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

Percentage Accurate: 94.9% → 97.7%

Time: 13.6s

Alternatives: 21

Speedup: 0.5×

• 36.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 66.8

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

   5. Simplified 66.8%

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

4. Final simplification 99.2%

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

Alternative 2: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, t + -2, x\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-184}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(b, -2, x\right)\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (+ t -2.0) x)) (t_2 (* y (- b z))))
   (if (<= y -2e+88)
     t_2
     (if (<= y -4.6e+31)
       t_1
       (if (<= y 1.5e-184)
         (+ a (+ z (fma b -2.0 x)))
         (if (<= y 6.7e+53) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, (t + -2.0), x);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2e+88) {
		tmp = t_2;
	} else if (y <= -4.6e+31) {
		tmp = t_1;
	} else if (y <= 1.5e-184) {
		tmp = a + (z + fma(b, -2.0, x));
	} else if (y <= 6.7e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(b, Float64(t + -2.0), x)
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2e+88)
		tmp = t_2;
	elseif (y <= -4.6e+31)
		tmp = t_1;
	elseif (y <= 1.5e-184)
		tmp = Float64(a + Float64(z + fma(b, -2.0, x)));
	elseif (y <= 6.7e+53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t + -2.0), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+88], t$95$2, If[LessEqual[y, -4.6e+31], t$95$1, If[LessEqual[y, 1.5e-184], N[(a + N[(z + N[(b * -2.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.7e+53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999992e88 or 6.6999999999999997e53 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.4

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

   5. Simplified 75.4%

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

   if -1.99999999999999992e88 < y < -4.5999999999999999e31 or 1.49999999999999996e-184 < y < 6.6999999999999997e53

   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 inf

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

   5. Simplified 71.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 67.8

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

   8. Simplified 67.8%

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

   if -4.5999999999999999e31 < y < 1.49999999999999996e-184

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. +-lowering-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. +-lowering-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around 0

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

      1. +-lowering-+.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. +-lowering-+.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 63.7

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

   8. Simplified 63.7%

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

Alternative 3: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := \mathsf{fma}\left(b, y + \left(t + -2\right), t\_1\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 0.0014:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x)) (t_2 (fma b (+ y (+ t -2.0)) t_1)))
   (if (<= b -5.2e-63) t_2 (if (<= b 0.0014) (fma a (- 1.0 t) t_1) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double t_2 = fma(b, (y + (t + -2.0)), t_1);
	double tmp;
	if (b <= -5.2e-63) {
		tmp = t_2;
	} else if (b <= 0.0014) {
		tmp = fma(a, (1.0 - t), t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	t_2 = fma(b, Float64(y + Float64(t + -2.0)), t_1)
	tmp = 0.0
	if (b <= -5.2e-63)
		tmp = t_2;
	elseif (b <= 0.0014)
		tmp = fma(a, Float64(1.0 - t), t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -5.2e-63], t$95$2, If[LessEqual[b, 0.0014], N[(a * N[(1.0 - t), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.2000000000000003e-63 or 0.00139999999999999999 < b

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. +-lowering-+.f64 N/A

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

      7. sub-neg N/A

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

      8. +-lowering-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 90.9

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

   5. Simplified 90.9%

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

   if -5.2000000000000003e-63 < b < 0.00139999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 95.1%

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

Alternative 4: 83.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -1.55e+25)
     t_1
     (if (<= b 3.4e+24) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -1.55e+25) {
		tmp = t_1;
	} else if (b <= 3.4e+24) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -1.55e+25)
		tmp = t_1;
	elseif (b <= 3.4e+24)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+25], t$95$1, If[LessEqual[b, 3.4e+24], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5499999999999999e25 or 3.4000000000000001e24 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 83.2%

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

   if -1.5499999999999999e25 < b < 3.4000000000000001e24

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 91.7%

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

Alternative 5: 60.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-192}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -5.2e-63)
     t_1
     (if (<= b 5.6e-192)
       (fma a (- 1.0 t) x)
       (if (<= b 1.35e+24) (fma z (- 1.0 y) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -5.2e-63) {
		tmp = t_1;
	} else if (b <= 5.6e-192) {
		tmp = fma(a, (1.0 - t), x);
	} else if (b <= 1.35e+24) {
		tmp = fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -5.2e-63)
		tmp = t_1;
	elseif (b <= 5.6e-192)
		tmp = fma(a, Float64(1.0 - t), x);
	elseif (b <= 1.35e+24)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e-63], t$95$1, If[LessEqual[b, 5.6e-192], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[b, 1.35e+24], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2000000000000003e-63 or 1.35e24 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. +-lowering-+.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval 73.0

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

   5. Simplified 73.0%

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

   if -5.2000000000000003e-63 < b < 5.60000000000000007e-192

   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. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 98.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 62.8

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

   8. Simplified 62.8%

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

   if 5.60000000000000007e-192 < b < 1.35e24

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. +-lowering-+.f64 N/A

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

      7. sub-neg N/A

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

      8. +-lowering-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 72.1

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

   5. Simplified 72.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 62.3

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

   8. Simplified 62.3%

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

Alternative 6: 71.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y, -z, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -9.2e-72)
     t_1
     (if (<= b 4.2e+23) (fma a (- 1.0 t) (fma y (- z) z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -9.2e-72) {
		tmp = t_1;
	} else if (b <= 4.2e+23) {
		tmp = fma(a, (1.0 - t), fma(y, -z, z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -9.2e-72)
		tmp = t_1;
	elseif (b <= 4.2e+23)
		tmp = fma(a, Float64(1.0 - t), fma(y, Float64(-z), z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e-72], t$95$1, If[LessEqual[b, 4.2e+23], N[(a * N[(1.0 - t), $MachinePrecision] + N[(y * (-z) + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.19999999999999978e-72 or 4.2000000000000003e23 < b

   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 inf

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

   5. Simplified 79.9%

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

   if -9.19999999999999978e-72 < b < 4.2000000000000003e23

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 95.2%

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

   6. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. *-rgt-identity N/A

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

      9. accelerator-lowering-fma.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-lowering-neg.f64 74.2

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

   8. Simplified 74.2%

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

Alternative 7: 57.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-167}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(b, t + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -2e+49)
     t_1
     (if (<= y 1.9e-167)
       (fma a (- 1.0 t) x)
       (if (<= y 8.2e+46) (fma b (+ t -2.0) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -2e+49) {
		tmp = t_1;
	} else if (y <= 1.9e-167) {
		tmp = fma(a, (1.0 - t), x);
	} else if (y <= 8.2e+46) {
		tmp = fma(b, (t + -2.0), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2e+49)
		tmp = t_1;
	elseif (y <= 1.9e-167)
		tmp = fma(a, Float64(1.0 - t), x);
	elseif (y <= 8.2e+46)
		tmp = fma(b, Float64(t + -2.0), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+49], t$95$1, If[LessEqual[y, 1.9e-167], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 8.2e+46], N[(b * N[(t + -2.0), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999989e49 or 8.19999999999999999e46 < y

   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 y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 72.9

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

   5. Simplified 72.9%

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

   if -1.99999999999999989e49 < y < 1.89999999999999984e-167

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 75.2%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 53.6

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

   8. Simplified 53.6%

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

   if 1.89999999999999984e-167 < y < 8.19999999999999999e46

   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 inf

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

   5. Simplified 71.0%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 68.0

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

   8. Simplified 68.0%

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

Alternative 8: 71.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -5.2e-63) t_1 (if (<= b 3.2e+23) (fma a (- 1.0 t) (+ x z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -5.2e-63) {
		tmp = t_1;
	} else if (b <= 3.2e+23) {
		tmp = fma(a, (1.0 - t), (x + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -5.2e-63)
		tmp = t_1;
	elseif (b <= 3.2e+23)
		tmp = fma(a, Float64(1.0 - t), Float64(x + z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e-63], t$95$1, If[LessEqual[b, 3.2e+23], N[(a * N[(1.0 - t), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.2000000000000003e-63 or 3.2e23 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 79.8%

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

   if -5.2000000000000003e-63 < b < 3.2e23

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. +-lowering-+.f64 73.2

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

   8. Simplified 73.2%

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

Alternative 9: 38.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+194}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.8e+194)
   (- (* y z))
   (if (<= y -9.5e+107)
     (* (+ y t) b)
     (if (<= y 1.72e+62) (fma b t x) (fma b y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.8e+194) {
		tmp = -(y * z);
	} else if (y <= -9.5e+107) {
		tmp = (y + t) * b;
	} else if (y <= 1.72e+62) {
		tmp = fma(b, t, x);
	} else {
		tmp = fma(b, y, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.8e+194)
		tmp = Float64(-Float64(y * z));
	elseif (y <= -9.5e+107)
		tmp = Float64(Float64(y + t) * b);
	elseif (y <= 1.72e+62)
		tmp = fma(b, t, x);
	else
		tmp = fma(b, y, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.8e+194], (-N[(y * z), $MachinePrecision]), If[LessEqual[y, -9.5e+107], N[(N[(y + t), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[y, 1.72e+62], N[(b * t + x), $MachinePrecision], N[(b * y + a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.8e194

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 85.2

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

   5. Simplified 85.2%

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

   6. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 60.5

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

   8. Simplified 60.5%

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

   if -4.8e194 < y < -9.50000000000000019e107

   1. Initial program 91.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. +-lowering-+.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval 60.2

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

   5. Simplified 60.2%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 60.2%

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

   if -9.50000000000000019e107 < y < 1.7200000000000001e62

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 50.8

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

   8. Simplified 50.8%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 41.2%

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

   if 1.7200000000000001e62 < y

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. +-lowering-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. +-lowering-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 88.1%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 50.6%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{y}, a\right) \]
   10. Step-by-step derivation

   11. Simplified 50.6%

       \[\leadsto \mathsf{fma}\left(b, \color{blue}{y}, a\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+194}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;\left(y + t\right) \cdot b\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -5.2e-63) t_1 (if (<= b 3.6e+24) (fma a (- 1.0 t) (+ x z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -5.2e-63) {
		tmp = t_1;
	} else if (b <= 3.6e+24) {
		tmp = fma(a, (1.0 - t), (x + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -5.2e-63)
		tmp = t_1;
	elseif (b <= 3.6e+24)
		tmp = fma(a, Float64(1.0 - t), Float64(x + z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e-63], t$95$1, If[LessEqual[b, 3.6e+24], N[(a * N[(1.0 - t), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.2000000000000003e-63 or 3.59999999999999983e24 < b

   1. Initial program 95.2%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. +-lowering-+.f64 N/A

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

      5. sub-neg N/A

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

      6. +-lowering-+.f64 N/A

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

      7. metadata-eval 73.0

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

   5. Simplified 73.0%

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

   if -5.2000000000000003e-63 < b < 3.59999999999999983e24

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 95.2%

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

   6. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. +-lowering-+.f64 73.2

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

   8. Simplified 73.2%

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

Alternative 11: 65.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+58}:\\ \;\;\;\;z + \mathsf{fma}\left(b, t + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.9e+84) t_1 (if (<= y 6e+58) (+ z (fma b (+ t -2.0) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.9e+84) {
		tmp = t_1;
	} else if (y <= 6e+58) {
		tmp = z + fma(b, (t + -2.0), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.9e+84)
		tmp = t_1;
	elseif (y <= 6e+58)
		tmp = Float64(z + fma(b, Float64(t + -2.0), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+84], t$95$1, If[LessEqual[y, 6e+58], N[(z + N[(b * N[(t + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e84 or 6.0000000000000005e58 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.4

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

   5. Simplified 75.4%

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

   if -1.9e84 < y < 6.0000000000000005e58

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. +-lowering-+.f64 N/A

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

      7. sub-neg N/A

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

      8. +-lowering-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 71.4

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. +-lowering-+.f64 N/A

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

      9. metadata-eval 67.0

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

   8. Simplified 67.0%

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

Alternative 12: 25.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.7e+126)
   (* t b)
   (if (<= t -3.3e-291) x (if (<= t 1.8e-5) a (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.7e+126) {
		tmp = t * b;
	} else if (t <= -3.3e-291) {
		tmp = x;
	} else if (t <= 1.8e-5) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4.7d+126)) then
        tmp = t * b
    else if (t <= (-3.3d-291)) then
        tmp = x
    else if (t <= 1.8d-5) then
        tmp = a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.7e+126) {
		tmp = t * b;
	} else if (t <= -3.3e-291) {
		tmp = x;
	} else if (t <= 1.8e-5) {
		tmp = a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.7e+126:
		tmp = t * b
	elif t <= -3.3e-291:
		tmp = x
	elif t <= 1.8e-5:
		tmp = a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.7e+126)
		tmp = Float64(t * b);
	elseif (t <= -3.3e-291)
		tmp = x;
	elseif (t <= 1.8e-5)
		tmp = a;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.7e+126)
		tmp = t * b;
	elseif (t <= -3.3e-291)
		tmp = x;
	elseif (t <= 1.8e-5)
		tmp = a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.7e+126], N[(t * b), $MachinePrecision], If[LessEqual[t, -3.3e-291], x, If[LessEqual[t, 1.8e-5], a, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6999999999999999e126 or 1.80000000000000005e-5 < t

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. +-lowering-+.f64 N/A

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

      7. sub-neg N/A

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

      8. +-lowering-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 72.6

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

   5. Simplified 72.6%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 36.5

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

   8. Simplified 36.5%

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

   if -4.6999999999999999e126 < t < -3.2999999999999999e-291

   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 inf

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

   5. Simplified 21.2%

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

   if -3.2999999999999999e-291 < t < 1.80000000000000005e-5

   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 t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. +-lowering-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. +-lowering-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 98.4%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 25.1%

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

4. Final simplification 28.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 38000000:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -4.8e+49) t_1 (if (<= y 38000000.0) (fma a (- 1.0 t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -4.8e+49) {
		tmp = t_1;
	} else if (y <= 38000000.0) {
		tmp = fma(a, (1.0 - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -4.8e+49)
		tmp = t_1;
	elseif (y <= 38000000.0)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+49], t$95$1, If[LessEqual[y, 38000000.0], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e49 or 3.8e7 < y

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 72.0

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

   5. Simplified 72.0%

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

   if -4.8e49 < y < 3.8e7

   1. Initial program 99.2%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

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

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

      6. mul-1-neg N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 71.4%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 52.2

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

   8. Simplified 52.2%

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

Alternative 14: 50.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.25e+82) t_1 (if (<= y 2.4e+46) (fma b t x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.25e+82) {
		tmp = t_1;
	} else if (y <= 2.4e+46) {
		tmp = fma(b, t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.25e+82)
		tmp = t_1;
	elseif (y <= 2.4e+46)
		tmp = fma(b, t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+82], t$95$1, If[LessEqual[y, 2.4e+46], N[(b * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000004e82 or 2.40000000000000008e46 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.4

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

   5. Simplified 75.4%

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

   if -1.25000000000000004e82 < y < 2.40000000000000008e46

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.9%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 51.5

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

   8. Simplified 51.5%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 41.6%

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

Alternative 15: 50.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(b, y, a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -9.2e+79) t_1 (if (<= t 1.8e-5) (fma b y a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -9.2e+79) {
		tmp = t_1;
	} else if (t <= 1.8e-5) {
		tmp = fma(b, y, a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -9.2e+79)
		tmp = t_1;
	elseif (t <= 1.8e-5)
		tmp = fma(b, y, a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+79], t$95$1, If[LessEqual[t, 1.8e-5], N[(b * y + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.2000000000000002e79 or 1.80000000000000005e-5 < 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. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 62.3

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

   5. Simplified 62.3%

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

   if -9.2000000000000002e79 < t < 1.80000000000000005e-5

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. +-lowering-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. +-lowering-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 96.5%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 52.2%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{y}, a\right) \]
   10. Step-by-step derivation

   11. Simplified 42.1%

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

Alternative 16: 39.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(b, y, a\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e+108)
   (fma b y a)
   (if (<= y 1.25e+50) (fma b t x) (fma b y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e+108) {
		tmp = fma(b, y, a);
	} else if (y <= 1.25e+50) {
		tmp = fma(b, t, x);
	} else {
		tmp = fma(b, y, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e+108)
		tmp = fma(b, y, a);
	elseif (y <= 1.25e+50)
		tmp = fma(b, t, x);
	else
		tmp = fma(b, y, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e+108], N[(b * y + a), $MachinePrecision], If[LessEqual[y, 1.25e+50], N[(b * t + x), $MachinePrecision], N[(b * y + a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e108 or 1.25e50 < y

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. +-lowering-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. +-lowering-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 86.8%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 49.3%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{y}, a\right) \]
   10. Step-by-step derivation

   11. Simplified 49.3%

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

   if -1.8e108 < y < 1.25e50

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 50.8

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

   8. Simplified 50.8%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 41.2%

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

Alternative 17: 38.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+110}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(b, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.15e+110) (* y b) (if (<= y 8e+64) (fma b t x) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.15e+110) {
		tmp = y * b;
	} else if (y <= 8e+64) {
		tmp = fma(b, t, x);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.15e+110)
		tmp = Float64(y * b);
	elseif (y <= 8e+64)
		tmp = fma(b, t, x);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.15e+110], N[(y * b), $MachinePrecision], If[LessEqual[y, 8e+64], N[(b * t + x), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15000000000000003e110 or 8.00000000000000017e64 < y

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 76.3

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

   5. Simplified 76.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 45.1

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

   8. Simplified 45.1%

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

   if -2.15000000000000003e110 < y < 8.00000000000000017e64

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 50.8

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

   8. Simplified 50.8%

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

   9. Taylor expanded in t around inf

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

   11. Simplified 41.2%

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

Alternative 18: 32.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 850000000000:\\ \;\;\;\;\mathsf{fma}\left(b, -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.5e+107)
   (* y b)
   (if (<= y 850000000000.0) (fma b -2.0 x) (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.5e+107) {
		tmp = y * b;
	} else if (y <= 850000000000.0) {
		tmp = fma(b, -2.0, x);
	} else {
		tmp = y * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.5e+107)
		tmp = Float64(y * b);
	elseif (y <= 850000000000.0)
		tmp = fma(b, -2.0, x);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.5e+107], N[(y * b), $MachinePrecision], If[LessEqual[y, 850000000000.0], N[(b * -2.0 + x), $MachinePrecision], N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000019e107 or 8.5e11 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.2

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

   5. Simplified 75.2%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 44.7

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

   8. Simplified 44.7%

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

   if -9.50000000000000019e107 < y < 8.5e11

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.5%

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

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 51.1

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

   8. Simplified 51.1%

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

   9. Taylor expanded in t around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. accelerator-lowering-fma.f64 31.0

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

   11. Simplified 31.0%

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

Alternative 19: 26.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-34}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e-34) (* t b) (if (<= b 1.85e-44) x (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e-34) {
		tmp = t * b;
	} else if (b <= 1.85e-44) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.7d-34)) then
        tmp = t * b
    else if (b <= 1.85d-44) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e-34) {
		tmp = t * b;
	} else if (b <= 1.85e-44) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e-34:
		tmp = t * b
	elif b <= 1.85e-44:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e-34)
		tmp = Float64(t * b);
	elseif (b <= 1.85e-44)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e-34)
		tmp = t * b;
	elseif (b <= 1.85e-44)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e-34], N[(t * b), $MachinePrecision], If[LessEqual[b, 1.85e-44], x, N[(y * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.69999999999999988e-34

   1. Initial program 93.8%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. +-lowering-+.f64 N/A

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

      7. sub-neg N/A

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

      8. +-lowering-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

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

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

      13. mul-1-neg N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. --lowering--.f64 86.4

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

   5. Simplified 86.4%

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

   6. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 39.8

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

   8. Simplified 39.8%

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

   if -3.69999999999999988e-34 < b < 1.85e-44

   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 inf

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

   5. Simplified 23.4%

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

   if 1.85e-44 < b

   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 y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 56.3

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

   5. Simplified 56.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 43.5

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

   8. Simplified 43.5%

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

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-34}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 20.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+179}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+178}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.7e+179) a (if (<= a 2e+178) x a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.7e+179) {
		tmp = a;
	} else if (a <= 2e+178) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-4.7d+179)) then
        tmp = a
    else if (a <= 2d+178) then
        tmp = x
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.7e+179) {
		tmp = a;
	} else if (a <= 2e+178) {
		tmp = x;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.7e+179:
		tmp = a
	elif a <= 2e+178:
		tmp = x
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.7e+179)
		tmp = a;
	elseif (a <= 2e+178)
		tmp = x;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.7e+179)
		tmp = a;
	elseif (a <= 2e+178)
		tmp = x;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.7e+179], a, If[LessEqual[a, 2e+178], x, a]]

Derivation

1. Split input into 2 regimes

2. if a < -4.70000000000000007e179 or 2.0000000000000001e178 < 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 t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. +-lowering-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. +-lowering-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

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

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

      19. mul-1-neg N/A

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

      20. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 68.9%

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

   6. Taylor expanded in a around inf

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

   8. Simplified 34.2%

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

   if -4.70000000000000007e179 < a < 2.0000000000000001e178

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 17.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 10.8% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in t around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. accelerator-lowering-fma.f64 N/A

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

   4. sub-neg N/A

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

   5. +-lowering-+.f64 N/A

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

   6. metadata-eval N/A

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

   7. sub-neg N/A

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

   8. +-commutative N/A

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

   9. distribute-neg-in N/A

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

   10. mul-1-neg N/A

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

   11. remove-double-neg N/A

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

   12. associate-+l+ N/A

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

   13. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

   14. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x - z \cdot \left(y - 1\right)\right)}\right) \]

   15. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(x - z \cdot \left(y - 1\right)\right)}\right) \]

   16. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

   18. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right)\right) \]

   19. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right)\right) \]

   20. accelerator-lowering-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

5. Simplified 73.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + -2, a + \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

6. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a} \]
7. Step-by-step derivation

8. Simplified 11.0%

   \[\leadsto \color{blue}{a} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024205 
(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)))