1, If[LessEqual[t, 3.2e+31], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.69999999999999973e47 or 3.2000000000000001e31 < t

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 70.9%

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

   if -6.69999999999999973e47 < t < -4.6e9 or -4.4999999999999998e-209 < t < -1.92000000000000008e-268 or 7.99999999999999943e-39 < t < 4.2e-10

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 71.1%

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

   if -4.6e9 < t < -4.4999999999999998e-209 or -1.92000000000000008e-268 < t < 7.99999999999999943e-39 or 4.2e-10 < t < 3.2000000000000001e31

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 75.3%

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

   4. Taylor expanded in t around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. sub-neg 73.7%

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

      3. metadata-eval 73.7%

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

      4. neg-mul-1 73.7%

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

      5. fma-undefine 73.7%

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

   6. Simplified 73.7%

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

   7. Taylor expanded in y around 0 58.2%

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

      1. associate--l+ 58.2%

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

      2. cancel-sign-sub-inv 58.2%

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

      3. metadata-eval 58.2%

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

      4. *-lft-identity 58.2%

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

   9. Simplified 58.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.7 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4600000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-209}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-39}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+31}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 235:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (* z (- 1.0 y))))
        (t_2 (* b (- (+ y t) 2.0)))
        (t_3 (+ x (* a (- 1.0 t)))))
   (if (<= b -6.2e+60)
     t_2
     (if (<= b -3.2e+20)
       t_1
       (if (<= b -3.2e-12)
         t_3
         (if (<= b -4e-84)
           t_1
           (if (<= b 235.0) t_3 (if (<= b 1.55e+126) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -6.2e+60) {
		tmp = t_2;
	} else if (b <= -3.2e+20) {
		tmp = t_1;
	} else if (b <= -3.2e-12) {
		tmp = t_3;
	} else if (b <= -4e-84) {
		tmp = t_1;
	} else if (b <= 235.0) {
		tmp = t_3;
	} else if (b <= 1.55e+126) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a + (z * (1.0d0 - y))
    t_2 = b * ((y + t) - 2.0d0)
    t_3 = x + (a * (1.0d0 - t))
    if (b <= (-6.2d+60)) then
        tmp = t_2
    else if (b <= (-3.2d+20)) then
        tmp = t_1
    else if (b <= (-3.2d-12)) then
        tmp = t_3
    else if (b <= (-4d-84)) then
        tmp = t_1
    else if (b <= 235.0d0) then
        tmp = t_3
    else if (b <= 1.55d+126) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z * (1.0 - y));
	double t_2 = b * ((y + t) - 2.0);
	double t_3 = x + (a * (1.0 - t));
	double tmp;
	if (b <= -6.2e+60) {
		tmp = t_2;
	} else if (b <= -3.2e+20) {
		tmp = t_1;
	} else if (b <= -3.2e-12) {
		tmp = t_3;
	} else if (b <= -4e-84) {
		tmp = t_1;
	} else if (b <= 235.0) {
		tmp = t_3;
	} else if (b <= 1.55e+126) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z * (1.0 - y))
	t_2 = b * ((y + t) - 2.0)
	t_3 = x + (a * (1.0 - t))
	tmp = 0
	if b <= -6.2e+60:
		tmp = t_2
	elif b <= -3.2e+20:
		tmp = t_1
	elif b <= -3.2e-12:
		tmp = t_3
	elif b <= -4e-84:
		tmp = t_1
	elif b <= 235.0:
		tmp = t_3
	elif b <= 1.55e+126:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(y + t) - 2.0))
	t_3 = Float64(x + Float64(a * Float64(1.0 - t)))
	tmp = 0.0
	if (b <= -6.2e+60)
		tmp = t_2;
	elseif (b <= -3.2e+20)
		tmp = t_1;
	elseif (b <= -3.2e-12)
		tmp = t_3;
	elseif (b <= -4e-84)
		tmp = t_1;
	elseif (b <= 235.0)
		tmp = t_3;
	elseif (b <= 1.55e+126)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z * (1.0 - y));
	t_2 = b * ((y + t) - 2.0);
	t_3 = x + (a * (1.0 - t));
	tmp = 0.0;
	if (b <= -6.2e+60)
		tmp = t_2;
	elseif (b <= -3.2e+20)
		tmp = t_1;
	elseif (b <= -3.2e-12)
		tmp = t_3;
	elseif (b <= -4e-84)
		tmp = t_1;
	elseif (b <= 235.0)
		tmp = t_3;
	elseif (b <= 1.55e+126)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+60], t$95$2, If[LessEqual[b, -3.2e+20], t$95$1, If[LessEqual[b, -3.2e-12], t$95$3, If[LessEqual[b, -4e-84], t$95$1, If[LessEqual[b, 235.0], t$95$3, If[LessEqual[b, 1.55e+126], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.2000000000000001e60 or 1.55e126 < b

   1. Initial program 92.0%

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

   3. Taylor expanded in b around inf 83.0%

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

   if -6.2000000000000001e60 < b < -3.2e20 or -3.2000000000000001e-12 < b < -4.0000000000000001e-84 or 235 < b < 1.55e126

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0 87.1%

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

   4. Taylor expanded in t around 0 75.1%

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

      1. +-commutative 75.1%

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

      2. sub-neg 75.1%

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

      3. metadata-eval 75.1%

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

      4. neg-mul-1 75.1%

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

      5. fma-undefine 75.1%

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

   6. Simplified 75.1%

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

   7. Taylor expanded in x around 0 63.8%

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

   if -3.2e20 < b < -3.2000000000000001e-12 or -4.0000000000000001e-84 < b < 235

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0 89.5%

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

   4. Taylor expanded in z around 0 64.4%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{+20}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-84}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 235:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+126}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := a + \left(x + z\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-265}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (+ a (+ x z))))
   (if (<= t -1.5e+54)
     t_1
     (if (<= t -6.5e-265)
       (+ a (* z (- 1.0 y)))
       (if (<= t 5.2e-39)
         t_2
         (if (<= t 2.95e-8) (* y (- b z)) (if (<= t 6e+32) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = a + (x + z);
	double tmp;
	if (t <= -1.5e+54) {
		tmp = t_1;
	} else if (t <= -6.5e-265) {
		tmp = a + (z * (1.0 - y));
	} else if (t <= 5.2e-39) {
		tmp = t_2;
	} else if (t <= 2.95e-8) {
		tmp = y * (b - z);
	} else if (t <= 6e+32) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = a + (x + z)
    if (t <= (-1.5d+54)) then
        tmp = t_1
    else if (t <= (-6.5d-265)) then
        tmp = a + (z * (1.0d0 - y))
    else if (t <= 5.2d-39) then
        tmp = t_2
    else if (t <= 2.95d-8) then
        tmp = y * (b - z)
    else if (t <= 6d+32) then
        tmp = t_2
    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 t_2 = a + (x + z);
	double tmp;
	if (t <= -1.5e+54) {
		tmp = t_1;
	} else if (t <= -6.5e-265) {
		tmp = a + (z * (1.0 - y));
	} else if (t <= 5.2e-39) {
		tmp = t_2;
	} else if (t <= 2.95e-8) {
		tmp = y * (b - z);
	} else if (t <= 6e+32) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = a + (x + z)
	tmp = 0
	if t <= -1.5e+54:
		tmp = t_1
	elif t <= -6.5e-265:
		tmp = a + (z * (1.0 - y))
	elif t <= 5.2e-39:
		tmp = t_2
	elif t <= 2.95e-8:
		tmp = y * (b - z)
	elif t <= 6e+32:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(a + Float64(x + z))
	tmp = 0.0
	if (t <= -1.5e+54)
		tmp = t_1;
	elseif (t <= -6.5e-265)
		tmp = Float64(a + Float64(z * Float64(1.0 - y)));
	elseif (t <= 5.2e-39)
		tmp = t_2;
	elseif (t <= 2.95e-8)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 6e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = a + (x + z);
	tmp = 0.0;
	if (t <= -1.5e+54)
		tmp = t_1;
	elseif (t <= -6.5e-265)
		tmp = a + (z * (1.0 - y));
	elseif (t <= 5.2e-39)
		tmp = t_2;
	elseif (t <= 2.95e-8)
		tmp = y * (b - z);
	elseif (t <= 6e+32)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+54], t$95$1, If[LessEqual[t, -6.5e-265], N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-39], t$95$2, If[LessEqual[t, 2.95e-8], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+32], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4999999999999999e54 or 6e32 < 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 71.2%

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

   if -1.4999999999999999e54 < t < -6.5000000000000005e-265

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 71.5%

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

   4. Taylor expanded in t around 0 69.7%

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

      1. +-commutative 69.7%

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

      2. sub-neg 69.7%

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

      3. metadata-eval 69.7%

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

      4. neg-mul-1 69.7%

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

      5. fma-undefine 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in x around 0 55.5%

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

   if -6.5000000000000005e-265 < t < 5.2e-39 or 2.9499999999999999e-8 < t < 6e32

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 75.2%

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

   4. Taylor expanded in t around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. sub-neg 72.9%

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

      3. metadata-eval 72.9%

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

      4. neg-mul-1 72.9%

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

      5. fma-undefine 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in y around 0 62.1%

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

      1. associate--l+ 62.1%

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

      2. cancel-sign-sub-inv 62.1%

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

      3. metadata-eval 62.1%

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

      4. *-lft-identity 62.1%

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

   9. Simplified 62.1%

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

   if 5.2e-39 < t < 2.9499999999999999e-8

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 81.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-265}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-39}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+32}:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-38}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 12600000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.4e+14)
     t_1
     (if (<= t 3.7e-38)
       (+ x a)
       (if (<= t 1.32e-11) (* y (- z)) (if (<= t 12600000.0) (+ x a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.4e+14) {
		tmp = t_1;
	} else if (t <= 3.7e-38) {
		tmp = x + a;
	} else if (t <= 1.32e-11) {
		tmp = y * -z;
	} else if (t <= 12600000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-4.4d+14)) then
        tmp = t_1
    else if (t <= 3.7d-38) then
        tmp = x + a
    else if (t <= 1.32d-11) then
        tmp = y * -z
    else if (t <= 12600000.0d0) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.4e+14) {
		tmp = t_1;
	} else if (t <= 3.7e-38) {
		tmp = x + a;
	} else if (t <= 1.32e-11) {
		tmp = y * -z;
	} else if (t <= 12600000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -4.4e+14:
		tmp = t_1
	elif t <= 3.7e-38:
		tmp = x + a
	elif t <= 1.32e-11:
		tmp = y * -z
	elif t <= 12600000.0:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.4e+14)
		tmp = t_1;
	elseif (t <= 3.7e-38)
		tmp = Float64(x + a);
	elseif (t <= 1.32e-11)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 12600000.0)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -4.4e+14)
		tmp = t_1;
	elseif (t <= 3.7e-38)
		tmp = x + a;
	elseif (t <= 1.32e-11)
		tmp = y * -z;
	elseif (t <= 12600000.0)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.4e+14], t$95$1, If[LessEqual[t, 3.7e-38], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.32e-11], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 12600000.0], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4e14 or 1.26e7 < t

   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 inf 67.4%

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

   if -4.4e14 < t < 3.7e-38 or 1.32e-11 < t < 1.26e7

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 73.1%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. sub-neg 72.5%

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

      3. metadata-eval 72.5%

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

      4. neg-mul-1 72.5%

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

      5. fma-undefine 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in z around 0 39.5%

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

   if 3.7e-38 < t < 1.32e-11

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 77.9%

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

   4. Taylor expanded in b around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-rgt-neg-in 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-38}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 12600000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-39}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 76000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -7.6e+46)
     t_2
     (if (<= t -9e-269)
       t_1
       (if (<= t 7.5e-39) (+ x a) (if (<= t 76000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.6e+46) {
		tmp = t_2;
	} else if (t <= -9e-269) {
		tmp = t_1;
	} else if (t <= 7.5e-39) {
		tmp = x + a;
	} else if (t <= 76000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-7.6d+46)) then
        tmp = t_2
    else if (t <= (-9d-269)) then
        tmp = t_1
    else if (t <= 7.5d-39) then
        tmp = x + a
    else if (t <= 76000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.6e+46) {
		tmp = t_2;
	} else if (t <= -9e-269) {
		tmp = t_1;
	} else if (t <= 7.5e-39) {
		tmp = x + a;
	} else if (t <= 76000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.6e+46:
		tmp = t_2
	elif t <= -9e-269:
		tmp = t_1
	elif t <= 7.5e-39:
		tmp = x + a
	elif t <= 76000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.6e+46)
		tmp = t_2;
	elseif (t <= -9e-269)
		tmp = t_1;
	elseif (t <= 7.5e-39)
		tmp = Float64(x + a);
	elseif (t <= 76000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.6e+46)
		tmp = t_2;
	elseif (t <= -9e-269)
		tmp = t_1;
	elseif (t <= 7.5e-39)
		tmp = x + a;
	elseif (t <= 76000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e+46], t$95$2, If[LessEqual[t, -9e-269], t$95$1, If[LessEqual[t, 7.5e-39], N[(x + a), $MachinePrecision], If[LessEqual[t, 76000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.5999999999999998e46 or 7.6e7 < t

   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 t around inf 69.5%

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

   if -7.5999999999999998e46 < t < -9.0000000000000003e-269 or 7.49999999999999971e-39 < t < 7.6e7

   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 48.4%

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

   if -9.0000000000000003e-269 < t < 7.49999999999999971e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 75.2%

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

   4. Taylor expanded in t around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. sub-neg 75.2%

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

      3. metadata-eval 75.2%

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

      4. neg-mul-1 75.2%

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

      5. fma-undefine 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in z around 0 47.5%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-39}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 76000000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;a \leq -1.42 \cdot 10^{-78} \lor \neg \left(a \leq 7.5 \cdot 10^{+159}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (or (<= a -1.42e-78) (not (<= a 7.5e+159)))
     (+ x (+ (* a (- 1.0 t)) t_1))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((a <= -1.42e-78) || !(a <= 7.5e+159)) {
		tmp = x + ((a * (1.0 - t)) + t_1);
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if ((a <= (-1.42d-78)) .or. (.not. (a <= 7.5d+159))) then
        tmp = x + ((a * (1.0d0 - t)) + t_1)
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if ((a <= -1.42e-78) || !(a <= 7.5e+159)) {
		tmp = x + ((a * (1.0 - t)) + t_1);
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if (a <= -1.42e-78) or not (a <= 7.5e+159):
		tmp = x + ((a * (1.0 - t)) + t_1)
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((a <= -1.42e-78) || !(a <= 7.5e+159))
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if ((a <= -1.42e-78) || ~((a <= 7.5e+159)))
		tmp = x + ((a * (1.0 - t)) + t_1);
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.42e-78], N[Not[LessEqual[a, 7.5e+159]], $MachinePrecision]], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.41999999999999999e-78 or 7.4999999999999997e159 < a

   1. Initial program 94.0%

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

   3. Taylor expanded in b around 0 85.9%

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

   if -1.41999999999999999e-78 < a < 7.4999999999999997e159

   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 96.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-78} \lor \neg \left(a \leq 7.5 \cdot 10^{+159}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-38}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -6.5e+38)
     t_1
     (if (<= t 3.9e-38)
       (+ x a)
       (if (<= t 3.3e-11) (* y (- z)) (if (<= t 1.55e+38) (+ x a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -6.5e+38) {
		tmp = t_1;
	} else if (t <= 3.9e-38) {
		tmp = x + a;
	} else if (t <= 3.3e-11) {
		tmp = y * -z;
	} else if (t <= 1.55e+38) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-6.5d+38)) then
        tmp = t_1
    else if (t <= 3.9d-38) then
        tmp = x + a
    else if (t <= 3.3d-11) then
        tmp = y * -z
    else if (t <= 1.55d+38) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -6.5e+38) {
		tmp = t_1;
	} else if (t <= 3.9e-38) {
		tmp = x + a;
	} else if (t <= 3.3e-11) {
		tmp = y * -z;
	} else if (t <= 1.55e+38) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -6.5e+38:
		tmp = t_1
	elif t <= 3.9e-38:
		tmp = x + a
	elif t <= 3.3e-11:
		tmp = y * -z
	elif t <= 1.55e+38:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -6.5e+38)
		tmp = t_1;
	elseif (t <= 3.9e-38)
		tmp = Float64(x + a);
	elseif (t <= 3.3e-11)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 1.55e+38)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -6.5e+38)
		tmp = t_1;
	elseif (t <= 3.9e-38)
		tmp = x + a;
	elseif (t <= 3.3e-11)
		tmp = y * -z;
	elseif (t <= 1.55e+38)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -6.5e+38], t$95$1, If[LessEqual[t, 3.9e-38], N[(x + a), $MachinePrecision], If[LessEqual[t, 3.3e-11], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 1.55e+38], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5e38 or 1.55000000000000009e38 < t

   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 0 70.8%

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

   4. Taylor expanded in t around inf 48.4%

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

      1. associate-*r* 48.4%

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

      2. neg-mul-1 48.4%

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

   6. Simplified 48.4%

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

   if -6.5e38 < t < 3.8999999999999999e-38 or 3.3000000000000002e-11 < t < 1.55000000000000009e38

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 73.1%

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

   4. Taylor expanded in t around 0 71.7%

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

      1. +-commutative 71.7%

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

      2. sub-neg 71.7%

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

      3. metadata-eval 71.7%

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

      4. neg-mul-1 71.7%

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

      5. fma-undefine 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in z around 0 38.2%

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

   if 3.8999999999999999e-38 < t < 3.3000000000000002e-11

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 77.9%

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

   4. Taylor expanded in b around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-rgt-neg-in 78.2%

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

   6. Simplified 78.2%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-38}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;b \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 250:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 10^{+124}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ y t) 2.0))))
   (if (<= b -1.35e+45)
     t_1
     (if (<= b 250.0)
       (+ x (+ z (* a (- 1.0 t))))
       (if (<= b 1e+124) (+ x (+ a (* z (- 1.0 y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.35e+45) {
		tmp = t_1;
	} else if (b <= 250.0) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (b <= 1e+124) {
		tmp = x + (a + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((y + t) - 2.0d0)
    if (b <= (-1.35d+45)) then
        tmp = t_1
    else if (b <= 250.0d0) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else if (b <= 1d+124) then
        tmp = x + (a + (z * (1.0d0 - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((y + t) - 2.0);
	double tmp;
	if (b <= -1.35e+45) {
		tmp = t_1;
	} else if (b <= 250.0) {
		tmp = x + (z + (a * (1.0 - t)));
	} else if (b <= 1e+124) {
		tmp = x + (a + (z * (1.0 - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((y + t) - 2.0)
	tmp = 0
	if b <= -1.35e+45:
		tmp = t_1
	elif b <= 250.0:
		tmp = x + (z + (a * (1.0 - t)))
	elif b <= 1e+124:
		tmp = x + (a + (z * (1.0 - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(y + t) - 2.0))
	tmp = 0.0
	if (b <= -1.35e+45)
		tmp = t_1;
	elseif (b <= 250.0)
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	elseif (b <= 1e+124)
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((y + t) - 2.0);
	tmp = 0.0;
	if (b <= -1.35e+45)
		tmp = t_1;
	elseif (b <= 250.0)
		tmp = x + (z + (a * (1.0 - t)));
	elseif (b <= 1e+124)
		tmp = x + (a + (z * (1.0 - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.35e+45], t$95$1, If[LessEqual[b, 250.0], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+124], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.34999999999999992e45 or 9.99999999999999948e123 < b

   1. Initial program 92.4%

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

   3. Taylor expanded in b around inf 81.6%

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

   if -1.34999999999999992e45 < b < 250

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 90.6%

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

   4. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

   6. Simplified 71.2%

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

   if 250 < b < 9.99999999999999948e123

   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 b around 0 79.0%

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

   4. Taylor expanded in t around 0 74.7%

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

      1. sub-neg 74.7%

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

      2. sub-neg 74.7%

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

      3. metadata-eval 74.7%

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

      4. distribute-neg-in 74.7%

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

      5. neg-mul-1 74.7%

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

      6. remove-double-neg 74.7%

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

      7. distribute-rgt-in 74.7%

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

      8. +-commutative 74.7%

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

      9. distribute-neg-in 74.7%

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

      10. distribute-lft-neg-in 74.7%

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

      11. metadata-eval 74.7%

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

      12. mul-1-neg 74.7%

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

      13. associate-*r* 74.7%

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

      14. distribute-rgt-in 74.7%

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

      15. neg-mul-1 74.7%

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

      16. sub-neg 74.7%

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

   6. Simplified 74.7%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq 250:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 10^{+124}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+33} \lor \neg \left(a \leq 5.5 \cdot 10^{+135}\right):\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -2.3e+33) (not (<= a 5.5e+135)))
   (+ x (+ z (* a (- 1.0 t))))
   (+ (* (+ y (+ t -2.0)) b) (- x (* y z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.3e+33) || !(a <= 5.5e+135)) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-2.3d+33)) .or. (.not. (a <= 5.5d+135))) then
        tmp = x + (z + (a * (1.0d0 - t)))
    else
        tmp = ((y + (t + (-2.0d0))) * b) + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -2.3e+33) || !(a <= 5.5e+135)) {
		tmp = x + (z + (a * (1.0 - t)));
	} else {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -2.3e+33) or not (a <= 5.5e+135):
		tmp = x + (z + (a * (1.0 - t)))
	else:
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -2.3e+33) || !(a <= 5.5e+135))
		tmp = Float64(x + Float64(z + Float64(a * Float64(1.0 - t))));
	else
		tmp = Float64(Float64(Float64(y + Float64(t + -2.0)) * b) + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -2.3e+33) || ~((a <= 5.5e+135)))
		tmp = x + (z + (a * (1.0 - t)));
	else
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -2.3e+33], N[Not[LessEqual[a, 5.5e+135]], $MachinePrecision]], N[(x + N[(z + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.30000000000000011e33 or 5.4999999999999999e135 < a

   1. Initial program 93.0%

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

   3. Taylor expanded in b around 0 85.4%

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

   4. Taylor expanded in y around 0 73.7%

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

      1. mul-1-neg 73.7%

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

   6. Simplified 73.7%

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

   if -2.30000000000000011e33 < a < 5.4999999999999999e135

   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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate-+l- 99.9%

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

      8. fma-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. metadata-eval 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 80.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+33} \lor \neg \left(a \leq 5.5 \cdot 10^{+135}\right):\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+44} \lor \neg \left(b \leq 9.5 \cdot 10^{+122}\right):\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7e+44) (not (<= b 9.5e+122)))
   (+ (* (+ y (+ t -2.0)) b) (- x (* y z)))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7e+44) || !(b <= 9.5e+122)) {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-7d+44)) .or. (.not. (b <= 9.5d+122))) then
        tmp = ((y + (t + (-2.0d0))) * b) + (x - (y * z))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7e+44) || !(b <= 9.5e+122)) {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7e+44) or not (b <= 9.5e+122):
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7e+44) || !(b <= 9.5e+122))
		tmp = Float64(Float64(Float64(y + Float64(t + -2.0)) * b) + Float64(x - Float64(y * z)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7e+44) || ~((b <= 9.5e+122)))
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7e+44], N[Not[LessEqual[b, 9.5e+122]], $MachinePrecision]], N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.9999999999999998e44 or 9.49999999999999986e122 < b

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. fma-define 97.5%

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

      3. associate--l+ 97.5%

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

      4. sub-neg 97.5%

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

      5. metadata-eval 97.5%

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

      6. sub-neg 97.5%

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

      7. associate-+l- 97.5%

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

      8. fma-neg 97.5%

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

      9. sub-neg 97.5%

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

      10. metadata-eval 97.5%

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

      11. remove-double-neg 97.5%

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

      12. sub-neg 97.5%

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

      13. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around inf 86.7%

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

   if -6.9999999999999998e44 < b < 9.49999999999999986e122

   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 b around 0 89.5%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+44} \lor \neg \left(b \leq 9.5 \cdot 10^{+122}\right):\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;a + \left(x + b \cdot \left(t + \left(y + -2\right)\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+122}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.4e+44)
   (+ a (+ x (* b (+ t (+ y -2.0)))))
   (if (<= b 9e+122)
     (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))
     (+ (* (+ y (+ t -2.0)) b) (- x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e+44) {
		tmp = a + (x + (b * (t + (y + -2.0))));
	} else if (b <= 9e+122) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.4d+44)) then
        tmp = a + (x + (b * (t + (y + (-2.0d0)))))
    else if (b <= 9d+122) then
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    else
        tmp = ((y + (t + (-2.0d0))) * b) + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e+44) {
		tmp = a + (x + (b * (t + (y + -2.0))));
	} else if (b <= 9e+122) {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	} else {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.4e+44:
		tmp = a + (x + (b * (t + (y + -2.0))))
	elif b <= 9e+122:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	else:
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.4e+44)
		tmp = Float64(a + Float64(x + Float64(b * Float64(t + Float64(y + -2.0)))));
	elseif (b <= 9e+122)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(Float64(y + Float64(t + -2.0)) * b) + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.4e+44)
		tmp = a + (x + (b * (t + (y + -2.0))));
	elseif (b <= 9e+122)
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	else
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.4e+44], N[(a + N[(x + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e+122], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4e44

   1. Initial program 93.7%

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

   3. Taylor expanded in t around 0 89.6%

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

   4. Taylor expanded in z around 0 85.8%

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

   5. Taylor expanded in a around 0 79.7%

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

      1. sub-neg 79.7%

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

      2. metadata-eval 79.7%

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

      3. distribute-lft-out 88.0%

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

   7. Simplified 88.0%

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

   if -3.4e44 < b < 8.99999999999999995e122

   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 b around 0 89.5%

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

   if 8.99999999999999995e122 < b

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. fma-define 96.9%

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

      3. associate--l+ 96.9%

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

      4. sub-neg 96.9%

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

      5. metadata-eval 96.9%

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

      6. sub-neg 96.9%

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

      7. associate-+l- 96.9%

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

      8. fma-neg 96.9%

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

      9. sub-neg 96.9%

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

      10. metadata-eval 96.9%

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

      11. remove-double-neg 96.9%

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

      12. sub-neg 96.9%

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

      13. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in y around inf 91.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+44}:\\ \;\;\;\;a + \left(x + b \cdot \left(t + \left(y + -2\right)\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+122}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 84.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+45}:\\ \;\;\;\;a + \left(x + b \cdot \left(t + \left(y + -2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+122}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + \left(z - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e+45)
   (+ a (+ x (* b (+ t (+ y -2.0)))))
   (if (<= b 1.9e+122)
     (+ x (+ (* a (- 1.0 t)) (- z (* y z))))
     (+ (* (+ y (+ t -2.0)) b) (- x (* y z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e+45) {
		tmp = a + (x + (b * (t + (y + -2.0))));
	} else if (b <= 1.9e+122) {
		tmp = x + ((a * (1.0 - t)) + (z - (y * z)));
	} else {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1d+45)) then
        tmp = a + (x + (b * (t + (y + (-2.0d0)))))
    else if (b <= 1.9d+122) then
        tmp = x + ((a * (1.0d0 - t)) + (z - (y * z)))
    else
        tmp = ((y + (t + (-2.0d0))) * b) + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e+45) {
		tmp = a + (x + (b * (t + (y + -2.0))));
	} else if (b <= 1.9e+122) {
		tmp = x + ((a * (1.0 - t)) + (z - (y * z)));
	} else {
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e+45:
		tmp = a + (x + (b * (t + (y + -2.0))))
	elif b <= 1.9e+122:
		tmp = x + ((a * (1.0 - t)) + (z - (y * z)))
	else:
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e+45)
		tmp = Float64(a + Float64(x + Float64(b * Float64(t + Float64(y + -2.0)))));
	elseif (b <= 1.9e+122)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z - Float64(y * z))));
	else
		tmp = Float64(Float64(Float64(y + Float64(t + -2.0)) * b) + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1e+45)
		tmp = a + (x + (b * (t + (y + -2.0))));
	elseif (b <= 1.9e+122)
		tmp = x + ((a * (1.0 - t)) + (z - (y * z)));
	else
		tmp = ((y + (t + -2.0)) * b) + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e+45], N[(a + N[(x + N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e+122], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.9999999999999993e44

   1. Initial program 93.7%

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

   3. Taylor expanded in t around 0 89.6%

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

   4. Taylor expanded in z around 0 85.8%

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

   5. Taylor expanded in a around 0 79.7%

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

      1. sub-neg 79.7%

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

      2. metadata-eval 79.7%

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

      3. distribute-lft-out 88.0%

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

   7. Simplified 88.0%

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

   if -9.9999999999999993e44 < b < 1.8999999999999999e122

   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 b around 0 89.5%

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

   4. Taylor expanded in y around 0 89.5%

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

   if 1.8999999999999999e122 < b

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. fma-define 96.9%

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

      3. associate--l+ 96.9%

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

      4. sub-neg 96.9%

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

      5. metadata-eval 96.9%

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

      6. sub-neg 96.9%

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

      7. associate-+l- 96.9%

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

      8. fma-neg 96.9%

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

      9. sub-neg 96.9%

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

      10. metadata-eval 96.9%

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

      11. remove-double-neg 96.9%

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

      12. sub-neg 96.9%

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

      13. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in y around inf 91.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+45}:\\ \;\;\;\;a + \left(x + b \cdot \left(t + \left(y + -2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+122}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + \left(z - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(t + -2\right)\right) \cdot b + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+55} \lor \neg \left(t \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.05e+55) (not (<= t 1.9e+34)))
   (* t (- b a))
   (+ x (+ a (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e+55) || !(t <= 1.9e+34)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.05d+55)) .or. (.not. (t <= 1.9d+34))) then
        tmp = t * (b - a)
    else
        tmp = x + (a + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.05e+55) || !(t <= 1.9e+34)) {
		tmp = t * (b - a);
	} else {
		tmp = x + (a + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.05e+55) or not (t <= 1.9e+34):
		tmp = t * (b - a)
	else:
		tmp = x + (a + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.05e+55) || !(t <= 1.9e+34))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.05e+55) || ~((t <= 1.9e+34)))
		tmp = t * (b - a);
	else
		tmp = x + (a + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.05e+55], N[Not[LessEqual[t, 1.9e+34]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e55 or 1.9000000000000001e34 < 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 71.2%

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

   if -1.05e55 < t < 1.9000000000000001e34

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 73.4%

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

   4. Taylor expanded in t around 0 71.4%

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

      1. sub-neg 71.4%

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

      2. sub-neg 71.4%

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

      3. metadata-eval 71.4%

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

      4. distribute-neg-in 71.4%

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

      5. neg-mul-1 71.4%

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

      6. remove-double-neg 71.4%

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

      7. distribute-rgt-in 71.5%

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

      8. +-commutative 71.5%

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

      9. distribute-neg-in 71.5%

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

      10. distribute-lft-neg-in 71.5%

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

      11. metadata-eval 71.5%

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

      12. mul-1-neg 71.5%

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

      13. associate-*r* 71.5%

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

      14. distribute-rgt-in 71.4%

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

      15. neg-mul-1 71.4%

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

      16. sub-neg 71.4%

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

   6. Simplified 71.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+55} \lor \neg \left(t \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+135} \lor \neg \left(y \leq 2.8 \cdot 10^{+112}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e+135) (not (<= y 2.8e+112))) (* y (- z)) (* a (- 1.0 t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+135) || !(y <= 2.8e+112)) {
		tmp = y * -z;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d+135)) .or. (.not. (y <= 2.8d+112))) then
        tmp = y * -z
    else
        tmp = a * (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+135) || !(y <= 2.8e+112)) {
		tmp = y * -z;
	} else {
		tmp = a * (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e+135) or not (y <= 2.8e+112):
		tmp = y * -z
	else:
		tmp = a * (1.0 - t)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e+135) || !(y <= 2.8e+112))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(a * Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e+135) || ~((y <= 2.8e+112)))
		tmp = y * -z;
	else
		tmp = a * (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e+135], N[Not[LessEqual[y, 2.8e+112]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3000000000000001e135 or 2.8000000000000001e112 < y

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 71.2%

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

   4. Taylor expanded in b around 0 48.1%

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

      1. mul-1-neg 48.1%

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

      2. distribute-rgt-neg-in 48.1%

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

   6. Simplified 48.1%

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

   if -2.3000000000000001e135 < y < 2.8000000000000001e112

   1. Initial program 98.2%

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

   3. Taylor expanded in a around inf 39.2%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+135} \lor \neg \left(y \leq 2.8 \cdot 10^{+112}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 33.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+95} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.7e+95) (not (<= z 24.0))) (* y (- z)) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+95) || !(z <= 24.0)) {
		tmp = y * -z;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.7d+95)) .or. (.not. (z <= 24.0d0))) then
        tmp = y * -z
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.7e+95) || !(z <= 24.0)) {
		tmp = y * -z;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.7e+95) or not (z <= 24.0):
		tmp = y * -z
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.7e+95) || !(z <= 24.0))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.7e+95) || ~((z <= 24.0)))
		tmp = y * -z;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.7e+95], N[Not[LessEqual[z, 24.0]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e95 or 24 < z

   1. Initial program 95.7%

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

   3. Taylor expanded in y around inf 44.1%

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

   4. Taylor expanded in b around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. distribute-rgt-neg-in 39.2%

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

   6. Simplified 39.2%

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

   if -2.7e95 < z < 24

   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 b around 0 62.9%

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

   4. Taylor expanded in t around 0 34.4%

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

      1. +-commutative 34.4%

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

      2. sub-neg 34.4%

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

      3. metadata-eval 34.4%

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

      4. neg-mul-1 34.4%

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

      5. fma-undefine 34.4%

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

   6. Simplified 34.4%

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

   7. Taylor expanded in z around 0 31.7%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+95} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+130}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+181}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9e+130) z (if (<= z 2.6e+181) (+ x a) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9e+130) {
		tmp = z;
	} else if (z <= 2.6e+181) {
		tmp = x + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-9d+130)) then
        tmp = z
    else if (z <= 2.6d+181) then
        tmp = x + a
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9e+130) {
		tmp = z;
	} else if (z <= 2.6e+181) {
		tmp = x + a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -9e+130:
		tmp = z
	elif z <= 2.6e+181:
		tmp = x + a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9e+130)
		tmp = z;
	elseif (z <= 2.6e+181)
		tmp = Float64(x + a);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -9e+130)
		tmp = z;
	elseif (z <= 2.6e+181)
		tmp = x + a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9e+130], z, If[LessEqual[z, 2.6e+181], N[(x + a), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -9.00000000000000078e130 or 2.6e181 < z

   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 z around inf 76.7%

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

   4. Taylor expanded in y around 0 76.7%

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

   5. Taylor expanded in y around 0 34.8%

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

   if -9.00000000000000078e130 < z < 2.6e181

   1. Initial program 97.3%

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

   3. Taylor expanded in b around 0 64.8%

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

   4. Taylor expanded in t around 0 40.0%

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

      1. +-commutative 40.0%

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

      2. sub-neg 40.0%

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

      3. metadata-eval 40.0%

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

      4. neg-mul-1 40.0%

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

      5. fma-undefine 40.0%

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

   6. Simplified 40.0%

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

   7. Taylor expanded in z around 0 28.8%

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

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+130}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+181}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.75e+111) z (if (<= z 1.4e+152) x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+111) {
		tmp = z;
	} else if (z <= 1.4e+152) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.75d+111)) then
        tmp = z
    else if (z <= 1.4d+152) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.75e+111) {
		tmp = z;
	} else if (z <= 1.4e+152) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.75e+111:
		tmp = z
	elif z <= 1.4e+152:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.75e+111)
		tmp = z;
	elseif (z <= 1.4e+152)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.75e+111)
		tmp = z;
	elseif (z <= 1.4e+152)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.75e+111], z, If[LessEqual[z, 1.4e+152], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e111 or 1.4000000000000001e152 < z

   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 z around inf 74.6%

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

   4. Taylor expanded in y around 0 74.6%

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

   5. Taylor expanded in y around 0 30.8%

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

   if -1.7500000000000001e111 < z < 1.4000000000000001e152

   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 x around inf 20.5%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+111}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 18.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+49}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= a -7.6e+49) a x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.6e+49) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-7.6d+49)) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -7.6e+49) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -7.6e+49:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -7.6e+49)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -7.6e+49)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -7.6e+49], a, x]

Derivation

1. Split input into 2 regimes

2. if a < -7.5999999999999997e49

   1. Initial program 94.9%

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

   3. Taylor expanded in b around 0 84.5%

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

   4. Taylor expanded in t around 0 47.7%

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

      1. +-commutative 47.7%

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

      2. sub-neg 47.7%

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

      3. metadata-eval 47.7%

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

      4. neg-mul-1 47.7%

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

      5. fma-undefine 47.7%

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

   6. Simplified 47.7%

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

   7. Taylor expanded in a around inf 25.5%

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

   if -7.5999999999999997e49 < a

   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 x around inf 18.5%

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

4. Final simplification 20.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+49}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 11.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Taylor expanded in b around 0 72.2%

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

4. Taylor expanded in t around 0 51.5%

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

   1. +-commutative 51.5%

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

   2. sub-neg 51.5%

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

   3. metadata-eval 51.5%

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

   4. neg-mul-1 51.5%

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

   5. fma-undefine 51.5%

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

6. Simplified 51.5%

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

7. Taylor expanded in a around inf 10.4%

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

8. Final simplification 10.4%

   \[\leadsto a \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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)))