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

Percentage Accurate: 95.3% → 97.7%

Time: 10.9s

Alternatives: 21

Speedup: 0.5×

• 35.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   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 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 40.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 73.3%

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

Alternative 2: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(-2, b, z + x\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -2.8e+130)
     t_1
     (if (<= b -7.6e+17)
       (fma (- t 2.0) b (+ z x))
       (if (<= b -2.25e-38)
         (fma (- b z) y (fma -2.0 b (+ z x)))
         (if (<= b 1.7e+137) (fma (- 1.0 y) z (- x (* a (- t 1.0)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -2.8e+130) {
		tmp = t_1;
	} else if (b <= -7.6e+17) {
		tmp = fma((t - 2.0), b, (z + x));
	} else if (b <= -2.25e-38) {
		tmp = fma((b - z), y, fma(-2.0, b, (z + x)));
	} else if (b <= 1.7e+137) {
		tmp = fma((1.0 - y), z, (x - (a * (t - 1.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -2.8e+130)
		tmp = t_1;
	elseif (b <= -7.6e+17)
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	elseif (b <= -2.25e-38)
		tmp = fma(Float64(b - z), y, fma(-2.0, b, Float64(z + x)));
	elseif (b <= 1.7e+137)
		tmp = fma(Float64(1.0 - y), z, Float64(x - Float64(a * Float64(t - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.8e+130], t$95$1, If[LessEqual[b, -7.6e+17], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.25e-38], N[(N[(b - z), $MachinePrecision] * y + N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+137], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.7999999999999999e130 or 1.69999999999999993e137 < b

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 90.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 89.8%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 79.7%

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

   if -2.7999999999999999e130 < b < -7.6e17

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 90.8

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

   5. Applied rewrites 90.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 87.1%

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

   if -7.6e17 < b < -2.25000000000000004e-38

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 96.4%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 96.4%

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

   if -2.25000000000000004e-38 < b < 1.69999999999999993e137

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.7%

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

Alternative 3: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-38} \lor \neg \left(b \leq 1.46 \cdot 10^{+40}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.55e-38) (not (<= b 1.46e+40)))
   (fma (- b z) y (fma (- t 2.0) b (+ z x)))
   (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.55e-38) || !(b <= 1.46e+40)) {
		tmp = fma((b - z), y, fma((t - 2.0), b, (z + x)));
	} else {
		tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (b * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.55e-38) || !(b <= 1.46e+40))
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, Float64(z + x)));
	else
		tmp = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(b * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.55e-38], N[Not[LessEqual[b, 1.46e+40]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.54999999999999991e-38 or 1.46e40 < b

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 91.8%

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

   if -1.54999999999999991e-38 < b < 1.46e40

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 96.3

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

   5. Applied rewrites 96.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-38} \lor \neg \left(b \leq 1.46 \cdot 10^{+40}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-80}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 320000000000:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)) (t_2 (* (- b z) y)))
   (if (<= y -4.2e+50)
     t_2
     (if (<= y -2.9e-210)
       t_1
       (if (<= y 1.45e-80)
         (fma -2.0 b (+ z x))
         (if (<= y 7e-17)
           t_1
           (if (<= y 320000000000.0) (* (- 1.0 t) a) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double t_2 = (b - z) * y;
	double tmp;
	if (y <= -4.2e+50) {
		tmp = t_2;
	} else if (y <= -2.9e-210) {
		tmp = t_1;
	} else if (y <= 1.45e-80) {
		tmp = fma(-2.0, b, (z + x));
	} else if (y <= 7e-17) {
		tmp = t_1;
	} else if (y <= 320000000000.0) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	t_2 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.2e+50)
		tmp = t_2;
	elseif (y <= -2.9e-210)
		tmp = t_1;
	elseif (y <= 1.45e-80)
		tmp = fma(-2.0, b, Float64(z + x));
	elseif (y <= 7e-17)
		tmp = t_1;
	elseif (y <= 320000000000.0)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.2e+50], t$95$2, If[LessEqual[y, -2.9e-210], t$95$1, If[LessEqual[y, 1.45e-80], N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-17], t$95$1, If[LessEqual[y, 320000000000.0], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.1999999999999999e50 or 3.2e11 < y

   1. Initial program 91.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.7

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

   5. Applied rewrites 67.7%

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

   if -4.1999999999999999e50 < y < -2.90000000000000006e-210 or 1.44999999999999999e-80 < y < 7.0000000000000003e-17

   1. Initial program 95.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.7

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

   5. Applied rewrites 51.7%

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

   if -2.90000000000000006e-210 < y < 1.44999999999999999e-80

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 98.1

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 83.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 64.2%

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

   if 7.0000000000000003e-17 < y < 3.2e11

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.5

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

   5. Applied rewrites 71.5%

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

Alternative 5: 39.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 2\right) \cdot b\\ t_2 := \mathsf{fma}\left(-z, y, z\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+155}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -12500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-139}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 2.0) b)) (t_2 (fma (- z) y z)))
   (if (<= b -3.6e+155)
     (* (- y 2.0) b)
     (if (<= b -12500000000000.0)
       t_1
       (if (<= b -2.9e-56)
         t_2
         (if (<= b 1.95e-139)
           (* (- 1.0 t) a)
           (if (<= b 1.15e+66) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 2.0) * b;
	double t_2 = fma(-z, y, z);
	double tmp;
	if (b <= -3.6e+155) {
		tmp = (y - 2.0) * b;
	} else if (b <= -12500000000000.0) {
		tmp = t_1;
	} else if (b <= -2.9e-56) {
		tmp = t_2;
	} else if (b <= 1.95e-139) {
		tmp = (1.0 - t) * a;
	} else if (b <= 1.15e+66) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 2.0) * b)
	t_2 = fma(Float64(-z), y, z)
	tmp = 0.0
	if (b <= -3.6e+155)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= -12500000000000.0)
		tmp = t_1;
	elseif (b <= -2.9e-56)
		tmp = t_2;
	elseif (b <= 1.95e-139)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (b <= 1.15e+66)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[((-z) * y + z), $MachinePrecision]}, If[LessEqual[b, -3.6e+155], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -12500000000000.0], t$95$1, If[LessEqual[b, -2.9e-56], t$95$2, If[LessEqual[b, 1.95e-139], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 1.15e+66], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.60000000000000007e155

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 92.7%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 84.9%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 55.0%

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

   if -3.60000000000000007e155 < b < -1.25e13 or 1.15e66 < b

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 65.7%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 47.9%

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

   if -1.25e13 < b < -2.89999999999999991e-56 or 1.95000000000000005e-139 < b < 1.15e66

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 84.7%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 48.4%

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

   if -2.89999999999999991e-56 < b < 1.95000000000000005e-139

   1. Initial program 96.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 48.9

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

   5. Applied rewrites 48.9%

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

Alternative 6: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-38}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - a \cdot \left(t - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.4e+132)
     t_1
     (if (<= b -1.55e-38)
       (fma (- z) y (fma (- t 2.0) b (+ z x)))
       (if (<= b 1.7e+137) (fma (- 1.0 y) z (- x (* a (- t 1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.4e+132) {
		tmp = t_1;
	} else if (b <= -1.55e-38) {
		tmp = fma(-z, y, fma((t - 2.0), b, (z + x)));
	} else if (b <= 1.7e+137) {
		tmp = fma((1.0 - y), z, (x - (a * (t - 1.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -1.4e+132)
		tmp = t_1;
	elseif (b <= -1.55e-38)
		tmp = fma(Float64(-z), y, fma(Float64(t - 2.0), b, Float64(z + x)));
	elseif (b <= 1.7e+137)
		tmp = fma(Float64(1.0 - y), z, Float64(x - Float64(a * Float64(t - 1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.4e+132], t$95$1, If[LessEqual[b, -1.55e-38], N[((-z) * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+137], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4e132 or 1.69999999999999993e137 < b

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 90.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 89.8%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 79.7%

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

   if -1.4e132 < b < -1.54999999999999991e-38

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 96.4%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 84.0%

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

   if -1.54999999999999991e-38 < b < 1.69999999999999993e137

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.7%

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

Alternative 7: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(-2, b, z + x\right)\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+73}:\\ \;\;\;\;\left(x - a \cdot \left(t - 1\right)\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b z) y (fma -2.0 b (+ z x)))))
   (if (<= y -3.8e-12)
     t_1
     (if (<= y 7e-17)
       (fma (- t 2.0) b (+ z x))
       (if (<= y 3.6e+73) (+ (- x (* a (- t 1.0))) (* b y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - z), y, fma(-2.0, b, (z + x)));
	double tmp;
	if (y <= -3.8e-12) {
		tmp = t_1;
	} else if (y <= 7e-17) {
		tmp = fma((t - 2.0), b, (z + x));
	} else if (y <= 3.6e+73) {
		tmp = (x - (a * (t - 1.0))) + (b * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - z), y, fma(-2.0, b, Float64(z + x)))
	tmp = 0.0
	if (y <= -3.8e-12)
		tmp = t_1;
	elseif (y <= 7e-17)
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	elseif (y <= 3.6e+73)
		tmp = Float64(Float64(x - Float64(a * Float64(t - 1.0))) + Float64(b * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y + N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-12], t$95$1, If[LessEqual[y, 7e-17], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+73], N[(N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.79999999999999996e-12 or 3.5999999999999999e73 < y

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 81.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 80.6%

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

   if -3.79999999999999996e-12 < y < 7.0000000000000003e-17

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 96.3

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.5%

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

   if 7.0000000000000003e-17 < y < 3.5999999999999999e73

   1. Initial program 96.8%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 40.2

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

   5. Applied rewrites 40.2%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 34.0

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

   8. Applied rewrites 34.0%

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

   9. Taylor expanded in a around 0

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

       1. fp-cancel-sub-sign-inv N/A

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

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

       4. lower-fma.f64 N/A

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

       5. mul-1-neg N/A

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

       6. lower-neg.f64 N/A

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

       7. lower--.f64 49.6

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

   11. Applied rewrites 49.6%

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

   12. Taylor expanded in z around 0

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

       1. lower--.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 71.7

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

   14. Applied rewrites 71.7%

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

Alternative 8: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(-2, b, z + x\right)\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \mathbf{elif}\;y \leq 3400000000:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b z) y (fma -2.0 b (+ z x)))))
   (if (<= y -3.8e-12)
     t_1
     (if (<= y 7e-17)
       (fma (- t 2.0) b (+ z x))
       (if (<= y 3400000000.0) (* (- 1.0 t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - z), y, fma(-2.0, b, (z + x)));
	double tmp;
	if (y <= -3.8e-12) {
		tmp = t_1;
	} else if (y <= 7e-17) {
		tmp = fma((t - 2.0), b, (z + x));
	} else if (y <= 3400000000.0) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - z), y, fma(-2.0, b, Float64(z + x)))
	tmp = 0.0
	if (y <= -3.8e-12)
		tmp = t_1;
	elseif (y <= 7e-17)
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	elseif (y <= 3400000000.0)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y + N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-12], t$95$1, If[LessEqual[y, 7e-17], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3400000000.0], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.79999999999999996e-12 or 3.4e9 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 80.3%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 77.2%

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

   if -3.79999999999999996e-12 < y < 7.0000000000000003e-17

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 96.3

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.5%

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

   if 7.0000000000000003e-17 < y < 3.4e9

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.5

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

   5. Applied rewrites 71.5%

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

Alternative 9: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+238}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;y \leq -0.0032 \lor \neg \left(y \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e+238)
   (* (- b z) y)
   (if (or (<= y -0.0032) (not (<= y 7e-17)))
     (+ (fma (- 1.0 y) z x) (* b y))
     (fma (- t 2.0) b (+ z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+238) {
		tmp = (b - z) * y;
	} else if ((y <= -0.0032) || !(y <= 7e-17)) {
		tmp = fma((1.0 - y), z, x) + (b * y);
	} else {
		tmp = fma((t - 2.0), b, (z + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e+238)
		tmp = Float64(Float64(b - z) * y);
	elseif ((y <= -0.0032) || !(y <= 7e-17))
		tmp = Float64(fma(Float64(1.0 - y), z, x) + Float64(b * y));
	else
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e+238], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[y, -0.0032], N[Not[LessEqual[y, 7e-17]], $MachinePrecision]], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + N[(b * y), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e238

   1. Initial program 75.0%

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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 87.9

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

   5. Applied rewrites 87.9%

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

   if -2.2e238 < y < -0.00320000000000000015 or 7.0000000000000003e-17 < y

   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 t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 45.6

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

   5. Applied rewrites 45.6%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 40.2

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

   8. Applied rewrites 40.2%

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

   9. Taylor expanded in a around 0

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

       1. fp-cancel-sub-sign-inv N/A

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

       2. +-commutative N/A

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

       3. mul-1-neg N/A

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

       4. lower-fma.f64 N/A

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

       5. mul-1-neg N/A

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

       6. lower-neg.f64 N/A

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

       7. lower--.f64 71.5

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

   11. Applied rewrites 71.5%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 71.5%

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

   if -0.00320000000000000015 < y < 7.0000000000000003e-17

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 96.1

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

   5. Applied rewrites 96.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+238}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;y \leq -0.0032 \lor \neg \left(y \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.18 \cdot 10^{-113}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-137}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+65}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -9.5e-10)
     t_1
     (if (<= b -1.18e-113)
       (fma -2.0 b (+ z x))
       (if (<= b 1.95e-137)
         (* (- 1.0 t) a)
         (if (<= b 8e+65) (* (- b z) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -9.5e-10) {
		tmp = t_1;
	} else if (b <= -1.18e-113) {
		tmp = fma(-2.0, b, (z + x));
	} else if (b <= 1.95e-137) {
		tmp = (1.0 - t) * a;
	} else if (b <= 8e+65) {
		tmp = (b - z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t + y) - 2.0) * b)
	tmp = 0.0
	if (b <= -9.5e-10)
		tmp = t_1;
	elseif (b <= -1.18e-113)
		tmp = fma(-2.0, b, Float64(z + x));
	elseif (b <= 1.95e-137)
		tmp = Float64(Float64(1.0 - t) * a);
	elseif (b <= 8e+65)
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -9.5e-10], t$95$1, If[LessEqual[b, -1.18e-113], N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e-137], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[b, 8e+65], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.50000000000000028e-10 or 7.9999999999999999e65 < b

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 90.8%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 71.3%

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

   if -9.50000000000000028e-10 < b < -1.18e-113

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 84.6

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 64.2%

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

   if -1.18e-113 < b < 1.95e-137

   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 a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.9

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

   5. Applied rewrites 49.9%

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

   if 1.95e-137 < b < 7.9999999999999999e65

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 53.1

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

   5. Applied rewrites 53.1%

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

Alternative 11: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-45} \lor \neg \left(b \leq 4.1 \cdot 10^{-28}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - a \cdot \left(t - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.6e-45) (not (<= b 4.1e-28)))
   (fma (- b z) y (fma (- t 2.0) b (+ z x)))
   (fma (- 1.0 y) z (- x (* a (- t 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.6e-45) || !(b <= 4.1e-28)) {
		tmp = fma((b - z), y, fma((t - 2.0), b, (z + x)));
	} else {
		tmp = fma((1.0 - y), z, (x - (a * (t - 1.0))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.6e-45) || !(b <= 4.1e-28))
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, Float64(z + x)));
	else
		tmp = fma(Float64(1.0 - y), z, Float64(x - Float64(a * Float64(t - 1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.6e-45], N[Not[LessEqual[b, 4.1e-28]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z + N[(x - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.60000000000000004e-45 or 4.1000000000000002e-28 < b

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 90.6%

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

   if -1.60000000000000004e-45 < b < 4.1000000000000002e-28

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 98.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-45} \lor \neg \left(b \leq 4.1 \cdot 10^{-28}\right):\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x - a \cdot \left(t - 1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 81.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5:\\ \;\;\;\;\mathsf{fma}\left(-z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(-2, b, z + x\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.5)
   (fma (- z) y (fma (- t 2.0) b (+ z x)))
   (if (<= t 8.2e+78)
     (fma (- b z) y (+ (fma -2.0 b (+ z x)) a))
     (* (- b a) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.5) {
		tmp = fma(-z, y, fma((t - 2.0), b, (z + x)));
	} else if (t <= 8.2e+78) {
		tmp = fma((b - z), y, (fma(-2.0, b, (z + x)) + a));
	} else {
		tmp = (b - a) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.5)
		tmp = fma(Float64(-z), y, fma(Float64(t - 2.0), b, Float64(z + x)));
	elseif (t <= 8.2e+78)
		tmp = fma(Float64(b - z), y, Float64(fma(-2.0, b, Float64(z + x)) + a));
	else
		tmp = Float64(Float64(b - a) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.5], N[((-z) * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+78], N[(N[(b - z), $MachinePrecision] * y + N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 75.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 72.2%

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

   if -3.5 < t < 8.1999999999999994e78

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 96.0%

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

   if 8.1999999999999994e78 < t

   1. Initial program 91.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.6

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

   5. Applied rewrites 76.6%

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

Alternative 13: 28.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+25}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-242}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+37}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.3e+25)
   (* b y)
   (if (<= y 1.3e-242)
     (* b t)
     (if (<= y 2.6e-68) (* 1.0 z) (if (<= y 1.52e+37) (* b t) (* (- y) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.3e+25) {
		tmp = b * y;
	} else if (y <= 1.3e-242) {
		tmp = b * t;
	} else if (y <= 2.6e-68) {
		tmp = 1.0 * z;
	} else if (y <= 1.52e+37) {
		tmp = b * t;
	} else {
		tmp = -y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.3d+25)) then
        tmp = b * y
    else if (y <= 1.3d-242) then
        tmp = b * t
    else if (y <= 2.6d-68) then
        tmp = 1.0d0 * z
    else if (y <= 1.52d+37) then
        tmp = b * t
    else
        tmp = -y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.3e+25) {
		tmp = b * y;
	} else if (y <= 1.3e-242) {
		tmp = b * t;
	} else if (y <= 2.6e-68) {
		tmp = 1.0 * z;
	} else if (y <= 1.52e+37) {
		tmp = b * t;
	} else {
		tmp = -y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.3e+25:
		tmp = b * y
	elif y <= 1.3e-242:
		tmp = b * t
	elif y <= 2.6e-68:
		tmp = 1.0 * z
	elif y <= 1.52e+37:
		tmp = b * t
	else:
		tmp = -y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.3e+25)
		tmp = Float64(b * y);
	elseif (y <= 1.3e-242)
		tmp = Float64(b * t);
	elseif (y <= 2.6e-68)
		tmp = Float64(1.0 * z);
	elseif (y <= 1.52e+37)
		tmp = Float64(b * t);
	else
		tmp = Float64(Float64(-y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.3e+25)
		tmp = b * y;
	elseif (y <= 1.3e-242)
		tmp = b * t;
	elseif (y <= 2.6e-68)
		tmp = 1.0 * z;
	elseif (y <= 1.52e+37)
		tmp = b * t;
	else
		tmp = -y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.3e+25], N[(b * y), $MachinePrecision], If[LessEqual[y, 1.3e-242], N[(b * t), $MachinePrecision], If[LessEqual[y, 2.6e-68], N[(1.0 * z), $MachinePrecision], If[LessEqual[y, 1.52e+37], N[(b * t), $MachinePrecision], N[((-y) * z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.29999999999999961e25

   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 y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 82.8%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 45.1%

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

   12. Taylor expanded in y around inf

       \[\leadsto b \cdot y \]
   13. Step-by-step derivation

   14. Applied rewrites 40.4%

       \[\leadsto b \cdot y \]

   if -7.29999999999999961e25 < y < 1.30000000000000009e-242 or 2.5999999999999998e-68 < y < 1.5200000000000001e37

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 75.1%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 41.5%

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

   12. Taylor expanded in t around inf

       \[\leadsto b \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 32.7%

       \[\leadsto b \cdot t \]

   if 1.30000000000000009e-242 < y < 2.5999999999999998e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 40.1

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

   5. Applied rewrites 40.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 40.1%

      \[\leadsto 1 \cdot z \]

   if 1.5200000000000001e37 < y

   1. Initial program 87.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.5

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

   5. Applied rewrites 43.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 43.5%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+25}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-242}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+37}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+25}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-242}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+73}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.3e+25)
   (* b y)
   (if (<= y 1.3e-242)
     (* b t)
     (if (<= y 2.6e-68) (* 1.0 z) (if (<= y 4.1e+73) (* b t) (* b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.3e+25) {
		tmp = b * y;
	} else if (y <= 1.3e-242) {
		tmp = b * t;
	} else if (y <= 2.6e-68) {
		tmp = 1.0 * z;
	} else if (y <= 4.1e+73) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.3d+25)) then
        tmp = b * y
    else if (y <= 1.3d-242) then
        tmp = b * t
    else if (y <= 2.6d-68) then
        tmp = 1.0d0 * z
    else if (y <= 4.1d+73) then
        tmp = b * t
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.3e+25) {
		tmp = b * y;
	} else if (y <= 1.3e-242) {
		tmp = b * t;
	} else if (y <= 2.6e-68) {
		tmp = 1.0 * z;
	} else if (y <= 4.1e+73) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.3e+25:
		tmp = b * y
	elif y <= 1.3e-242:
		tmp = b * t
	elif y <= 2.6e-68:
		tmp = 1.0 * z
	elif y <= 4.1e+73:
		tmp = b * t
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.3e+25)
		tmp = Float64(b * y);
	elseif (y <= 1.3e-242)
		tmp = Float64(b * t);
	elseif (y <= 2.6e-68)
		tmp = Float64(1.0 * z);
	elseif (y <= 4.1e+73)
		tmp = Float64(b * t);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.3e+25)
		tmp = b * y;
	elseif (y <= 1.3e-242)
		tmp = b * t;
	elseif (y <= 2.6e-68)
		tmp = 1.0 * z;
	elseif (y <= 4.1e+73)
		tmp = b * t;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.3e+25], N[(b * y), $MachinePrecision], If[LessEqual[y, 1.3e-242], N[(b * t), $MachinePrecision], If[LessEqual[y, 2.6e-68], N[(1.0 * z), $MachinePrecision], If[LessEqual[y, 4.1e+73], N[(b * t), $MachinePrecision], N[(b * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.29999999999999961e25 or 4.0999999999999998e73 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 82.4%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 41.9%

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

   12. Taylor expanded in y around inf

       \[\leadsto b \cdot y \]
   13. Step-by-step derivation

   14. Applied rewrites 39.0%

       \[\leadsto b \cdot y \]

   if -7.29999999999999961e25 < y < 1.30000000000000009e-242 or 2.5999999999999998e-68 < y < 4.0999999999999998e73

   1. Initial program 95.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 95.9%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 74.1%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 39.6%

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

   12. Taylor expanded in t around inf

       \[\leadsto b \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 30.8%

       \[\leadsto b \cdot t \]

   if 1.30000000000000009e-242 < y < 2.5999999999999998e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 40.1

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

   5. Applied rewrites 40.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 40.1%

      \[\leadsto 1 \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+25}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-242}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-68}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+73}:\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+155}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -12500000000000 \lor \neg \left(b \leq 1.15 \cdot 10^{+66}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e+155)
   (* (- y 2.0) b)
   (if (or (<= b -12500000000000.0) (not (<= b 1.15e+66)))
     (* (- t 2.0) b)
     (fma (- z) y z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+155) {
		tmp = (y - 2.0) * b;
	} else if ((b <= -12500000000000.0) || !(b <= 1.15e+66)) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = fma(-z, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e+155)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif ((b <= -12500000000000.0) || !(b <= 1.15e+66))
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = fma(Float64(-z), y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e+155], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[Or[LessEqual[b, -12500000000000.0], N[Not[LessEqual[b, 1.15e+66]], $MachinePrecision]], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], N[((-z) * y + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.60000000000000007e155

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 92.7%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 84.9%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 55.0%

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

   if -3.60000000000000007e155 < b < -1.25e13 or 1.15e66 < b

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 90.0%

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

   9. Taylor expanded in b around -inf

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

   11. Applied rewrites 65.7%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 47.9%

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

   if -1.25e13 < b < 1.15e66

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 66.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 37.6%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+155}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -12500000000000 \lor \neg \left(b \leq 1.15 \cdot 10^{+66}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 320000000000:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.2e+50)
     t_1
     (if (<= y 7e-17)
       (* (- b a) t)
       (if (<= y 320000000000.0) (* (- 1.0 t) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.2e+50) {
		tmp = t_1;
	} else if (y <= 7e-17) {
		tmp = (b - a) * t;
	} else if (y <= 320000000000.0) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-4.2d+50)) then
        tmp = t_1
    else if (y <= 7d-17) then
        tmp = (b - a) * t
    else if (y <= 320000000000.0d0) then
        tmp = (1.0d0 - t) * a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.2e+50) {
		tmp = t_1;
	} else if (y <= 7e-17) {
		tmp = (b - a) * t;
	} else if (y <= 320000000000.0) {
		tmp = (1.0 - t) * a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -4.2e+50:
		tmp = t_1
	elif y <= 7e-17:
		tmp = (b - a) * t
	elif y <= 320000000000.0:
		tmp = (1.0 - t) * a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.2e+50)
		tmp = t_1;
	elseif (y <= 7e-17)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 320000000000.0)
		tmp = Float64(Float64(1.0 - t) * a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -4.2e+50)
		tmp = t_1;
	elseif (y <= 7e-17)
		tmp = (b - a) * t;
	elseif (y <= 320000000000.0)
		tmp = (1.0 - t) * a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.2e+50], t$95$1, If[LessEqual[y, 7e-17], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 320000000000.0], N[(N[(1.0 - t), $MachinePrecision] * a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1999999999999999e50 or 3.2e11 < y

   1. Initial program 91.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 67.7

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

   5. Applied rewrites 67.7%

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

   if -4.1999999999999999e50 < y < 7.0000000000000003e-17

   1. Initial program 96.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 42.3

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

   5. Applied rewrites 42.3%

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

   if 7.0000000000000003e-17 < y < 3.2e11

   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 inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.5

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

   5. Applied rewrites 71.5%

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

Alternative 17: 47.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -14500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-170}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b a) t)))
   (if (<= t -14500000000000.0)
     t_1
     (if (<= t 2.8e-170)
       (* (- y 2.0) b)
       (if (<= t 4.5e+76) (fma (- z) y z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - a) * t;
	double tmp;
	if (t <= -14500000000000.0) {
		tmp = t_1;
	} else if (t <= 2.8e-170) {
		tmp = (y - 2.0) * b;
	} else if (t <= 4.5e+76) {
		tmp = fma(-z, y, z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -14500000000000.0)
		tmp = t_1;
	elseif (t <= 2.8e-170)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 4.5e+76)
		tmp = fma(Float64(-z), y, z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -14500000000000.0], t$95$1, If[LessEqual[t, 2.8e-170], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 4.5e+76], N[((-z) * y + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e13 or 4.4999999999999997e76 < t

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 68.9

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

   5. Applied rewrites 68.9%

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

   if -1.45e13 < t < 2.79999999999999995e-170

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - z}, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x + z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.2%

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right) \]

   9. Taylor expanded in b around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot y + -1 \cdot \left(t - 2\right)\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 40.2%

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

   12. Taylor expanded in t around 0

       \[\leadsto \left(y - 2\right) \cdot b \]
   13. Step-by-step derivation

   14. Applied rewrites 38.2%

       \[\leadsto \left(y - 2\right) \cdot b \]

   if 2.79999999999999995e-170 < t < 4.4999999999999997e76

   1. Initial program 93.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot \left(b - z\right) + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - z\right) \cdot y + \color{blue}{\left(\left(b \cdot \left(t - 2\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - z\right) \cdot y + \left(\color{blue}{\left(x + b \cdot \left(t - 2\right)\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - z}, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   5. Applied rewrites 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x + z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 77.5%

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right) \]

   9. Taylor expanded in z around inf

      \[\leadsto z \cdot \color{blue}{\left(1 + -1 \cdot y\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 34.5%

       \[\leadsto \mathsf{fma}\left(-z, \color{blue}{y}, z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 66.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+48} \lor \neg \left(y \leq 3.2 \cdot 10^{+36}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.8e+48) (not (<= y 3.2e+36)))
   (* (- b z) y)
   (fma (- t 2.0) b (+ z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.8e+48) || !(y <= 3.2e+36)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((t - 2.0), b, (z + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.8e+48) || !(y <= 3.2e+36))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.8e+48], N[Not[LessEqual[y, 3.2e+36]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.8000000000000002e48 or 3.1999999999999999e36 < y

   1. Initial program 90.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 70.2

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 70.2%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -7.8000000000000002e48 < y < 3.1999999999999999e36

   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 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      5. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      6. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, \color{blue}{x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)}\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, x - \color{blue}{\left(a \cdot \left(t - 1\right) + -1 \cdot z\right)}\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, x - \left(\color{blue}{\left(t - 1\right) \cdot a} + -1 \cdot z\right)\right) \]

      9. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(t - 2, b, x - \color{blue}{\mathsf{fma}\left(t - 1, a, -1 \cdot z\right)}\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(\color{blue}{t - 1}, a, -1 \cdot z\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, \color{blue}{\mathsf{neg}\left(z\right)}\right)\right) \]

      12. lower-neg.f64 91.2

          \[\leadsto \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, \color{blue}{-z}\right)\right) \]

   5. Applied rewrites 91.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(t - 2, b, x + z\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 70.8%

      \[\leadsto \mathsf{fma}\left(t - 2, b, z + x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+48} \lor \neg \left(y \leq 3.2 \cdot 10^{+36}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.3e+51) (* b y) (if (<= y 1.6e+36) (* (- t 2.0) b) (* (- y) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+51) {
		tmp = b * y;
	} else if (y <= 1.6e+36) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = -y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.3d+51)) then
        tmp = b * y
    else if (y <= 1.6d+36) then
        tmp = (t - 2.0d0) * b
    else
        tmp = -y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+51) {
		tmp = b * y;
	} else if (y <= 1.6e+36) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = -y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.3e+51:
		tmp = b * y
	elif y <= 1.6e+36:
		tmp = (t - 2.0) * b
	else:
		tmp = -y * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.3e+51)
		tmp = Float64(b * y);
	elseif (y <= 1.6e+36)
		tmp = Float64(Float64(t - 2.0) * b);
	else
		tmp = Float64(Float64(-y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.3e+51)
		tmp = b * y;
	elseif (y <= 1.6e+36)
		tmp = (t - 2.0) * b;
	else
		tmp = -y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.3e+51], N[(b * y), $MachinePrecision], If[LessEqual[y, 1.6e+36], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], N[((-y) * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3000000000000001e51

   1. Initial program 93.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot \left(b - z\right) + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - z\right) \cdot y + \color{blue}{\left(\left(b \cdot \left(t - 2\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - z\right) \cdot y + \left(\color{blue}{\left(x + b \cdot \left(t - 2\right)\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - z}, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   5. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x + z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.7%

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right) \]

   9. Taylor expanded in b around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot y + -1 \cdot \left(t - 2\right)\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 46.2%

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

   12. Taylor expanded in y around inf

       \[\leadsto b \cdot y \]
   13. Step-by-step derivation

   14. Applied rewrites 42.6%

       \[\leadsto b \cdot y \]

   if -1.3000000000000001e51 < y < 1.5999999999999999e36

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot \left(b - z\right) + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - z\right) \cdot y + \color{blue}{\left(\left(b \cdot \left(t - 2\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - z\right) \cdot y + \left(\color{blue}{\left(x + b \cdot \left(t - 2\right)\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - z}, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   5. Applied rewrites 97.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x + z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.9%

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right) \]

   9. Taylor expanded in b around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot y + -1 \cdot \left(t - 2\right)\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 38.6%

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

   12. Taylor expanded in y around 0

       \[\leadsto \left(t - 2\right) \cdot b \]
   13. Step-by-step derivation

   14. Applied rewrites 35.7%

       \[\leadsto \left(t - 2\right) \cdot b \]

   if 1.5999999999999999e36 < y

   1. Initial program 87.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

      3. lower--.f64 42.8

         \[\leadsto \color{blue}{\left(1 - y\right)} \cdot z \]

   5. Applied rewrites 42.8%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 42.8%

      \[\leadsto \left(-y\right) \cdot z \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+51}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 27.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+25} \lor \neg \left(y \leq 4.1 \cdot 10^{+73}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.3e+25) (not (<= y 4.1e+73))) (* b y) (* b t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.3e+25) || !(y <= 4.1e+73)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.3d+25)) .or. (.not. (y <= 4.1d+73))) then
        tmp = b * y
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.3e+25) || !(y <= 4.1e+73)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.3e+25) or not (y <= 4.1e+73):
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.3e+25) || !(y <= 4.1e+73))
		tmp = Float64(b * y);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.3e+25) || ~((y <= 4.1e+73)))
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.3e+25], N[Not[LessEqual[y, 4.1e+73]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.29999999999999961e25 or 4.0999999999999998e73 < y

   1. Initial program 90.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot \left(b - z\right) + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - z\right) \cdot y + \color{blue}{\left(\left(b \cdot \left(t - 2\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - z\right) \cdot y + \left(\color{blue}{\left(x + b \cdot \left(t - 2\right)\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - z}, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   5. Applied rewrites 96.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x + z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 82.4%

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right) \]

   9. Taylor expanded in b around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot y + -1 \cdot \left(t - 2\right)\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 41.9%

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

   12. Taylor expanded in y around inf

       \[\leadsto b \cdot y \]
   13. Step-by-step derivation

   14. Applied rewrites 39.0%

       \[\leadsto b \cdot y \]

   if -7.29999999999999961e25 < y < 4.0999999999999998e73

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{y \cdot \left(b - z\right) + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - z\right) \cdot y + \color{blue}{\left(\left(b \cdot \left(t - 2\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - z\right) \cdot y + \left(\color{blue}{\left(x + b \cdot \left(t - 2\right)\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - z}, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   5. Applied rewrites 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x + z\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 74.8%

      \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right) \]

   9. Taylor expanded in b around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot y + -1 \cdot \left(t - 2\right)\right)\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 37.2%

       \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

   12. Taylor expanded in t around inf

       \[\leadsto b \cdot t \]
   13. Step-by-step derivation

   14. Applied rewrites 26.8%

       \[\leadsto b \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.3 \cdot 10^{+25} \lor \neg \left(y \leq 4.1 \cdot 10^{+73}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 17.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ b \cdot t \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* b t))

C

double code(double x, double y, double z, double t, double a, double b) {
	return b * t;
}

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 = b * t
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return b * t;
}

Python

def code(x, y, z, t, a, b):
	return b * t

Julia

function code(x, y, z, t, a, b)
	return Float64(b * t)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = b * t;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(b * t), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right) \]

   2. associate--l+ N/A

      \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + y \cdot \left(b - z\right)\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(y \cdot \left(b - z\right) + b \cdot \left(t - 2\right)\right)} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

   4. associate-+l+ N/A

      \[\leadsto \color{blue}{y \cdot \left(b - z\right) + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right)} \]

   5. *-commutative N/A

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} + \left(b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   6. associate--l+ N/A

      \[\leadsto \left(b - z\right) \cdot y + \color{blue}{\left(\left(b \cdot \left(t - 2\right) + x\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

   7. +-commutative N/A

      \[\leadsto \left(b - z\right) \cdot y + \left(\color{blue}{\left(x + b \cdot \left(t - 2\right)\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

   9. lower--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{b - z}, y, \left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

   10. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(b \cdot \left(t - 2\right) + x\right)} - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) \]

   11. associate--l+ N/A

       \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{b \cdot \left(t - 2\right) + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\left(t - 2\right) \cdot b} + \left(x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

   13. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(b - z, y, \color{blue}{\mathsf{fma}\left(t - 2, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)}\right) \]

   14. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(\color{blue}{t - 2}, b, x - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)\right) \]

5. Applied rewrites 96.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x - \mathsf{fma}\left(t - 1, a, -z\right)\right)\right)} \]

6. Taylor expanded in a around 0

   \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x + z\right)\right) \]
7. Step-by-step derivation

8. Applied rewrites 78.0%

   \[\leadsto \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, z + x\right)\right) \]

9. Taylor expanded in b around -inf

   \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot y + -1 \cdot \left(t - 2\right)\right)\right)} \]
10. Step-by-step derivation

11. Applied rewrites 39.2%

    \[\leadsto \left(\left(t + y\right) - 2\right) \cdot \color{blue}{b} \]

12. Taylor expanded in t around inf

    \[\leadsto b \cdot t \]
13. Step-by-step derivation

14. Applied rewrites 19.5%

    \[\leadsto b \cdot t \]

15. Final simplification 19.5%

    \[\leadsto b \cdot t \]
16. Add Preprocessing

Reproduce

herbie shell --seed 2024337 
(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)))