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

Percentage Accurate: 95.2% → 97.8%

Time: 11.4s

Alternatives: 27

Speedup: 1.2×

• 36.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 42.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* (- (+ t y) 2.0) b) (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)))))
   (if (<= t_1 -2e+303) (* b t) (if (<= t_1 5e+300) (+ (+ z x) a) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = b * t;
	} else if (t_1 <= 5e+300) {
		tmp = (z + x) + a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((t + y) - 2.0d0) * b) + ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a))
    if (t_1 <= (-2d+303)) then
        tmp = b * t
    else if (t_1 <= 5d+300) then
        tmp = (z + x) + a
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = b * t;
	} else if (t_1 <= 5e+300) {
		tmp = (z + x) + a;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a))
	tmp = 0
	if t_1 <= -2e+303:
		tmp = b * t
	elif t_1 <= 5e+300:
		tmp = (z + x) + a
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(t + y) - 2.0) * b) + Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)))
	tmp = 0.0
	if (t_1 <= -2e+303)
		tmp = Float64(b * t);
	elseif (t_1 <= 5e+300)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	tmp = 0.0;
	if (t_1 <= -2e+303)
		tmp = b * t;
	elseif (t_1 <= 5e+300)
		tmp = (z + x) + a;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+303], N[(b * t), $MachinePrecision], If[LessEqual[t$95$1, 5e+300], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 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)) < -2e303

   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 x around 0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 84.4

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

   8. Applied rewrites 84.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 35.6%

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

   if -2e303 < (+.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)) < 5.00000000000000026e300

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 85.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 62.6%

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

   12. Taylor expanded in y around 0

       \[\leadsto a + \left(x + z\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 57.1%

       \[\leadsto \left(z + x\right) + a \]

   if 5.00000000000000026e300 < (+.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 83.3%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.6%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \leq -2 \cdot 10^{+303}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \leq 5 \cdot 10^{+300}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 33.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* (- (+ t y) 2.0) b) (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)))))
   (if (<= t_1 -2e+303) (* b t) (if (<= t_1 5e+300) (+ a x) (* b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = b * t;
	} else if (t_1 <= 5e+300) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((t + y) - 2.0d0) * b) + ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a))
    if (t_1 <= (-2d+303)) then
        tmp = b * t
    else if (t_1 <= 5d+300) then
        tmp = a + x
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	double tmp;
	if (t_1 <= -2e+303) {
		tmp = b * t;
	} else if (t_1 <= 5e+300) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a))
	tmp = 0
	if t_1 <= -2e+303:
		tmp = b * t
	elif t_1 <= 5e+300:
		tmp = a + x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(t + y) - 2.0) * b) + Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)))
	tmp = 0.0
	if (t_1 <= -2e+303)
		tmp = Float64(b * t);
	elseif (t_1 <= 5e+300)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((t + y) - 2.0) * b) + ((x - ((y - 1.0) * z)) - ((t - 1.0) * a));
	tmp = 0.0;
	if (t_1 <= -2e+303)
		tmp = b * t;
	elseif (t_1 <= 5e+300)
		tmp = a + x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] + N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+303], N[(b * t), $MachinePrecision], If[LessEqual[t$95$1, 5e+300], N[(a + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 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)) < -2e303

   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 x around 0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 84.4

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

   8. Applied rewrites 84.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 35.6%

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

   if -2e303 < (+.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)) < 5.00000000000000026e300

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 85.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 62.6%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 37.6%

       \[\leadsto a + x \]

   if 5.00000000000000026e300 < (+.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 83.3%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 38.6%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \leq -2 \cdot 10^{+303}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;\left(\left(t + y\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \leq 5 \cdot 10^{+300}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 155000:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, a\right) + \mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b a) t (fma (- y 2.0) b (fma (- 1.0 y) z a)))))
   (if (<= z -5e-69)
     t_1
     (if (<= z 155000.0) (+ (fma (- b a) t a) (fma (- y 2.0) b x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, fma((y - 2.0), b, fma((1.0 - y), z, a)));
	double tmp;
	if (z <= -5e-69) {
		tmp = t_1;
	} else if (z <= 155000.0) {
		tmp = fma((b - a), t, a) + fma((y - 2.0), b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, fma(Float64(1.0 - y), z, a)))
	tmp = 0.0
	if (z <= -5e-69)
		tmp = t_1;
	elseif (z <= 155000.0)
		tmp = Float64(fma(Float64(b - a), t, a) + fma(Float64(y - 2.0), b, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-69], t$95$1, If[LessEqual[z, 155000.0], N[(N[(N[(b - a), $MachinePrecision] * t + a), $MachinePrecision] + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000033e-69 or 155000 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.1%

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

   if -5.00000000000000033e-69 < z < 155000

   1. Initial program 98.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 97.5

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

   5. Applied rewrites 97.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 98.3%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-69}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \mathbf{elif}\;z \leq 155000:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, a\right) + \mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.46 \cdot 10^{+144}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t + y\right), -b, \left(-b\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.46e+144)
   (* (- (+ t y) 2.0) b)
   (if (<= b -2.55e+41)
     (fma (- 1.0 y) z (fma (- y 2.0) b x))
     (if (<= b 1.02e+93)
       (fma (- 1.0 t) a (+ (fma (- z) y x) z))
       (fma (- (+ t y)) (- b) (* (- b) 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.46e+144) {
		tmp = ((t + y) - 2.0) * b;
	} else if (b <= -2.55e+41) {
		tmp = fma((1.0 - y), z, fma((y - 2.0), b, x));
	} else if (b <= 1.02e+93) {
		tmp = fma((1.0 - t), a, (fma(-z, y, x) + z));
	} else {
		tmp = fma(-(t + y), -b, (-b * 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.46e+144)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	elseif (b <= -2.55e+41)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(y - 2.0), b, x));
	elseif (b <= 1.02e+93)
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(-z), y, x) + z));
	else
		tmp = fma(Float64(-Float64(t + y)), Float64(-b), Float64(Float64(-b) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.46e+144], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -2.55e+41], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e+93], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[((-z) * y + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[((-N[(t + y), $MachinePrecision]) * (-b) + N[((-b) * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.46e144

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.9%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 71.9%

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

   12. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 93.9

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

   14. Applied rewrites 93.9%

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

   if -1.46e144 < b < -2.54999999999999989e41

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 89.7%

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

   if -2.54999999999999989e41 < b < 1.0200000000000001e93

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.4%

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

   if 1.0200000000000001e93 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 82.7%

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

   10. Applied rewrites 82.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.46 \cdot 10^{+144}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t + y\right), -b, \left(-b\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.46 \cdot 10^{+144}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t + y\right), -b, \left(-b\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.46e+144)
   (* (- (+ t y) 2.0) b)
   (if (<= b -2.55e+41)
     (fma (- 1.0 y) z (fma (- y 2.0) b x))
     (if (<= b 1.02e+93)
       (fma (- 1.0 t) a (fma (- 1.0 y) z x))
       (fma (- (+ t y)) (- b) (* (- b) 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.46e+144) {
		tmp = ((t + y) - 2.0) * b;
	} else if (b <= -2.55e+41) {
		tmp = fma((1.0 - y), z, fma((y - 2.0), b, x));
	} else if (b <= 1.02e+93) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = fma(-(t + y), -b, (-b * 2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.46e+144)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	elseif (b <= -2.55e+41)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(y - 2.0), b, x));
	elseif (b <= 1.02e+93)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = fma(Float64(-Float64(t + y)), Float64(-b), Float64(Float64(-b) * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.46e+144], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -2.55e+41], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e+93], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], N[((-N[(t + y), $MachinePrecision]) * (-b) + N[((-b) * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.46e144

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.9%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 71.9%

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

   12. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 93.9

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

   14. Applied rewrites 93.9%

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

   if -1.46e144 < b < -2.54999999999999989e41

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 89.7%

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

   if -2.54999999999999989e41 < b < 1.0200000000000001e93

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.4%

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

   if 1.0200000000000001e93 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 82.7%

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

   10. Applied rewrites 82.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.46 \cdot 10^{+144}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-\left(t + y\right), -b, \left(-b\right) \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.46 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.46e+144)
     t_1
     (if (<= b -2.55e+41)
       (fma (- 1.0 y) z (fma (- y 2.0) b x))
       (if (<= b 1.02e+93) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.46e+144) {
		tmp = t_1;
	} else if (b <= -2.55e+41) {
		tmp = fma((1.0 - y), z, fma((y - 2.0), b, x));
	} else if (b <= 1.02e+93) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.46e+144)
		tmp = t_1;
	elseif (b <= -2.55e+41)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(y - 2.0), b, x));
	elseif (b <= 1.02e+93)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.46e+144], t$95$1, If[LessEqual[b, -2.55e+41], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e+93], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.46e144 or 1.0200000000000001e93 < b

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 66.3%

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

   12. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 87.6

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

   14. Applied rewrites 87.6%

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

   if -1.46e144 < b < -2.54999999999999989e41

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 99.8

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

   8. Applied rewrites 99.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 89.7%

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

   if -2.54999999999999989e41 < b < 1.0200000000000001e93

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.4%

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

Alternative 8: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.25e+117)
     t_1
     (if (<= b -2.55e+41)
       (+ (fma -2.0 b (fma (- b z) y z)) a)
       (if (<= b 1.02e+93) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.25e+117) {
		tmp = t_1;
	} else if (b <= -2.55e+41) {
		tmp = fma(-2.0, b, fma((b - z), y, z)) + a;
	} else if (b <= 1.02e+93) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.25e+117)
		tmp = t_1;
	elseif (b <= -2.55e+41)
		tmp = Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + a);
	elseif (b <= 1.02e+93)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.25e+117], t$95$1, If[LessEqual[b, -2.55e+41], N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[b, 1.02e+93], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.24999999999999996e117 or 1.0200000000000001e93 < b

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 66.0%

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

   12. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 86.8

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

   14. Applied rewrites 86.8%

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

   if -1.24999999999999996e117 < b < -2.54999999999999989e41

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 93.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 86.4%

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

   if -2.54999999999999989e41 < b < 1.0200000000000001e93

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.4%

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

Alternative 9: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, a\right)\\ t_2 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-43}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z a)) (t_2 (* (- (+ t y) 2.0) b)))
   (if (<= b -6e+35)
     t_2
     (if (<= b -1.85e-230)
       t_1
       (if (<= b 5.2e-43) (fma (- 1.0 t) a x) (if (<= b 7e+92) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, a);
	double t_2 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -6e+35) {
		tmp = t_2;
	} else if (b <= -1.85e-230) {
		tmp = t_1;
	} else if (b <= 5.2e-43) {
		tmp = fma((1.0 - t), a, x);
	} else if (b <= 7e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, a)
	t_2 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -6e+35)
		tmp = t_2;
	elseif (b <= -1.85e-230)
		tmp = t_1;
	elseif (b <= 5.2e-43)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (b <= 7e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -6e+35], t$95$2, If[LessEqual[b, -1.85e-230], t$95$1, If[LessEqual[b, 5.2e-43], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[b, 7e+92], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.99999999999999981e35 or 6.99999999999999972e92 < b

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.3%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 68.2%

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

   12. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 81.4

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

   14. Applied rewrites 81.4%

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

   if -5.99999999999999981e35 < b < -1.84999999999999991e-230 or 5.2e-43 < b < 6.99999999999999972e92

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 71.3%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 65.2%

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

   if -1.84999999999999991e-230 < b < 5.2e-43

   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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 70.0

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

   5. Applied rewrites 70.0%

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

   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 64.1%

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

Alternative 10: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -240000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-193}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-265}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 17.5:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -240000000.0)
     t_1
     (if (<= y -1e-193)
       (+ (+ z x) a)
       (if (<= y -5e-265)
         (* (- b a) t)
         (if (<= y 17.5) (+ (fma -2.0 b z) a) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -240000000.0) {
		tmp = t_1;
	} else if (y <= -1e-193) {
		tmp = (z + x) + a;
	} else if (y <= -5e-265) {
		tmp = (b - a) * t;
	} else if (y <= 17.5) {
		tmp = fma(-2.0, b, z) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -240000000.0)
		tmp = t_1;
	elseif (y <= -1e-193)
		tmp = Float64(Float64(z + x) + a);
	elseif (y <= -5e-265)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 17.5)
		tmp = Float64(fma(-2.0, b, z) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -240000000.0], t$95$1, If[LessEqual[y, -1e-193], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[y, -5e-265], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 17.5], N[(N[(-2.0 * b + z), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4e8 or 17.5 < y

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.4

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

   5. Applied rewrites 69.4%

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

   if -2.4e8 < y < -1e-193

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 73.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 63.7%

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

   12. Taylor expanded in y around 0

       \[\leadsto a + \left(x + z\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 62.3%

       \[\leadsto \left(z + x\right) + a \]

   if -1e-193 < y < -5.0000000000000001e-265

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 70.1

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

   5. Applied rewrites 70.1%

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

   if -5.0000000000000001e-265 < y < 17.5

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 58.3%

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

   12. Taylor expanded in y around 0

       \[\leadsto \left(z + -2 \cdot b\right) + a \]
   13. Step-by-step derivation

   14. Applied rewrites 57.1%

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

Alternative 11: 57.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - 2, b, a\right)\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-190}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a\right)\\ \mathbf{elif}\;t \leq 14600:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y 2.0) b a)) (t_2 (* (- b a) t)))
   (if (<= t -1.08e+40)
     t_2
     (if (<= t -1.65e-115)
       t_1
       (if (<= t 5.2e-190) (fma (- 1.0 y) z a) (if (<= t 14600.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((y - 2.0), b, a);
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -1.08e+40) {
		tmp = t_2;
	} else if (t <= -1.65e-115) {
		tmp = t_1;
	} else if (t <= 5.2e-190) {
		tmp = fma((1.0 - y), z, a);
	} else if (t <= 14600.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(y - 2.0), b, a)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.08e+40)
		tmp = t_2;
	elseif (t <= -1.65e-115)
		tmp = t_1;
	elseif (t <= 5.2e-190)
		tmp = fma(Float64(1.0 - y), z, a);
	elseif (t <= 14600.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.08e+40], t$95$2, If[LessEqual[t, -1.65e-115], t$95$1, If[LessEqual[t, 5.2e-190], N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision], If[LessEqual[t, 14600.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08000000000000001e40 or 14600 < t

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.0

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

   5. Applied rewrites 64.0%

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

   if -1.08000000000000001e40 < t < -1.64999999999999995e-115 or 5.1999999999999996e-190 < t < 14600

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 94.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 84.2%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 66.5%

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

   if -1.64999999999999995e-115 < t < 5.1999999999999996e-190

   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 x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 100.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 85.0%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 63.5%

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

Alternative 12: 87.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, t\_1\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= z -1.45e+72)
     (fma (- 1.0 y) z t_1)
     (if (<= z 2.6e+20)
       (fma (- 1.0 t) a t_1)
       (fma (- 1.0 t) a (+ (fma (- z) y x) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (z <= -1.45e+72) {
		tmp = fma((1.0 - y), z, t_1);
	} else if (z <= 2.6e+20) {
		tmp = fma((1.0 - t), a, t_1);
	} else {
		tmp = fma((1.0 - t), a, (fma(-z, y, x) + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (z <= -1.45e+72)
		tmp = fma(Float64(1.0 - y), z, t_1);
	elseif (z <= 2.6e+20)
		tmp = fma(Float64(1.0 - t), a, t_1);
	else
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(-z), y, x) + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[z, -1.45e+72], N[(N[(1.0 - y), $MachinePrecision] * z + t$95$1), $MachinePrecision], If[LessEqual[z, 2.6e+20], N[(N[(1.0 - t), $MachinePrecision] * a + t$95$1), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[((-z) * y + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000009e72

   1. Initial program 96.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 90.4

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

   8. Applied rewrites 90.4%

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

   if -1.45000000000000009e72 < z < 2.6e20

   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 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 95.2

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

   5. Applied rewrites 95.2%

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

   if 2.6e20 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.8%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e+75)
   (fma (- 1.0 y) z (+ (fma (- y 2.0) b x) a))
   (if (<= z 2.6e+20)
     (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
     (fma (- 1.0 t) a (+ (fma (- z) y x) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+75) {
		tmp = fma((1.0 - y), z, (fma((y - 2.0), b, x) + a));
	} else if (z <= 2.6e+20) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = fma((1.0 - t), a, (fma(-z, y, x) + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e+75)
		tmp = fma(Float64(1.0 - y), z, Float64(fma(Float64(y - 2.0), b, x) + a));
	elseif (z <= 2.6e+20)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(-z), y, x) + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e+75], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+20], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[((-z) * y + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999997e75

   1. Initial program 96.0%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. +-commutative N/A

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

      4. distribute-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. associate-+l+ N/A

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-fma.f64 N/A

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

      12. sub-neg N/A

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

      13. metadata-eval N/A

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

      14. distribute-lft-in N/A

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

      15. metadata-eval N/A

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

      16. +-commutative N/A

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

      17. neg-mul-1 N/A

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

      18. sub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-+.f64 N/A

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

   5. Applied rewrites 87.0%

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

   if -4.19999999999999997e75 < z < 2.6e20

   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 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 95.2

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

   5. Applied rewrites 95.2%

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

   if 2.6e20 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + \left(a + x\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e+75)
   (+ (fma -2.0 b (fma (- b z) y z)) (+ a x))
   (if (<= z 2.6e+20)
     (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
     (fma (- 1.0 t) a (+ (fma (- z) y x) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+75) {
		tmp = fma(-2.0, b, fma((b - z), y, z)) + (a + x);
	} else if (z <= 2.6e+20) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = fma((1.0 - t), a, (fma(-z, y, x) + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e+75)
		tmp = Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + Float64(a + x));
	elseif (z <= 2.6e+20)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(-z), y, x) + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e+75], N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+20], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[((-z) * y + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999997e75

   1. Initial program 96.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 87.0%

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

   if -4.19999999999999997e75 < z < 2.6e20

   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 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 95.2

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

   5. Applied rewrites 95.2%

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

   if 2.6e20 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + \left(a + x\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 85.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + \left(a + x\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, a\right) + \mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+39)
   (+ (fma -2.0 b (fma (- b z) y z)) (+ a x))
   (if (<= z 2e+19)
     (+ (fma (- b a) t a) (fma (- y 2.0) b x))
     (fma (- 1.0 t) a (+ (fma (- z) y x) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+39) {
		tmp = fma(-2.0, b, fma((b - z), y, z)) + (a + x);
	} else if (z <= 2e+19) {
		tmp = fma((b - a), t, a) + fma((y - 2.0), b, x);
	} else {
		tmp = fma((1.0 - t), a, (fma(-z, y, x) + z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+39)
		tmp = Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + Float64(a + x));
	elseif (z <= 2e+19)
		tmp = Float64(fma(Float64(b - a), t, a) + fma(Float64(y - 2.0), b, x));
	else
		tmp = fma(Float64(1.0 - t), a, Float64(fma(Float64(-z), y, x) + z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+39], N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + N[(a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+19], N[(N[(N[(b - a), $MachinePrecision] * t + a), $MachinePrecision] + N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[((-z) * y + x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e39

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 86.1%

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

   if -1.8999999999999999e39 < z < 2e19

   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 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 95.0%

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

   if 2e19 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.8%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + \left(a + x\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, a\right) + \mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, x\right) + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 84.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-a\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + \left(a + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -8.8e+116)
   (fma t b (* (- a) t))
   (if (<= t 1.28e+106)
     (+ (fma -2.0 b (fma (- b z) y z)) (+ a x))
     (fma (- 1.0 t) a (fma (- t 2.0) b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -8.8e+116) {
		tmp = fma(t, b, (-a * t));
	} else if (t <= 1.28e+106) {
		tmp = fma(-2.0, b, fma((b - z), y, z)) + (a + x);
	} else {
		tmp = fma((1.0 - t), a, fma((t - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -8.8e+116)
		tmp = fma(t, b, Float64(Float64(-a) * t));
	elseif (t <= 1.28e+106)
		tmp = Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + Float64(a + x));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(t - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -8.8e+116], N[(t * b + N[((-a) * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.28e+106], N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + N[(a + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.799999999999999e116

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   7. Applied rewrites 77.1%

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

   if -8.799999999999999e116 < t < 1.28e106

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 94.3%

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

   if 1.28e106 < t

   1. Initial program 89.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.2%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-a\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + \left(a + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 72.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-a\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 170000000:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+148}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.4e+116)
   (fma t b (* (- a) t))
   (if (<= t 170000000.0)
     (+ (fma -2.0 b (fma (- b z) y z)) a)
     (if (<= t 5.2e+148) (+ (fma (- t 2.0) b z) x) (* (- b a) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.4e+116) {
		tmp = fma(t, b, (-a * t));
	} else if (t <= 170000000.0) {
		tmp = fma(-2.0, b, fma((b - z), y, z)) + a;
	} else if (t <= 5.2e+148) {
		tmp = fma((t - 2.0), b, z) + x;
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.4e+116)
		tmp = fma(t, b, Float64(Float64(-a) * t));
	elseif (t <= 170000000.0)
		tmp = Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + a);
	elseif (t <= 5.2e+148)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	else
		tmp = Float64(Float64(b - a) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.4e+116], N[(t * b + N[((-a) * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 170000000.0], N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t, 5.2e+148], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.40000000000000023e116

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   7. Applied rewrites 77.1%

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

   if -3.40000000000000023e116 < t < 1.7e8

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 96.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 83.2%

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

   if 1.7e8 < t < 5.2e148

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in a around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 91.3

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

   8. Applied rewrites 91.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 74.9%

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

   if 5.2e148 < t

   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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.1

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

   5. Applied rewrites 79.1%

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

Alternative 18: 74.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+116}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-a\right) \cdot t\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.4e+116)
   (fma t b (* (- a) t))
   (if (<= t 3.3e+49)
     (+ (fma -2.0 b (fma (- b z) y z)) a)
     (fma (- 1.0 t) a (fma (- t 2.0) b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.4e+116) {
		tmp = fma(t, b, (-a * t));
	} else if (t <= 3.3e+49) {
		tmp = fma(-2.0, b, fma((b - z), y, z)) + a;
	} else {
		tmp = fma((1.0 - t), a, fma((t - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.4e+116)
		tmp = fma(t, b, Float64(Float64(-a) * t));
	elseif (t <= 3.3e+49)
		tmp = Float64(fma(-2.0, b, fma(Float64(b - z), y, z)) + a);
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(t - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.4e+116], N[(t * b + N[((-a) * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+49], N[(N[(-2.0 * b + N[(N[(b - z), $MachinePrecision] * y + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.40000000000000023e116

   1. Initial program 95.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   7. Applied rewrites 77.1%

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

   if -3.40000000000000023e116 < t < 3.2999999999999998e49

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 94.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 81.8%

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

   if 3.2999999999999998e49 < t

   1. Initial program 91.3%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 85.5

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.4%

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

Alternative 19: 52.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, a\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-295}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z a)))
   (if (<= z -5.8e+29)
     t_1
     (if (<= z -2.35e-295)
       (fma (- y 2.0) b a)
       (if (<= z 8.5e+16) (fma (- 1.0 t) a x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, a);
	double tmp;
	if (z <= -5.8e+29) {
		tmp = t_1;
	} else if (z <= -2.35e-295) {
		tmp = fma((y - 2.0), b, a);
	} else if (z <= 8.5e+16) {
		tmp = fma((1.0 - t), a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, a)
	tmp = 0.0
	if (z <= -5.8e+29)
		tmp = t_1;
	elseif (z <= -2.35e-295)
		tmp = fma(Float64(y - 2.0), b, a);
	elseif (z <= 8.5e+16)
		tmp = fma(Float64(1.0 - t), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision]}, If[LessEqual[z, -5.8e+29], t$95$1, If[LessEqual[z, -2.35e-295], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision], If[LessEqual[z, 8.5e+16], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7999999999999999e29 or 8.5e16 < z

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 85.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 80.7%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 72.4%

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

   if -5.7999999999999999e29 < z < -2.3499999999999999e-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 x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.2%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 61.3%

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

   12. Taylor expanded in z around 0

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

   14. Applied rewrites 54.8%

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

   if -2.3499999999999999e-295 < z < 8.5e16

   1. Initial program 97.4%

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

   3. Taylor expanded in 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 98.7

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

   5. Applied rewrites 98.7%

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

   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 60.6%

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

Alternative 20: 55.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+61}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -1.08e+40)
     t_1
     (if (<= t -1.5e-7)
       (* (- y 2.0) b)
       (if (<= t 4.6e+61) (+ (+ z x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -1.08e+40) {
		tmp = t_1;
	} else if (t <= -1.5e-7) {
		tmp = (y - 2.0) * b;
	} else if (t <= 4.6e+61) {
		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 - a) * t
    if (t <= (-1.08d+40)) then
        tmp = t_1
    else if (t <= (-1.5d-7)) then
        tmp = (y - 2.0d0) * b
    else if (t <= 4.6d+61) 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 - a) * t;
	double tmp;
	if (t <= -1.08e+40) {
		tmp = t_1;
	} else if (t <= -1.5e-7) {
		tmp = (y - 2.0) * b;
	} else if (t <= 4.6e+61) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - a) * t
	tmp = 0
	if t <= -1.08e+40:
		tmp = t_1
	elif t <= -1.5e-7:
		tmp = (y - 2.0) * b
	elif t <= 4.6e+61:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.08e+40)
		tmp = t_1;
	elseif (t <= -1.5e-7)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 4.6e+61)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - a) * t;
	tmp = 0.0;
	if (t <= -1.08e+40)
		tmp = t_1;
	elseif (t <= -1.5e-7)
		tmp = (y - 2.0) * b;
	elseif (t <= 4.6e+61)
		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[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.08e+40], t$95$1, If[LessEqual[t, -1.5e-7], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 4.6e+61], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.08000000000000001e40 or 4.5999999999999999e61 < t

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.5

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

   5. Applied rewrites 68.5%

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

   if -1.08000000000000001e40 < t < -1.4999999999999999e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.0%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 63.3%

       \[\leadsto \left(y - 2\right) \cdot b \]

   if -1.4999999999999999e-7 < t < 4.5999999999999999e61

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 97.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 68.9%

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

   12. Taylor expanded in y around 0

       \[\leadsto a + \left(x + z\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 52.8%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 69.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -9e+116) t_1 (if (<= b 7e+92) (fma (- 1.0 y) z (+ a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -9e+116) {
		tmp = t_1;
	} else if (b <= 7e+92) {
		tmp = fma((1.0 - y), z, (a + x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -9e+116)
		tmp = t_1;
	elseif (b <= 7e+92)
		tmp = fma(Float64(1.0 - y), z, Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9e+116], t$95$1, If[LessEqual[b, 7e+92], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.00000000000000032e116 or 6.99999999999999972e92 < b

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.6%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 66.0%

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

   12. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 86.8

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

   14. Applied rewrites 86.8%

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

   if -9.00000000000000032e116 < b < 6.99999999999999972e92

   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 x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 71.7%

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

Alternative 22: 57.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -240000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 320000000:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -240000000.0) t_1 (if (<= y 320000000.0) (+ (+ z x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -240000000.0) {
		tmp = t_1;
	} else if (y <= 320000000.0) {
		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 - z) * y
    if (y <= (-240000000.0d0)) then
        tmp = t_1
    else if (y <= 320000000.0d0) 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 - z) * y;
	double tmp;
	if (y <= -240000000.0) {
		tmp = t_1;
	} else if (y <= 320000000.0) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -240000000.0:
		tmp = t_1
	elif y <= 320000000.0:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -240000000.0)
		tmp = t_1;
	elseif (y <= 320000000.0)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -240000000.0)
		tmp = t_1;
	elseif (y <= 320000000.0)
		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[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -240000000.0], t$95$1, If[LessEqual[y, 320000000.0], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e8 or 3.2e8 < y

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 70.0

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

   5. Applied rewrites 70.0%

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

   if -2.4e8 < y < 3.2e8

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 67.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 54.3%

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

   12. Taylor expanded in y around 0

       \[\leadsto a + \left(x + z\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 53.8%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 45.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+92}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y 2.0) b)))
   (if (<= b -1.8e+86) t_1 (if (<= b 2.8e+92) (+ (+ z x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y - 2.0) * b;
	double tmp;
	if (b <= -1.8e+86) {
		tmp = t_1;
	} else if (b <= 2.8e+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 = (y - 2.0d0) * b
    if (b <= (-1.8d+86)) then
        tmp = t_1
    else if (b <= 2.8d+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 = (y - 2.0) * b;
	double tmp;
	if (b <= -1.8e+86) {
		tmp = t_1;
	} else if (b <= 2.8e+92) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y - 2.0) * b
	tmp = 0
	if b <= -1.8e+86:
		tmp = t_1
	elif b <= 2.8e+92:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y - 2.0) * b)
	tmp = 0.0
	if (b <= -1.8e+86)
		tmp = t_1;
	elseif (b <= 2.8e+92)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.8e+86)
		tmp = t_1;
	elseif (b <= 2.8e+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[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.8e+86], t$95$1, If[LessEqual[b, 2.8e+92], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.80000000000000003e86 or 2.80000000000000001e92 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.6%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 57.3%

       \[\leadsto \left(y - 2\right) \cdot b \]

   if -1.80000000000000003e86 < b < 2.80000000000000001e92

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 78.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 71.9%

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

   12. Taylor expanded in y around 0

       \[\leadsto a + \left(x + z\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 51.3%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 43.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50000000000:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+36}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -50000000000.0)
   (* b y)
   (if (<= y 4.8e+36) (+ (+ z x) a) (* (- z) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -50000000000.0) {
		tmp = b * y;
	} else if (y <= 4.8e+36) {
		tmp = (z + x) + a;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-50000000000.0d0)) then
        tmp = b * y
    else if (y <= 4.8d+36) then
        tmp = (z + x) + a
    else
        tmp = -z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -50000000000.0) {
		tmp = b * y;
	} else if (y <= 4.8e+36) {
		tmp = (z + x) + a;
	} else {
		tmp = -z * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -50000000000.0:
		tmp = b * y
	elif y <= 4.8e+36:
		tmp = (z + x) + a
	else:
		tmp = -z * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -50000000000.0)
		tmp = Float64(b * y);
	elseif (y <= 4.8e+36)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(Float64(-z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -50000000000.0)
		tmp = b * y;
	elseif (y <= 4.8e+36)
		tmp = (z + x) + a;
	else
		tmp = -z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -50000000000.0], N[(b * y), $MachinePrecision], If[LessEqual[y, 4.8e+36], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[((-z) * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e10

   1. Initial program 95.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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. *-commutative N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower-+.f64 79.6

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

   5. Applied rewrites 79.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.5%

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

   if -5e10 < y < 4.79999999999999985e36

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, z + \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 67.0%

      \[\leadsto \left(a + x\right) + \color{blue}{\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a + \left(x + \color{blue}{\left(z + -1 \cdot \left(y \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 53.6%

       \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]

   12. Taylor expanded in y around 0

       \[\leadsto a + \left(x + z\right) \]
   13. Step-by-step derivation

   14. Applied rewrites 52.4%

       \[\leadsto \left(z + x\right) + a \]

   if 4.79999999999999985e36 < y

   1. Initial program 96.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 80.9

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 80.9%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot z\right) \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 51.9%

      \[\leadsto \left(-z\right) \cdot y \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 25: 32.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+35}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+92}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e+35) (* b y) (if (<= b 7.5e+92) (+ a x) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+35) {
		tmp = b * y;
	} else if (b <= 7.5e+92) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d+35)) then
        tmp = b * y
    else if (b <= 7.5d+92) then
        tmp = a + x
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+35) {
		tmp = b * y;
	} else if (b <= 7.5e+92) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e+35:
		tmp = b * y
	elif b <= 7.5e+92:
		tmp = a + x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e+35)
		tmp = Float64(b * y);
	elseif (b <= 7.5e+92)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e+35)
		tmp = b * y;
	elseif (b <= 7.5e+92)
		tmp = a + x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e+35], N[(b * y), $MachinePrecision], If[LessEqual[b, 7.5e+92], N[(a + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.80000000000000029e35 or 7.49999999999999946e92 < b

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(-1 + t\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot -1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1} + -1 \cdot t, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. lower-+.f64 88.5

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 88.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 38.9%

      \[\leadsto b \cdot \color{blue}{y} \]

   if -4.80000000000000029e35 < b < 7.49999999999999946e92

   1. Initial program 99.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, z + \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.8%

      \[\leadsto \left(a + x\right) + \color{blue}{\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a + \left(x + \color{blue}{\left(z + -1 \cdot \left(y \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 73.5%

       \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto a + x \]
   13. Step-by-step derivation

   14. Applied rewrites 35.2%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 26: 26.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+155}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+93}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+155) (* -2.0 b) (if (<= b 2.05e+93) (+ a x) (* -2.0 b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+155) {
		tmp = -2.0 * b;
	} else if (b <= 2.05e+93) {
		tmp = a + x;
	} else {
		tmp = -2.0 * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d+155)) then
        tmp = (-2.0d0) * b
    else if (b <= 2.05d+93) then
        tmp = a + x
    else
        tmp = (-2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+155) {
		tmp = -2.0 * b;
	} else if (b <= 2.05e+93) {
		tmp = a + x;
	} else {
		tmp = -2.0 * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+155:
		tmp = -2.0 * b
	elif b <= 2.05e+93:
		tmp = a + x
	else:
		tmp = -2.0 * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+155)
		tmp = Float64(-2.0 * b);
	elseif (b <= 2.05e+93)
		tmp = Float64(a + x);
	else
		tmp = Float64(-2.0 * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+155)
		tmp = -2.0 * b;
	elseif (b <= 2.05e+93)
		tmp = a + x;
	else
		tmp = -2.0 * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+155], N[(-2.0 * b), $MachinePrecision], If[LessEqual[b, 2.05e+93], N[(a + x), $MachinePrecision], N[(-2.0 * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.5000000000000006e155 or 2.0500000000000001e93 < b

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 93.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, z + \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 68.4%

      \[\leadsto \left(a + x\right) + \color{blue}{\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right)} \]

   9. Taylor expanded in b around inf

      \[\leadsto b \cdot \left(y - \color{blue}{2}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 59.1%

       \[\leadsto \left(y - 2\right) \cdot b \]

   12. Taylor expanded in y around 0

       \[\leadsto -2 \cdot b \]
   13. Step-by-step derivation

   14. Applied rewrites 20.3%

       \[\leadsto -2 \cdot b \]

   if -9.5000000000000006e155 < b < 2.0500000000000001e93

   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 x around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, z + \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 79.2%

      \[\leadsto \left(a + x\right) + \color{blue}{\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto a + \left(x + \color{blue}{\left(z + -1 \cdot \left(y \cdot z\right)\right)}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 70.0%

       \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]

   12. Taylor expanded in z around 0

       \[\leadsto a + x \]
   13. Step-by-step derivation

   14. Applied rewrites 32.3%

       \[\leadsto a + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 27: 24.4% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ a + x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ a x))

C

double code(double x, double y, double z, double t, double a, double b) {
	return a + x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a + x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a + x;
}

Python

def code(x, y, z, t, a, b):
	return a + x

Julia

function code(x, y, z, t, a, b)
	return Float64(a + x)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a + x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + x), $MachinePrecision]

Derivation

1. Initial program 96.8%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]

5. Applied rewrites 98.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, z + \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right)\right)} \]

6. Taylor expanded in t around 0

   \[\leadsto a + \color{blue}{\left(x + \left(z + \left(-2 \cdot b + y \cdot \left(b - z\right)\right)\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 75.8%

   \[\leadsto \left(a + x\right) + \color{blue}{\mathsf{fma}\left(-2, b, \mathsf{fma}\left(b - z, y, z\right)\right)} \]

9. Taylor expanded in b around 0

   \[\leadsto a + \left(x + \color{blue}{\left(z + -1 \cdot \left(y \cdot z\right)\right)}\right) \]
10. Step-by-step derivation

11. Applied rewrites 53.4%

    \[\leadsto \mathsf{fma}\left(1 - y, z, a + x\right) \]

12. Taylor expanded in z around 0

    \[\leadsto a + x \]
13. Step-by-step derivation

14. Applied rewrites 24.2%

    \[\leadsto a + x \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024331 
(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)))