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

Percentage Accurate: 95.1% → 98.1%

Time: 11.9s

Alternatives: 22

Speedup: 0.5×

• 36.8% 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: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 87.5%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 87.5%

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

4. Final simplification 99.6%

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

Alternative 2: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-129}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))))
   (if (<= b -8.8e-23)
     t_1
     (if (<= b 3.2e-129)
       (fma (- 1.0 y) z (fma (- 1.0 t) a x))
       (if (<= b 8.5e-23) (fma (- b z) y (fma (- t 2.0) b (+ z x))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	double tmp;
	if (b <= -8.8e-23) {
		tmp = t_1;
	} else if (b <= 3.2e-129) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else if (b <= 8.5e-23) {
		tmp = fma((b - z), y, fma((t - 2.0), b, (z + x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x))
	tmp = 0.0
	if (b <= -8.8e-23)
		tmp = t_1;
	elseif (b <= 3.2e-129)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	elseif (b <= 8.5e-23)
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, Float64(z + 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 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e-23], t$95$1, If[LessEqual[b, 3.2e-129], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-23], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.7999999999999998e-23 or 8.4999999999999996e-23 < b

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 87.9

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

   5. Applied rewrites 87.9%

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

   if -8.7999999999999998e-23 < b < 3.2000000000000003e-129

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 95.3%

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

   if 3.2000000000000003e-129 < b < 8.4999999999999996e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 93.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-129}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z\right)\right)\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b z) y (fma (- t 2.0) b (fma (- 1.0 t) a z)))))
   (if (<= z -2.2e-20)
     t_1
     (if (<= z 4.7e-11) (fma (- 1.0 t) a (fma (- (+ t 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 - z), y, fma((t - 2.0), b, fma((1.0 - t), a, z)));
	double tmp;
	if (z <= -2.2e-20) {
		tmp = t_1;
	} else if (z <= 4.7e-11) {
		tmp = fma((1.0 - t), a, fma(((t + 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 - z), y, fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, z)))
	tmp = 0.0
	if (z <= -2.2e-20)
		tmp = t_1;
	elseif (z <= 4.7e-11)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + 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 - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-20], t$95$1, If[LessEqual[z, 4.7e-11], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.19999999999999991e-20 or 4.69999999999999993e-11 < z

   1. Initial program 93.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.0%

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

   if -2.19999999999999991e-20 < z < 4.69999999999999993e-11

   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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 96.8

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

   5. Applied rewrites 96.8%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-20}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z\right)\right)\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, x\right)\\ t_2 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -1 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+231}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y) z x)) (t_2 (* (- a) t)))
   (if (<= t -1e+137)
     t_2
     (if (<= t -2.1e-25)
       t_1
       (if (<= t -8.5e-206)
         (* (- y 2.0) b)
         (if (<= t 3.6e+37) t_1 (if (<= t 1.05e+231) (* b t) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-y, z, x);
	double t_2 = -a * t;
	double tmp;
	if (t <= -1e+137) {
		tmp = t_2;
	} else if (t <= -2.1e-25) {
		tmp = t_1;
	} else if (t <= -8.5e-206) {
		tmp = (y - 2.0) * b;
	} else if (t <= 3.6e+37) {
		tmp = t_1;
	} else if (t <= 1.05e+231) {
		tmp = b * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-y), z, x)
	t_2 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -1e+137)
		tmp = t_2;
	elseif (t <= -2.1e-25)
		tmp = t_1;
	elseif (t <= -8.5e-206)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 3.6e+37)
		tmp = t_1;
	elseif (t <= 1.05e+231)
		tmp = Float64(b * t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z + x), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -1e+137], t$95$2, If[LessEqual[t, -2.1e-25], t$95$1, If[LessEqual[t, -8.5e-206], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 3.6e+37], t$95$1, If[LessEqual[t, 1.05e+231], N[(b * t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1e137 or 1.04999999999999992e231 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   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 86.1

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.0%

      \[\leadsto \left(-a\right) \cdot t \]

   if -1e137 < t < -2.10000000000000002e-25 or -8.5000000000000005e-206 < t < 3.59999999999999998e37

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 57.6%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 46.5%

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

   if -2.10000000000000002e-25 < t < -8.5000000000000005e-206

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf

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

      1. *-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. +-commutative N/A

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

      5. lower-+.f64 51.5

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

   5. Applied rewrites 51.5%

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

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 51.5%

      \[\leadsto \left(y - 2\right) \cdot b \]

   if 3.59999999999999998e37 < t < 1.04999999999999992e231

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 50.6

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

   5. Applied rewrites 50.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.9%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, x\right)\\ t_2 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -1 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-205}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+231}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y) z x)) (t_2 (* (- a) t)))
   (if (<= t -1e+137)
     t_2
     (if (<= t -1.15e-79)
       t_1
       (if (<= t -1.2e-205)
         (* b y)
         (if (<= t 3.6e+37) t_1 (if (<= t 1.05e+231) (* b t) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-y, z, x);
	double t_2 = -a * t;
	double tmp;
	if (t <= -1e+137) {
		tmp = t_2;
	} else if (t <= -1.15e-79) {
		tmp = t_1;
	} else if (t <= -1.2e-205) {
		tmp = b * y;
	} else if (t <= 3.6e+37) {
		tmp = t_1;
	} else if (t <= 1.05e+231) {
		tmp = b * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-y), z, x)
	t_2 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -1e+137)
		tmp = t_2;
	elseif (t <= -1.15e-79)
		tmp = t_1;
	elseif (t <= -1.2e-205)
		tmp = Float64(b * y);
	elseif (t <= 3.6e+37)
		tmp = t_1;
	elseif (t <= 1.05e+231)
		tmp = Float64(b * t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z + x), $MachinePrecision]}, Block[{t$95$2 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -1e+137], t$95$2, If[LessEqual[t, -1.15e-79], t$95$1, If[LessEqual[t, -1.2e-205], N[(b * y), $MachinePrecision], If[LessEqual[t, 3.6e+37], t$95$1, If[LessEqual[t, 1.05e+231], N[(b * t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1e137 or 1.04999999999999992e231 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   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 86.1

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.0%

      \[\leadsto \left(-a\right) \cdot t \]

   if -1e137 < t < -1.15000000000000006e-79 or -1.2000000000000001e-205 < t < 3.59999999999999998e37

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 56.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 45.6%

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

   if -1.15000000000000006e-79 < t < -1.2000000000000001e-205

   1. Initial program 96.5%

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

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 86.4

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

   5. Applied rewrites 86.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 43.5%

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

   if 3.59999999999999998e37 < t < 1.04999999999999992e231

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 50.6

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

   5. Applied rewrites 50.6%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 43.9%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 33.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot t\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-79}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-139}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+27}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+231}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- a) t)))
   (if (<= t -7.6e+118)
     t_1
     (if (<= t -1.15e-79)
       (+ z x)
       (if (<= t -3.7e-139)
         (* b y)
         (if (<= t 1.45e+27) (+ z x) (if (<= t 1.05e+231) (* b t) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -7.6e+118) {
		tmp = t_1;
	} else if (t <= -1.15e-79) {
		tmp = z + x;
	} else if (t <= -3.7e-139) {
		tmp = b * y;
	} else if (t <= 1.45e+27) {
		tmp = z + x;
	} else if (t <= 1.05e+231) {
		tmp = b * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * t
    if (t <= (-7.6d+118)) then
        tmp = t_1
    else if (t <= (-1.15d-79)) then
        tmp = z + x
    else if (t <= (-3.7d-139)) then
        tmp = b * y
    else if (t <= 1.45d+27) then
        tmp = z + x
    else if (t <= 1.05d+231) then
        tmp = b * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a * t;
	double tmp;
	if (t <= -7.6e+118) {
		tmp = t_1;
	} else if (t <= -1.15e-79) {
		tmp = z + x;
	} else if (t <= -3.7e-139) {
		tmp = b * y;
	} else if (t <= 1.45e+27) {
		tmp = z + x;
	} else if (t <= 1.05e+231) {
		tmp = b * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a * t
	tmp = 0
	if t <= -7.6e+118:
		tmp = t_1
	elif t <= -1.15e-79:
		tmp = z + x
	elif t <= -3.7e-139:
		tmp = b * y
	elif t <= 1.45e+27:
		tmp = z + x
	elif t <= 1.05e+231:
		tmp = b * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) * t)
	tmp = 0.0
	if (t <= -7.6e+118)
		tmp = t_1;
	elseif (t <= -1.15e-79)
		tmp = Float64(z + x);
	elseif (t <= -3.7e-139)
		tmp = Float64(b * y);
	elseif (t <= 1.45e+27)
		tmp = Float64(z + x);
	elseif (t <= 1.05e+231)
		tmp = Float64(b * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a * t;
	tmp = 0.0;
	if (t <= -7.6e+118)
		tmp = t_1;
	elseif (t <= -1.15e-79)
		tmp = z + x;
	elseif (t <= -3.7e-139)
		tmp = b * y;
	elseif (t <= 1.45e+27)
		tmp = z + x;
	elseif (t <= 1.05e+231)
		tmp = b * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) * t), $MachinePrecision]}, If[LessEqual[t, -7.6e+118], t$95$1, If[LessEqual[t, -1.15e-79], N[(z + x), $MachinePrecision], If[LessEqual[t, -3.7e-139], N[(b * y), $MachinePrecision], If[LessEqual[t, 1.45e+27], N[(z + x), $MachinePrecision], If[LessEqual[t, 1.05e+231], N[(b * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.60000000000000033e118 or 1.04999999999999992e231 < t

   1. Initial program 90.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 84.8

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.7%

      \[\leadsto \left(-a\right) \cdot t \]

   if -7.60000000000000033e118 < t < -1.15000000000000006e-79 or -3.70000000000000005e-139 < t < 1.4500000000000001e27

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 55.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 35.9%

       \[\leadsto z + x \]

   if -1.15000000000000006e-79 < t < -3.70000000000000005e-139

   1. Initial program 94.1%

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

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 60.0%

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

   if 1.4500000000000001e27 < t < 1.04999999999999992e231

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 50.7

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

   5. Applied rewrites 50.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 44.2%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, a + x\right)\\ t_2 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-138}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (+ a x))) (t_2 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -9.8e+73)
     t_2
     (if (<= b -3.8e-96)
       t_1
       (if (<= b 5.4e-138)
         (fma (- 1.0 y) z (* (- 1.0 t) a))
         (if (<= b 1.6e+35) 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 + x));
	double t_2 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -9.8e+73) {
		tmp = t_2;
	} else if (b <= -3.8e-96) {
		tmp = t_1;
	} else if (b <= 5.4e-138) {
		tmp = fma((1.0 - y), z, ((1.0 - t) * a));
	} else if (b <= 1.6e+35) {
		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, Float64(a + x))
	t_2 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -9.8e+73)
		tmp = t_2;
	elseif (b <= -3.8e-96)
		tmp = t_1;
	elseif (b <= 5.4e-138)
		tmp = fma(Float64(1.0 - y), z, Float64(Float64(1.0 - t) * a));
	elseif (b <= 1.6e+35)
		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 + N[(a + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -9.8e+73], t$95$2, If[LessEqual[b, -3.8e-96], t$95$1, If[LessEqual[b, 5.4e-138], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+35], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.7999999999999998e73 or 1.59999999999999991e35 < b

   1. Initial program 92.4%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 88.6

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 74.3%

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

   if -9.7999999999999998e73 < b < -3.8000000000000001e-96 or 5.40000000000000057e-138 < b < 1.59999999999999991e35

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 69.7%

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

   if -3.8000000000000001e-96 < b < 5.40000000000000057e-138

   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

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

   5. Applied rewrites 88.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 83.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-96}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-138}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \left(1 - t\right) \cdot a\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -2.8e+111)
     t_2
     (if (<= b 1.1e-140)
       t_1
       (if (<= b 8.3e-23) (fma (- 1.0 y) z x) (if (<= b 8e+85) 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 - t), a, x);
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.8e+111) {
		tmp = t_2;
	} else if (b <= 1.1e-140) {
		tmp = t_1;
	} else if (b <= 8.3e-23) {
		tmp = fma((1.0 - y), z, x);
	} else if (b <= 8e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, x)
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.8e+111)
		tmp = t_2;
	elseif (b <= 1.1e-140)
		tmp = t_1;
	elseif (b <= 8.3e-23)
		tmp = fma(Float64(1.0 - y), z, x);
	elseif (b <= 8e+85)
		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 - t), $MachinePrecision] * a + x), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+111], t$95$2, If[LessEqual[b, 1.1e-140], t$95$1, If[LessEqual[b, 8.3e-23], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[b, 8e+85], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.7999999999999999e111 or 8.0000000000000001e85 < b

   1. Initial program 90.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. 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. +-commutative N/A

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

      5. lower-+.f64 75.8

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

   5. Applied rewrites 75.8%

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

   if -2.7999999999999999e111 < b < 1.1e-140 or 8.29999999999999986e-23 < b < 8.0000000000000001e85

   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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 75.3

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

   5. Applied rewrites 75.3%

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

   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 62.0%

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

   if 1.1e-140 < b < 8.29999999999999986e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 77.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 71.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-140}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - z, y, \left(1 - t\right) \cdot a\right)\\ \mathbf{if}\;a \leq -5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-238}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, \mathsf{fma}\left(t - 2, b, z\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b z) y (* (- 1.0 t) a))))
   (if (<= a -5e+81)
     t_1
     (if (<= a -5.1e-238)
       (fma (- z) y (fma (- t 2.0) b z))
       (if (<= a 1.45e+45) (fma (- (+ t 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 - z), y, ((1.0 - t) * a));
	double tmp;
	if (a <= -5e+81) {
		tmp = t_1;
	} else if (a <= -5.1e-238) {
		tmp = fma(-z, y, fma((t - 2.0), b, z));
	} else if (a <= 1.45e+45) {
		tmp = fma(((t + 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 - z), y, Float64(Float64(1.0 - t) * a))
	tmp = 0.0
	if (a <= -5e+81)
		tmp = t_1;
	elseif (a <= -5.1e-238)
		tmp = fma(Float64(-z), y, fma(Float64(t - 2.0), b, z));
	elseif (a <= 1.45e+45)
		tmp = fma(Float64(Float64(t + 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 - z), $MachinePrecision] * y + N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e+81], t$95$1, If[LessEqual[a, -5.1e-238], N[((-z) * y + N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+45], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.9999999999999998e81 or 1.4499999999999999e45 < a

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 91.1%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 81.8%

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

   if -4.9999999999999998e81 < a < -5.1000000000000001e-238

   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

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 67.6%

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

   if -5.1000000000000001e-238 < a < 1.4499999999999999e45

   1. Initial program 96.5%

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

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 72.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \left(1 - t\right) \cdot a\right)\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-238}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, \mathsf{fma}\left(t - 2, b, z\right)\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \left(1 - t\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, x\right)\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-205}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z x)) (t_2 (* (- b a) t)))
   (if (<= t -4.5e+135)
     t_2
     (if (<= t -1.15e-79)
       t_1
       (if (<= t -1.25e-205) (* (- y 2.0) b) (if (<= t 5.2e+33) 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, x);
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -4.5e+135) {
		tmp = t_2;
	} else if (t <= -1.15e-79) {
		tmp = t_1;
	} else if (t <= -1.25e-205) {
		tmp = (y - 2.0) * b;
	} else if (t <= 5.2e+33) {
		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, x)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -4.5e+135)
		tmp = t_2;
	elseif (t <= -1.15e-79)
		tmp = t_1;
	elseif (t <= -1.25e-205)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 5.2e+33)
		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 + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.5e+135], t$95$2, If[LessEqual[t, -1.15e-79], t$95$1, If[LessEqual[t, -1.25e-205], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 5.2e+33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.50000000000000007e135 or 5.1999999999999995e33 < t

   1. Initial program 94.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   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 79.8

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

   5. Applied rewrites 79.8%

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

   if -4.50000000000000007e135 < t < -1.15000000000000006e-79 or -1.25e-205 < t < 5.1999999999999995e33

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 56.9%

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

   if -1.15000000000000006e-79 < t < -1.25e-205

   1. Initial program 96.5%

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

   3. Taylor expanded in b around inf

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

      1. *-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. +-commutative N/A

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

      5. lower-+.f64 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 56.6%

      \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-117}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, x\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)) (t_2 (* (- b z) y)))
   (if (<= y -2.2e+108)
     t_2
     (if (<= y -1.8e+22)
       t_1
       (if (<= y -3.5e-117)
         (fma (- t 2.0) b x)
         (if (<= y 1.7e+86) 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 - t), a, x);
	double t_2 = (b - z) * y;
	double tmp;
	if (y <= -2.2e+108) {
		tmp = t_2;
	} else if (y <= -1.8e+22) {
		tmp = t_1;
	} else if (y <= -3.5e-117) {
		tmp = fma((t - 2.0), b, x);
	} else if (y <= 1.7e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, x)
	t_2 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -2.2e+108)
		tmp = t_2;
	elseif (y <= -1.8e+22)
		tmp = t_1;
	elseif (y <= -3.5e-117)
		tmp = fma(Float64(t - 2.0), b, x);
	elseif (y <= 1.7e+86)
		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 - t), $MachinePrecision] * a + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.2e+108], t$95$2, If[LessEqual[y, -1.8e+22], t$95$1, If[LessEqual[y, -3.5e-117], N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[y, 1.7e+86], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e108 or 1.6999999999999999e86 < y

   1. Initial program 92.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 70.6

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

   5. Applied rewrites 70.6%

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

   if -2.2000000000000001e108 < y < -1.8e22 or -3.4999999999999998e-117 < y < 1.6999999999999999e86

   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 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 79.7

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

   5. Applied rewrites 79.7%

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

   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 56.4%

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

   if -1.8e22 < y < -3.4999999999999998e-117

   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 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 92.8

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 75.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(t - 2, b, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 72.8%

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

Alternative 12: 87.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{if}\;b \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))))
   (if (<= b -8.8e-23)
     t_1
     (if (<= b 8.5e-22) (fma (- 1.0 y) z (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 - t), a, fma(((t + y) - 2.0), b, x));
	double tmp;
	if (b <= -8.8e-23) {
		tmp = t_1;
	} else if (b <= 8.5e-22) {
		tmp = fma((1.0 - y), z, 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 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x))
	tmp = 0.0
	if (b <= -8.8e-23)
		tmp = t_1;
	elseif (b <= 8.5e-22)
		tmp = fma(Float64(1.0 - y), z, 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 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.8e-23], t$95$1, If[LessEqual[b, 8.5e-22], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.7999999999999998e-23 or 8.5000000000000001e-22 < b

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 87.9

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

   5. Applied rewrites 87.9%

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

   if -8.7999999999999998e-23 < b < 8.5000000000000001e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 91.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, x\right)\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y) z x)) (t_2 (* (- b a) t)))
   (if (<= t -1.35e+38)
     t_2
     (if (<= t -2.1e-25)
       t_1
       (if (<= t -8.5e-206) (* (- y 2.0) b) (if (<= t 1.2e+33) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-y, z, x);
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -1.35e+38) {
		tmp = t_2;
	} else if (t <= -2.1e-25) {
		tmp = t_1;
	} else if (t <= -8.5e-206) {
		tmp = (y - 2.0) * b;
	} else if (t <= 1.2e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-y), z, x)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -1.35e+38)
		tmp = t_2;
	elseif (t <= -2.1e-25)
		tmp = t_1;
	elseif (t <= -8.5e-206)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 1.2e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.35e+38], t$95$2, If[LessEqual[t, -2.1e-25], t$95$1, If[LessEqual[t, -8.5e-206], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 1.2e+33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.34999999999999998e38 or 1.2e33 < t

   1. Initial program 95.7%

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

   3. Taylor expanded in 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 73.0

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

   5. Applied rewrites 73.0%

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

   if -1.34999999999999998e38 < t < -2.10000000000000002e-25 or -8.5000000000000005e-206 < t < 1.2e33

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 60.0%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 48.8%

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

   if -2.10000000000000002e-25 < t < -8.5000000000000005e-206

   1. Initial program 97.2%

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

   3. Taylor expanded in b around inf

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

      1. *-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. +-commutative N/A

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

      5. lower-+.f64 51.5

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

   5. Applied rewrites 51.5%

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

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 51.5%

      \[\leadsto \left(y - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 84.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z\right)\right)\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+111)
   (fma (- b z) y (fma (- t 2.0) b z))
   (if (<= b 8.3e+99)
     (fma (- 1.0 y) z (fma (- 1.0 t) a x))
     (fma (- b z) y (* (- t 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+111) {
		tmp = fma((b - z), y, fma((t - 2.0), b, z));
	} else if (b <= 8.3e+99) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = fma((b - z), y, ((t - 2.0) * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+111)
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, z));
	elseif (b <= 8.3e+99)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = fma(Float64(b - z), y, Float64(Float64(t - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+111], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.3e+99], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.7999999999999999e111

   1. Initial program 90.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 95.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 86.6%

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

   if -2.7999999999999999e111 < b < 8.3e99

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 84.6%

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

   if 8.3e99 < b

   1. Initial program 89.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 92.3%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 79.4%

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

Alternative 15: 84.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.8e+75)
   (fma (- (+ t y) 2.0) b x)
   (if (<= b 8.3e+99)
     (fma (- 1.0 y) z (fma (- 1.0 t) a x))
     (fma (- b z) y (* (- t 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.8e+75) {
		tmp = fma(((t + y) - 2.0), b, x);
	} else if (b <= 8.3e+99) {
		tmp = fma((1.0 - y), z, fma((1.0 - t), a, x));
	} else {
		tmp = fma((b - z), y, ((t - 2.0) * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.8e+75)
		tmp = fma(Float64(Float64(t + y) - 2.0), b, x);
	elseif (b <= 8.3e+99)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(1.0 - t), a, x));
	else
		tmp = fma(Float64(b - z), y, Float64(Float64(t - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.8e+75], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[b, 8.3e+99], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.80000000000000012e75

   1. Initial program 92.4%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 90.7

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

   5. Applied rewrites 90.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.8%

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

   if -2.80000000000000012e75 < b < 8.3e99

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 86.2%

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

   if 8.3e99 < b

   1. Initial program 89.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. 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 92.3%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 79.4%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 8.3 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \left(t - 2\right) \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-79}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-139}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+27}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.4e+150)
   (* b t)
   (if (<= t -1.15e-79)
     (+ z x)
     (if (<= t -3.7e-139) (* b y) (if (<= t 1.45e+27) (+ z x) (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.4e+150) {
		tmp = b * t;
	} else if (t <= -1.15e-79) {
		tmp = z + x;
	} else if (t <= -3.7e-139) {
		tmp = b * y;
	} else if (t <= 1.45e+27) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.4d+150)) then
        tmp = b * t
    else if (t <= (-1.15d-79)) then
        tmp = z + x
    else if (t <= (-3.7d-139)) then
        tmp = b * y
    else if (t <= 1.45d+27) then
        tmp = z + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.4e+150) {
		tmp = b * t;
	} else if (t <= -1.15e-79) {
		tmp = z + x;
	} else if (t <= -3.7e-139) {
		tmp = b * y;
	} else if (t <= 1.45e+27) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.4e+150:
		tmp = b * t
	elif t <= -1.15e-79:
		tmp = z + x
	elif t <= -3.7e-139:
		tmp = b * y
	elif t <= 1.45e+27:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.4e+150)
		tmp = Float64(b * t);
	elseif (t <= -1.15e-79)
		tmp = Float64(z + x);
	elseif (t <= -3.7e-139)
		tmp = Float64(b * y);
	elseif (t <= 1.45e+27)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.4e+150)
		tmp = b * t;
	elseif (t <= -1.15e-79)
		tmp = z + x;
	elseif (t <= -3.7e-139)
		tmp = b * y;
	elseif (t <= 1.45e+27)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.4e+150], N[(b * t), $MachinePrecision], If[LessEqual[t, -1.15e-79], N[(z + x), $MachinePrecision], If[LessEqual[t, -3.7e-139], N[(b * y), $MachinePrecision], If[LessEqual[t, 1.45e+27], N[(z + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.40000000000000031e150 or 1.4500000000000001e27 < t

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf

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

      1. *-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. +-commutative N/A

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

      5. lower-+.f64 43.8

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

   5. Applied rewrites 43.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 39.0%

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

   if -6.40000000000000031e150 < t < -1.15000000000000006e-79 or -3.70000000000000005e-139 < t < 1.4500000000000001e27

   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 b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 54.4%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 35.2%

       \[\leadsto z + x \]

   if -1.15000000000000006e-79 < t < -3.70000000000000005e-139

   1. Initial program 94.1%

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

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 60.0%

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

Alternative 17: 44.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-152}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- 1.0 t) a)))
   (if (<= a -1.55e+117)
     t_1
     (if (<= a -2.85e-152) (+ z x) (if (<= a 1.8e+45) (fma (- y) z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 - t) * a;
	double tmp;
	if (a <= -1.55e+117) {
		tmp = t_1;
	} else if (a <= -2.85e-152) {
		tmp = z + x;
	} else if (a <= 1.8e+45) {
		tmp = fma(-y, z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 - t) * a)
	tmp = 0.0
	if (a <= -1.55e+117)
		tmp = t_1;
	elseif (a <= -2.85e-152)
		tmp = Float64(z + x);
	elseif (a <= 1.8e+45)
		tmp = fma(Float64(-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[(1.0 - t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -1.55e+117], t$95$1, If[LessEqual[a, -2.85e-152], N[(z + x), $MachinePrecision], If[LessEqual[a, 1.8e+45], N[((-y) * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.54999999999999988e117 or 1.8e45 < a

   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 a around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 67.1

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

   5. Applied rewrites 67.1%

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

   if -1.54999999999999988e117 < a < -2.8500000000000002e-152

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 54.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 44.0%

       \[\leadsto z + x \]

   if -2.8500000000000002e-152 < a < 1.8e45

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 53.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 47.4%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 38.0%

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

Alternative 18: 36.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot z\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+164}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+47}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- y) z)))
   (if (<= y -2.05e+164)
     (* b y)
     (if (<= y -1.55e+101) t_1 (if (<= y 3e+47) (+ z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -y * z;
	double tmp;
	if (y <= -2.05e+164) {
		tmp = b * y;
	} else if (y <= -1.55e+101) {
		tmp = t_1;
	} else if (y <= 3e+47) {
		tmp = z + x;
	} 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 * z
    if (y <= (-2.05d+164)) then
        tmp = b * y
    else if (y <= (-1.55d+101)) then
        tmp = t_1
    else if (y <= 3d+47) then
        tmp = z + x
    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 * z;
	double tmp;
	if (y <= -2.05e+164) {
		tmp = b * y;
	} else if (y <= -1.55e+101) {
		tmp = t_1;
	} else if (y <= 3e+47) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -y * z
	tmp = 0
	if y <= -2.05e+164:
		tmp = b * y
	elif y <= -1.55e+101:
		tmp = t_1
	elif y <= 3e+47:
		tmp = z + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-y) * z)
	tmp = 0.0
	if (y <= -2.05e+164)
		tmp = Float64(b * y);
	elseif (y <= -1.55e+101)
		tmp = t_1;
	elseif (y <= 3e+47)
		tmp = Float64(z + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -y * z;
	tmp = 0.0;
	if (y <= -2.05e+164)
		tmp = b * y;
	elseif (y <= -1.55e+101)
		tmp = t_1;
	elseif (y <= 3e+47)
		tmp = z + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-y) * z), $MachinePrecision]}, If[LessEqual[y, -2.05e+164], N[(b * y), $MachinePrecision], If[LessEqual[y, -1.55e+101], t$95$1, If[LessEqual[y, 3e+47], N[(z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05000000000000008e164

   1. Initial program 87.0%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 79.1

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

   5. Applied rewrites 79.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 58.1%

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

   if -2.05000000000000008e164 < y < -1.55e101 or 3.0000000000000001e47 < y

   1. Initial program 94.2%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 69.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 44.1%

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

   if -1.55e101 < y < 3.0000000000000001e47

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 70.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 35.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 33.7%

       \[\leadsto z + x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 65.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -4.5e+135)
     t_1
     (if (<= t 1.2e+33) (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 = (b - a) * t;
	double tmp;
	if (t <= -4.5e+135) {
		tmp = t_1;
	} else if (t <= 1.2e+33) {
		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(b - a) * t)
	tmp = 0.0
	if (t <= -4.5e+135)
		tmp = t_1;
	elseif (t <= 1.2e+33)
		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[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.5e+135], t$95$1, If[LessEqual[t, 1.2e+33], N[(N[(1.0 - y), $MachinePrecision] * z + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.50000000000000007e135 or 1.2e33 < t

   1. Initial program 94.8%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   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 79.8

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

   5. Applied rewrites 79.8%

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

   if -4.50000000000000007e135 < t < 1.2e33

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 71.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 66.5%

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

Alternative 20: 62.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)))
   (if (<= a -1.55e+82)
     t_1
     (if (<= a 4.4e+115) (fma (- (+ t 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((1.0 - t), a, x);
	double tmp;
	if (a <= -1.55e+82) {
		tmp = t_1;
	} else if (a <= 4.4e+115) {
		tmp = fma(((t + y) - 2.0), b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, x)
	tmp = 0.0
	if (a <= -1.55e+82)
		tmp = t_1;
	elseif (a <= 4.4e+115)
		tmp = fma(Float64(Float64(t + 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[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[a, -1.55e+82], t$95$1, If[LessEqual[a, 4.4e+115], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55000000000000016e82 or 4.4000000000000001e115 < a

   1. Initial program 94.7%

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

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 87.4

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

   5. Applied rewrites 87.4%

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

   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 77.3%

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

   if -1.55000000000000016e82 < a < 4.4000000000000001e115

   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 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. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative 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. +-commutative N/A

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

      20. lower-+.f64 71.3

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 62.3%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+115}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+27}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.4e+150) (* b t) (if (<= t 1.45e+27) (+ z x) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.4e+150) {
		tmp = b * t;
	} else if (t <= 1.45e+27) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-6.4d+150)) then
        tmp = b * t
    else if (t <= 1.45d+27) then
        tmp = z + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.4e+150) {
		tmp = b * t;
	} else if (t <= 1.45e+27) {
		tmp = z + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.4e+150:
		tmp = b * t
	elif t <= 1.45e+27:
		tmp = z + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.4e+150)
		tmp = Float64(b * t);
	elseif (t <= 1.45e+27)
		tmp = Float64(z + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6.4e+150)
		tmp = b * t;
	elseif (t <= 1.45e+27)
		tmp = z + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.4e+150], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.45e+27], N[(z + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.40000000000000031e150 or 1.4500000000000001e27 < t

   1. Initial program 94.7%

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

   3. Taylor expanded in b around inf

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

      1. *-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. +-commutative N/A

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

      5. lower-+.f64 43.8

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

   5. Applied rewrites 43.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 39.0%

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

   if -6.40000000000000031e150 < t < 1.4500000000000001e27

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate--r+ N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. *-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. +-commutative N/A

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

      15. neg-mul-1 N/A

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

      16. sub-neg N/A

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

      17. lower--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. *-commutative N/A

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

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

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

      22. mul-1-neg N/A

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

      23. lower-fma.f64 N/A

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 50.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 32.3%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 24.6% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ z + x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return z + 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 = z + x
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(z + x)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + x), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in b around 0

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

   1. +-commutative N/A

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

   2. associate--r+ N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. associate-+r- N/A

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

   6. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right) \cdot z}\right)\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

   7. distribute-lft-neg-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} + \left(x - a \cdot \left(t - 1\right)\right) \]

   8. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \cdot z + \left(x - a \cdot \left(t - 1\right)\right) \]

   9. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(y - 1\right), z, x - a \cdot \left(t - 1\right)\right)} \]

   10. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}, z, x - a \cdot \left(t - 1\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(-1 \cdot \left(y + \color{blue}{-1}\right), z, x - a \cdot \left(t - 1\right)\right) \]

   12. distribute-lft-in N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot y + -1 \cdot -1}, z, x - a \cdot \left(t - 1\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(-1 \cdot y + \color{blue}{1}, z, x - a \cdot \left(t - 1\right)\right) \]

   14. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot y}, z, x - a \cdot \left(t - 1\right)\right) \]

   15. neg-mul-1 N/A

       \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}, z, x - a \cdot \left(t - 1\right)\right) \]

   16. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x - a \cdot \left(t - 1\right)\right) \]

   17. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 - y}, z, x - a \cdot \left(t - 1\right)\right) \]

   18. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

   19. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

   20. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + x\right) \]

   21. distribute-lft-neg-in N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + x\right) \]

   22. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + x\right) \]

   23. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(1 - y, z, \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x\right)}\right) \]

5. Applied rewrites 67.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(1 - t, a, x\right)\right)} \]

6. Taylor expanded in a around 0

   \[\leadsto x + \color{blue}{z \cdot \left(1 - y\right)} \]
7. Step-by-step derivation

8. Applied rewrites 38.6%

   \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, x\right) \]

9. Taylor expanded in y around 0

   \[\leadsto x + z \]
10. Step-by-step derivation

11. Applied rewrites 23.9%

    \[\leadsto z + x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024284 
(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)))