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

Percentage Accurate: 94.8% → 97.8%

Time: 16.6s

Alternatives: 23

Speedup: 0.5×

• 36.1% 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: 94.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 78.0%

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

4. Final simplification 99.2%

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

Alternative 2: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-def 98.0%

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

   3. associate--l+ 98.0%

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

   4. sub-neg 98.0%

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

   5. metadata-eval 98.0%

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

   6. sub-neg 98.0%

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

   7. associate--l+ 98.0%

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

   8. *-commutative 98.0%

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

   9. distribute-rgt-neg-in 98.0%

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

   10. fma-neg 98.8%

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

   11. neg-sub0 98.8%

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

   12. sub-neg 98.8%

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

   13. +-commutative 98.8%

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

   14. associate--r+ 98.8%

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

   15. metadata-eval 98.8%

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

   16. metadata-eval 98.8%

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

   17. *-commutative 98.8%

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

   18. distribute-rgt-neg-in 98.8%

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

   19. neg-sub0 98.8%

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

   20. sub-neg 98.8%

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

   21. +-commutative 98.8%

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

   22. associate--r+ 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -165000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-169}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-301}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-259}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -165000.0)
     t_2
     (if (<= t -7.2e-169)
       (+ x a)
       (if (<= t -7.6e-271)
         t_1
         (if (<= t 1.02e-301)
           (+ x a)
           (if (<= t 7e-259)
             (* b (+ y -2.0))
             (if (<= t 2.6e-170)
               (+ x a)
               (if (<= t 1.15e-117)
                 t_1
                 (if (<= t 2.6e+14) (+ x a) 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 <= -165000.0) {
		tmp = t_2;
	} else if (t <= -7.2e-169) {
		tmp = x + a;
	} else if (t <= -7.6e-271) {
		tmp = t_1;
	} else if (t <= 1.02e-301) {
		tmp = x + a;
	} else if (t <= 7e-259) {
		tmp = b * (y + -2.0);
	} else if (t <= 2.6e-170) {
		tmp = x + a;
	} else if (t <= 1.15e-117) {
		tmp = t_1;
	} else if (t <= 2.6e+14) {
		tmp = x + a;
	} 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 <= (-165000.0d0)) then
        tmp = t_2
    else if (t <= (-7.2d-169)) then
        tmp = x + a
    else if (t <= (-7.6d-271)) then
        tmp = t_1
    else if (t <= 1.02d-301) then
        tmp = x + a
    else if (t <= 7d-259) then
        tmp = b * (y + (-2.0d0))
    else if (t <= 2.6d-170) then
        tmp = x + a
    else if (t <= 1.15d-117) then
        tmp = t_1
    else if (t <= 2.6d+14) then
        tmp = x + a
    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 <= -165000.0) {
		tmp = t_2;
	} else if (t <= -7.2e-169) {
		tmp = x + a;
	} else if (t <= -7.6e-271) {
		tmp = t_1;
	} else if (t <= 1.02e-301) {
		tmp = x + a;
	} else if (t <= 7e-259) {
		tmp = b * (y + -2.0);
	} else if (t <= 2.6e-170) {
		tmp = x + a;
	} else if (t <= 1.15e-117) {
		tmp = t_1;
	} else if (t <= 2.6e+14) {
		tmp = x + a;
	} 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 <= -165000.0:
		tmp = t_2
	elif t <= -7.2e-169:
		tmp = x + a
	elif t <= -7.6e-271:
		tmp = t_1
	elif t <= 1.02e-301:
		tmp = x + a
	elif t <= 7e-259:
		tmp = b * (y + -2.0)
	elif t <= 2.6e-170:
		tmp = x + a
	elif t <= 1.15e-117:
		tmp = t_1
	elif t <= 2.6e+14:
		tmp = x + a
	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 <= -165000.0)
		tmp = t_2;
	elseif (t <= -7.2e-169)
		tmp = Float64(x + a);
	elseif (t <= -7.6e-271)
		tmp = t_1;
	elseif (t <= 1.02e-301)
		tmp = Float64(x + a);
	elseif (t <= 7e-259)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (t <= 2.6e-170)
		tmp = Float64(x + a);
	elseif (t <= 1.15e-117)
		tmp = t_1;
	elseif (t <= 2.6e+14)
		tmp = Float64(x + a);
	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 <= -165000.0)
		tmp = t_2;
	elseif (t <= -7.2e-169)
		tmp = x + a;
	elseif (t <= -7.6e-271)
		tmp = t_1;
	elseif (t <= 1.02e-301)
		tmp = x + a;
	elseif (t <= 7e-259)
		tmp = b * (y + -2.0);
	elseif (t <= 2.6e-170)
		tmp = x + a;
	elseif (t <= 1.15e-117)
		tmp = t_1;
	elseif (t <= 2.6e+14)
		tmp = x + a;
	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, -165000.0], t$95$2, If[LessEqual[t, -7.2e-169], N[(x + a), $MachinePrecision], If[LessEqual[t, -7.6e-271], t$95$1, If[LessEqual[t, 1.02e-301], N[(x + a), $MachinePrecision], If[LessEqual[t, 7e-259], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-170], N[(x + a), $MachinePrecision], If[LessEqual[t, 1.15e-117], t$95$1, If[LessEqual[t, 2.6e+14], N[(x + a), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -165000 or 2.6e14 < t

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf 66.8%

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

   if -165000 < t < -7.20000000000000003e-169 or -7.60000000000000019e-271 < t < 1.0200000000000001e-301 or 7.0000000000000005e-259 < t < 2.6000000000000001e-170 or 1.14999999999999997e-117 < t < 2.6e14

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. fma-def 99.0%

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

      3. associate--l+ 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

      6. sub-neg 99.0%

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

      7. associate--l+ 99.0%

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

      8. *-commutative 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. fma-neg 99.0%

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

      11. neg-sub0 99.0%

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

      12. sub-neg 99.0%

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

      13. +-commutative 99.0%

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

      14. associate--r+ 99.0%

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

      15. metadata-eval 99.0%

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

      16. metadata-eval 99.0%

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

      17. *-commutative 99.0%

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

      18. distribute-rgt-neg-in 99.0%

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

      19. neg-sub0 99.0%

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

      20. sub-neg 99.0%

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

      21. +-commutative 99.0%

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

      22. associate--r+ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 75.2%

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

   5. Taylor expanded in t around 0 72.2%

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

   6. Taylor expanded in b around 0 50.0%

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

      1. +-commutative 50.0%

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

   8. Simplified 50.0%

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

   if -7.20000000000000003e-169 < t < -7.60000000000000019e-271 or 2.6000000000000001e-170 < t < 1.14999999999999997e-117

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 54.0%

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

   if 1.0200000000000001e-301 < t < 7.0000000000000005e-259

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 78.0%

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

   3. Taylor expanded in y around 0 78.0%

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

   4. Taylor expanded in t around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. *-commutative 78.0%

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

      3. distribute-lft-in 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -165000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-169}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-301}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-259}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 4: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-211}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t))))
        (t_2 (+ x (* b (- (+ y t) 2.0))))
        (t_3 (+ x (* z (- 1.0 y)))))
   (if (<= b -4.2e+36)
     t_2
     (if (<= b -9e-137)
       t_1
       (if (<= b 1.15e-305)
         t_3
         (if (<= b 3.2e-267)
           t_1
           (if (<= b 2.5e-211) t_3 (if (<= b 8.2e-80) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -4.2e+36) {
		tmp = t_2;
	} else if (b <= -9e-137) {
		tmp = t_1;
	} else if (b <= 1.15e-305) {
		tmp = t_3;
	} else if (b <= 3.2e-267) {
		tmp = t_1;
	} else if (b <= 2.5e-211) {
		tmp = t_3;
	} else if (b <= 8.2e-80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a * (1.0d0 - t))
    t_2 = x + (b * ((y + t) - 2.0d0))
    t_3 = x + (z * (1.0d0 - y))
    if (b <= (-4.2d+36)) then
        tmp = t_2
    else if (b <= (-9d-137)) then
        tmp = t_1
    else if (b <= 1.15d-305) then
        tmp = t_3
    else if (b <= 3.2d-267) then
        tmp = t_1
    else if (b <= 2.5d-211) then
        tmp = t_3
    else if (b <= 8.2d-80) 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 + (a * (1.0 - t));
	double t_2 = x + (b * ((y + t) - 2.0));
	double t_3 = x + (z * (1.0 - y));
	double tmp;
	if (b <= -4.2e+36) {
		tmp = t_2;
	} else if (b <= -9e-137) {
		tmp = t_1;
	} else if (b <= 1.15e-305) {
		tmp = t_3;
	} else if (b <= 3.2e-267) {
		tmp = t_1;
	} else if (b <= 2.5e-211) {
		tmp = t_3;
	} else if (b <= 8.2e-80) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (b * ((y + t) - 2.0))
	t_3 = x + (z * (1.0 - y))
	tmp = 0
	if b <= -4.2e+36:
		tmp = t_2
	elif b <= -9e-137:
		tmp = t_1
	elif b <= 1.15e-305:
		tmp = t_3
	elif b <= 3.2e-267:
		tmp = t_1
	elif b <= 2.5e-211:
		tmp = t_3
	elif b <= 8.2e-80:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	t_3 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (b <= -4.2e+36)
		tmp = t_2;
	elseif (b <= -9e-137)
		tmp = t_1;
	elseif (b <= 1.15e-305)
		tmp = t_3;
	elseif (b <= 3.2e-267)
		tmp = t_1;
	elseif (b <= 2.5e-211)
		tmp = t_3;
	elseif (b <= 8.2e-80)
		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 + (a * (1.0 - t));
	t_2 = x + (b * ((y + t) - 2.0));
	t_3 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (b <= -4.2e+36)
		tmp = t_2;
	elseif (b <= -9e-137)
		tmp = t_1;
	elseif (b <= 1.15e-305)
		tmp = t_3;
	elseif (b <= 3.2e-267)
		tmp = t_1;
	elseif (b <= 2.5e-211)
		tmp = t_3;
	elseif (b <= 8.2e-80)
		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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+36], t$95$2, If[LessEqual[b, -9e-137], t$95$1, If[LessEqual[b, 1.15e-305], t$95$3, If[LessEqual[b, 3.2e-267], t$95$1, If[LessEqual[b, 2.5e-211], t$95$3, If[LessEqual[b, 8.2e-80], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.20000000000000009e36 or 8.1999999999999999e-80 < b

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 79.5%

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

   3. Taylor expanded in a around 0 68.4%

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

   if -4.20000000000000009e36 < b < -8.9999999999999994e-137 or 1.15e-305 < b < 3.19999999999999986e-267 or 2.5000000000000001e-211 < b < 8.1999999999999999e-80

   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 z around 0 87.7%

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

   3. Taylor expanded in b around 0 77.1%

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

   if -8.9999999999999994e-137 < b < 1.15e-305 or 3.19999999999999986e-267 < b < 2.5000000000000001e-211

   1. Initial program 98.2%

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

   2. Taylor expanded in a around 0 77.5%

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

   3. Taylor expanded in b around 0 75.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+36}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-137}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-267}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-211}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-80}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \end{array} \]

Alternative 5: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+252}:\\ \;\;\;\;x + \left(t_2 + t_1\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+96} \lor \neg \left(z \leq 3.9 \cdot 10^{+114}\right):\\ \;\;\;\;t_3 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (* a (- 1.0 t)))
        (t_3 (+ x (* b (- (+ y t) 2.0)))))
   (if (<= z -7e+252)
     (+ x (+ t_2 t_1))
     (if (or (<= z -2e+96) (not (<= z 3.9e+114))) (+ t_3 t_1) (+ t_3 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 = a * (1.0 - t);
	double t_3 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (z <= -7e+252) {
		tmp = x + (t_2 + t_1);
	} else if ((z <= -2e+96) || !(z <= 3.9e+114)) {
		tmp = t_3 + t_1;
	} else {
		tmp = t_3 + t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = a * (1.0d0 - t)
    t_3 = x + (b * ((y + t) - 2.0d0))
    if (z <= (-7d+252)) then
        tmp = x + (t_2 + t_1)
    else if ((z <= (-2d+96)) .or. (.not. (z <= 3.9d+114))) then
        tmp = t_3 + t_1
    else
        tmp = t_3 + 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 = a * (1.0 - t);
	double t_3 = x + (b * ((y + t) - 2.0));
	double tmp;
	if (z <= -7e+252) {
		tmp = x + (t_2 + t_1);
	} else if ((z <= -2e+96) || !(z <= 3.9e+114)) {
		tmp = t_3 + t_1;
	} else {
		tmp = t_3 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = a * (1.0 - t)
	t_3 = x + (b * ((y + t) - 2.0))
	tmp = 0
	if z <= -7e+252:
		tmp = x + (t_2 + t_1)
	elif (z <= -2e+96) or not (z <= 3.9e+114):
		tmp = t_3 + t_1
	else:
		tmp = t_3 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(a * Float64(1.0 - t))
	t_3 = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)))
	tmp = 0.0
	if (z <= -7e+252)
		tmp = Float64(x + Float64(t_2 + t_1));
	elseif ((z <= -2e+96) || !(z <= 3.9e+114))
		tmp = Float64(t_3 + t_1);
	else
		tmp = Float64(t_3 + 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 = a * (1.0 - t);
	t_3 = x + (b * ((y + t) - 2.0));
	tmp = 0.0;
	if (z <= -7e+252)
		tmp = x + (t_2 + t_1);
	elseif ((z <= -2e+96) || ~((z <= 3.9e+114)))
		tmp = t_3 + t_1;
	else
		tmp = t_3 + 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[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+252], N[(x + N[(t$95$2 + t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2e+96], N[Not[LessEqual[z, 3.9e+114]], $MachinePrecision]], N[(t$95$3 + t$95$1), $MachinePrecision], N[(t$95$3 + t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999999e252

   1. Initial program 94.1%

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

   2. Taylor expanded in b around 0 100.0%

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

   if -6.9999999999999999e252 < z < -2.0000000000000001e96 or 3.9000000000000001e114 < z

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0 90.7%

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

   if -2.0000000000000001e96 < z < 3.9000000000000001e114

   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. Taylor expanded in z around 0 91.4%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+252}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+96} \lor \neg \left(z \leq 3.9 \cdot 10^{+114}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 6: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+253}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + t_1\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+91} \lor \neg \left(z \leq 1.15 \cdot 10^{+114}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -1.35e+253)
     (+ x (+ (* a (- 1.0 t)) t_1))
     (if (or (<= z -5.4e+91) (not (<= z 1.15e+114)))
       (+ (+ x (* b (- (+ y t) 2.0))) t_1)
       (+ a (+ x (+ (* t (- b a)) (* b (- y 2.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.35e+253) {
		tmp = x + ((a * (1.0 - t)) + t_1);
	} else if ((z <= -5.4e+91) || !(z <= 1.15e+114)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = a + (x + ((t * (b - 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) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (z <= (-1.35d+253)) then
        tmp = x + ((a * (1.0d0 - t)) + t_1)
    else if ((z <= (-5.4d+91)) .or. (.not. (z <= 1.15d+114))) then
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    else
        tmp = a + (x + ((t * (b - 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 t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.35e+253) {
		tmp = x + ((a * (1.0 - t)) + t_1);
	} else if ((z <= -5.4e+91) || !(z <= 1.15e+114)) {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	} else {
		tmp = a + (x + ((t * (b - a)) + (b * (y - 2.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if z <= -1.35e+253:
		tmp = x + ((a * (1.0 - t)) + t_1)
	elif (z <= -5.4e+91) or not (z <= 1.15e+114):
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	else:
		tmp = a + (x + ((t * (b - a)) + (b * (y - 2.0))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.35e+253)
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + t_1));
	elseif ((z <= -5.4e+91) || !(z <= 1.15e+114))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	else
		tmp = Float64(a + Float64(x + Float64(Float64(t * Float64(b - a)) + Float64(b * Float64(y - 2.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.35e+253)
		tmp = x + ((a * (1.0 - t)) + t_1);
	elseif ((z <= -5.4e+91) || ~((z <= 1.15e+114)))
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	else
		tmp = a + (x + ((t * (b - a)) + (b * (y - 2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+253], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5.4e+91], N[Not[LessEqual[z, 1.15e+114]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(a + N[(x + N[(N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000001e253

   1. Initial program 94.1%

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

   2. Taylor expanded in b around 0 100.0%

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

   if -1.35000000000000001e253 < z < -5.4e91 or 1.15e114 < z

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0 90.7%

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

   if -5.4e91 < z < 1.15e114

   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. Taylor expanded in t around 0 97.6%

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

   3. Taylor expanded in z around 0 92.0%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+253}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+91} \lor \neg \left(z \leq 1.15 \cdot 10^{+114}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right)\right)\\ \end{array} \]

Alternative 7: 43.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-161}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+20}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* z (- 1.0 y))))
   (if (<= z -3.5e+91)
     t_2
     (if (<= z -7.5e-18)
       t_1
       (if (<= z 1.7e-161)
         (+ x a)
         (if (<= z 6.6e-51)
           (* b (- (+ y t) 2.0))
           (if (<= z 1.12e+20)
             (+ x a)
             (if (<= z 6.5e+54)
               (* y (- b z))
               (if (<= z 1.45e+144) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (z <= -3.5e+91) {
		tmp = t_2;
	} else if (z <= -7.5e-18) {
		tmp = t_1;
	} else if (z <= 1.7e-161) {
		tmp = x + a;
	} else if (z <= 6.6e-51) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 1.12e+20) {
		tmp = x + a;
	} else if (z <= 6.5e+54) {
		tmp = y * (b - z);
	} else if (z <= 1.45e+144) {
		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 = t * (b - a)
    t_2 = z * (1.0d0 - y)
    if (z <= (-3.5d+91)) then
        tmp = t_2
    else if (z <= (-7.5d-18)) then
        tmp = t_1
    else if (z <= 1.7d-161) then
        tmp = x + a
    else if (z <= 6.6d-51) then
        tmp = b * ((y + t) - 2.0d0)
    else if (z <= 1.12d+20) then
        tmp = x + a
    else if (z <= 6.5d+54) then
        tmp = y * (b - z)
    else if (z <= 1.45d+144) 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 = t * (b - a);
	double t_2 = z * (1.0 - y);
	double tmp;
	if (z <= -3.5e+91) {
		tmp = t_2;
	} else if (z <= -7.5e-18) {
		tmp = t_1;
	} else if (z <= 1.7e-161) {
		tmp = x + a;
	} else if (z <= 6.6e-51) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 1.12e+20) {
		tmp = x + a;
	} else if (z <= 6.5e+54) {
		tmp = y * (b - z);
	} else if (z <= 1.45e+144) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = z * (1.0 - y)
	tmp = 0
	if z <= -3.5e+91:
		tmp = t_2
	elif z <= -7.5e-18:
		tmp = t_1
	elif z <= 1.7e-161:
		tmp = x + a
	elif z <= 6.6e-51:
		tmp = b * ((y + t) - 2.0)
	elif z <= 1.12e+20:
		tmp = x + a
	elif z <= 6.5e+54:
		tmp = y * (b - z)
	elif z <= 1.45e+144:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -3.5e+91)
		tmp = t_2;
	elseif (z <= -7.5e-18)
		tmp = t_1;
	elseif (z <= 1.7e-161)
		tmp = Float64(x + a);
	elseif (z <= 6.6e-51)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (z <= 1.12e+20)
		tmp = Float64(x + a);
	elseif (z <= 6.5e+54)
		tmp = Float64(y * Float64(b - z));
	elseif (z <= 1.45e+144)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -3.5e+91)
		tmp = t_2;
	elseif (z <= -7.5e-18)
		tmp = t_1;
	elseif (z <= 1.7e-161)
		tmp = x + a;
	elseif (z <= 6.6e-51)
		tmp = b * ((y + t) - 2.0);
	elseif (z <= 1.12e+20)
		tmp = x + a;
	elseif (z <= 6.5e+54)
		tmp = y * (b - z);
	elseif (z <= 1.45e+144)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+91], t$95$2, If[LessEqual[z, -7.5e-18], t$95$1, If[LessEqual[z, 1.7e-161], N[(x + a), $MachinePrecision], If[LessEqual[z, 6.6e-51], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+20], N[(x + a), $MachinePrecision], If[LessEqual[z, 6.5e+54], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+144], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.50000000000000001e91 or 1.44999999999999999e144 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf 67.2%

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

   if -3.50000000000000001e91 < z < -7.50000000000000015e-18 or 6.5e54 < z < 1.44999999999999999e144

   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 t around inf 60.9%

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

   if -7.50000000000000015e-18 < z < 1.69999999999999991e-161 or 6.59999999999999946e-51 < z < 1.12e20

   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. Step-by-step derivation

      1. +-commutative 98.0%

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

      2. fma-def 99.0%

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

      3. associate--l+ 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

      6. sub-neg 99.0%

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

      7. associate--l+ 99.0%

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

      8. *-commutative 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. fma-neg 99.0%

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

      11. neg-sub0 99.0%

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

      12. sub-neg 99.0%

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

      13. +-commutative 99.0%

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

      14. associate--r+ 99.0%

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

      15. metadata-eval 99.0%

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

      16. metadata-eval 99.0%

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

      17. *-commutative 99.0%

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

      18. distribute-rgt-neg-in 99.0%

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

      19. neg-sub0 99.0%

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

      20. sub-neg 99.0%

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

      21. +-commutative 99.0%

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

      22. associate--r+ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 94.3%

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

   5. Taylor expanded in t around 0 71.5%

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

   6. Taylor expanded in b around 0 48.2%

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

      1. +-commutative 48.2%

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

   8. Simplified 48.2%

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

   if 1.69999999999999991e-161 < z < 6.59999999999999946e-51

   1. Initial program 96.2%

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

   2. Taylor expanded in b around inf 51.6%

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

   if 1.12e20 < z < 6.5e54

   1. Initial program 77.8%

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

   2. Taylor expanded in y around inf 76.8%

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-161}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+20}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 8: 55.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* a (- 1.0 t)))) (t_2 (+ x (* z (- 1.0 y)))))
   (if (<= z -2.5e+77)
     t_2
     (if (<= z 1.9e-102)
       t_1
       (if (<= z 1.05e-49)
         (* b (- (+ y t) 2.0))
         (if (<= z 2.3e+24)
           t_1
           (if (<= z 1.25e+70)
             (* y (- b z))
             (if (<= z 1.06e+114) (* t (- b a)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a * (1.0 - t));
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -2.5e+77) {
		tmp = t_2;
	} else if (z <= 1.9e-102) {
		tmp = t_1;
	} else if (z <= 1.05e-49) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 2.3e+24) {
		tmp = t_1;
	} else if (z <= 1.25e+70) {
		tmp = y * (b - z);
	} else if (z <= 1.06e+114) {
		tmp = t * (b - a);
	} 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 + (a * (1.0d0 - t))
    t_2 = x + (z * (1.0d0 - y))
    if (z <= (-2.5d+77)) then
        tmp = t_2
    else if (z <= 1.9d-102) then
        tmp = t_1
    else if (z <= 1.05d-49) then
        tmp = b * ((y + t) - 2.0d0)
    else if (z <= 2.3d+24) then
        tmp = t_1
    else if (z <= 1.25d+70) then
        tmp = y * (b - z)
    else if (z <= 1.06d+114) then
        tmp = t * (b - a)
    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 + (a * (1.0 - t));
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -2.5e+77) {
		tmp = t_2;
	} else if (z <= 1.9e-102) {
		tmp = t_1;
	} else if (z <= 1.05e-49) {
		tmp = b * ((y + t) - 2.0);
	} else if (z <= 2.3e+24) {
		tmp = t_1;
	} else if (z <= 1.25e+70) {
		tmp = y * (b - z);
	} else if (z <= 1.06e+114) {
		tmp = t * (b - a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a * (1.0 - t))
	t_2 = x + (z * (1.0 - y))
	tmp = 0
	if z <= -2.5e+77:
		tmp = t_2
	elif z <= 1.9e-102:
		tmp = t_1
	elif z <= 1.05e-49:
		tmp = b * ((y + t) - 2.0)
	elif z <= 2.3e+24:
		tmp = t_1
	elif z <= 1.25e+70:
		tmp = y * (b - z)
	elif z <= 1.06e+114:
		tmp = t * (b - a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a * Float64(1.0 - t)))
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (z <= -2.5e+77)
		tmp = t_2;
	elseif (z <= 1.9e-102)
		tmp = t_1;
	elseif (z <= 1.05e-49)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif (z <= 2.3e+24)
		tmp = t_1;
	elseif (z <= 1.25e+70)
		tmp = Float64(y * Float64(b - z));
	elseif (z <= 1.06e+114)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a * (1.0 - t));
	t_2 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (z <= -2.5e+77)
		tmp = t_2;
	elseif (z <= 1.9e-102)
		tmp = t_1;
	elseif (z <= 1.05e-49)
		tmp = b * ((y + t) - 2.0);
	elseif (z <= 2.3e+24)
		tmp = t_1;
	elseif (z <= 1.25e+70)
		tmp = y * (b - z);
	elseif (z <= 1.06e+114)
		tmp = t * (b - a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+77], t$95$2, If[LessEqual[z, 1.9e-102], t$95$1, If[LessEqual[z, 1.05e-49], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+24], t$95$1, If[LessEqual[z, 1.25e+70], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+114], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.50000000000000002e77 or 1.05999999999999993e114 < z

   1. Initial program 95.2%

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

   2. Taylor expanded in a around 0 87.2%

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

   3. Taylor expanded in b around 0 75.2%

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

   if -2.50000000000000002e77 < z < 1.90000000000000013e-102 or 1.0499999999999999e-49 < z < 2.2999999999999999e24

   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 93.8%

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

   3. Taylor expanded in b around 0 62.9%

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

   if 1.90000000000000013e-102 < z < 1.0499999999999999e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 65.0%

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

   if 2.2999999999999999e24 < z < 1.2500000000000001e70

   1. Initial program 80.0%

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

   2. Taylor expanded in y around inf 79.1%

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

   if 1.2500000000000001e70 < z < 1.05999999999999993e114

   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 t around inf 78.2%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+77}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-102}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 9: 85.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+42} \lor \neg \left(z \leq 3.8 \cdot 10^{+157}\right):\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= z -1.6e+42) (not (<= z 3.8e+157)))
     (+ x (+ t_1 (* z (- 1.0 y))))
     (+ (+ x (* b (- (+ y t) 2.0))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((z <= -1.6e+42) || !(z <= 3.8e+157)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((z <= (-1.6d+42)) .or. (.not. (z <= 3.8d+157))) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = (x + (b * ((y + t) - 2.0d0))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if ((z <= -1.6e+42) || !(z <= 3.8e+157)) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (z <= -1.6e+42) or not (z <= 3.8e+157):
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = (x + (b * ((y + t) - 2.0))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((z <= -1.6e+42) || !(z <= 3.8e+157))
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(y + t) - 2.0))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if ((z <= -1.6e+42) || ~((z <= 3.8e+157)))
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = (x + (b * ((y + t) - 2.0))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.6e+42], N[Not[LessEqual[z, 3.8e+157]], $MachinePrecision]], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000001e42 or 3.8000000000000001e157 < z

   1. Initial program 95.0%

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

   2. Taylor expanded in b around 0 86.0%

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

   if -1.60000000000000001e42 < z < 3.8000000000000001e157

   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. Taylor expanded in z around 0 90.6%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+42} \lor \neg \left(z \leq 3.8 \cdot 10^{+157}\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(y + t\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 10: 25.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-49}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.9e+26)
   (* y b)
   (if (<= y -1.8e-99)
     z
     (if (<= y -1.7e-288)
       x
       (if (<= y 3.4e-289)
         z
         (if (<= y 3.4e-121)
           x
           (if (<= y 4.8e-49)
             (* -2.0 b)
             (if (<= y 2e+153) (* t b) (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e+26) {
		tmp = y * b;
	} else if (y <= -1.8e-99) {
		tmp = z;
	} else if (y <= -1.7e-288) {
		tmp = x;
	} else if (y <= 3.4e-289) {
		tmp = z;
	} else if (y <= 3.4e-121) {
		tmp = x;
	} else if (y <= 4.8e-49) {
		tmp = -2.0 * b;
	} else if (y <= 2e+153) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.9d+26)) then
        tmp = y * b
    else if (y <= (-1.8d-99)) then
        tmp = z
    else if (y <= (-1.7d-288)) then
        tmp = x
    else if (y <= 3.4d-289) then
        tmp = z
    else if (y <= 3.4d-121) then
        tmp = x
    else if (y <= 4.8d-49) then
        tmp = (-2.0d0) * b
    else if (y <= 2d+153) then
        tmp = t * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.9e+26) {
		tmp = y * b;
	} else if (y <= -1.8e-99) {
		tmp = z;
	} else if (y <= -1.7e-288) {
		tmp = x;
	} else if (y <= 3.4e-289) {
		tmp = z;
	} else if (y <= 3.4e-121) {
		tmp = x;
	} else if (y <= 4.8e-49) {
		tmp = -2.0 * b;
	} else if (y <= 2e+153) {
		tmp = t * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.9e+26:
		tmp = y * b
	elif y <= -1.8e-99:
		tmp = z
	elif y <= -1.7e-288:
		tmp = x
	elif y <= 3.4e-289:
		tmp = z
	elif y <= 3.4e-121:
		tmp = x
	elif y <= 4.8e-49:
		tmp = -2.0 * b
	elif y <= 2e+153:
		tmp = t * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.9e+26)
		tmp = Float64(y * b);
	elseif (y <= -1.8e-99)
		tmp = z;
	elseif (y <= -1.7e-288)
		tmp = x;
	elseif (y <= 3.4e-289)
		tmp = z;
	elseif (y <= 3.4e-121)
		tmp = x;
	elseif (y <= 4.8e-49)
		tmp = Float64(-2.0 * b);
	elseif (y <= 2e+153)
		tmp = Float64(t * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.9e+26)
		tmp = y * b;
	elseif (y <= -1.8e-99)
		tmp = z;
	elseif (y <= -1.7e-288)
		tmp = x;
	elseif (y <= 3.4e-289)
		tmp = z;
	elseif (y <= 3.4e-121)
		tmp = x;
	elseif (y <= 4.8e-49)
		tmp = -2.0 * b;
	elseif (y <= 2e+153)
		tmp = t * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.9e+26], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.8e-99], z, If[LessEqual[y, -1.7e-288], x, If[LessEqual[y, 3.4e-289], z, If[LessEqual[y, 3.4e-121], x, If[LessEqual[y, 4.8e-49], N[(-2.0 * b), $MachinePrecision], If[LessEqual[y, 2e+153], N[(t * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.9000000000000001e26 or 2e153 < y

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. fma-def 96.2%

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

      3. associate--l+ 96.2%

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

      4. sub-neg 96.2%

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

      5. metadata-eval 96.2%

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

      6. sub-neg 96.2%

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

      7. associate--l+ 96.2%

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

      8. *-commutative 96.2%

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

      9. distribute-rgt-neg-in 96.2%

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

      10. fma-neg 97.4%

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

      11. neg-sub0 97.4%

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

      12. sub-neg 97.4%

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

      13. +-commutative 97.4%

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

      14. associate--r+ 97.4%

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

      15. metadata-eval 97.4%

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

      16. metadata-eval 97.4%

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

      17. *-commutative 97.4%

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

      18. distribute-rgt-neg-in 97.4%

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

      19. neg-sub0 97.4%

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

      20. sub-neg 97.4%

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

      21. +-commutative 97.4%

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

      22. associate--r+ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 75.1%

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

   5. Taylor expanded in y around inf 43.9%

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

   if -1.9000000000000001e26 < y < -1.8e-99 or -1.69999999999999986e-288 < y < 3.40000000000000018e-289

   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 z around inf 42.9%

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

   3. Taylor expanded in y around 0 35.8%

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

   if -1.8e-99 < y < -1.69999999999999986e-288 or 3.40000000000000018e-289 < y < 3.40000000000000001e-121

   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 x around inf 37.2%

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

   if 3.40000000000000001e-121 < y < 4.79999999999999985e-49

   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 b around inf 51.5%

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

   3. Taylor expanded in y around 0 51.5%

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

   4. Taylor expanded in t around 0 43.9%

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

      1. *-commutative 43.9%

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

   6. Simplified 43.9%

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

   7. Taylor expanded in y around 0 43.9%

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

      1. *-commutative 43.9%

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

   9. Simplified 43.9%

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

   if 4.79999999999999985e-49 < y < 2e153

   1. Initial program 97.6%

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

   2. Taylor expanded in b around inf 36.5%

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

   3. Taylor expanded in y around 0 36.4%

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

   4. Taylor expanded in t around inf 27.0%

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

      1. *-commutative 27.0%

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

   6. Simplified 27.0%

      \[\leadsto \color{blue}{t \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-289}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-49}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 11: 83.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+108} \lor \neg \left(b \leq 6 \cdot 10^{+113}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.08e+108) (not (<= b 6e+113)))
   (+ x (* b (- (+ y t) 2.0)))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.08e+108) || !(b <= 6e+113)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.08d+108)) .or. (.not. (b <= 6d+113))) then
        tmp = x + (b * ((y + t) - 2.0d0))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.08e+108) || !(b <= 6e+113)) {
		tmp = x + (b * ((y + t) - 2.0));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.08e+108) or not (b <= 6e+113):
		tmp = x + (b * ((y + t) - 2.0))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.08e+108) || !(b <= 6e+113))
		tmp = Float64(x + Float64(b * Float64(Float64(y + t) - 2.0)));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.08e+108) || ~((b <= 6e+113)))
		tmp = x + (b * ((y + t) - 2.0));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.08e+108], N[Not[LessEqual[b, 6e+113]], $MachinePrecision]], N[(x + N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.0800000000000001e108 or 6e113 < b

   1. Initial program 92.5%

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

   2. Taylor expanded in z around 0 82.5%

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

   3. Taylor expanded in a around 0 78.6%

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

   if -1.0800000000000001e108 < b < 6e113

   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 0 84.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.08 \cdot 10^{+108} \lor \neg \left(b \leq 6 \cdot 10^{+113}\right):\\ \;\;\;\;x + b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 12: 25.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-100}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-288}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0032:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e+25)
   (* y b)
   (if (<= y -5e-100)
     z
     (if (<= y -1.8e-288)
       x
       (if (<= y 1.3e-288)
         z
         (if (<= y 2.7e-121) x (if (<= y 0.0032) (* -2.0 b) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+25) {
		tmp = y * b;
	} else if (y <= -5e-100) {
		tmp = z;
	} else if (y <= -1.8e-288) {
		tmp = x;
	} else if (y <= 1.3e-288) {
		tmp = z;
	} else if (y <= 2.7e-121) {
		tmp = x;
	} else if (y <= 0.0032) {
		tmp = -2.0 * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7d+25)) then
        tmp = y * b
    else if (y <= (-5d-100)) then
        tmp = z
    else if (y <= (-1.8d-288)) then
        tmp = x
    else if (y <= 1.3d-288) then
        tmp = z
    else if (y <= 2.7d-121) then
        tmp = x
    else if (y <= 0.0032d0) then
        tmp = (-2.0d0) * b
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e+25) {
		tmp = y * b;
	} else if (y <= -5e-100) {
		tmp = z;
	} else if (y <= -1.8e-288) {
		tmp = x;
	} else if (y <= 1.3e-288) {
		tmp = z;
	} else if (y <= 2.7e-121) {
		tmp = x;
	} else if (y <= 0.0032) {
		tmp = -2.0 * b;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e+25:
		tmp = y * b
	elif y <= -5e-100:
		tmp = z
	elif y <= -1.8e-288:
		tmp = x
	elif y <= 1.3e-288:
		tmp = z
	elif y <= 2.7e-121:
		tmp = x
	elif y <= 0.0032:
		tmp = -2.0 * b
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e+25)
		tmp = Float64(y * b);
	elseif (y <= -5e-100)
		tmp = z;
	elseif (y <= -1.8e-288)
		tmp = x;
	elseif (y <= 1.3e-288)
		tmp = z;
	elseif (y <= 2.7e-121)
		tmp = x;
	elseif (y <= 0.0032)
		tmp = Float64(-2.0 * b);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7e+25)
		tmp = y * b;
	elseif (y <= -5e-100)
		tmp = z;
	elseif (y <= -1.8e-288)
		tmp = x;
	elseif (y <= 1.3e-288)
		tmp = z;
	elseif (y <= 2.7e-121)
		tmp = x;
	elseif (y <= 0.0032)
		tmp = -2.0 * b;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e+25], N[(y * b), $MachinePrecision], If[LessEqual[y, -5e-100], z, If[LessEqual[y, -1.8e-288], x, If[LessEqual[y, 1.3e-288], z, If[LessEqual[y, 2.7e-121], x, If[LessEqual[y, 0.0032], N[(-2.0 * b), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.99999999999999999e25 or 0.00320000000000000015 < y

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. fma-def 96.4%

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

      3. associate--l+ 96.4%

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

      4. sub-neg 96.4%

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

      5. metadata-eval 96.4%

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

      6. sub-neg 96.4%

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

      7. associate--l+ 96.4%

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

      8. *-commutative 96.4%

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

      9. distribute-rgt-neg-in 96.4%

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

      10. fma-neg 98.2%

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

      11. neg-sub0 98.2%

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

      12. sub-neg 98.2%

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

      13. +-commutative 98.2%

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

      14. associate--r+ 98.2%

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

      15. metadata-eval 98.2%

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

      16. metadata-eval 98.2%

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

      17. *-commutative 98.2%

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

      18. distribute-rgt-neg-in 98.2%

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

      19. neg-sub0 98.2%

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

      20. sub-neg 98.2%

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

      21. +-commutative 98.2%

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

      22. associate--r+ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 73.2%

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

   5. Taylor expanded in y around inf 34.5%

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

   if -6.99999999999999999e25 < y < -5.0000000000000001e-100 or -1.8000000000000001e-288 < y < 1.29999999999999995e-288

   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 z around inf 42.9%

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

   3. Taylor expanded in y around 0 35.8%

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

   if -5.0000000000000001e-100 < y < -1.8000000000000001e-288 or 1.29999999999999995e-288 < y < 2.7000000000000002e-121

   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 x around inf 37.2%

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

   if 2.7000000000000002e-121 < y < 0.00320000000000000015

   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 b around inf 47.6%

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

   3. Taylor expanded in y around 0 47.6%

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

   4. Taylor expanded in t around 0 28.1%

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

      1. *-commutative 28.1%

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

   6. Simplified 28.1%

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

   7. Taylor expanded in y around 0 28.1%

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

      1. *-commutative 28.1%

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

   9. Simplified 28.1%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+25}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-100}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-288}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-288}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0032:\\ \;\;\;\;-2 \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 13: 54.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+82} \lor \neg \left(y \leq 4.45 \cdot 10^{+120}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.28e+66)
     t_1
     (if (<= y 5e-99)
       (+ x (* a (- 1.0 t)))
       (if (<= y 5e+16)
         (* b (- (+ y t) 2.0))
         (if (or (<= y 3.6e+82) (not (<= y 4.45e+120))) t_1 (* t (- b a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.28e+66) {
		tmp = t_1;
	} else if (y <= 5e-99) {
		tmp = x + (a * (1.0 - t));
	} else if (y <= 5e+16) {
		tmp = b * ((y + t) - 2.0);
	} else if ((y <= 3.6e+82) || !(y <= 4.45e+120)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-1.28d+66)) then
        tmp = t_1
    else if (y <= 5d-99) then
        tmp = x + (a * (1.0d0 - t))
    else if (y <= 5d+16) then
        tmp = b * ((y + t) - 2.0d0)
    else if ((y <= 3.6d+82) .or. (.not. (y <= 4.45d+120))) then
        tmp = t_1
    else
        tmp = 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 t_1 = y * (b - z);
	double tmp;
	if (y <= -1.28e+66) {
		tmp = t_1;
	} else if (y <= 5e-99) {
		tmp = x + (a * (1.0 - t));
	} else if (y <= 5e+16) {
		tmp = b * ((y + t) - 2.0);
	} else if ((y <= 3.6e+82) || !(y <= 4.45e+120)) {
		tmp = t_1;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -1.28e+66:
		tmp = t_1
	elif y <= 5e-99:
		tmp = x + (a * (1.0 - t))
	elif y <= 5e+16:
		tmp = b * ((y + t) - 2.0)
	elif (y <= 3.6e+82) or not (y <= 4.45e+120):
		tmp = t_1
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.28e+66)
		tmp = t_1;
	elseif (y <= 5e-99)
		tmp = Float64(x + Float64(a * Float64(1.0 - t)));
	elseif (y <= 5e+16)
		tmp = Float64(b * Float64(Float64(y + t) - 2.0));
	elseif ((y <= 3.6e+82) || !(y <= 4.45e+120))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.28e+66)
		tmp = t_1;
	elseif (y <= 5e-99)
		tmp = x + (a * (1.0 - t));
	elseif (y <= 5e+16)
		tmp = b * ((y + t) - 2.0);
	elseif ((y <= 3.6e+82) || ~((y <= 4.45e+120)))
		tmp = t_1;
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.28e+66], t$95$1, If[LessEqual[y, 5e-99], N[(x + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+16], N[(b * N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.6e+82], N[Not[LessEqual[y, 4.45e+120]], $MachinePrecision]], t$95$1, N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.28000000000000003e66 or 5e16 < y < 3.60000000000000014e82 or 4.4499999999999997e120 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf 69.8%

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

   if -1.28000000000000003e66 < y < 4.99999999999999969e-99

   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. Taylor expanded in z around 0 75.8%

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

   3. Taylor expanded in b around 0 61.6%

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

   if 4.99999999999999969e-99 < y < 5e16

   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 b around inf 51.2%

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

   if 3.60000000000000014e82 < y < 4.4499999999999997e120

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf 72.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+16}:\\ \;\;\;\;b \cdot \left(\left(y + t\right) - 2\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+82} \lor \neg \left(y \leq 4.45 \cdot 10^{+120}\right):\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 14: 54.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-239}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-116}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7.5e+23)
     t_1
     (if (<= t 4.6e-239)
       (+ a (* b (- y 2.0)))
       (if (<= t 8e-170)
         (+ x a)
         (if (<= t 5.4e-116)
           (* y (- b z))
           (if (<= t 2.5e+14) (+ x a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7.5e+23) {
		tmp = t_1;
	} else if (t <= 4.6e-239) {
		tmp = a + (b * (y - 2.0));
	} else if (t <= 8e-170) {
		tmp = x + a;
	} else if (t <= 5.4e-116) {
		tmp = y * (b - z);
	} else if (t <= 2.5e+14) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-7.5d+23)) then
        tmp = t_1
    else if (t <= 4.6d-239) then
        tmp = a + (b * (y - 2.0d0))
    else if (t <= 8d-170) then
        tmp = x + a
    else if (t <= 5.4d-116) then
        tmp = y * (b - z)
    else if (t <= 2.5d+14) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7.5e+23) {
		tmp = t_1;
	} else if (t <= 4.6e-239) {
		tmp = a + (b * (y - 2.0));
	} else if (t <= 8e-170) {
		tmp = x + a;
	} else if (t <= 5.4e-116) {
		tmp = y * (b - z);
	} else if (t <= 2.5e+14) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -7.5e+23:
		tmp = t_1
	elif t <= 4.6e-239:
		tmp = a + (b * (y - 2.0))
	elif t <= 8e-170:
		tmp = x + a
	elif t <= 5.4e-116:
		tmp = y * (b - z)
	elif t <= 2.5e+14:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.5e+23)
		tmp = t_1;
	elseif (t <= 4.6e-239)
		tmp = Float64(a + Float64(b * Float64(y - 2.0)));
	elseif (t <= 8e-170)
		tmp = Float64(x + a);
	elseif (t <= 5.4e-116)
		tmp = Float64(y * Float64(b - z));
	elseif (t <= 2.5e+14)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.5e+23)
		tmp = t_1;
	elseif (t <= 4.6e-239)
		tmp = a + (b * (y - 2.0));
	elseif (t <= 8e-170)
		tmp = x + a;
	elseif (t <= 5.4e-116)
		tmp = y * (b - z);
	elseif (t <= 2.5e+14)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+23], t$95$1, If[LessEqual[t, 4.6e-239], N[(a + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-170], N[(x + a), $MachinePrecision], If[LessEqual[t, 5.4e-116], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+14], N[(x + a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.49999999999999987e23 or 2.5e14 < t

   1. Initial program 92.5%

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

   2. Taylor expanded in t around inf 67.7%

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

   if -7.49999999999999987e23 < t < 4.5999999999999998e-239

   1. Initial program 98.9%

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

      1. +-commutative 98.9%

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

      2. fma-def 98.9%

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

      3. associate--l+ 98.9%

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

      4. sub-neg 98.9%

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

      5. metadata-eval 98.9%

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

      6. sub-neg 98.9%

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

      7. associate--l+ 98.9%

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

      8. *-commutative 98.9%

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

      9. distribute-rgt-neg-in 98.9%

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

      10. fma-neg 98.9%

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

      11. neg-sub0 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. associate--r+ 98.9%

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

      15. metadata-eval 98.9%

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

      16. metadata-eval 98.9%

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

      17. *-commutative 98.9%

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

      18. distribute-rgt-neg-in 98.9%

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

      19. neg-sub0 98.9%

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

      20. sub-neg 98.9%

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

      21. +-commutative 98.9%

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

      22. associate--r+ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 71.7%

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

   5. Taylor expanded in t around 0 70.7%

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

   6. Taylor expanded in x around 0 56.1%

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

   if 4.5999999999999998e-239 < t < 7.99999999999999987e-170 or 5.4e-116 < t < 2.5e14

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

      6. sub-neg 99.9%

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

      7. associate--l+ 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. fma-neg 99.9%

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

      11. neg-sub0 99.9%

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

      12. sub-neg 99.9%

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

      13. +-commutative 99.9%

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

      14. associate--r+ 99.9%

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

      15. metadata-eval 99.9%

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

      16. metadata-eval 99.9%

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

      17. *-commutative 99.9%

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

      18. distribute-rgt-neg-in 99.9%

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

      19. neg-sub0 99.9%

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

      20. sub-neg 99.9%

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

      21. +-commutative 99.9%

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

      22. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 78.6%

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

   5. Taylor expanded in t around 0 71.0%

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

   6. Taylor expanded in b around 0 49.7%

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

      1. +-commutative 49.7%

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

   8. Simplified 49.7%

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

   if 7.99999999999999987e-170 < t < 5.4e-116

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 56.5%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-239}:\\ \;\;\;\;a + b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-170}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-116}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+14}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 15: 60.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+30}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (+ x (* z (- 1.0 y)))))
   (if (<= z -8.5e+56)
     t_2
     (if (<= z -1.25e-7)
       t_1
       (if (<= z 6.4e+30)
         (+ a (+ x (* b (- y 2.0))))
         (if (<= z 1.06e+114) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -8.5e+56) {
		tmp = t_2;
	} else if (z <= -1.25e-7) {
		tmp = t_1;
	} else if (z <= 6.4e+30) {
		tmp = a + (x + (b * (y - 2.0)));
	} else if (z <= 1.06e+114) {
		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 = t * (b - a)
    t_2 = x + (z * (1.0d0 - y))
    if (z <= (-8.5d+56)) then
        tmp = t_2
    else if (z <= (-1.25d-7)) then
        tmp = t_1
    else if (z <= 6.4d+30) then
        tmp = a + (x + (b * (y - 2.0d0)))
    else if (z <= 1.06d+114) 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 = t * (b - a);
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (z <= -8.5e+56) {
		tmp = t_2;
	} else if (z <= -1.25e-7) {
		tmp = t_1;
	} else if (z <= 6.4e+30) {
		tmp = a + (x + (b * (y - 2.0)));
	} else if (z <= 1.06e+114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = x + (z * (1.0 - y))
	tmp = 0
	if z <= -8.5e+56:
		tmp = t_2
	elif z <= -1.25e-7:
		tmp = t_1
	elif z <= 6.4e+30:
		tmp = a + (x + (b * (y - 2.0)))
	elif z <= 1.06e+114:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (z <= -8.5e+56)
		tmp = t_2;
	elseif (z <= -1.25e-7)
		tmp = t_1;
	elseif (z <= 6.4e+30)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y - 2.0))));
	elseif (z <= 1.06e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (z <= -8.5e+56)
		tmp = t_2;
	elseif (z <= -1.25e-7)
		tmp = t_1;
	elseif (z <= 6.4e+30)
		tmp = a + (x + (b * (y - 2.0)));
	elseif (z <= 1.06e+114)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+56], t$95$2, If[LessEqual[z, -1.25e-7], t$95$1, If[LessEqual[z, 6.4e+30], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e+114], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999998e56 or 1.05999999999999993e114 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in a around 0 86.6%

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

   3. Taylor expanded in b around 0 74.9%

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

   if -8.4999999999999998e56 < z < -1.24999999999999994e-7 or 6.39999999999999945e30 < z < 1.05999999999999993e114

   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 t around inf 66.0%

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

   if -1.24999999999999994e-7 < z < 6.39999999999999945e30

   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. Step-by-step derivation

      1. +-commutative 96.3%

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

      2. fma-def 98.5%

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

      3. associate--l+ 98.5%

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

      4. sub-neg 98.5%

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

      5. metadata-eval 98.5%

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

      6. sub-neg 98.5%

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

      7. associate--l+ 98.5%

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

      8. *-commutative 98.5%

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

      9. distribute-rgt-neg-in 98.5%

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

      10. fma-neg 98.5%

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

      11. neg-sub0 98.5%

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

      12. sub-neg 98.5%

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

      13. +-commutative 98.5%

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

      14. associate--r+ 98.5%

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

      15. metadata-eval 98.5%

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

      16. metadata-eval 98.5%

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

      17. *-commutative 98.5%

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

      18. distribute-rgt-neg-in 98.5%

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

      19. neg-sub0 98.5%

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

      20. sub-neg 98.5%

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

      21. +-commutative 98.5%

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

      22. associate--r+ 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around 0 94.2%

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

   5. Taylor expanded in t around 0 68.1%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+56}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+30}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 16: 35.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -9.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-116}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -7.9 \cdot 10^{-202}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -9.6e+48)
     t_1
     (if (<= a -2e-116)
       (* y b)
       (if (<= a -7.9e-202) z (if (<= a 3.3e-37) (+ x a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -9.6e+48) {
		tmp = t_1;
	} else if (a <= -2e-116) {
		tmp = y * b;
	} else if (a <= -7.9e-202) {
		tmp = z;
	} else if (a <= 3.3e-37) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-9.6d+48)) then
        tmp = t_1
    else if (a <= (-2d-116)) then
        tmp = y * b
    else if (a <= (-7.9d-202)) then
        tmp = z
    else if (a <= 3.3d-37) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -9.6e+48) {
		tmp = t_1;
	} else if (a <= -2e-116) {
		tmp = y * b;
	} else if (a <= -7.9e-202) {
		tmp = z;
	} else if (a <= 3.3e-37) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -9.6e+48:
		tmp = t_1
	elif a <= -2e-116:
		tmp = y * b
	elif a <= -7.9e-202:
		tmp = z
	elif a <= 3.3e-37:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -9.6e+48)
		tmp = t_1;
	elseif (a <= -2e-116)
		tmp = Float64(y * b);
	elseif (a <= -7.9e-202)
		tmp = z;
	elseif (a <= 3.3e-37)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -9.6e+48)
		tmp = t_1;
	elseif (a <= -2e-116)
		tmp = y * b;
	elseif (a <= -7.9e-202)
		tmp = z;
	elseif (a <= 3.3e-37)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.6e+48], t$95$1, If[LessEqual[a, -2e-116], N[(y * b), $MachinePrecision], If[LessEqual[a, -7.9e-202], z, If[LessEqual[a, 3.3e-37], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.6000000000000004e48 or 3.29999999999999982e-37 < a

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 54.0%

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

   if -9.6000000000000004e48 < a < -2e-116

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. fma-def 96.4%

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

      3. associate--l+ 96.4%

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

      4. sub-neg 96.4%

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

      5. metadata-eval 96.4%

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

      6. sub-neg 96.4%

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

      7. associate--l+ 96.4%

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

      8. *-commutative 96.4%

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

      9. distribute-rgt-neg-in 96.4%

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

      10. fma-neg 96.4%

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

      11. neg-sub0 96.4%

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

      12. sub-neg 96.4%

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

      13. +-commutative 96.4%

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

      14. associate--r+ 96.4%

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

      15. metadata-eval 96.4%

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

      16. metadata-eval 96.4%

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

      17. *-commutative 96.4%

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

      18. distribute-rgt-neg-in 96.4%

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

      19. neg-sub0 96.4%

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

      20. sub-neg 96.4%

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

      21. +-commutative 96.4%

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

      22. associate--r+ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 86.2%

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

   5. Taylor expanded in y around inf 30.2%

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

   if -2e-116 < a < -7.9000000000000001e-202

   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 z around inf 50.1%

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

   3. Taylor expanded in y around 0 40.3%

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

   if -7.9000000000000001e-202 < a < 3.29999999999999982e-37

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      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 z around 0 68.9%

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

   5. Taylor expanded in t around 0 53.1%

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

   6. Taylor expanded in b around 0 32.6%

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

      1. +-commutative 32.6%

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

   8. Simplified 32.6%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.6 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-116}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -7.9 \cdot 10^{-202}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 17: 37.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-155}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -4.5e+48)
     t_1
     (if (<= a -2.8e-148)
       (* b (+ y -2.0))
       (if (<= a 6.5e-155) (+ x a) (if (<= a 2.4e+73) (* b (- t 2.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e+48) {
		tmp = t_1;
	} else if (a <= -2.8e-148) {
		tmp = b * (y + -2.0);
	} else if (a <= 6.5e-155) {
		tmp = x + a;
	} else if (a <= 2.4e+73) {
		tmp = b * (t - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-4.5d+48)) then
        tmp = t_1
    else if (a <= (-2.8d-148)) then
        tmp = b * (y + (-2.0d0))
    else if (a <= 6.5d-155) then
        tmp = x + a
    else if (a <= 2.4d+73) then
        tmp = b * (t - 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.5e+48) {
		tmp = t_1;
	} else if (a <= -2.8e-148) {
		tmp = b * (y + -2.0);
	} else if (a <= 6.5e-155) {
		tmp = x + a;
	} else if (a <= 2.4e+73) {
		tmp = b * (t - 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -4.5e+48:
		tmp = t_1
	elif a <= -2.8e-148:
		tmp = b * (y + -2.0)
	elif a <= 6.5e-155:
		tmp = x + a
	elif a <= 2.4e+73:
		tmp = b * (t - 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.5e+48)
		tmp = t_1;
	elseif (a <= -2.8e-148)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (a <= 6.5e-155)
		tmp = Float64(x + a);
	elseif (a <= 2.4e+73)
		tmp = Float64(b * Float64(t - 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.5e+48)
		tmp = t_1;
	elseif (a <= -2.8e-148)
		tmp = b * (y + -2.0);
	elseif (a <= 6.5e-155)
		tmp = x + a;
	elseif (a <= 2.4e+73)
		tmp = b * (t - 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+48], t$95$1, If[LessEqual[a, -2.8e-148], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-155], N[(x + a), $MachinePrecision], If[LessEqual[a, 2.4e+73], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.49999999999999995e48 or 2.40000000000000002e73 < a

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 60.3%

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

   if -4.49999999999999995e48 < a < -2.8e-148

   1. Initial program 96.9%

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

   2. Taylor expanded in b around inf 55.2%

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

   3. Taylor expanded in y around 0 55.2%

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

   4. Taylor expanded in t around 0 36.7%

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

      1. +-commutative 36.7%

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

      2. *-commutative 36.7%

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

      3. distribute-lft-in 36.7%

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

   6. Simplified 36.7%

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

   if -2.8e-148 < a < 6.5e-155

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      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 z around 0 66.4%

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

   5. Taylor expanded in t around 0 53.0%

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

   6. Taylor expanded in b around 0 35.5%

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

      1. +-commutative 35.5%

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

   8. Simplified 35.5%

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

   if 6.5e-155 < a < 2.40000000000000002e73

   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 b around inf 43.4%

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

   3. Taylor expanded in y around 0 33.9%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-155}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+73}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 18: 49.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -55000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-301}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -55000000.0)
     t_1
     (if (<= t 1.02e-301)
       (+ x a)
       (if (<= t 7.5e-266)
         (* b (+ y -2.0))
         (if (<= t 7.2e+18) (+ x a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -55000000.0) {
		tmp = t_1;
	} else if (t <= 1.02e-301) {
		tmp = x + a;
	} else if (t <= 7.5e-266) {
		tmp = b * (y + -2.0);
	} else if (t <= 7.2e+18) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-55000000.0d0)) then
        tmp = t_1
    else if (t <= 1.02d-301) then
        tmp = x + a
    else if (t <= 7.5d-266) then
        tmp = b * (y + (-2.0d0))
    else if (t <= 7.2d+18) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -55000000.0) {
		tmp = t_1;
	} else if (t <= 1.02e-301) {
		tmp = x + a;
	} else if (t <= 7.5e-266) {
		tmp = b * (y + -2.0);
	} else if (t <= 7.2e+18) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -55000000.0:
		tmp = t_1
	elif t <= 1.02e-301:
		tmp = x + a
	elif t <= 7.5e-266:
		tmp = b * (y + -2.0)
	elif t <= 7.2e+18:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -55000000.0)
		tmp = t_1;
	elseif (t <= 1.02e-301)
		tmp = Float64(x + a);
	elseif (t <= 7.5e-266)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (t <= 7.2e+18)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -55000000.0)
		tmp = t_1;
	elseif (t <= 1.02e-301)
		tmp = x + a;
	elseif (t <= 7.5e-266)
		tmp = b * (y + -2.0);
	elseif (t <= 7.2e+18)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -55000000.0], t$95$1, If[LessEqual[t, 1.02e-301], N[(x + a), $MachinePrecision], If[LessEqual[t, 7.5e-266], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+18], N[(x + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5e7 or 7.2e18 < t

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf 66.8%

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

   if -5.5e7 < t < 1.0200000000000001e-301 or 7.4999999999999995e-266 < t < 7.2e18

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. fma-def 99.2%

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

      3. associate--l+ 99.2%

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

      4. sub-neg 99.2%

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

      5. metadata-eval 99.2%

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

      6. sub-neg 99.2%

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

      7. associate--l+ 99.2%

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

      8. *-commutative 99.2%

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

      9. distribute-rgt-neg-in 99.2%

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

      10. fma-neg 99.2%

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

      11. neg-sub0 99.2%

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

      12. sub-neg 99.2%

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

      13. +-commutative 99.2%

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

      14. associate--r+ 99.2%

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

      15. metadata-eval 99.2%

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

      16. metadata-eval 99.2%

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

      17. *-commutative 99.2%

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

      18. distribute-rgt-neg-in 99.2%

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

      19. neg-sub0 99.2%

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

      20. sub-neg 99.2%

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

      21. +-commutative 99.2%

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

      22. associate--r+ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 67.5%

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

   5. Taylor expanded in t around 0 65.3%

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

   6. Taylor expanded in b around 0 42.7%

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

      1. +-commutative 42.7%

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

   8. Simplified 42.7%

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

   if 1.0200000000000001e-301 < t < 7.4999999999999995e-266

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 78.0%

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

   3. Taylor expanded in y around 0 78.0%

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

   4. Taylor expanded in t around 0 78.0%

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

      1. +-commutative 78.0%

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

      2. *-commutative 78.0%

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

      3. distribute-lft-in 78.0%

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

   6. Simplified 78.0%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -55000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-301}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-266}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+18}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 19: 36.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.05 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.55 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -4.05e+48)
     t_1
     (if (<= a -3.55e-146) (* b (+ y -2.0)) (if (<= a 3.7e-37) (+ x a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.05e+48) {
		tmp = t_1;
	} else if (a <= -3.55e-146) {
		tmp = b * (y + -2.0);
	} else if (a <= 3.7e-37) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-4.05d+48)) then
        tmp = t_1
    else if (a <= (-3.55d-146)) then
        tmp = b * (y + (-2.0d0))
    else if (a <= 3.7d-37) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -4.05e+48) {
		tmp = t_1;
	} else if (a <= -3.55e-146) {
		tmp = b * (y + -2.0);
	} else if (a <= 3.7e-37) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -4.05e+48:
		tmp = t_1
	elif a <= -3.55e-146:
		tmp = b * (y + -2.0)
	elif a <= 3.7e-37:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -4.05e+48)
		tmp = t_1;
	elseif (a <= -3.55e-146)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (a <= 3.7e-37)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -4.05e+48)
		tmp = t_1;
	elseif (a <= -3.55e-146)
		tmp = b * (y + -2.0);
	elseif (a <= 3.7e-37)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.05e+48], t$95$1, If[LessEqual[a, -3.55e-146], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.7e-37], N[(x + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.0499999999999999e48 or 3.7e-37 < a

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 54.0%

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

   if -4.0499999999999999e48 < a < -3.5500000000000002e-146

   1. Initial program 96.9%

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

   2. Taylor expanded in b around inf 55.2%

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

   3. Taylor expanded in y around 0 55.2%

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

   4. Taylor expanded in t around 0 36.7%

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

      1. +-commutative 36.7%

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

      2. *-commutative 36.7%

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

      3. distribute-lft-in 36.7%

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

   6. Simplified 36.7%

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

   if -3.5500000000000002e-146 < a < 3.7e-37

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      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 z around 0 65.7%

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

   5. Taylor expanded in t around 0 49.5%

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

   6. Taylor expanded in b around 0 31.5%

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

      1. +-commutative 31.5%

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

   8. Simplified 31.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.05 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -3.55 \cdot 10^{-146}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-37}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 20: 33.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+23} \lor \neg \left(t \leq 1.8 \cdot 10^{+142}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2e+23) (not (<= t 1.8e+142))) (* t b) (+ x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e+23) || !(t <= 1.8e+142)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2d+23)) .or. (.not. (t <= 1.8d+142))) then
        tmp = t * b
    else
        tmp = x + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e+23) || !(t <= 1.8e+142)) {
		tmp = t * b;
	} else {
		tmp = x + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2e+23) or not (t <= 1.8e+142):
		tmp = t * b
	else:
		tmp = x + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2e+23) || !(t <= 1.8e+142))
		tmp = Float64(t * b);
	else
		tmp = Float64(x + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2e+23) || ~((t <= 1.8e+142)))
		tmp = t * b;
	else
		tmp = x + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2e+23], N[Not[LessEqual[t, 1.8e+142]], $MachinePrecision]], N[(t * b), $MachinePrecision], N[(x + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999998e23 or 1.8000000000000001e142 < t

   1. Initial program 90.4%

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

   2. Taylor expanded in b around inf 42.5%

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

   3. Taylor expanded in y around 0 41.3%

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

   4. Taylor expanded in t around inf 36.9%

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

      1. *-commutative 36.9%

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

   6. Simplified 36.9%

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

   if -1.9999999999999998e23 < t < 1.8000000000000001e142

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. fma-def 99.4%

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

      3. associate--l+ 99.4%

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

      4. sub-neg 99.4%

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

      5. metadata-eval 99.4%

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

      6. sub-neg 99.4%

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

      7. associate--l+ 99.4%

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

      8. *-commutative 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. fma-neg 99.4%

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

      11. neg-sub0 99.4%

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

      12. sub-neg 99.4%

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

      13. +-commutative 99.4%

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

      14. associate--r+ 99.4%

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

      15. metadata-eval 99.4%

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

      16. metadata-eval 99.4%

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

      17. *-commutative 99.4%

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

      18. distribute-rgt-neg-in 99.4%

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

      19. neg-sub0 99.4%

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

      20. sub-neg 99.4%

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

      21. +-commutative 99.4%

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

      22. associate--r+ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 71.0%

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

   5. Taylor expanded in t around 0 61.7%

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

   6. Taylor expanded in b around 0 37.1%

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

      1. +-commutative 37.1%

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

   8. Simplified 37.1%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+23} \lor \neg \left(t \leq 1.8 \cdot 10^{+142}\right):\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 21: 20.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+91}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.25e+41) x (if (<= x 7.5e+91) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e+41) {
		tmp = x;
	} else if (x <= 7.5e+91) {
		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 <= (-1.25d+41)) then
        tmp = x
    else if (x <= 7.5d+91) 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 <= -1.25e+41) {
		tmp = x;
	} else if (x <= 7.5e+91) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.25e+41:
		tmp = x
	elif x <= 7.5e+91:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.25e+41)
		tmp = x;
	elseif (x <= 7.5e+91)
		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 <= -1.25e+41)
		tmp = x;
	elseif (x <= 7.5e+91)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.25e+41], x, If[LessEqual[x, 7.5e+91], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000006e41 or 7.50000000000000033e91 < x

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 38.0%

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

   if -1.25000000000000006e41 < x < 7.50000000000000033e91

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 38.3%

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

   3. Taylor expanded in t around 0 16.8%

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

4. Final simplification 25.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+91}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 20.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6e+45) x (if (<= x 2.35e+91) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+45) {
		tmp = x;
	} else if (x <= 2.35e+91) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6d+45)) then
        tmp = x
    else if (x <= 2.35d+91) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6e+45) {
		tmp = x;
	} else if (x <= 2.35e+91) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6e+45:
		tmp = x
	elif x <= 2.35e+91:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6e+45)
		tmp = x;
	elseif (x <= 2.35e+91)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6e+45)
		tmp = x;
	elseif (x <= 2.35e+91)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6e+45], x, If[LessEqual[x, 2.35e+91], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.00000000000000021e45 or 2.3499999999999999e91 < x

   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 x around inf 39.0%

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

   if -6.00000000000000021e45 < x < 2.3499999999999999e91

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 29.8%

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

   3. Taylor expanded in y around 0 16.6%

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

4. Final simplification 25.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 11.3% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in a around inf 30.5%

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

3. Taylor expanded in t around 0 12.6%

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

4. Final simplification 12.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023310 
(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)))