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

Percentage Accurate: 95.5% → 97.8%

Time: 12.4s

Alternatives: 20

Speedup: 0.9×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+244}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+244)
   (* (- (+ t y) 2.0) b)
   (fma (- b a) t (fma (- y 2.0) b (- x (fma (- y 1.0) z (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+244) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma((b - a), t, fma((y - 2.0), b, (x - fma((y - 1.0), z, -a))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+244)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, Float64(x - fma(Float64(y - 1.0), z, Float64(-a)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+244], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.5e244

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -7.5e244 < b

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower--.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 99.1

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

   5. Applied rewrites 99.1%

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

Alternative 2: 96.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 2 \cdot 10^{+286}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z + x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \end{array} \end{array} \]

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))
      2e+286)
   (fma (- b z) y (fma (- t 2.0) b (fma (- 1.0 t) a (+ z x))))
   (fma (- 1.0 t) a (fma (- (+ t y) 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 ((((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)) <= 2e+286) {
		tmp = fma((b - z), y, fma((t - 2.0), b, fma((1.0 - t), a, (z + x))));
	} else {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, fma(-z, y, z)));
	}
	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)) <= 2e+286)
		tmp = fma(Float64(b - z), y, fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, Float64(z + x))));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-z), y, z)));
	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], 2e+286], N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y + z), $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)) < 2.00000000000000007e286

   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. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

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

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

      15. +-commutative N/A

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

      16. associate--l+ N/A

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

   5. Applied rewrites 100.0%

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

   if 2.00000000000000007e286 < (+.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 73.7%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. distribute-lft-out-- N/A

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

      11. *-rgt-identity N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-lft-neg-out N/A

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

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

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

      18. *-commutative N/A

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

   5. Applied rewrites 91.2%

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

Alternative 3: 87.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z + x\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+195}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -8.2e+126)
   (fma (- t 2.0) b (fma (- 1.0 t) a (+ z x)))
   (if (<= x 7e+195)
     (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b (fma (- z) y z)))
     (fma (- y 2.0) b (- x (fma (- y 1.0) z (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -8.2e+126) {
		tmp = fma((t - 2.0), b, fma((1.0 - t), a, (z + x)));
	} else if (x <= 7e+195) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, fma(-z, y, z)));
	} else {
		tmp = fma((y - 2.0), b, (x - fma((y - 1.0), z, -a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -8.2e+126)
		tmp = fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, Float64(z + x)));
	elseif (x <= 7e+195)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-z), y, z)));
	else
		tmp = fma(Float64(y - 2.0), b, Float64(x - fma(Float64(y - 1.0), z, Float64(-a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -8.2e+126], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+195], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2000000000000001e126

   1. Initial program 94.7%

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

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

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 82.5%

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

   if -8.2000000000000001e126 < x < 7.0000000000000005e195

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. distribute-lft-out-- N/A

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

      11. *-rgt-identity N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-lft-neg-out N/A

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

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

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

      18. *-commutative N/A

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

   5. Applied rewrites 96.1%

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

   if 7.0000000000000005e195 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 92.5

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

   5. Applied rewrites 92.5%

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

Alternative 4: 82.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -3.15 \cdot 10^{+218}:\\ \;\;\;\;t\_1 \cdot b\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-93}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z + x\right)\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, \left(-z\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -3.15e+218)
     (* t_1 b)
     (if (<= b -8.5e-93)
       (fma (- t 2.0) b (fma (- 1.0 t) a (+ z x)))
       (if (<= b 1.15e+79)
         (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))
         (fma t_1 b (* (- z) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -3.15e+218) {
		tmp = t_1 * b;
	} else if (b <= -8.5e-93) {
		tmp = fma((t - 2.0), b, fma((1.0 - t), a, (z + x)));
	} else if (b <= 1.15e+79) {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	} else {
		tmp = fma(t_1, b, (-z * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -3.15e+218)
		tmp = Float64(t_1 * b);
	elseif (b <= -8.5e-93)
		tmp = fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, Float64(z + x)));
	elseif (b <= 1.15e+79)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	else
		tmp = fma(t_1, b, Float64(Float64(-z) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -3.15e+218], N[(t$95$1 * b), $MachinePrecision], If[LessEqual[b, -8.5e-93], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+79], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.1499999999999998e218

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 96.2

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

   5. Applied rewrites 96.2%

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

   if -3.1499999999999998e218 < b < -8.5000000000000007e-93

   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 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. +-commutative N/A

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 77.1%

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

   if -8.5000000000000007e-93 < b < 1.15e79

   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 t around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower--.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 94.3%

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

   if 1.15e79 < b

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 86.5

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

   5. Applied rewrites 86.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 88.8

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-+.f64 88.8

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

   7. Applied rewrites 88.8%

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

Alternative 5: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+89} \lor \neg \left(y \leq 0.0033\right):\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z + x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.5e+89) (not (<= y 0.0033)))
   (fma (- y 2.0) b (- x (fma (- y 1.0) z (- a))))
   (fma (- t 2.0) b (fma (- 1.0 t) a (+ z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.5e+89) || !(y <= 0.0033)) {
		tmp = fma((y - 2.0), b, (x - fma((y - 1.0), z, -a)));
	} else {
		tmp = fma((t - 2.0), b, fma((1.0 - t), a, (z + x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.5e+89) || !(y <= 0.0033))
		tmp = fma(Float64(y - 2.0), b, Float64(x - fma(Float64(y - 1.0), z, Float64(-a))));
	else
		tmp = fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, Float64(z + x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.5e+89], N[Not[LessEqual[y, 0.0033]], $MachinePrecision]], N[(N[(y - 2.0), $MachinePrecision] * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999976e89 or 0.0033 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. lower--.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 84.0

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

   5. Applied rewrites 84.0%

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

   if -5.49999999999999976e89 < y < 0.0033

   1. Initial program 96.5%

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

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

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 93.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+89} \lor \neg \left(y \leq 0.0033\right):\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z + x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-45}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.85e+220)
     t_1
     (if (<= b -2.45e-45)
       (fma (- t 2.0) b (+ z x))
       (if (<= b 7.5e+74) (fma (- 1.0 t) a (fma (- z) y z)) 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 <= -1.85e+220) {
		tmp = t_1;
	} else if (b <= -2.45e-45) {
		tmp = fma((t - 2.0), b, (z + x));
	} else if (b <= 7.5e+74) {
		tmp = fma((1.0 - t), a, fma(-z, y, z));
	} 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 <= -1.85e+220)
		tmp = t_1;
	elseif (b <= -2.45e-45)
		tmp = fma(Float64(t - 2.0), b, Float64(z + x));
	elseif (b <= 7.5e+74)
		tmp = fma(Float64(1.0 - t), a, 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[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.85e+220], t$95$1, If[LessEqual[b, -2.45e-45], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+74], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.85e220 or 7.5e74 < b

   1. Initial program 84.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 90.2

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

   5. Applied rewrites 90.2%

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

   if -1.85e220 < b < -2.4499999999999999e-45

   1. Initial program 93.7%

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

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

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 68.6%

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

   if -2.4499999999999999e-45 < b < 7.5e74

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. distribute-lft-out-- N/A

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

      11. *-rgt-identity N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-lft-neg-out N/A

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

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

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

      18. *-commutative N/A

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

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 74.3%

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

Alternative 7: 82.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+48} \lor \neg \left(b \leq 1.15 \cdot 10^{+79}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.35e+48) (not (<= b 1.15e+79)))
   (fma (- (+ t y) 2.0) b (* (- z) y))
   (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.35e+48) || !(b <= 1.15e+79)) {
		tmp = fma(((t + y) - 2.0), b, (-z * y));
	} else {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.35e+48) || !(b <= 1.15e+79))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(-z) * y));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.35e+48], N[Not[LessEqual[b, 1.15e+79]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.35000000000000006e48 or 1.15e79 < b

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 78.1

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

   5. Applied rewrites 78.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 81.6

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-+.f64 81.6

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

   7. Applied rewrites 81.6%

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

   if -2.35000000000000006e48 < b < 1.15e79

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lower--.f64 N/A

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

      17. mul-1-neg N/A

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

      18. lower-neg.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 89.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+48} \lor \neg \left(b \leq 1.15 \cdot 10^{+79}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.58 \lor \neg \left(y \leq 3.85 \cdot 10^{-7}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.58) (not (<= y 3.85e-7)))
   (fma (- (+ t y) 2.0) 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 <= -1.58) || !(y <= 3.85e-7)) {
		tmp = fma(((t + y) - 2.0), 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 <= -1.58) || !(y <= 3.85e-7))
		tmp = fma(Float64(Float64(t + y) - 2.0), b, Float64(Float64(-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, -1.58], N[Not[LessEqual[y, 3.85e-7]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + N[((-z) * y), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5800000000000001 or 3.8500000000000002e-7 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 69.0

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

   5. Applied rewrites 69.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 72.0

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

      5. lift-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lift-+.f64 72.0

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

   7. Applied rewrites 72.0%

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

   if -1.5800000000000001 < y < 3.8500000000000002e-7

   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

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

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 85.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.58 \lor \neg \left(y \leq 3.85 \cdot 10^{-7}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, \left(-z\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-7} \lor \neg \left(y \leq 0.00073\right):\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.9e-7) (not (<= y 0.00073)))
   (fma (- 1.0 y) z (fma (- y 2.0) b a))
   (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 <= -3.9e-7) || !(y <= 0.00073)) {
		tmp = fma((1.0 - y), z, fma((y - 2.0), b, a));
	} 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 <= -3.9e-7) || !(y <= 0.00073))
		tmp = fma(Float64(1.0 - y), z, fma(Float64(y - 2.0), b, a));
	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, -3.9e-7], N[Not[LessEqual[y, 0.00073]], $MachinePrecision]], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.90000000000000025e-7 or 7.2999999999999996e-4 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. *-commutative N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. distribute-lft-out-- N/A

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

      11. *-rgt-identity N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-lft-neg-out N/A

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

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

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

      16. +-commutative N/A

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

      17. associate--l+ N/A

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

      18. *-commutative N/A

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

   5. Applied rewrites 88.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 70.5%

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

   if -3.90000000000000025e-7 < y < 7.2999999999999996e-4

   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

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

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 85.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-7} \lor \neg \left(y \leq 0.00073\right):\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -6 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-165}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 780:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -6e+89)
     t_1
     (if (<= y -1.45e-165)
       (* (- b a) t)
       (if (<= y 780.0) (+ (fma -2.0 b (+ z x)) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -6e+89) {
		tmp = t_1;
	} else if (y <= -1.45e-165) {
		tmp = (b - a) * t;
	} else if (y <= 780.0) {
		tmp = fma(-2.0, b, (z + x)) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -6e+89)
		tmp = t_1;
	elseif (y <= -1.45e-165)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 780.0)
		tmp = Float64(fma(-2.0, b, Float64(z + x)) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -6e+89], t$95$1, If[LessEqual[y, -1.45e-165], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 780.0], N[(N[(-2.0 * b + N[(z + x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000025e89 or 780 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in 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 71.6

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

   5. Applied rewrites 71.6%

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

   if -6.00000000000000025e89 < y < -1.45e-165

   1. Initial program 98.2%

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

   3. Taylor expanded in 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 55.6

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

   5. Applied rewrites 55.6%

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

   if -1.45e-165 < y < 780

   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 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. +-commutative N/A

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 94.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 67.8%

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

Alternative 11: 26.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+40}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-102}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-174}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+95}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.8e+40)
   (* b t)
   (if (<= t -5.5e-102)
     (* b y)
     (if (<= t 4.5e-174) (* 1.0 z) (if (<= t 5.2e+95) (* b y) (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.8e+40) {
		tmp = b * t;
	} else if (t <= -5.5e-102) {
		tmp = b * y;
	} else if (t <= 4.5e-174) {
		tmp = 1.0 * z;
	} else if (t <= 5.2e+95) {
		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 (t <= (-6.8d+40)) then
        tmp = b * t
    else if (t <= (-5.5d-102)) then
        tmp = b * y
    else if (t <= 4.5d-174) then
        tmp = 1.0d0 * z
    else if (t <= 5.2d+95) 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 (t <= -6.8e+40) {
		tmp = b * t;
	} else if (t <= -5.5e-102) {
		tmp = b * y;
	} else if (t <= 4.5e-174) {
		tmp = 1.0 * z;
	} else if (t <= 5.2e+95) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.8e+40:
		tmp = b * t
	elif t <= -5.5e-102:
		tmp = b * y
	elif t <= 4.5e-174:
		tmp = 1.0 * z
	elif t <= 5.2e+95:
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.8e+40)
		tmp = Float64(b * t);
	elseif (t <= -5.5e-102)
		tmp = Float64(b * y);
	elseif (t <= 4.5e-174)
		tmp = Float64(1.0 * z);
	elseif (t <= 5.2e+95)
		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 (t <= -6.8e+40)
		tmp = b * t;
	elseif (t <= -5.5e-102)
		tmp = b * y;
	elseif (t <= 4.5e-174)
		tmp = 1.0 * z;
	elseif (t <= 5.2e+95)
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.8e+40], N[(b * t), $MachinePrecision], If[LessEqual[t, -5.5e-102], N[(b * y), $MachinePrecision], If[LessEqual[t, 4.5e-174], N[(1.0 * z), $MachinePrecision], If[LessEqual[t, 5.2e+95], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.79999999999999977e40 or 5.19999999999999981e95 < t

   1. Initial program 92.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 53.3

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

   5. Applied rewrites 53.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 48.0%

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

   if -6.79999999999999977e40 < t < -5.4999999999999997e-102 or 4.49999999999999964e-174 < t < 5.19999999999999981e95

   1. Initial program 93.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 40.7

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

   5. Applied rewrites 40.7%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 28.8%

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

   if -5.4999999999999997e-102 < t < 4.49999999999999964e-174

   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 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 46.0

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 23.8%

      \[\leadsto 1 \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 48.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -6 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-139}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 450000:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -6e+89)
     t_1
     (if (<= y -2.15e-139)
       (* (- b a) t)
       (if (<= y 450000.0) (* (- t 2.0) b) 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 <= -6e+89) {
		tmp = t_1;
	} else if (y <= -2.15e-139) {
		tmp = (b - a) * t;
	} else if (y <= 450000.0) {
		tmp = (t - 2.0) * b;
	} 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 <= (-6d+89)) then
        tmp = t_1
    else if (y <= (-2.15d-139)) then
        tmp = (b - a) * t
    else if (y <= 450000.0d0) then
        tmp = (t - 2.0d0) * b
    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 <= -6e+89) {
		tmp = t_1;
	} else if (y <= -2.15e-139) {
		tmp = (b - a) * t;
	} else if (y <= 450000.0) {
		tmp = (t - 2.0) * b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -6e+89:
		tmp = t_1
	elif y <= -2.15e-139:
		tmp = (b - a) * t
	elif y <= 450000.0:
		tmp = (t - 2.0) * b
	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 <= -6e+89)
		tmp = t_1;
	elseif (y <= -2.15e-139)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 450000.0)
		tmp = Float64(Float64(t - 2.0) * b);
	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 <= -6e+89)
		tmp = t_1;
	elseif (y <= -2.15e-139)
		tmp = (b - a) * t;
	elseif (y <= 450000.0)
		tmp = (t - 2.0) * b;
	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, -6e+89], t$95$1, If[LessEqual[y, -2.15e-139], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 450000.0], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000025e89 or 4.5e5 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in 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 71.6

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

   5. Applied rewrites 71.6%

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

   if -6.00000000000000025e89 < y < -2.15000000000000009e-139

   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 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 52.2

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

   5. Applied rewrites 52.2%

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

   if -2.15000000000000009e-139 < y < 4.5e5

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 49.8

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

   5. Applied rewrites 49.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 49.1%

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

Alternative 13: 65.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+89} \lor \neg \left(y \leq 700000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6e+89) (not (<= y 700000.0)))
   (* (- 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 <= -6e+89) || !(y <= 700000.0)) {
		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 <= -6e+89) || !(y <= 700000.0))
		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, -6e+89], N[Not[LessEqual[y, 700000.0]], $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 < -6.00000000000000025e89 or 7e5 < y

   1. Initial program 90.9%

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

   3. Taylor expanded in 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 71.6

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

   5. Applied rewrites 71.6%

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

   if -6.00000000000000025e89 < y < 7e5

   1. Initial program 96.5%

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

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

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

      7. associate--r+ N/A

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

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

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

      9. +-commutative N/A

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

      10. associate--l+ N/A

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 77.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+89} \lor \neg \left(y \leq 700000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-12} \lor \neg \left(b \leq 2.4 \cdot 10^{+66}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1e-12) (not (<= b 2.4e+66)))
   (* (- (+ t y) 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 <= -1e-12) || !(b <= 2.4e+66)) {
		tmp = ((t + y) - 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 <= -1e-12) || !(b <= 2.4e+66))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = fma(Float64(-z), y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1e-12], N[Not[LessEqual[b, 2.4e+66]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[((-z) * y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.9999999999999998e-13 or 2.4000000000000002e66 < b

   1. Initial program 88.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 74.3

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

   5. Applied rewrites 74.3%

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

   if -9.9999999999999998e-13 < b < 2.4000000000000002e66

   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 50.0

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

   5. Applied rewrites 50.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 50.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-12} \lor \neg \left(b \leq 2.4 \cdot 10^{+66}\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+173} \lor \neg \left(t \leq 2.2 \cdot 10^{+37}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.05e+173) (not (<= t 2.2e+37)))
   (* (- b a) t)
   (fma (- z) y z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.05e+173) || !(t <= 2.2e+37)) {
		tmp = (b - a) * t;
	} else {
		tmp = fma(-z, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.05e+173) || !(t <= 2.2e+37))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = fma(Float64(-z), y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.05e+173], N[Not[LessEqual[t, 2.2e+37]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[((-z) * y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.04999999999999988e173 or 2.2000000000000001e37 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   if -2.04999999999999988e173 < t < 2.2000000000000001e37

   1. Initial program 96.9%

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

   3. Taylor expanded in 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 42.9

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

   5. Applied rewrites 42.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 42.9%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+173} \lor \neg \left(t \leq 2.2 \cdot 10^{+37}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-12} \lor \neg \left(b \leq 1.85 \cdot 10^{+86}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1e-12) (not (<= b 1.85e+86))) (* (- 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 <= -1e-12) || !(b <= 1.85e+86)) {
		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 <= -1e-12) || !(b <= 1.85e+86))
		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[Or[LessEqual[b, -1e-12], N[Not[LessEqual[b, 1.85e+86]], $MachinePrecision]], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision], N[((-z) * y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.9999999999999998e-13 or 1.84999999999999996e86 < b

   1. Initial program 88.2%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.1%

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

   if -9.9999999999999998e-13 < b < 1.84999999999999996e86

   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 49.2

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 49.2%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-12} \lor \neg \left(b \leq 1.85 \cdot 10^{+86}\right):\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 35.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+173} \lor \neg \left(t \leq 5.4 \cdot 10^{+95}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e+173) (not (<= t 5.4e+95))) (* b t) (fma (- z) y z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e+173) || !(t <= 5.4e+95)) {
		tmp = b * t;
	} else {
		tmp = fma(-z, y, z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.6e+173) || !(t <= 5.4e+95))
		tmp = Float64(b * t);
	else
		tmp = fma(Float64(-z), y, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.6e+173], N[Not[LessEqual[t, 5.4e+95]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[((-z) * y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5999999999999999e173 or 5.4e95 < t

   1. Initial program 90.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 61.8

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 56.0%

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

   if -2.5999999999999999e173 < t < 5.4e95

   1. Initial program 96.0%

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

   3. Taylor expanded in 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 41.8

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

   5. Applied rewrites 41.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 41.8%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+173} \lor \neg \left(t \leq 5.4 \cdot 10^{+95}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+55} \lor \neg \left(y \leq 510000\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.6e+55) (not (<= y 510000.0))) (* (- y) z) (* b t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.6e+55) || !(y <= 510000.0)) {
		tmp = -y * z;
	} 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 <= (-8.6d+55)) .or. (.not. (y <= 510000.0d0))) then
        tmp = -y * z
    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 <= -8.6e+55) || !(y <= 510000.0)) {
		tmp = -y * z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.6e+55) or not (y <= 510000.0):
		tmp = -y * z
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.6e+55) || !(y <= 510000.0))
		tmp = Float64(Float64(-y) * z);
	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 <= -8.6e+55) || ~((y <= 510000.0)))
		tmp = -y * z;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.6e+55], N[Not[LessEqual[y, 510000.0]], $MachinePrecision]], N[((-y) * z), $MachinePrecision], N[(b * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5999999999999998e55 or 5.1e5 < 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 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 45.8

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

   5. Applied rewrites 45.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.3%

      \[\leadsto \left(-y\right) \cdot z \]

   if -8.5999999999999998e55 < y < 5.1e5

   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 b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 46.3

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

   5. Applied rewrites 46.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 31.5%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+55} \lor \neg \left(y \leq 510000\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+89} \lor \neg \left(y \leq 1.75 \cdot 10^{+124}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6e+89) (not (<= y 1.75e+124))) (* b y) (* b t)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -6e+89) || !(y <= 1.75e+124)) {
		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 <= (-6d+89)) .or. (.not. (y <= 1.75d+124))) 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 <= -6e+89) || !(y <= 1.75e+124)) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -6e+89) or not (y <= 1.75e+124):
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -6e+89) || !(y <= 1.75e+124))
		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 <= -6e+89) || ~((y <= 1.75e+124)))
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -6e+89], N[Not[LessEqual[y, 1.75e+124]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000025e89 or 1.7500000000000001e124 < y

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 39.8

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

   5. Applied rewrites 39.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 35.7%

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

   if -6.00000000000000025e89 < y < 1.7500000000000001e124

   1. Initial program 96.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 43.8

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

   5. Applied rewrites 43.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 30.7%

      \[\leadsto b \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+89} \lor \neg \left(y \leq 1.75 \cdot 10^{+124}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 18.6% 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 b around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-+.f64 42.5

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

5. Applied rewrites 42.5%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 23.5%

   \[\leadsto b \cdot \color{blue}{t} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024338 
(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)))