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

Percentage Accurate: 95.5% → 98.0%

Time: 19.4s

Alternatives: 21

Speedup: 0.5×

• 35.1% 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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 27.3%

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

      3. associate--l+ 27.3%

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

      4. sub-neg 27.3%

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

      5. metadata-eval 27.3%

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

      6. sub-neg 27.3%

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

      7. associate--l+ 27.3%

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

      8. *-commutative 27.3%

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

      9. distribute-rgt-neg-in 27.3%

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

      10. fma-neg 27.3%

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

      11. neg-sub0 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 27.3%

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

      17. *-commutative 27.3%

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

      18. distribute-rgt-neg-in 27.3%

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

      19. neg-sub0 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 27.3%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 27.3%

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

   4. Taylor expanded in y around 0 9.7%

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

   5. Taylor expanded in t around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   7. Simplified 64.3%

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

4. Final simplification 98.5%

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

Alternative 2: 52.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot a\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_4 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -58000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-211}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-256}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-113}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* t a)))
        (t_2 (* a (- 1.0 t)))
        (t_3 (* (- (+ y t) 2.0) b))
        (t_4 (* z (- 1.0 y))))
   (if (<= b -58000.0)
     t_3
     (if (<= b -4.6e-187)
       t_1
       (if (<= b -5e-211)
         t_4
         (if (<= b -4.1e-271)
           t_1
           (if (<= b 6e-256)
             t_4
             (if (<= b 2.6e-135)
               t_2
               (if (<= b 3.5e-113)
                 t_4
                 (if (<= b 1.95e-103) t_2 (if (<= b 2.5e+21) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * a);
	double t_2 = a * (1.0 - t);
	double t_3 = ((y + t) - 2.0) * b;
	double t_4 = z * (1.0 - y);
	double tmp;
	if (b <= -58000.0) {
		tmp = t_3;
	} else if (b <= -4.6e-187) {
		tmp = t_1;
	} else if (b <= -5e-211) {
		tmp = t_4;
	} else if (b <= -4.1e-271) {
		tmp = t_1;
	} else if (b <= 6e-256) {
		tmp = t_4;
	} else if (b <= 2.6e-135) {
		tmp = t_2;
	} else if (b <= 3.5e-113) {
		tmp = t_4;
	} else if (b <= 1.95e-103) {
		tmp = t_2;
	} else if (b <= 2.5e+21) {
		tmp = t_1;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = x - (t * a)
    t_2 = a * (1.0d0 - t)
    t_3 = ((y + t) - 2.0d0) * b
    t_4 = z * (1.0d0 - y)
    if (b <= (-58000.0d0)) then
        tmp = t_3
    else if (b <= (-4.6d-187)) then
        tmp = t_1
    else if (b <= (-5d-211)) then
        tmp = t_4
    else if (b <= (-4.1d-271)) then
        tmp = t_1
    else if (b <= 6d-256) then
        tmp = t_4
    else if (b <= 2.6d-135) then
        tmp = t_2
    else if (b <= 3.5d-113) then
        tmp = t_4
    else if (b <= 1.95d-103) then
        tmp = t_2
    else if (b <= 2.5d+21) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (t * a);
	double t_2 = a * (1.0 - t);
	double t_3 = ((y + t) - 2.0) * b;
	double t_4 = z * (1.0 - y);
	double tmp;
	if (b <= -58000.0) {
		tmp = t_3;
	} else if (b <= -4.6e-187) {
		tmp = t_1;
	} else if (b <= -5e-211) {
		tmp = t_4;
	} else if (b <= -4.1e-271) {
		tmp = t_1;
	} else if (b <= 6e-256) {
		tmp = t_4;
	} else if (b <= 2.6e-135) {
		tmp = t_2;
	} else if (b <= 3.5e-113) {
		tmp = t_4;
	} else if (b <= 1.95e-103) {
		tmp = t_2;
	} else if (b <= 2.5e+21) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (t * a)
	t_2 = a * (1.0 - t)
	t_3 = ((y + t) - 2.0) * b
	t_4 = z * (1.0 - y)
	tmp = 0
	if b <= -58000.0:
		tmp = t_3
	elif b <= -4.6e-187:
		tmp = t_1
	elif b <= -5e-211:
		tmp = t_4
	elif b <= -4.1e-271:
		tmp = t_1
	elif b <= 6e-256:
		tmp = t_4
	elif b <= 2.6e-135:
		tmp = t_2
	elif b <= 3.5e-113:
		tmp = t_4
	elif b <= 1.95e-103:
		tmp = t_2
	elif b <= 2.5e+21:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(t * a))
	t_2 = Float64(a * Float64(1.0 - t))
	t_3 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_4 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (b <= -58000.0)
		tmp = t_3;
	elseif (b <= -4.6e-187)
		tmp = t_1;
	elseif (b <= -5e-211)
		tmp = t_4;
	elseif (b <= -4.1e-271)
		tmp = t_1;
	elseif (b <= 6e-256)
		tmp = t_4;
	elseif (b <= 2.6e-135)
		tmp = t_2;
	elseif (b <= 3.5e-113)
		tmp = t_4;
	elseif (b <= 1.95e-103)
		tmp = t_2;
	elseif (b <= 2.5e+21)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (t * a);
	t_2 = a * (1.0 - t);
	t_3 = ((y + t) - 2.0) * b;
	t_4 = z * (1.0 - y);
	tmp = 0.0;
	if (b <= -58000.0)
		tmp = t_3;
	elseif (b <= -4.6e-187)
		tmp = t_1;
	elseif (b <= -5e-211)
		tmp = t_4;
	elseif (b <= -4.1e-271)
		tmp = t_1;
	elseif (b <= 6e-256)
		tmp = t_4;
	elseif (b <= 2.6e-135)
		tmp = t_2;
	elseif (b <= 3.5e-113)
		tmp = t_4;
	elseif (b <= 1.95e-103)
		tmp = t_2;
	elseif (b <= 2.5e+21)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -58000.0], t$95$3, If[LessEqual[b, -4.6e-187], t$95$1, If[LessEqual[b, -5e-211], t$95$4, If[LessEqual[b, -4.1e-271], t$95$1, If[LessEqual[b, 6e-256], t$95$4, If[LessEqual[b, 2.6e-135], t$95$2, If[LessEqual[b, 3.5e-113], t$95$4, If[LessEqual[b, 1.95e-103], t$95$2, If[LessEqual[b, 2.5e+21], t$95$1, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -58000 or 2.5e21 < 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. Taylor expanded in b around inf 72.8%

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

   if -58000 < b < -4.59999999999999996e-187 or -5.0000000000000002e-211 < b < -4.1000000000000003e-271 or 1.9500000000000001e-103 < b < 2.5e21

   1. Initial program 100.0%

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

   2. Taylor expanded in b around 0 92.9%

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

   3. Taylor expanded in t around inf 55.2%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   4. Step-by-step derivation

      1. *-commutative 55.2%

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

   5. Simplified 55.2%

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

   if -4.59999999999999996e-187 < b < -5.0000000000000002e-211 or -4.1000000000000003e-271 < b < 5.9999999999999996e-256 or 2.60000000000000004e-135 < b < 3.50000000000000029e-113

   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. Taylor expanded in z around inf 75.1%

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

   if 5.9999999999999996e-256 < b < 2.60000000000000004e-135 or 3.50000000000000029e-113 < b < 1.9500000000000001e-103

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 68.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -58000:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-187}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-211}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-271}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-256}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-113}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 3: 81.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+189} \lor \neg \left(y \leq 7.7 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + \left(b \cdot \left(t - 2\right) + a \cdot \left(1 - t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+189) (not (<= y 7.7e+58)))
   (* y (- b z))
   (+ x (+ z (+ (* b (- t 2.0)) (* a (- 1.0 t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+189) || !(y <= 7.7e+58)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + ((b * (t - 2.0)) + (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 <= (-2.7d+189)) .or. (.not. (y <= 7.7d+58))) then
        tmp = y * (b - z)
    else
        tmp = x + (z + ((b * (t - 2.0d0)) + (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 <= -2.7e+189) || !(y <= 7.7e+58)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + ((b * (t - 2.0)) + (a * (1.0 - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e+189) or not (y <= 7.7e+58):
		tmp = y * (b - z)
	else:
		tmp = x + (z + ((b * (t - 2.0)) + (a * (1.0 - t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e+189) || !(y <= 7.7e+58))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(z + Float64(Float64(b * Float64(t - 2.0)) + 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 <= -2.7e+189) || ~((y <= 7.7e+58)))
		tmp = y * (b - z);
	else
		tmp = x + (z + ((b * (t - 2.0)) + (a * (1.0 - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e+189], N[Not[LessEqual[y, 7.7e+58]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999994e189 or 7.70000000000000053e58 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 81.7%

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

   if -2.69999999999999994e189 < y < 7.70000000000000053e58

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. fma-def 96.7%

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

      3. associate--l+ 96.7%

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

      4. sub-neg 96.7%

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

      5. metadata-eval 96.7%

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

      6. sub-neg 96.7%

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

      7. associate--l+ 96.7%

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

      8. *-commutative 96.7%

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

      9. distribute-rgt-neg-in 96.7%

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

      10. fma-neg 96.7%

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

      11. neg-sub0 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 96.7%

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

      17. *-commutative 96.7%

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

      18. distribute-rgt-neg-in 96.7%

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

      19. neg-sub0 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 96.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 96.7%

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

   4. Taylor expanded in y around 0 91.0%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+189} \lor \neg \left(y \leq 7.7 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + \left(b \cdot \left(t - 2\right) + a \cdot \left(1 - t\right)\right)\right)\\ \end{array} \]

Alternative 4: 47.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-93}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.98 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))) (t_2 (* t (- b a))))
   (if (<= t -7.5e+51)
     t_2
     (if (<= t -2.4e-63)
       t_1
       (if (<= t -8e-93)
         a
         (if (<= t -1.98e-115)
           t_1
           (if (<= t 1.45e-213)
             (* b (- y 2.0))
             (if (<= t 1.05e+38) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.5e+51) {
		tmp = t_2;
	} else if (t <= -2.4e-63) {
		tmp = t_1;
	} else if (t <= -8e-93) {
		tmp = a;
	} else if (t <= -1.98e-115) {
		tmp = t_1;
	} else if (t <= 1.45e-213) {
		tmp = b * (y - 2.0);
	} else if (t <= 1.05e+38) {
		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 = z * (1.0d0 - y)
    t_2 = t * (b - a)
    if (t <= (-7.5d+51)) then
        tmp = t_2
    else if (t <= (-2.4d-63)) then
        tmp = t_1
    else if (t <= (-8d-93)) then
        tmp = a
    else if (t <= (-1.98d-115)) then
        tmp = t_1
    else if (t <= 1.45d-213) then
        tmp = b * (y - 2.0d0)
    else if (t <= 1.05d+38) 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 = z * (1.0 - y);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.5e+51) {
		tmp = t_2;
	} else if (t <= -2.4e-63) {
		tmp = t_1;
	} else if (t <= -8e-93) {
		tmp = a;
	} else if (t <= -1.98e-115) {
		tmp = t_1;
	} else if (t <= 1.45e-213) {
		tmp = b * (y - 2.0);
	} else if (t <= 1.05e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.5e+51:
		tmp = t_2
	elif t <= -2.4e-63:
		tmp = t_1
	elif t <= -8e-93:
		tmp = a
	elif t <= -1.98e-115:
		tmp = t_1
	elif t <= 1.45e-213:
		tmp = b * (y - 2.0)
	elif t <= 1.05e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.5e+51)
		tmp = t_2;
	elseif (t <= -2.4e-63)
		tmp = t_1;
	elseif (t <= -8e-93)
		tmp = a;
	elseif (t <= -1.98e-115)
		tmp = t_1;
	elseif (t <= 1.45e-213)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 1.05e+38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.5e+51)
		tmp = t_2;
	elseif (t <= -2.4e-63)
		tmp = t_1;
	elseif (t <= -8e-93)
		tmp = a;
	elseif (t <= -1.98e-115)
		tmp = t_1;
	elseif (t <= 1.45e-213)
		tmp = b * (y - 2.0);
	elseif (t <= 1.05e+38)
		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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+51], t$95$2, If[LessEqual[t, -2.4e-63], t$95$1, If[LessEqual[t, -8e-93], a, If[LessEqual[t, -1.98e-115], t$95$1, If[LessEqual[t, 1.45e-213], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+38], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.4999999999999999e51 or 1.05e38 < 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. Taylor expanded in t around inf 68.0%

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

   if -7.4999999999999999e51 < t < -2.4000000000000001e-63 or -7.9999999999999992e-93 < t < -1.97999999999999989e-115 or 1.45e-213 < t < 1.05e38

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 42.8%

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

   if -2.4000000000000001e-63 < t < -7.9999999999999992e-93

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 64.3%

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

   3. Taylor expanded in t around 0 64.3%

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

   if -1.97999999999999989e-115 < t < 1.45e-213

   1. Initial program 97.9%

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

   2. Taylor expanded in b around inf 50.2%

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

   3. Taylor expanded in t around 0 50.2%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-93}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.98 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 5: 74.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(\left(y + -1\right) \cdot z - a\right)\\ t_2 := x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-215}:\\ \;\;\;\;\left(x + a\right) + b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (- (* (+ y -1.0) z) a))) (t_2 (+ x (+ z (* t (- b a))))))
   (if (<= t -1.7e+31)
     t_2
     (if (<= t -6.2e-119)
       t_1
       (if (<= t 4.1e-215)
         (+ (+ x a) (* b (+ y -2.0)))
         (if (<= t 1.95e+21) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y + -1.0) * z) - a);
	double t_2 = x + (z + (t * (b - a)));
	double tmp;
	if (t <= -1.7e+31) {
		tmp = t_2;
	} else if (t <= -6.2e-119) {
		tmp = t_1;
	} else if (t <= 4.1e-215) {
		tmp = (x + a) + (b * (y + -2.0));
	} else if (t <= 1.95e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (((y + (-1.0d0)) * z) - a)
    t_2 = x + (z + (t * (b - a)))
    if (t <= (-1.7d+31)) then
        tmp = t_2
    else if (t <= (-6.2d-119)) then
        tmp = t_1
    else if (t <= 4.1d-215) then
        tmp = (x + a) + (b * (y + (-2.0d0)))
    else if (t <= 1.95d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (((y + -1.0) * z) - a);
	double t_2 = x + (z + (t * (b - a)));
	double tmp;
	if (t <= -1.7e+31) {
		tmp = t_2;
	} else if (t <= -6.2e-119) {
		tmp = t_1;
	} else if (t <= 4.1e-215) {
		tmp = (x + a) + (b * (y + -2.0));
	} else if (t <= 1.95e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (((y + -1.0) * z) - a)
	t_2 = x + (z + (t * (b - a)))
	tmp = 0
	if t <= -1.7e+31:
		tmp = t_2
	elif t <= -6.2e-119:
		tmp = t_1
	elif t <= 4.1e-215:
		tmp = (x + a) + (b * (y + -2.0))
	elif t <= 1.95e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(Float64(y + -1.0) * z) - a))
	t_2 = Float64(x + Float64(z + Float64(t * Float64(b - a))))
	tmp = 0.0
	if (t <= -1.7e+31)
		tmp = t_2;
	elseif (t <= -6.2e-119)
		tmp = t_1;
	elseif (t <= 4.1e-215)
		tmp = Float64(Float64(x + a) + Float64(b * Float64(y + -2.0)));
	elseif (t <= 1.95e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (((y + -1.0) * z) - a);
	t_2 = x + (z + (t * (b - a)));
	tmp = 0.0;
	if (t <= -1.7e+31)
		tmp = t_2;
	elseif (t <= -6.2e-119)
		tmp = t_1;
	elseif (t <= 4.1e-215)
		tmp = (x + a) + (b * (y + -2.0));
	elseif (t <= 1.95e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+31], t$95$2, If[LessEqual[t, -6.2e-119], t$95$1, If[LessEqual[t, 4.1e-215], N[(N[(x + a), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6999999999999999e31 or 1.95e21 < t

   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. Step-by-step derivation

      1. +-commutative 93.0%

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

      2. fma-def 93.7%

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

      3. associate--l+ 93.7%

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

      4. sub-neg 93.7%

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

      5. metadata-eval 93.7%

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

      6. sub-neg 93.7%

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

      7. associate--l+ 93.7%

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

      8. *-commutative 93.7%

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

      9. distribute-rgt-neg-in 93.7%

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

      10. fma-neg 93.7%

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

      11. neg-sub0 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 93.7%

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

      17. *-commutative 93.7%

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

      18. distribute-rgt-neg-in 93.7%

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

      19. neg-sub0 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 78.5%

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

   5. Taylor expanded in t around inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. unsub-neg 83.1%

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

   7. Simplified 83.1%

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

   if -1.6999999999999999e31 < t < -6.19999999999999956e-119 or 4.09999999999999985e-215 < t < 1.95e21

   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. Taylor expanded in b around 0 79.6%

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

   3. Taylor expanded in t around 0 78.9%

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

      1. mul-1-neg 78.9%

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

   5. Simplified 78.9%

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

   if -6.19999999999999956e-119 < t < 4.09999999999999985e-215

   1. Initial program 97.9%

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

   2. Taylor expanded in z around 0 81.5%

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

      1. sub-neg 81.5%

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

      2. metadata-eval 81.5%

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

      3. *-commutative 81.5%

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

      4. cancel-sign-sub-inv 81.5%

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

      5. neg-sub0 81.5%

         \[\leadsto \left(x + \color{blue}{\left(0 - \left(t + -1\right)\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. +-commutative 81.5%

         \[\leadsto \left(x + \left(0 - \color{blue}{\left(-1 + t\right)}\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. associate--r+ 81.5%

         \[\leadsto \left(x + \color{blue}{\left(\left(0 - -1\right) - t\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. metadata-eval 81.5%

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

      9. *-commutative 81.5%

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

      10. +-commutative 81.5%

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

      11. fma-def 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in t around 0 81.5%

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

      1. associate-+r+ 81.5%

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

      2. +-commutative 81.5%

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

      3. sub-neg 81.5%

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

      4. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+31}:\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-119}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-215}:\\ \;\;\;\;\left(x + a\right) + b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+21}:\\ \;\;\;\;x - \left(\left(y + -1\right) \cdot z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \end{array} \]

Alternative 6: 80.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+16} \lor \neg \left(b \leq 1.42 \cdot 10^{+119}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.5e+16) (not (<= b 1.42e+119)))
   (* (- (+ y t) 2.0) b)
   (+ x (+ (* z (- 1.0 y)) (* a (- 1.0 t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+16) || !(b <= 1.42e+119)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.5d+16)) .or. (.not. (b <= 1.42d+119))) then
        tmp = ((y + t) - 2.0d0) * b
    else
        tmp = x + ((z * (1.0d0 - y)) + (a * (1.0d0 - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+16) || !(b <= 1.42e+119)) {
		tmp = ((y + t) - 2.0) * b;
	} else {
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.5e+16) or not (b <= 1.42e+119):
		tmp = ((y + t) - 2.0) * b
	else:
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.5e+16) || !(b <= 1.42e+119))
		tmp = Float64(Float64(Float64(y + t) - 2.0) * b);
	else
		tmp = Float64(x + Float64(Float64(z * Float64(1.0 - y)) + Float64(a * Float64(1.0 - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.5e+16) || ~((b <= 1.42e+119)))
		tmp = ((y + t) - 2.0) * b;
	else
		tmp = x + ((z * (1.0 - y)) + (a * (1.0 - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.5e+16], N[Not[LessEqual[b, 1.42e+119]], $MachinePrecision]], N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(x + N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.5e16 or 1.4199999999999999e119 < b

   1. Initial program 90.7%

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

   2. Taylor expanded in b around inf 78.1%

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

   if -4.5e16 < b < 1.4199999999999999e119

   1. Initial program 98.7%

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

   2. Taylor expanded in b around 0 92.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+16} \lor \neg \left(b \leq 1.42 \cdot 10^{+119}\right):\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 7: 44.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-165}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* t (- b a))))
   (if (<= t -1.6e+31)
     t_2
     (if (<= t -4e-65)
       t_1
       (if (<= t -9.5e-165)
         (* a (- 1.0 t))
         (if (<= t 5.2e-128) (* b (- y 2.0)) (if (<= t 1.15e+38) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.6e+31) {
		tmp = t_2;
	} else if (t <= -4e-65) {
		tmp = t_1;
	} else if (t <= -9.5e-165) {
		tmp = a * (1.0 - t);
	} else if (t <= 5.2e-128) {
		tmp = b * (y - 2.0);
	} else if (t <= 1.15e+38) {
		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 * -z
    t_2 = t * (b - a)
    if (t <= (-1.6d+31)) then
        tmp = t_2
    else if (t <= (-4d-65)) then
        tmp = t_1
    else if (t <= (-9.5d-165)) then
        tmp = a * (1.0d0 - t)
    else if (t <= 5.2d-128) then
        tmp = b * (y - 2.0d0)
    else if (t <= 1.15d+38) 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 * -z;
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.6e+31) {
		tmp = t_2;
	} else if (t <= -4e-65) {
		tmp = t_1;
	} else if (t <= -9.5e-165) {
		tmp = a * (1.0 - t);
	} else if (t <= 5.2e-128) {
		tmp = b * (y - 2.0);
	} else if (t <= 1.15e+38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = t * (b - a)
	tmp = 0
	if t <= -1.6e+31:
		tmp = t_2
	elif t <= -4e-65:
		tmp = t_1
	elif t <= -9.5e-165:
		tmp = a * (1.0 - t)
	elif t <= 5.2e-128:
		tmp = b * (y - 2.0)
	elif t <= 1.15e+38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.6e+31)
		tmp = t_2;
	elseif (t <= -4e-65)
		tmp = t_1;
	elseif (t <= -9.5e-165)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 5.2e-128)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 1.15e+38)
		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 * -z;
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -1.6e+31)
		tmp = t_2;
	elseif (t <= -4e-65)
		tmp = t_1;
	elseif (t <= -9.5e-165)
		tmp = a * (1.0 - t);
	elseif (t <= 5.2e-128)
		tmp = b * (y - 2.0);
	elseif (t <= 1.15e+38)
		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 * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+31], t$95$2, If[LessEqual[t, -4e-65], t$95$1, If[LessEqual[t, -9.5e-165], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-128], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+38], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6e31 or 1.1500000000000001e38 < 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. Taylor expanded in t around inf 68.0%

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

   if -1.6e31 < t < -3.99999999999999969e-65 or 5.19999999999999961e-128 < t < 1.1500000000000001e38

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 42.9%

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

   3. Taylor expanded in b around 0 33.1%

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

      1. mul-1-neg 33.1%

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

      2. distribute-rgt-neg-out 33.1%

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

   5. Simplified 33.1%

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

   if -3.99999999999999969e-65 < t < -9.49999999999999973e-165

   1. Initial program 95.7%

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

   2. Taylor expanded in a around inf 44.9%

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

   if -9.49999999999999973e-165 < t < 5.19999999999999961e-128

   1. Initial program 98.3%

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

   2. Taylor expanded in b around inf 43.8%

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

   3. Taylor expanded in t around 0 43.8%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-165}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 8: 69.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;x + \left(z + \left(a + b \cdot -2\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+21}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ z (* t (- b a))))))
   (if (<= t -1.6e+31)
     t_1
     (if (<= t 1.25e-120)
       (+ x (+ z (+ a (* b -2.0))))
       (if (<= t 1.55e+21) (+ 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 = x + (z + (t * (b - a)));
	double tmp;
	if (t <= -1.6e+31) {
		tmp = t_1;
	} else if (t <= 1.25e-120) {
		tmp = x + (z + (a + (b * -2.0)));
	} else if (t <= 1.55e+21) {
		tmp = 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 = x + (z + (t * (b - a)))
    if (t <= (-1.6d+31)) then
        tmp = t_1
    else if (t <= 1.25d-120) then
        tmp = x + (z + (a + (b * (-2.0d0))))
    else if (t <= 1.55d+21) then
        tmp = 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 = x + (z + (t * (b - a)));
	double tmp;
	if (t <= -1.6e+31) {
		tmp = t_1;
	} else if (t <= 1.25e-120) {
		tmp = x + (z + (a + (b * -2.0)));
	} else if (t <= 1.55e+21) {
		tmp = a + (z * (1.0 - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z + (t * (b - a)))
	tmp = 0
	if t <= -1.6e+31:
		tmp = t_1
	elif t <= 1.25e-120:
		tmp = x + (z + (a + (b * -2.0)))
	elif t <= 1.55e+21:
		tmp = a + (z * (1.0 - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z + Float64(t * Float64(b - a))))
	tmp = 0.0
	if (t <= -1.6e+31)
		tmp = t_1;
	elseif (t <= 1.25e-120)
		tmp = Float64(x + Float64(z + Float64(a + Float64(b * -2.0))));
	elseif (t <= 1.55e+21)
		tmp = 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 = x + (z + (t * (b - a)));
	tmp = 0.0;
	if (t <= -1.6e+31)
		tmp = t_1;
	elseif (t <= 1.25e-120)
		tmp = x + (z + (a + (b * -2.0)));
	elseif (t <= 1.55e+21)
		tmp = 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[(x + N[(z + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+31], t$95$1, If[LessEqual[t, 1.25e-120], N[(x + N[(z + N[(a + N[(b * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+21], N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e31 or 1.55e21 < t

   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. Step-by-step derivation

      1. +-commutative 93.0%

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

      2. fma-def 93.7%

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

      3. associate--l+ 93.7%

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

      4. sub-neg 93.7%

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

      5. metadata-eval 93.7%

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

      6. sub-neg 93.7%

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

      7. associate--l+ 93.7%

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

      8. *-commutative 93.7%

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

      9. distribute-rgt-neg-in 93.7%

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

      10. fma-neg 93.7%

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

      11. neg-sub0 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 93.7%

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

      17. *-commutative 93.7%

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

      18. distribute-rgt-neg-in 93.7%

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

      19. neg-sub0 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 93.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 78.5%

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

   5. Taylor expanded in t around inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. unsub-neg 83.1%

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

   7. Simplified 83.1%

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

   if -1.6e31 < t < 1.25000000000000002e-120

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 67.8%

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

   5. Taylor expanded in t around 0 67.8%

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

      1. *-commutative 67.8%

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

   7. Simplified 67.8%

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

   if 1.25000000000000002e-120 < t < 1.55e21

   1. Initial program 100.0%

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

   2. Taylor expanded in b around 0 82.6%

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

   3. Taylor expanded in x around 0 65.0%

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

      1. distribute-lft-in 65.0%

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

      2. mul-1-neg 65.0%

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

      3. mul-1-neg 65.0%

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

      4. sub-neg 65.0%

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

      5. metadata-eval 65.0%

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

      6. +-commutative 65.0%

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

      7. distribute-rgt-neg-in 65.0%

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

      8. fma-udef 65.0%

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

      9. neg-sub0 65.0%

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

      10. +-commutative 65.0%

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

      11. associate--r+ 65.0%

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

      12. metadata-eval 65.0%

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

      13. sub-neg 65.0%

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

      14. metadata-eval 65.0%

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

      15. fma-neg 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in t around 0 62.3%

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

      1. neg-mul-1 62.3%

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

   8. Simplified 62.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;x + \left(z + \left(a + b \cdot -2\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+21}:\\ \;\;\;\;a + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \end{array} \]

Alternative 9: 26.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ t_2 := y \cdot \left(-z\right)\\ \mathbf{if}\;b \leq -13000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.35 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))) (t_2 (* y (- z))))
   (if (<= b -13000000000.0)
     (* t b)
     (if (<= b -5.2e-149)
       t_2
       (if (<= b -1.3e-270)
         t_1
         (if (<= b 4.35e-256) t_2 (if (<= b 6.1e+119) t_1 (* t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (b <= -13000000000.0) {
		tmp = t * b;
	} else if (b <= -5.2e-149) {
		tmp = t_2;
	} else if (b <= -1.3e-270) {
		tmp = t_1;
	} else if (b <= 4.35e-256) {
		tmp = t_2;
	} else if (b <= 6.1e+119) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -a
    t_2 = y * -z
    if (b <= (-13000000000.0d0)) then
        tmp = t * b
    else if (b <= (-5.2d-149)) then
        tmp = t_2
    else if (b <= (-1.3d-270)) then
        tmp = t_1
    else if (b <= 4.35d-256) then
        tmp = t_2
    else if (b <= 6.1d+119) then
        tmp = t_1
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double t_2 = y * -z;
	double tmp;
	if (b <= -13000000000.0) {
		tmp = t * b;
	} else if (b <= -5.2e-149) {
		tmp = t_2;
	} else if (b <= -1.3e-270) {
		tmp = t_1;
	} else if (b <= 4.35e-256) {
		tmp = t_2;
	} else if (b <= 6.1e+119) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	t_2 = y * -z
	tmp = 0
	if b <= -13000000000.0:
		tmp = t * b
	elif b <= -5.2e-149:
		tmp = t_2
	elif b <= -1.3e-270:
		tmp = t_1
	elif b <= 4.35e-256:
		tmp = t_2
	elif b <= 6.1e+119:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	t_2 = Float64(y * Float64(-z))
	tmp = 0.0
	if (b <= -13000000000.0)
		tmp = Float64(t * b);
	elseif (b <= -5.2e-149)
		tmp = t_2;
	elseif (b <= -1.3e-270)
		tmp = t_1;
	elseif (b <= 4.35e-256)
		tmp = t_2;
	elseif (b <= 6.1e+119)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	t_2 = y * -z;
	tmp = 0.0;
	if (b <= -13000000000.0)
		tmp = t * b;
	elseif (b <= -5.2e-149)
		tmp = t_2;
	elseif (b <= -1.3e-270)
		tmp = t_1;
	elseif (b <= 4.35e-256)
		tmp = t_2;
	elseif (b <= 6.1e+119)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[b, -13000000000.0], N[(t * b), $MachinePrecision], If[LessEqual[b, -5.2e-149], t$95$2, If[LessEqual[b, -1.3e-270], t$95$1, If[LessEqual[b, 4.35e-256], t$95$2, If[LessEqual[b, 6.1e+119], t$95$1, N[(t * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3e10 or 6.1e119 < b

   1. Initial program 90.7%

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

   2. Taylor expanded in b around inf 78.1%

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

   3. Taylor expanded in t around inf 38.2%

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

   if -1.3e10 < b < -5.19999999999999998e-149 or -1.3000000000000001e-270 < b < 4.3499999999999999e-256

   1. Initial program 98.1%

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

   2. Taylor expanded in y around inf 39.5%

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

   3. Taylor expanded in b around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. distribute-rgt-neg-out 35.8%

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

   5. Simplified 35.8%

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

   if -5.19999999999999998e-149 < b < -1.3000000000000001e-270 or 4.3499999999999999e-256 < b < 6.1e119

   1. Initial program 99.1%

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

   2. Taylor expanded in b around 0 92.6%

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

   3. Taylor expanded in x around 0 77.6%

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

      1. distribute-lft-in 77.6%

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

      2. mul-1-neg 77.6%

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

      3. mul-1-neg 77.6%

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

      4. sub-neg 77.6%

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

      5. metadata-eval 77.6%

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

      6. +-commutative 77.6%

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

      7. distribute-rgt-neg-in 77.6%

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

      8. fma-udef 77.6%

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

      9. neg-sub0 77.6%

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

      10. +-commutative 77.6%

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

      11. associate--r+ 77.6%

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

      12. metadata-eval 77.6%

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

      13. sub-neg 77.6%

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

      14. metadata-eval 77.6%

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

      15. fma-neg 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around inf 36.0%

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

      1. mul-1-neg 36.0%

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

      2. distribute-lft-neg-out 36.0%

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

      3. *-commutative 36.0%

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

   8. Simplified 36.0%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -13000000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-149}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 4.35 \cdot 10^{-256}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 10: 33.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -5.8e+96)
     (* t b)
     (if (<= b -4.6e-293)
       t_1
       (if (<= b 2.75e-257) (* y (- z)) (if (<= b 1.2e+208) t_1 (* t b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -5.8e+96) {
		tmp = t * b;
	} else if (b <= -4.6e-293) {
		tmp = t_1;
	} else if (b <= 2.75e-257) {
		tmp = y * -z;
	} else if (b <= 1.2e+208) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-5.8d+96)) then
        tmp = t * b
    else if (b <= (-4.6d-293)) then
        tmp = t_1
    else if (b <= 2.75d-257) then
        tmp = y * -z
    else if (b <= 1.2d+208) then
        tmp = t_1
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -5.8e+96) {
		tmp = t * b;
	} else if (b <= -4.6e-293) {
		tmp = t_1;
	} else if (b <= 2.75e-257) {
		tmp = y * -z;
	} else if (b <= 1.2e+208) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -5.8e+96:
		tmp = t * b
	elif b <= -4.6e-293:
		tmp = t_1
	elif b <= 2.75e-257:
		tmp = y * -z
	elif b <= 1.2e+208:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -5.8e+96)
		tmp = Float64(t * b);
	elseif (b <= -4.6e-293)
		tmp = t_1;
	elseif (b <= 2.75e-257)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 1.2e+208)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -5.8e+96)
		tmp = t * b;
	elseif (b <= -4.6e-293)
		tmp = t_1;
	elseif (b <= 2.75e-257)
		tmp = y * -z;
	elseif (b <= 1.2e+208)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.8e+96], N[(t * b), $MachinePrecision], If[LessEqual[b, -4.6e-293], t$95$1, If[LessEqual[b, 2.75e-257], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 1.2e+208], t$95$1, N[(t * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.79999999999999955e96 or 1.19999999999999993e208 < b

   1. Initial program 89.2%

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

   2. Taylor expanded in b around inf 86.8%

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

   3. Taylor expanded in t around inf 48.3%

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

   if -5.79999999999999955e96 < b < -4.5999999999999999e-293 or 2.75000000000000012e-257 < b < 1.19999999999999993e208

   1. Initial program 98.3%

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

   2. Taylor expanded in a around inf 42.2%

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

   if -4.5999999999999999e-293 < b < 2.75000000000000012e-257

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 46.9%

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

   3. Taylor expanded in b around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. distribute-rgt-neg-out 46.9%

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

   5. Simplified 46.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+96}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 11: 38.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;b \leq -2.32 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* b (- t 2.0))))
   (if (<= b -2.32e+33)
     t_2
     (if (<= b -4.5e-293)
       t_1
       (if (<= b 5.3e-257) (* y (- z)) (if (<= b 1.1e+107) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -2.32e+33) {
		tmp = t_2;
	} else if (b <= -4.5e-293) {
		tmp = t_1;
	} else if (b <= 5.3e-257) {
		tmp = y * -z;
	} else if (b <= 1.1e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    t_2 = b * (t - 2.0d0)
    if (b <= (-2.32d+33)) then
        tmp = t_2
    else if (b <= (-4.5d-293)) then
        tmp = t_1
    else if (b <= 5.3d-257) then
        tmp = y * -z
    else if (b <= 1.1d+107) 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 * (1.0 - t);
	double t_2 = b * (t - 2.0);
	double tmp;
	if (b <= -2.32e+33) {
		tmp = t_2;
	} else if (b <= -4.5e-293) {
		tmp = t_1;
	} else if (b <= 5.3e-257) {
		tmp = y * -z;
	} else if (b <= 1.1e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	t_2 = b * (t - 2.0)
	tmp = 0
	if b <= -2.32e+33:
		tmp = t_2
	elif b <= -4.5e-293:
		tmp = t_1
	elif b <= 5.3e-257:
		tmp = y * -z
	elif b <= 1.1e+107:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	t_2 = Float64(b * Float64(t - 2.0))
	tmp = 0.0
	if (b <= -2.32e+33)
		tmp = t_2;
	elseif (b <= -4.5e-293)
		tmp = t_1;
	elseif (b <= 5.3e-257)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 1.1e+107)
		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 * (1.0 - t);
	t_2 = b * (t - 2.0);
	tmp = 0.0;
	if (b <= -2.32e+33)
		tmp = t_2;
	elseif (b <= -4.5e-293)
		tmp = t_1;
	elseif (b <= 5.3e-257)
		tmp = y * -z;
	elseif (b <= 1.1e+107)
		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[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.32e+33], t$95$2, If[LessEqual[b, -4.5e-293], t$95$1, If[LessEqual[b, 5.3e-257], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 1.1e+107], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.32000000000000002e33 or 1.1e107 < b

   1. Initial program 89.7%

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

   2. Taylor expanded in b around inf 78.1%

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

   3. Taylor expanded in y around 0 52.0%

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

   if -2.32000000000000002e33 < b < -4.5000000000000002e-293 or 5.3e-257 < b < 1.1e107

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 46.3%

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

   if -4.5000000000000002e-293 < b < 5.3e-257

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 46.9%

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

   3. Taylor expanded in b around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. distribute-rgt-neg-out 46.9%

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

   5. Simplified 46.9%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.32 \cdot 10^{+33}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 12: 50.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -7.5e+38)
     t_2
     (if (<= t -2.5e-180)
       t_1
       (if (<= t 1.45e-210) (* b (- y 2.0)) (if (<= t 2.45e+39) 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 <= -7.5e+38) {
		tmp = t_2;
	} else if (t <= -2.5e-180) {
		tmp = t_1;
	} else if (t <= 1.45e-210) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.45e+39) {
		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 <= (-7.5d+38)) then
        tmp = t_2
    else if (t <= (-2.5d-180)) then
        tmp = t_1
    else if (t <= 1.45d-210) then
        tmp = b * (y - 2.0d0)
    else if (t <= 2.45d+39) 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 <= -7.5e+38) {
		tmp = t_2;
	} else if (t <= -2.5e-180) {
		tmp = t_1;
	} else if (t <= 1.45e-210) {
		tmp = b * (y - 2.0);
	} else if (t <= 2.45e+39) {
		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 <= -7.5e+38:
		tmp = t_2
	elif t <= -2.5e-180:
		tmp = t_1
	elif t <= 1.45e-210:
		tmp = b * (y - 2.0)
	elif t <= 2.45e+39:
		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 <= -7.5e+38)
		tmp = t_2;
	elseif (t <= -2.5e-180)
		tmp = t_1;
	elseif (t <= 1.45e-210)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 2.45e+39)
		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 <= -7.5e+38)
		tmp = t_2;
	elseif (t <= -2.5e-180)
		tmp = t_1;
	elseif (t <= 1.45e-210)
		tmp = b * (y - 2.0);
	elseif (t <= 2.45e+39)
		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, -7.5e+38], t$95$2, If[LessEqual[t, -2.5e-180], t$95$1, If[LessEqual[t, 1.45e-210], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4999999999999999e38 or 2.44999999999999994e39 < 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. Taylor expanded in t around inf 68.0%

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

   if -7.4999999999999999e38 < t < -2.5000000000000001e-180 or 1.45000000000000003e-210 < t < 2.44999999999999994e39

   1. Initial program 97.9%

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

   2. Taylor expanded in y around inf 38.2%

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

   if -2.5000000000000001e-180 < t < 1.45000000000000003e-210

   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. Taylor expanded in b around inf 52.5%

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

   3. Taylor expanded in t around 0 52.5%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 13: 68.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+136} \lor \neg \left(y \leq 1.52 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.2e+136) (not (<= y 1.52e+29)))
   (* y (- b z))
   (+ x (+ z (* t (- b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.2e+136) || !(y <= 1.52e+29)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (t * (b - 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 ((y <= (-6.2d+136)) .or. (.not. (y <= 1.52d+29))) then
        tmp = y * (b - z)
    else
        tmp = x + (z + (t * (b - 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 ((y <= -6.2e+136) || !(y <= 1.52e+29)) {
		tmp = y * (b - z);
	} else {
		tmp = x + (z + (t * (b - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.2e+136) or not (y <= 1.52e+29):
		tmp = y * (b - z)
	else:
		tmp = x + (z + (t * (b - a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.2e+136) || !(y <= 1.52e+29))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(x + Float64(z + Float64(t * Float64(b - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.2e+136) || ~((y <= 1.52e+29)))
		tmp = y * (b - z);
	else
		tmp = x + (z + (t * (b - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.2e+136], N[Not[LessEqual[y, 1.52e+29]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999967e136 or 1.52e29 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 77.1%

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

   if -6.19999999999999967e136 < y < 1.52e29

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. fma-def 97.7%

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

      3. associate--l+ 97.7%

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

      4. sub-neg 97.7%

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

      5. metadata-eval 97.7%

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

      6. sub-neg 97.7%

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

      7. associate--l+ 97.7%

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

      8. *-commutative 97.7%

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

      9. distribute-rgt-neg-in 97.7%

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

      10. fma-neg 97.7%

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

      11. neg-sub0 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 97.7%

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

      17. *-commutative 97.7%

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

      18. distribute-rgt-neg-in 97.7%

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

      19. neg-sub0 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 97.7%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 97.7%

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

   4. Taylor expanded in y around 0 92.7%

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

   5. Taylor expanded in t around inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. unsub-neg 73.2%

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

   7. Simplified 73.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+136} \lor \neg \left(y \leq 1.52 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \end{array} \]

Alternative 14: 73.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+31} \lor \neg \left(t \leq 0.92\right):\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + b \cdot \left(y + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.6e+31) (not (<= t 0.92)))
   (+ x (+ z (* t (- b a))))
   (+ (+ x a) (* b (+ y -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.6e+31) || !(t <= 0.92)) {
		tmp = x + (z + (t * (b - a)));
	} else {
		tmp = (x + a) + (b * (y + -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.6d+31)) .or. (.not. (t <= 0.92d0))) then
        tmp = x + (z + (t * (b - a)))
    else
        tmp = (x + a) + (b * (y + (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.6e+31) || !(t <= 0.92)) {
		tmp = x + (z + (t * (b - a)));
	} else {
		tmp = (x + a) + (b * (y + -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.6e+31) or not (t <= 0.92):
		tmp = x + (z + (t * (b - a)))
	else:
		tmp = (x + a) + (b * (y + -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.6e+31) || !(t <= 0.92))
		tmp = Float64(x + Float64(z + Float64(t * Float64(b - a))));
	else
		tmp = Float64(Float64(x + a) + Float64(b * Float64(y + -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.6e+31) || ~((t <= 0.92)))
		tmp = x + (z + (t * (b - a)));
	else
		tmp = (x + a) + (b * (y + -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.6e+31], N[Not[LessEqual[t, 0.92]], $MachinePrecision]], N[(x + N[(z + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + a), $MachinePrecision] + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e31 or 0.92000000000000004 < t

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. fma-def 93.9%

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

      3. associate--l+ 93.9%

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

      4. sub-neg 93.9%

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

      5. metadata-eval 93.9%

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

      6. sub-neg 93.9%

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

      7. associate--l+ 93.9%

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

      8. *-commutative 93.9%

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

      9. distribute-rgt-neg-in 93.9%

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

      10. fma-neg 93.9%

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

      11. neg-sub0 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 93.9%

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

      17. *-commutative 93.9%

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

      18. distribute-rgt-neg-in 93.9%

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

      19. neg-sub0 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 93.9%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 77.9%

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

   5. Taylor expanded in t around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   7. Simplified 82.0%

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

   if -1.6e31 < t < 0.92000000000000004

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 70.0%

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

      1. sub-neg 70.0%

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

      2. metadata-eval 70.0%

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

      3. *-commutative 70.0%

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

      4. cancel-sign-sub-inv 70.0%

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

      5. neg-sub0 70.0%

         \[\leadsto \left(x + \color{blue}{\left(0 - \left(t + -1\right)\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      6. +-commutative 70.0%

         \[\leadsto \left(x + \left(0 - \color{blue}{\left(-1 + t\right)}\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      7. associate--r+ 70.0%

         \[\leadsto \left(x + \color{blue}{\left(\left(0 - -1\right) - t\right)} \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

      8. metadata-eval 70.0%

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

      9. *-commutative 70.0%

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

      10. +-commutative 70.0%

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

      11. fma-def 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 69.4%

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

      1. associate-+r+ 69.4%

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

      2. +-commutative 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

   7. Simplified 69.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+31} \lor \neg \left(t \leq 0.92\right):\\ \;\;\;\;x + \left(z + t \cdot \left(b - a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + a\right) + b \cdot \left(y + -2\right)\\ \end{array} \]

Alternative 15: 23.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+70}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-183}:\\ \;\;\;\;a\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-118}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.2e+70)
   (* t b)
   (if (<= b -1.6e-183)
     a
     (if (<= b 7.6e-118) z (if (<= b 8.8e+20) x (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+70) {
		tmp = t * b;
	} else if (b <= -1.6e-183) {
		tmp = a;
	} else if (b <= 7.6e-118) {
		tmp = z;
	} else if (b <= 8.8e+20) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.2d+70)) then
        tmp = t * b
    else if (b <= (-1.6d-183)) then
        tmp = a
    else if (b <= 7.6d-118) then
        tmp = z
    else if (b <= 8.8d+20) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+70) {
		tmp = t * b;
	} else if (b <= -1.6e-183) {
		tmp = a;
	} else if (b <= 7.6e-118) {
		tmp = z;
	} else if (b <= 8.8e+20) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.2e+70:
		tmp = t * b
	elif b <= -1.6e-183:
		tmp = a
	elif b <= 7.6e-118:
		tmp = z
	elif b <= 8.8e+20:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.2e+70)
		tmp = Float64(t * b);
	elseif (b <= -1.6e-183)
		tmp = a;
	elseif (b <= 7.6e-118)
		tmp = z;
	elseif (b <= 8.8e+20)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.2e+70)
		tmp = t * b;
	elseif (b <= -1.6e-183)
		tmp = a;
	elseif (b <= 7.6e-118)
		tmp = z;
	elseif (b <= 8.8e+20)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.2e+70], N[(t * b), $MachinePrecision], If[LessEqual[b, -1.6e-183], a, If[LessEqual[b, 7.6e-118], z, If[LessEqual[b, 8.8e+20], x, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.2000000000000006e70 or 8.8e20 < b

   1. Initial program 89.7%

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

   2. Taylor expanded in b around inf 75.1%

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

   3. Taylor expanded in t around inf 38.4%

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

   if -6.2000000000000006e70 < b < -1.6000000000000001e-183

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 39.5%

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

   3. Taylor expanded in t around 0 21.2%

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

   if -1.6000000000000001e-183 < b < 7.6000000000000002e-118

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. fma-def 98.6%

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

      3. associate--l+ 98.6%

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

      4. sub-neg 98.6%

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

      5. metadata-eval 98.6%

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

      6. sub-neg 98.6%

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

      7. associate--l+ 98.6%

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

      8. *-commutative 98.6%

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

      9. distribute-rgt-neg-in 98.6%

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

      10. fma-neg 98.6%

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

      11. neg-sub0 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 98.6%

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

      17. *-commutative 98.6%

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

      18. distribute-rgt-neg-in 98.6%

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

      19. neg-sub0 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 98.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 98.6%

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

   4. Taylor expanded in y around 0 78.4%

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

   5. Taylor expanded in z around inf 23.3%

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

   if 7.6000000000000002e-118 < b < 8.8e20

   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. Taylor expanded in x around inf 31.3%

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

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+70}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-183}:\\ \;\;\;\;a\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{-118}:\\ \;\;\;\;z\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 16: 57.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+127} \lor \neg \left(y \leq 175000000000\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.9e+127) (not (<= y 175000000000.0)))
   (* y (- b z))
   (+ z (* t (- b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6.9e+127) || !(y <= 175000000000.0)) {
		tmp = y * (b - z);
	} else {
		tmp = z + (t * (b - 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 ((y <= (-6.9d+127)) .or. (.not. (y <= 175000000000.0d0))) then
        tmp = y * (b - z)
    else
        tmp = z + (t * (b - 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 ((y <= -6.9e+127) || !(y <= 175000000000.0)) {
		tmp = y * (b - z);
	} else {
		tmp = z + (t * (b - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6.9e+127) or not (y <= 175000000000.0):
		tmp = y * (b - z)
	else:
		tmp = z + (t * (b - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6.9e+127) || !(y <= 175000000000.0))
		tmp = Float64(y * Float64(b - z));
	else
		tmp = Float64(z + Float64(t * Float64(b - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -6.9e+127) || ~((y <= 175000000000.0)))
		tmp = y * (b - z);
	else
		tmp = z + (t * (b - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6.9e+127], N[Not[LessEqual[y, 175000000000.0]], $MachinePrecision]], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8999999999999996e127 or 1.75e11 < y

   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. Taylor expanded in y around inf 75.1%

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

   if -6.8999999999999996e127 < y < 1.75e11

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. fma-def 97.6%

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

      3. associate--l+ 97.6%

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

      4. sub-neg 97.6%

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

      5. metadata-eval 97.6%

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

      6. sub-neg 97.6%

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

      7. associate--l+ 97.6%

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

      8. *-commutative 97.6%

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

      9. distribute-rgt-neg-in 97.6%

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

      10. fma-neg 97.6%

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

      11. neg-sub0 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 97.6%

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

      17. *-commutative 97.6%

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

      18. distribute-rgt-neg-in 97.6%

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

      19. neg-sub0 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 97.6%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 94.3%

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

   5. Taylor expanded in t around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

   7. Simplified 73.9%

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

   8. Taylor expanded in x around 0 57.7%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+127} \lor \neg \left(y \leq 175000000000\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 17: 25.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+70}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-151}:\\ \;\;\;\;a\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e+70)
   (* t b)
   (if (<= b -8.5e-151) a (if (<= b 1.45e+119) (* t (- a)) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+70) {
		tmp = t * b;
	} else if (b <= -8.5e-151) {
		tmp = a;
	} else if (b <= 1.45e+119) {
		tmp = t * -a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.65d+70)) then
        tmp = t * b
    else if (b <= (-8.5d-151)) then
        tmp = a
    else if (b <= 1.45d+119) then
        tmp = t * -a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+70) {
		tmp = t * b;
	} else if (b <= -8.5e-151) {
		tmp = a;
	} else if (b <= 1.45e+119) {
		tmp = t * -a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.65e+70:
		tmp = t * b
	elif b <= -8.5e-151:
		tmp = a
	elif b <= 1.45e+119:
		tmp = t * -a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e+70)
		tmp = Float64(t * b);
	elseif (b <= -8.5e-151)
		tmp = a;
	elseif (b <= 1.45e+119)
		tmp = Float64(t * Float64(-a));
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.65e+70)
		tmp = t * b;
	elseif (b <= -8.5e-151)
		tmp = a;
	elseif (b <= 1.45e+119)
		tmp = t * -a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e+70], N[(t * b), $MachinePrecision], If[LessEqual[b, -8.5e-151], a, If[LessEqual[b, 1.45e+119], N[(t * (-a)), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.65000000000000008e70 or 1.45000000000000004e119 < b

   1. Initial program 89.5%

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

   2. Taylor expanded in b around inf 79.8%

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

   3. Taylor expanded in t around inf 41.6%

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

   if -1.65000000000000008e70 < b < -8.49999999999999999e-151

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 36.4%

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

   3. Taylor expanded in t around 0 23.7%

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

   if -8.49999999999999999e-151 < b < 1.45000000000000004e119

   1. Initial program 98.3%

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

   2. Taylor expanded in b around 0 92.7%

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

   3. Taylor expanded in x around 0 76.3%

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

      1. distribute-lft-in 76.3%

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

      2. mul-1-neg 76.3%

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

      3. mul-1-neg 76.3%

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

      4. sub-neg 76.3%

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

      5. metadata-eval 76.3%

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

      6. +-commutative 76.3%

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

      7. distribute-rgt-neg-in 76.3%

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

      8. fma-udef 76.3%

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

      9. neg-sub0 76.3%

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

      10. +-commutative 76.3%

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

      11. associate--r+ 76.3%

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

      12. metadata-eval 76.3%

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

      13. sub-neg 76.3%

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

      14. metadata-eval 76.3%

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

      15. fma-neg 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in t around inf 32.6%

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

      1. mul-1-neg 32.6%

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

      2. distribute-lft-neg-out 32.6%

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

      3. *-commutative 32.6%

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

   8. Simplified 32.6%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+70}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-151}:\\ \;\;\;\;a\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+119}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 18: 21.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-290}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-17}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.1e+90)
   x
   (if (<= x -6e-290) a (if (<= x 9e-17) z (if (<= x 6.8e+109) a x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e+90) {
		tmp = x;
	} else if (x <= -6e-290) {
		tmp = a;
	} else if (x <= 9e-17) {
		tmp = z;
	} else if (x <= 6.8e+109) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.1d+90)) then
        tmp = x
    else if (x <= (-6d-290)) then
        tmp = a
    else if (x <= 9d-17) then
        tmp = z
    else if (x <= 6.8d+109) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e+90) {
		tmp = x;
	} else if (x <= -6e-290) {
		tmp = a;
	} else if (x <= 9e-17) {
		tmp = z;
	} else if (x <= 6.8e+109) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.1e+90:
		tmp = x
	elif x <= -6e-290:
		tmp = a
	elif x <= 9e-17:
		tmp = z
	elif x <= 6.8e+109:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.1e+90)
		tmp = x;
	elseif (x <= -6e-290)
		tmp = a;
	elseif (x <= 9e-17)
		tmp = z;
	elseif (x <= 6.8e+109)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.1e+90)
		tmp = x;
	elseif (x <= -6e-290)
		tmp = a;
	elseif (x <= 9e-17)
		tmp = z;
	elseif (x <= 6.8e+109)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.1e+90], x, If[LessEqual[x, -6e-290], a, If[LessEqual[x, 9e-17], z, If[LessEqual[x, 6.8e+109], a, x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.09999999999999995e90 or 6.80000000000000013e109 < x

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 39.1%

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

   if -1.09999999999999995e90 < x < -5.99999999999999985e-290 or 8.99999999999999957e-17 < x < 6.80000000000000013e109

   1. Initial program 96.5%

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

   2. Taylor expanded in a around inf 37.8%

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

   3. Taylor expanded in t around 0 18.6%

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

   if -5.99999999999999985e-290 < x < 8.99999999999999957e-17

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. fma-def 98.4%

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

      3. associate--l+ 98.4%

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

      4. sub-neg 98.4%

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

      5. metadata-eval 98.4%

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

      6. sub-neg 98.4%

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

      7. associate--l+ 98.4%

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

      8. *-commutative 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. fma-neg 98.4%

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

      11. neg-sub0 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      12. sub-neg 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(y + \left(-1\right)\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      13. +-commutative 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 0 - \color{blue}{\left(\left(-1\right) + y\right)}, -\left(t - 1\right) \cdot a\right)\right) \]

      14. associate--r+ 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \color{blue}{\left(0 - \left(-1\right)\right) - y}, -\left(t - 1\right) \cdot a\right)\right) \]

      15. metadata-eval 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, \left(0 - \color{blue}{-1}\right) - y, -\left(t - 1\right) \cdot a\right)\right) \]

      16. metadata-eval 98.4%

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

      17. *-commutative 98.4%

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

      18. distribute-rgt-neg-in 98.4%

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

      19. neg-sub0 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(0 - \left(t - 1\right)\right)}\right)\right) \]

      20. sub-neg 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(t + \left(-1\right)\right)}\right)\right)\right) \]

      21. +-commutative 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \left(0 - \color{blue}{\left(\left(-1\right) + t\right)}\right)\right)\right) \]

      22. associate--r+ 98.4%

          \[\leadsto \mathsf{fma}\left(y + \left(t + -2\right), b, x + \mathsf{fma}\left(z, 1 - y, a \cdot \color{blue}{\left(\left(0 - \left(-1\right)\right) - t\right)}\right)\right) \]

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 69.9%

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

   5. Taylor expanded in z around inf 17.2%

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

4. Final simplification 24.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-290}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-17}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 20.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-272}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+23}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.02e+92)
   x
   (if (<= x -6.5e-272) a (if (<= x 1.06e+23) (* b -2.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.02e+92) {
		tmp = x;
	} else if (x <= -6.5e-272) {
		tmp = a;
	} else if (x <= 1.06e+23) {
		tmp = b * -2.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.02d+92)) then
        tmp = x
    else if (x <= (-6.5d-272)) then
        tmp = a
    else if (x <= 1.06d+23) then
        tmp = b * (-2.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.02e+92) {
		tmp = x;
	} else if (x <= -6.5e-272) {
		tmp = a;
	} else if (x <= 1.06e+23) {
		tmp = b * -2.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.02e+92:
		tmp = x
	elif x <= -6.5e-272:
		tmp = a
	elif x <= 1.06e+23:
		tmp = b * -2.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.02e+92)
		tmp = x;
	elseif (x <= -6.5e-272)
		tmp = a;
	elseif (x <= 1.06e+23)
		tmp = Float64(b * -2.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.02e+92)
		tmp = x;
	elseif (x <= -6.5e-272)
		tmp = a;
	elseif (x <= 1.06e+23)
		tmp = b * -2.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.02e+92], x, If[LessEqual[x, -6.5e-272], a, If[LessEqual[x, 1.06e+23], N[(b * -2.0), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02000000000000003e92 or 1.06e23 < x

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf 34.5%

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

   if -1.02000000000000003e92 < x < -6.5e-272

   1. Initial program 97.5%

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

   2. Taylor expanded in a around inf 36.8%

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

   3. Taylor expanded in t around 0 21.5%

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

   if -6.5e-272 < x < 1.06e23

   1. Initial program 96.3%

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

   2. Taylor expanded in b around inf 46.3%

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

   3. Taylor expanded in y around 0 31.7%

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

   4. Taylor expanded in t around 0 17.1%

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

      1. *-commutative 17.1%

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

   6. Simplified 17.1%

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

4. Final simplification 25.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-272}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{+23}:\\ \;\;\;\;b \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 21.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8e+89) x (if (<= x 7.5e+109) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+89) {
		tmp = x;
	} else if (x <= 7.5e+109) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-8d+89)) then
        tmp = x
    else if (x <= 7.5d+109) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8e+89) {
		tmp = x;
	} else if (x <= 7.5e+109) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -8e+89:
		tmp = x
	elif x <= 7.5e+109:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8e+89)
		tmp = x;
	elseif (x <= 7.5e+109)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -8e+89)
		tmp = x;
	elseif (x <= 7.5e+109)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8e+89], x, If[LessEqual[x, 7.5e+109], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999996e89 or 7.50000000000000018e109 < x

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 39.1%

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

   if -7.99999999999999996e89 < x < 7.50000000000000018e109

   1. Initial program 96.0%

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

   2. Taylor expanded in a around inf 34.9%

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

   3. Taylor expanded in t around 0 15.3%

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

4. Final simplification 22.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+109}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 11.6% 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 95.7%

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

2. Taylor expanded in a around inf 32.3%

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

3. Taylor expanded in t around 0 12.6%

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

4. Final simplification 12.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023314 
(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)))