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

Percentage Accurate: 95.6% → 98.3%

Time: 13.3s

Alternatives: 20

Speedup: 0.5×

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 71.5

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

   5. Applied rewrites 71.5%

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

4. Final simplification 98.4%

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

Alternative 2: 42.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+301}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 -2e+301) (* t b) (if (<= t_1 2e+302) (+ z (+ x a)) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -2e+301) {
		tmp = t * b;
	} else if (t_1 <= 2e+302) {
		tmp = z + (x + a);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x + (z * (1.0d0 - y))) + (a * (1.0d0 - t))) + (((y + t) - 2.0d0) * b)
    if (t_1 <= (-2d+301)) then
        tmp = t * b
    else if (t_1 <= 2d+302) then
        tmp = z + (x + a)
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -2e+301) {
		tmp = t * b;
	} else if (t_1 <= 2e+302) {
		tmp = z + (x + a);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= -2e+301:
		tmp = t * b
	elif t_1 <= 2e+302:
		tmp = z + (x + a)
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= -2e+301)
		tmp = Float64(t * b);
	elseif (t_1 <= 2e+302)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= -2e+301)
		tmp = t * b;
	elseif (t_1 <= 2e+302)
		tmp = z + (x + a);
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+301], N[(t * b), $MachinePrecision], If[LessEqual[t$95$1, 2e+302], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -2.00000000000000011e301 or 2.0000000000000002e302 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 87.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 33.0%

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

   if -2.00000000000000011e301 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 2.0000000000000002e302

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 58.7%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq -2 \cdot 10^{+301}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 2 \cdot 10^{+302}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 33.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+290}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* (- (+ y t) 2.0) b))))
   (if (<= t_1 -1e+290) (* t b) (if (<= t_1 2e+302) (+ x a) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -1e+290) {
		tmp = t * b;
	} else if (t_1 <= 2e+302) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x + (z * (1.0d0 - y))) + (a * (1.0d0 - t))) + (((y + t) - 2.0d0) * b)
    if (t_1 <= (-1d+290)) then
        tmp = t * b
    else if (t_1 <= 2d+302) then
        tmp = x + a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -1e+290) {
		tmp = t * b;
	} else if (t_1 <= 2e+302) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= -1e+290:
		tmp = t * b
	elif t_1 <= 2e+302:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (t_1 <= -1e+290)
		tmp = Float64(t * b);
	elseif (t_1 <= 2e+302)
		tmp = Float64(x + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (t_1 <= -1e+290)
		tmp = t * b;
	elseif (t_1 <= 2e+302)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+290], N[(t * b), $MachinePrecision], If[LessEqual[t$95$1, 2e+302], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -1.00000000000000006e290 or 2.0000000000000002e302 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 87.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 74.9

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 33.3%

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

   if -1.00000000000000006e290 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 2.0000000000000002e302

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 73.7

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

   5. Applied rewrites 73.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 62.3%

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

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 45.8%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq -1 \cdot 10^{+290}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(t + -2\right)\\ t_2 := \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, t\_1, x\right)\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, t\_1, t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ t -2.0))) (t_2 (fma z (- 1.0 y) x)))
   (if (<= b -2.05e+133)
     (fma a (- 1.0 t) (fma b t_1 x))
     (if (<= b 1.45e-43) (fma a (- 1.0 t) t_2) (fma b t_1 t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (t + -2.0);
	double t_2 = fma(z, (1.0 - y), x);
	double tmp;
	if (b <= -2.05e+133) {
		tmp = fma(a, (1.0 - t), fma(b, t_1, x));
	} else if (b <= 1.45e-43) {
		tmp = fma(a, (1.0 - t), t_2);
	} else {
		tmp = fma(b, t_1, t_2);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(t + -2.0))
	t_2 = fma(z, Float64(1.0 - y), x)
	tmp = 0.0
	if (b <= -2.05e+133)
		tmp = fma(a, Float64(1.0 - t), fma(b, t_1, x));
	elseif (b <= 1.45e-43)
		tmp = fma(a, Float64(1.0 - t), t_2);
	else
		tmp = fma(b, t_1, t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[b, -2.05e+133], N[(a * N[(1.0 - t), $MachinePrecision] + N[(b * t$95$1 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-43], N[(a * N[(1.0 - t), $MachinePrecision] + t$95$2), $MachinePrecision], N[(b * t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05000000000000002e133

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 97.4

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

   5. Applied rewrites 97.4%

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

   if -2.05000000000000002e133 < b < 1.4500000000000001e-43

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 90.4%

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

   if 1.4500000000000001e-43 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 93.0

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

   5. Applied rewrites 93.0%

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

Alternative 5: 86.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + -2\right), x\right)\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) (fma b (+ y (+ t -2.0)) x))))
   (if (<= b -2.05e+133)
     t_1
     (if (<= b 1.45e-9) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), fma(b, (y + (t + -2.0)), x));
	double tmp;
	if (b <= -2.05e+133) {
		tmp = t_1;
	} else if (b <= 1.45e-9) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), fma(b, Float64(y + Float64(t + -2.0)), x))
	tmp = 0.0
	if (b <= -2.05e+133)
		tmp = t_1;
	elseif (b <= 1.45e-9)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+133], t$95$1, If[LessEqual[b, 1.45e-9], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.05000000000000002e133 or 1.44999999999999996e-9 < b

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 88.7

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

   5. Applied rewrites 88.7%

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

   if -2.05000000000000002e133 < b < 1.44999999999999996e-9

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 84.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + -2\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(b, t\_1, x\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, b \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y -2.0))))
   (if (<= b -2.05e+133)
     (fma b t_1 x)
     (if (<= b 2e+44)
       (fma a (- 1.0 t) (fma z (- 1.0 y) x))
       (fma a (- 1.0 t) (* b t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (y + -2.0);
	double tmp;
	if (b <= -2.05e+133) {
		tmp = fma(b, t_1, x);
	} else if (b <= 2e+44) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = fma(a, (1.0 - t), (b * t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(y + -2.0))
	tmp = 0.0
	if (b <= -2.05e+133)
		tmp = fma(b, t_1, x);
	elseif (b <= 2e+44)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = fma(a, Float64(1.0 - t), Float64(b * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.05e+133], N[(b * t$95$1 + x), $MachinePrecision], If[LessEqual[b, 2e+44], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision] + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05000000000000002e133

   1. Initial program 87.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 93.6%

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

   if -2.05000000000000002e133 < b < 2.0000000000000002e44

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 88.4%

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

   if 2.0000000000000002e44 < b

   1. Initial program 87.5%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in b around inf

      \[\leadsto \mathsf{fma}\left(a, 1 - t, b \cdot \left(\left(t + y\right) - 2\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 86.4%

      \[\leadsto \mathsf{fma}\left(a, 1 - t, b \cdot \left(t + \left(y + -2\right)\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 66.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-212}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(z, -y, x\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.5e+79)
     t_1
     (if (<= t 4.5e-212)
       (fma b (+ y -2.0) (fma z (- y) x))
       (if (<= t 5e+92) (fma z (- 1.0 y) (+ x a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.5e+79) {
		tmp = t_1;
	} else if (t <= 4.5e-212) {
		tmp = fma(b, (y + -2.0), fma(z, -y, x));
	} else if (t <= 5e+92) {
		tmp = fma(z, (1.0 - y), (x + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.5e+79)
		tmp = t_1;
	elseif (t <= 4.5e-212)
		tmp = fma(b, Float64(y + -2.0), fma(z, Float64(-y), x));
	elseif (t <= 5e+92)
		tmp = fma(z, Float64(1.0 - y), Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+79], t$95$1, If[LessEqual[t, 4.5e-212], N[(b * N[(y + -2.0), $MachinePrecision] + N[(z * (-y) + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+92], N[(z * N[(1.0 - y), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999994e79 or 5.00000000000000022e92 < t

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

   if -4.49999999999999994e79 < t < 4.4999999999999999e-212

   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. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 82.4

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

   5. Applied rewrites 82.4%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(z, 1 - y, x\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 81.5%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(z, -1 \cdot y, x\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 73.4%

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

   if 4.4999999999999999e-212 < t < 5.00000000000000022e92

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 78.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-212}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(z, -y, x\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-295}:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.5e+79)
     t_1
     (if (<= t -5.8e-295)
       (+ a (fma b (+ y -2.0) x))
       (if (<= t 5e+92) (fma z (- 1.0 y) (+ x a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.5e+79) {
		tmp = t_1;
	} else if (t <= -5.8e-295) {
		tmp = a + fma(b, (y + -2.0), x);
	} else if (t <= 5e+92) {
		tmp = fma(z, (1.0 - y), (x + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.5e+79)
		tmp = t_1;
	elseif (t <= -5.8e-295)
		tmp = Float64(a + fma(b, Float64(y + -2.0), x));
	elseif (t <= 5e+92)
		tmp = fma(z, Float64(1.0 - y), Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+79], t$95$1, If[LessEqual[t, -5.8e-295], N[(a + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+92], N[(z * N[(1.0 - y), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999994e79 or 5.00000000000000022e92 < t

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

   if -4.49999999999999994e79 < t < -5.8000000000000003e-295

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 76.6

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

   5. Applied rewrites 76.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 72.3%

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

   if -5.8000000000000003e-295 < t < 5.00000000000000022e92

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.8%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-295}:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, t + \left(y + -2\right), x\right)\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (+ t (+ y -2.0)) x)))
   (if (<= b -2.05e+133)
     t_1
     (if (<= b 1.18e+27) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, (t + (y + -2.0)), x);
	double tmp;
	if (b <= -2.05e+133) {
		tmp = t_1;
	} else if (b <= 1.18e+27) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(b, Float64(t + Float64(y + -2.0)), x)
	tmp = 0.0
	if (b <= -2.05e+133)
		tmp = t_1;
	elseif (b <= 1.18e+27)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[b, -2.05e+133], t$95$1, If[LessEqual[b, 1.18e+27], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.05000000000000002e133 or 1.18000000000000006e27 < b

   1. Initial program 87.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 92.5

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

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.5%

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

   if -2.05000000000000002e133 < b < 1.18000000000000006e27

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 61.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -8 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-305}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -8e+78)
     t_1
     (if (<= b 3.5e-305)
       (fma a (- 1.0 t) x)
       (if (<= b 2e+44) (fma z (- 1.0 y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -8e+78) {
		tmp = t_1;
	} else if (b <= 3.5e-305) {
		tmp = fma(a, (1.0 - t), x);
	} else if (b <= 2e+44) {
		tmp = fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -8e+78)
		tmp = t_1;
	elseif (b <= 3.5e-305)
		tmp = fma(a, Float64(1.0 - t), x);
	elseif (b <= 2e+44)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8e+78], t$95$1, If[LessEqual[b, 3.5e-305], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[b, 2e+44], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.00000000000000007e78 or 2.0000000000000002e44 < b

   1. Initial program 87.2%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 80.8

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

   5. Applied rewrites 80.8%

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

   if -8.00000000000000007e78 < b < 3.4999999999999998e-305

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 70.5

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.8%

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

   if 3.4999999999999998e-305 < b < 2.0000000000000002e44

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.6%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{1 - y}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 63.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-180}:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -4.5e+79)
     t_1
     (if (<= t 6.5e-180)
       (+ a (fma b (+ y -2.0) x))
       (if (<= t 5e+92) (fma z (- 1.0 y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -4.5e+79) {
		tmp = t_1;
	} else if (t <= 6.5e-180) {
		tmp = a + fma(b, (y + -2.0), x);
	} else if (t <= 5e+92) {
		tmp = fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -4.5e+79)
		tmp = t_1;
	elseif (t <= 6.5e-180)
		tmp = Float64(a + fma(b, Float64(y + -2.0), x));
	elseif (t <= 5e+92)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+79], t$95$1, If[LessEqual[t, 6.5e-180], N[(a + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+92], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999994e79 or 5.00000000000000022e92 < t

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

   if -4.49999999999999994e79 < t < 6.50000000000000013e-180

   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. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.1%

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

   if 6.50000000000000013e-180 < t < 5.00000000000000022e92

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 84.6

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 65.2%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{1 - y}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 54.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -720000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-215}:\\ \;\;\;\;a + \mathsf{fma}\left(b, -2, x\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+92}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -720000000000.0)
     t_1
     (if (<= t 4.8e-215)
       (+ a (fma b -2.0 x))
       (if (<= t 1.7e+92) (+ z (+ 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 <= -720000000000.0) {
		tmp = t_1;
	} else if (t <= 4.8e-215) {
		tmp = a + fma(b, -2.0, x);
	} else if (t <= 1.7e+92) {
		tmp = z + (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 <= -720000000000.0)
		tmp = t_1;
	elseif (t <= 4.8e-215)
		tmp = Float64(a + fma(b, -2.0, x));
	elseif (t <= 1.7e+92)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -720000000000.0], t$95$1, If[LessEqual[t, 4.8e-215], N[(a + N[(b * -2.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+92], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2e11 or 1.6999999999999999e92 < t

   1. Initial program 86.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -7.2e11 < t < 4.8000000000000002e-215

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 73.8

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 73.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 52.6%

       \[\leadsto a + \mathsf{fma}\left(b, -2, x\right) \]

   if 4.8000000000000002e-215 < t < 1.6999999999999999e92

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 53.2%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -720000000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-215}:\\ \;\;\;\;a + \mathsf{fma}\left(b, -2, x\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+92}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -1.28 \cdot 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+81}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -1.28e+238)
     t_1
     (if (<= t -2.6e+81) (* t b) (if (<= t 5e+92) (+ z (+ x a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.28e+238) {
		tmp = t_1;
	} else if (t <= -2.6e+81) {
		tmp = t * b;
	} else if (t <= 5e+92) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-1.28d+238)) then
        tmp = t_1
    else if (t <= (-2.6d+81)) then
        tmp = t * b
    else if (t <= 5d+92) then
        tmp = z + (x + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.28e+238) {
		tmp = t_1;
	} else if (t <= -2.6e+81) {
		tmp = t * b;
	} else if (t <= 5e+92) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -1.28e+238:
		tmp = t_1
	elif t <= -2.6e+81:
		tmp = t * b
	elif t <= 5e+92:
		tmp = z + (x + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -1.28e+238)
		tmp = t_1;
	elseif (t <= -2.6e+81)
		tmp = Float64(t * b);
	elseif (t <= 5e+92)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -1.28e+238)
		tmp = t_1;
	elseif (t <= -2.6e+81)
		tmp = t * b;
	elseif (t <= 5e+92)
		tmp = z + (x + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -1.28e+238], t$95$1, If[LessEqual[t, -2.6e+81], N[(t * b), $MachinePrecision], If[LessEqual[t, 5e+92], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.28000000000000007e238 or 5.00000000000000022e92 < t

   1. Initial program 86.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.6%

      \[\leadsto t \cdot \left(-a\right) \]

   if -1.28000000000000007e238 < t < -2.59999999999999992e81

   1. Initial program 83.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 78.0

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

   5. Applied rewrites 78.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 53.2%

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

   if -2.59999999999999992e81 < t < 5.00000000000000022e92

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 49.1%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{+238}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+81}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.26e+76) t_1 (if (<= t 5e+92) (fma z (- 1.0 y) x) 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 <= -1.26e+76) {
		tmp = t_1;
	} else if (t <= 5e+92) {
		tmp = fma(z, (1.0 - y), x);
	} 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 <= -1.26e+76)
		tmp = t_1;
	elseif (t <= 5e+92)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+76], t$95$1, If[LessEqual[t, 5e+92], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.26000000000000007e76 or 5.00000000000000022e92 < t

   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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 81.8

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

   5. Applied rewrites 81.8%

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

   if -1.26000000000000007e76 < t < 5.00000000000000022e92

   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. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 81.6

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

   5. Applied rewrites 81.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 55.8%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{1 - y}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 58.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2.05e+80) t_1 (if (<= y 2.5e+125) (fma a (- 1.0 t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2.05e+80) {
		tmp = t_1;
	} else if (y <= 2.5e+125) {
		tmp = fma(a, (1.0 - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.05e+80)
		tmp = t_1;
	elseif (y <= 2.5e+125)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e+80], t$95$1, If[LessEqual[y, 2.5e+125], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05000000000000001e80 or 2.49999999999999981e125 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

   if -2.05000000000000001e80 < y < 2.49999999999999981e125

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 81.4

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

   5. Applied rewrites 81.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 54.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+92}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -8.8e+77) t_1 (if (<= t 1.7e+92) (+ z (+ 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 <= -8.8e+77) {
		tmp = t_1;
	} else if (t <= 1.7e+92) {
		tmp = z + (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 <= (-8.8d+77)) then
        tmp = t_1
    else if (t <= 1.7d+92) then
        tmp = z + (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 <= -8.8e+77) {
		tmp = t_1;
	} else if (t <= 1.7e+92) {
		tmp = z + (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 <= -8.8e+77:
		tmp = t_1
	elif t <= 1.7e+92:
		tmp = z + (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 <= -8.8e+77)
		tmp = t_1;
	elseif (t <= 1.7e+92)
		tmp = Float64(z + 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 <= -8.8e+77)
		tmp = t_1;
	elseif (t <= 1.7e+92)
		tmp = z + (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, -8.8e+77], t$95$1, If[LessEqual[t, 1.7e+92], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8000000000000002e77 or 1.6999999999999999e92 < t

   1. Initial program 85.4%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

   if -8.8000000000000002e77 < t < 1.6999999999999999e92

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x - z \cdot \left(y - 1\right)\right)} \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x - z \cdot \left(y - 1\right)\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x - z \cdot \left(y - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x - z \cdot \left(y - 1\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x - z \cdot \left(y - 1\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 73.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + z \cdot \left(1 - y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 71.4%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{1 - y}, a + x\right) \]

   9. Taylor expanded in y around 0

      \[\leadsto a + \left(x + \color{blue}{z}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 49.4%

       \[\leadsto z + \left(a + \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+92}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+133}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+45}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.4e+133)
   (* b (+ y -2.0))
   (if (<= b 2.25e+45) (+ z (+ x a)) (* b (+ t -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.4e+133) {
		tmp = b * (y + -2.0);
	} else if (b <= 2.25e+45) {
		tmp = z + (x + a);
	} else {
		tmp = b * (t + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.4d+133)) then
        tmp = b * (y + (-2.0d0))
    else if (b <= 2.25d+45) then
        tmp = z + (x + a)
    else
        tmp = b * (t + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.4e+133) {
		tmp = b * (y + -2.0);
	} else if (b <= 2.25e+45) {
		tmp = z + (x + a);
	} else {
		tmp = b * (t + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.4e+133:
		tmp = b * (y + -2.0)
	elif b <= 2.25e+45:
		tmp = z + (x + a)
	else:
		tmp = b * (t + -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.4e+133)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (b <= 2.25e+45)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = Float64(b * Float64(t + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.4e+133)
		tmp = b * (y + -2.0);
	elseif (b <= 2.25e+45)
		tmp = z + (x + a);
	else
		tmp = b * (t + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.4e+133], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+45], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.3999999999999999e133

   1. Initial program 87.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right) \]

      3. associate-+r- N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      6. lower-+.f64 N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      7. metadata-eval 85.5

         \[\leadsto b \cdot \left(y + \left(t + \color{blue}{-2}\right)\right) \]

   5. Applied rewrites 85.5%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(t + -2\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto b \cdot \left(y + -2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 65.4%

      \[\leadsto b \cdot \left(y + -2\right) \]

   if -2.3999999999999999e133 < b < 2.2499999999999999e45

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) - z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)} - z \cdot \left(y - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x\right)} - z \cdot \left(y - 1\right) \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x - z \cdot \left(y - 1\right)\right)} \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x - z \cdot \left(y - 1\right)\right)} \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x - z \cdot \left(y - 1\right)\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x - z \cdot \left(y - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x - z \cdot \left(y - 1\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x - z \cdot \left(y - 1\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + z \cdot \left(1 - y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.8%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{1 - y}, a + x\right) \]

   9. Taylor expanded in y around 0

      \[\leadsto a + \left(x + \color{blue}{z}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 48.0%

       \[\leadsto z + \left(a + \color{blue}{x}\right) \]

   if 2.2499999999999999e45 < b

   1. Initial program 87.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right) \]

      3. associate-+r- N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      6. lower-+.f64 N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      7. metadata-eval 83.4

         \[\leadsto b \cdot \left(y + \left(t + \color{blue}{-2}\right)\right) \]

   5. Applied rewrites 83.4%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(t + -2\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(t - \color{blue}{2}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 60.8%

      \[\leadsto b \cdot \left(t + \color{blue}{-2}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+133}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+45}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 44.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -8.4 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+45}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ t -2.0))))
   (if (<= b -8.4e+133) t_1 (if (<= b 2.25e+45) (+ z (+ x a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t + -2.0);
	double tmp;
	if (b <= -8.4e+133) {
		tmp = t_1;
	} else if (b <= 2.25e+45) {
		tmp = z + (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 = b * (t + (-2.0d0))
    if (b <= (-8.4d+133)) then
        tmp = t_1
    else if (b <= 2.25d+45) then
        tmp = z + (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 = b * (t + -2.0);
	double tmp;
	if (b <= -8.4e+133) {
		tmp = t_1;
	} else if (b <= 2.25e+45) {
		tmp = z + (x + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t + -2.0)
	tmp = 0
	if b <= -8.4e+133:
		tmp = t_1
	elif b <= 2.25e+45:
		tmp = z + (x + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t + -2.0))
	tmp = 0.0
	if (b <= -8.4e+133)
		tmp = t_1;
	elseif (b <= 2.25e+45)
		tmp = Float64(z + Float64(x + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t + -2.0);
	tmp = 0.0;
	if (b <= -8.4e+133)
		tmp = t_1;
	elseif (b <= 2.25e+45)
		tmp = z + (x + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.4e+133], t$95$1, If[LessEqual[b, 2.25e+45], N[(z + N[(x + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.4e133 or 2.2499999999999999e45 < b

   1. Initial program 87.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right) \]

      3. associate-+r- N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      6. lower-+.f64 N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      7. metadata-eval 84.0

         \[\leadsto b \cdot \left(y + \left(t + \color{blue}{-2}\right)\right) \]

   5. Applied rewrites 84.0%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(t + -2\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto b \cdot \left(t - \color{blue}{2}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 58.7%

      \[\leadsto b \cdot \left(t + \color{blue}{-2}\right) \]

   if -8.4e133 < b < 2.2499999999999999e45

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) - z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)} - z \cdot \left(y - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x\right)} - z \cdot \left(y - 1\right) \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x - z \cdot \left(y - 1\right)\right)} \]

      5. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x - z \cdot \left(y - 1\right)\right)} \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x - z \cdot \left(y - 1\right)\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x - z \cdot \left(y - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x - z \cdot \left(y - 1\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x - z \cdot \left(y - 1\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 88.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + z \cdot \left(1 - y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.8%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{1 - y}, a + x\right) \]

   9. Taylor expanded in y around 0

      \[\leadsto a + \left(x + \color{blue}{z}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 48.0%

       \[\leadsto z + \left(a + \color{blue}{x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+133}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+45}:\\ \;\;\;\;z + \left(x + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+229}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5e+80) (* y b) (if (<= y 2.35e+229) (+ x a) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5e+80) {
		tmp = y * b;
	} else if (y <= 2.35e+229) {
		tmp = x + a;
	} 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 <= (-5d+80)) then
        tmp = y * b
    else if (y <= 2.35d+229) then
        tmp = x + a
    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 <= -5e+80) {
		tmp = y * b;
	} else if (y <= 2.35e+229) {
		tmp = x + a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5e+80:
		tmp = y * b
	elif y <= 2.35e+229:
		tmp = x + a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5e+80)
		tmp = Float64(y * b);
	elseif (y <= 2.35e+229)
		tmp = Float64(x + a);
	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 <= -5e+80)
		tmp = y * b;
	elseif (y <= 2.35e+229)
		tmp = x + a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5e+80], N[(y * b), $MachinePrecision], If[LessEqual[y, 2.35e+229], N[(x + a), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999961e80 or 2.35e229 < y

   1. Initial program 90.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)}\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{\left(y + t\right)} - 2, x\right)\right) \]

      17. associate-+r- N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x\right)\right) \]

      18. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x\right)\right) \]

      20. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x\right)\right) \]

      21. metadata-eval 67.3

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + \color{blue}{-2}\right), x\right)\right) \]

   5. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + -2\right), x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.2%

      \[\leadsto b \cdot \color{blue}{y} \]

   if -4.99999999999999961e80 < y < 2.35e229

   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. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      15. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)}\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{\left(y + t\right)} - 2, x\right)\right) \]

      17. associate-+r- N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x\right)\right) \]

      18. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x\right)\right) \]

      19. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x\right)\right) \]

      20. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x\right)\right) \]

      21. metadata-eval 78.5

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + \color{blue}{-2}\right), x\right)\right) \]

   5. Applied rewrites 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + -2\right), x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.4%

      \[\leadsto a + \color{blue}{\mathsf{fma}\left(b, y + -2, x\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 34.2%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+229}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 24.8% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ x + a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ x a))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + 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 = x + a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + a;
}

Python

def code(x, y, z, t, a, b):
	return x + a

Julia

function code(x, y, z, t, a, b)
	return Float64(x + a)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + a), $MachinePrecision]

Derivation

1. Initial program 94.5%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
4. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   3. distribute-rgt-neg-in N/A

      \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   4. mul-1-neg N/A

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   6. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   7. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   8. distribute-lft-in N/A

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot t + -1 \cdot -1}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(a, -1 \cdot t + \color{blue}{1}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   10. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + -1 \cdot t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   11. neg-mul-1 N/A

       \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   12. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   13. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

   15. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(b, \left(t + y\right) - 2, x\right)}\right) \]

   16. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{\left(y + t\right)} - 2, x\right)\right) \]

   17. associate-+r- N/A

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x\right)\right) \]

   18. lower-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x\right)\right) \]

   19. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x\right)\right) \]

   20. lower-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x\right)\right) \]

   21. metadata-eval 75.4

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + \color{blue}{-2}\right), x\right)\right) \]

5. Applied rewrites 75.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + -2\right), x\right)\right)} \]

6. Taylor expanded in t around 0

   \[\leadsto a + \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 48.5%

   \[\leadsto a + \color{blue}{\mathsf{fma}\left(b, y + -2, x\right)} \]

9. Taylor expanded in b around 0

   \[\leadsto a + x \]
10. Step-by-step derivation

11. Applied rewrites 27.3%

    \[\leadsto a + x \]

12. Final simplification 27.3%

    \[\leadsto x + a \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024221 
(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)))