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

Percentage Accurate: 95.5% → 97.7%

Time: 12.2s

Alternatives: 23

Speedup: 1.2×

• 35.9% 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: 97.7% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (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) {
	return fma((b - a), t, fma((y - 2.0), b, (x - fma((y - 1.0), z, -a))));
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := 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. 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. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. +-commutative N/A

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

   4. associate-+l+ N/A

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

   5. *-commutative N/A

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

   6. associate--l+ N/A

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

   7. +-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. associate--l+ N/A

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

   12. *-commutative N/A

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

   13. lower-fma.f64 N/A

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

   14. lower--.f64 N/A

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

5. Applied rewrites 98.0%

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

Alternative 2: 90.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19.5 \lor \neg \left(z \leq 3.3 \cdot 10^{-48}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -19.5) (not (<= z 3.3e-48)))
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b (fma (- z) y z)))
   (fma (- b a) t (+ (fma (- y 2.0) b x) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -19.5) || !(z <= 3.3e-48)) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, fma(-z, y, z)));
	} else {
		tmp = fma((b - a), t, (fma((y - 2.0), b, x) + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -19.5) || !(z <= 3.3e-48))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, fma(Float64(-z), y, z)));
	else
		tmp = fma(Float64(b - a), t, Float64(fma(Float64(y - 2.0), b, x) + a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -19.5], N[Not[LessEqual[z, 3.3e-48]], $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], N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -19.5 or 3.3e-48 < z

   1. Initial program 92.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. fp-cancel-sub-sign-inv N/A

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

      5. metadata-eval N/A

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

      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. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      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

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

   5. Applied rewrites 94.5%

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

   if -19.5 < z < 3.3e-48

   1. Initial program 99.1%

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

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

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   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 z around 0

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

   8. Applied rewrites 95.9%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -19.5 \lor \neg \left(z \leq 3.3 \cdot 10^{-48}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + x\right) + a\\ t_2 := \left(b - a\right) \cdot t\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-267}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-226}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ z x) a)) (t_2 (* (- b a) t)))
   (if (<= t -9.2e+51)
     t_2
     (if (<= t -7.5e-116)
       t_1
       (if (<= t -1.2e-267)
         (* (- 1.0 y) z)
         (if (<= t 4.5e-226) (* (- y 2.0) b) (if (<= t 3.9e+39) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + x) + a;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -9.2e+51) {
		tmp = t_2;
	} else if (t <= -7.5e-116) {
		tmp = t_1;
	} else if (t <= -1.2e-267) {
		tmp = (1.0 - y) * z;
	} else if (t <= 4.5e-226) {
		tmp = (y - 2.0) * b;
	} else if (t <= 3.9e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (z + x) + a
    t_2 = (b - a) * t
    if (t <= (-9.2d+51)) then
        tmp = t_2
    else if (t <= (-7.5d-116)) then
        tmp = t_1
    else if (t <= (-1.2d-267)) then
        tmp = (1.0d0 - y) * z
    else if (t <= 4.5d-226) then
        tmp = (y - 2.0d0) * b
    else if (t <= 3.9d+39) then
        tmp = t_1
    else
        tmp = t_2
    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 = (z + x) + a;
	double t_2 = (b - a) * t;
	double tmp;
	if (t <= -9.2e+51) {
		tmp = t_2;
	} else if (t <= -7.5e-116) {
		tmp = t_1;
	} else if (t <= -1.2e-267) {
		tmp = (1.0 - y) * z;
	} else if (t <= 4.5e-226) {
		tmp = (y - 2.0) * b;
	} else if (t <= 3.9e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + x) + a
	t_2 = (b - a) * t
	tmp = 0
	if t <= -9.2e+51:
		tmp = t_2
	elif t <= -7.5e-116:
		tmp = t_1
	elif t <= -1.2e-267:
		tmp = (1.0 - y) * z
	elif t <= 4.5e-226:
		tmp = (y - 2.0) * b
	elif t <= 3.9e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + x) + a)
	t_2 = Float64(Float64(b - a) * t)
	tmp = 0.0
	if (t <= -9.2e+51)
		tmp = t_2;
	elseif (t <= -7.5e-116)
		tmp = t_1;
	elseif (t <= -1.2e-267)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (t <= 4.5e-226)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (t <= 3.9e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + x) + a;
	t_2 = (b - a) * t;
	tmp = 0.0;
	if (t <= -9.2e+51)
		tmp = t_2;
	elseif (t <= -7.5e-116)
		tmp = t_1;
	elseif (t <= -1.2e-267)
		tmp = (1.0 - y) * z;
	elseif (t <= 4.5e-226)
		tmp = (y - 2.0) * b;
	elseif (t <= 3.9e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -9.2e+51], t$95$2, If[LessEqual[t, -7.5e-116], t$95$1, If[LessEqual[t, -1.2e-267], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t, 4.5e-226], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[t, 3.9e+39], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.2000000000000002e51 or 3.9000000000000001e39 < t

   1. Initial program 91.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 74.1

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

   5. Applied rewrites 74.1%

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

   if -9.2000000000000002e51 < t < -7.5000000000000004e-116 or 4.50000000000000011e-226 < t < 3.9000000000000001e39

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 64.3%

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

   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 56.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 44.7%

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

   if -7.5000000000000004e-116 < t < -1.1999999999999999e-267

   1. Initial program 96.6%

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

   3. Taylor expanded in 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 59.9

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

   5. Applied rewrites 59.9%

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

   if -1.1999999999999999e-267 < t < 4.50000000000000011e-226

   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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 74.1%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   10. 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 50.5

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

   11. Applied rewrites 50.5%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 50.5%

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

Alternative 4: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-26}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+127}:\\ \;\;\;\;b \cdot t + \mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.6e+34)
     t_1
     (if (<= y 2.45e-26)
       (+ (fma (- t 2.0) b z) x)
       (if (<= y 5.4e+127) (+ (* b t) (fma (- 1.0 t) a x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.6e+34) {
		tmp = t_1;
	} else if (y <= 2.45e-26) {
		tmp = fma((t - 2.0), b, z) + x;
	} else if (y <= 5.4e+127) {
		tmp = (b * t) + fma((1.0 - t), a, x);
	} 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 <= -3.6e+34)
		tmp = t_1;
	elseif (y <= 2.45e-26)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	elseif (y <= 5.4e+127)
		tmp = Float64(Float64(b * t) + fma(Float64(1.0 - t), a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.6e+34], t$95$1, If[LessEqual[y, 2.45e-26], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 5.4e+127], N[(N[(b * t), $MachinePrecision] + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e34 or 5.4000000000000004e127 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 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 79.6

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

   5. Applied rewrites 79.6%

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

   if -3.6e34 < y < 2.45e-26

   1. Initial program 98.3%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 96.6%

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

   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 74.3%

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

   if 2.45e-26 < y < 5.4000000000000004e127

   1. Initial program 96.8%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 63.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 62.8%

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

Alternative 5: 88.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+35} \lor \neg \left(b \leq 8 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7e+35) (not (<= b 8e+26)))
   (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))
   (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 <= -7e+35) || !(b <= 8e+26)) {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	} 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 <= -7e+35) || !(b <= 8e+26))
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	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, -7e+35], N[Not[LessEqual[b, 8e+26]], $MachinePrecision]], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.0000000000000001e35 or 8.00000000000000038e26 < b

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. associate-+r+ N/A

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

      4. +-commutative N/A

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

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

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

      6. associate-+l- N/A

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

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

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

      8. *-commutative N/A

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

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

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. *-lft-identity N/A

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

      13. metadata-eval N/A

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

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

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

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

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

      16. *-rgt-identity N/A

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

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

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

      18. mul-1-neg N/A

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

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

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

   5. Applied rewrites 88.3%

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

   if -7.0000000000000001e35 < b < 8.00000000000000038e26

   1. Initial program 98.4%

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

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

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.2%

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

   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 88.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+35} \lor \neg \left(b \leq 8 \cdot 10^{+26}\right):\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+37} \lor \neg \left(y \leq 5.2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e+37) (not (<= y 5.2e+127)))
   (* (- b z) y)
   (+ (fma (- t 2.0) b z) (fma (- 1.0 t) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+37) || !(y <= 5.2e+127)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((t - 2.0), b, z) + fma((1.0 - t), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e+37) || !(y <= 5.2e+127))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(fma(Float64(t - 2.0), b, z) + fma(Float64(1.0 - t), a, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e+37], N[Not[LessEqual[y, 5.2e+127]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000001e37 or 5.2000000000000004e127 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 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 79.6

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

   5. Applied rewrites 79.6%

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

   if -1.15000000000000001e37 < y < 5.2000000000000004e127

   1. Initial program 98.0%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 89.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+37} \lor \neg \left(y \leq 5.2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+81} \lor \neg \left(b \leq 1.9 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.42e+81) (not (<= b 1.9e+30)))
   (fma (- b a) t (+ (* (- y 2.0) b) a))
   (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 <= -1.42e+81) || !(b <= 1.9e+30)) {
		tmp = fma((b - a), t, (((y - 2.0) * b) + a));
	} 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 <= -1.42e+81) || !(b <= 1.9e+30))
		tmp = fma(Float64(b - a), t, Float64(Float64(Float64(y - 2.0) * b) + a));
	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, -1.42e+81], N[Not[LessEqual[b, 1.9e+30]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision] + a), $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 < -1.41999999999999998e81 or 1.9000000000000001e30 < b

   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 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. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 87.0%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 81.3%

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

   if -1.41999999999999998e81 < b < 1.9000000000000001e30

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.3%

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

   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 87.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+81} \lor \neg \left(b \leq 1.9 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b + a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(-z, y - 1, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, b, \left(t - 2\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e+47)
   (* (- (+ t y) 2.0) b)
   (if (<= b 5.2e+112)
     (fma (- 1.0 t) a (fma (- z) (- y 1.0) x))
     (fma y b (* (- t 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+47) {
		tmp = ((t + y) - 2.0) * b;
	} else if (b <= 5.2e+112) {
		tmp = fma((1.0 - t), a, fma(-z, (y - 1.0), x));
	} else {
		tmp = fma(y, b, ((t - 2.0) * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e+47)
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	elseif (b <= 5.2e+112)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(-z), Float64(y - 1.0), x));
	else
		tmp = fma(y, b, Float64(Float64(t - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e+47], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 5.2e+112], N[(N[(1.0 - t), $MachinePrecision] * a + N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(y * b + N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.8999999999999998e47

   1. Initial program 94.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 91.2%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   10. 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 84.2

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

   11. Applied rewrites 84.2%

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

   if -2.8999999999999998e47 < b < 5.2000000000000001e112

   1. Initial program 98.1%

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

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

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.4%

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

   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 83.9%

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

   if 5.2000000000000001e112 < b

   1. Initial program 88.9%

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

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 84.1%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. lower--.f64 N/A

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

       4. lower-+.f64 81.9

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

   11. Applied rewrites 81.9%

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

   13. Applied rewrites 82.0%

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

Alternative 9: 74.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+37} \lor \neg \left(y \leq 5.2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, x\right) + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e+37) (not (<= y 5.2e+127)))
   (* (- b z) y)
   (fma (- b a) t (+ (fma -2.0 b x) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+37) || !(y <= 5.2e+127)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((b - a), t, (fma(-2.0, b, x) + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e+37) || !(y <= 5.2e+127))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = fma(Float64(b - a), t, Float64(fma(-2.0, b, x) + a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e+37], N[Not[LessEqual[y, 5.2e+127]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(-2.0 * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000001e37 or 5.2000000000000004e127 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around 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 79.6

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

   5. Applied rewrites 79.6%

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

   if -1.15000000000000001e37 < y < 5.2000000000000004e127

   1. Initial program 98.0%

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

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

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 76.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+37} \lor \neg \left(y \leq 5.2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(-2, b, x\right) + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 97.2%

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

Alternative 11: 26.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+41}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-272}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-72}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+60}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.75e+41)
   (* b t)
   (if (<= t 1.75e-272)
     (* b y)
     (if (<= t 4.5e-72) (* -2.0 b) (if (<= t 2.1e+60) (* b y) (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.75e+41) {
		tmp = b * t;
	} else if (t <= 1.75e-272) {
		tmp = b * y;
	} else if (t <= 4.5e-72) {
		tmp = -2.0 * b;
	} else if (t <= 2.1e+60) {
		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 <= (-1.75d+41)) then
        tmp = b * t
    else if (t <= 1.75d-272) then
        tmp = b * y
    else if (t <= 4.5d-72) then
        tmp = (-2.0d0) * b
    else if (t <= 2.1d+60) 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 <= -1.75e+41) {
		tmp = b * t;
	} else if (t <= 1.75e-272) {
		tmp = b * y;
	} else if (t <= 4.5e-72) {
		tmp = -2.0 * b;
	} else if (t <= 2.1e+60) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.75e+41:
		tmp = b * t
	elif t <= 1.75e-272:
		tmp = b * y
	elif t <= 4.5e-72:
		tmp = -2.0 * b
	elif t <= 2.1e+60:
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.75e+41)
		tmp = Float64(b * t);
	elseif (t <= 1.75e-272)
		tmp = Float64(b * y);
	elseif (t <= 4.5e-72)
		tmp = Float64(-2.0 * b);
	elseif (t <= 2.1e+60)
		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 <= -1.75e+41)
		tmp = b * t;
	elseif (t <= 1.75e-272)
		tmp = b * y;
	elseif (t <= 4.5e-72)
		tmp = -2.0 * b;
	elseif (t <= 2.1e+60)
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.75e+41], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.75e-272], N[(b * y), $MachinePrecision], If[LessEqual[t, 4.5e-72], N[(-2.0 * b), $MachinePrecision], If[LessEqual[t, 2.1e+60], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.75e41 or 2.1000000000000001e60 < t

   1. Initial program 92.6%

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

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

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in b around -inf

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

   8. Applied rewrites 49.8%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 44.7%

       \[\leadsto b \cdot t \]

   if -1.75e41 < t < 1.7499999999999998e-272 or 4.5e-72 < t < 2.1000000000000001e60

   1. Initial program 96.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   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 -inf

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

   8. Applied rewrites 38.5%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 28.7%

       \[\leadsto b \cdot y \]

   if 1.7499999999999998e-272 < t < 4.5e-72

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 64.6%

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

   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 64.6%

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

   9. Taylor expanded in b around inf

      \[\leadsto -2 \cdot b \]
   10. Step-by-step derivation

   11. Applied rewrites 27.3%

       \[\leadsto -2 \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 52.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-253}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ t y) 2.0) b)))
   (if (<= b -1.45e+25)
     t_1
     (if (<= b 2.6e-253)
       (* (- 1.0 y) z)
       (if (<= b 1.9e+30) (+ (+ z x) a) 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 <= -1.45e+25) {
		tmp = t_1;
	} else if (b <= 2.6e-253) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.9e+30) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) - 2.0d0) * b
    if (b <= (-1.45d+25)) then
        tmp = t_1
    else if (b <= 2.6d-253) then
        tmp = (1.0d0 - y) * z
    else if (b <= 1.9d+30) then
        tmp = (z + x) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t + y) - 2.0) * b;
	double tmp;
	if (b <= -1.45e+25) {
		tmp = t_1;
	} else if (b <= 2.6e-253) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.9e+30) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t + y) - 2.0) * b
	tmp = 0
	if b <= -1.45e+25:
		tmp = t_1
	elif b <= 2.6e-253:
		tmp = (1.0 - y) * z
	elif b <= 1.9e+30:
		tmp = (z + x) + a
	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 <= -1.45e+25)
		tmp = t_1;
	elseif (b <= 2.6e-253)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 1.9e+30)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t + y) - 2.0) * b;
	tmp = 0.0;
	if (b <= -1.45e+25)
		tmp = t_1;
	elseif (b <= 2.6e-253)
		tmp = (1.0 - y) * z;
	elseif (b <= 1.9e+30)
		tmp = (z + x) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -1.45e+25], t$95$1, If[LessEqual[b, 2.6e-253], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 1.9e+30], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.44999999999999995e25 or 1.9000000000000001e30 < b

   1. Initial program 92.8%

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

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

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 86.6%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   10. 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 75.1

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

   11. Applied rewrites 75.1%

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

   if -1.44999999999999995e25 < b < 2.6e-253

   1. Initial program 97.3%

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

   3. Taylor expanded in 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 52.3

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

   5. Applied rewrites 52.3%

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

   if 2.6e-253 < b < 1.9000000000000001e30

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 76.0%

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

   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 51.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 49.7%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 54.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-51}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;y \leq 400000:\\ \;\;\;\;\mathsf{fma}\left(-2, b, z\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3.5e+33)
     t_1
     (if (<= y -1.7e-51)
       (* (- b a) t)
       (if (<= y 400000.0) (+ (fma -2.0 b z) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -3.5e+33) {
		tmp = t_1;
	} else if (y <= -1.7e-51) {
		tmp = (b - a) * t;
	} else if (y <= 400000.0) {
		tmp = fma(-2.0, b, z) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -3.5e+33)
		tmp = t_1;
	elseif (y <= -1.7e-51)
		tmp = Float64(Float64(b - a) * t);
	elseif (y <= 400000.0)
		tmp = Float64(fma(-2.0, b, z) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.5e+33], t$95$1, If[LessEqual[y, -1.7e-51], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 400000.0], N[(N[(-2.0 * b + z), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e33 or 4e5 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -3.5000000000000001e33 < y < -1.70000000000000001e-51

   1. Initial program 94.0%

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

   3. Taylor expanded in t around 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 54.5

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

   5. Applied rewrites 54.5%

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

   if -1.70000000000000001e-51 < y < 4e5

   1. Initial program 99.0%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 98.4%

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

   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 64.9%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 47.9%

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

Alternative 14: 41.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-253}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+113}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e+47)
   (* (- y 2.0) b)
   (if (<= b 2.6e-253)
     (* (- 1.0 y) z)
     (if (<= b 1.4e+113) (+ (+ z x) a) (* (- t 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+47) {
		tmp = (y - 2.0) * b;
	} else if (b <= 2.6e-253) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.4e+113) {
		tmp = (z + x) + a;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.9d+47)) then
        tmp = (y - 2.0d0) * b
    else if (b <= 2.6d-253) then
        tmp = (1.0d0 - y) * z
    else if (b <= 1.4d+113) then
        tmp = (z + x) + a
    else
        tmp = (t - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+47) {
		tmp = (y - 2.0) * b;
	} else if (b <= 2.6e-253) {
		tmp = (1.0 - y) * z;
	} else if (b <= 1.4e+113) {
		tmp = (z + x) + a;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e+47:
		tmp = (y - 2.0) * b
	elif b <= 2.6e-253:
		tmp = (1.0 - y) * z
	elif b <= 1.4e+113:
		tmp = (z + x) + a
	else:
		tmp = (t - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e+47)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= 2.6e-253)
		tmp = Float64(Float64(1.0 - y) * z);
	elseif (b <= 1.4e+113)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e+47)
		tmp = (y - 2.0) * b;
	elseif (b <= 2.6e-253)
		tmp = (1.0 - y) * z;
	elseif (b <= 1.4e+113)
		tmp = (z + x) + a;
	else
		tmp = (t - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e+47], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 2.6e-253], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 1.4e+113], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.8999999999999998e47

   1. Initial program 94.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 91.2%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   10. 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 84.2

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

   11. Applied rewrites 84.2%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 61.8%

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

   if -2.8999999999999998e47 < b < 2.6e-253

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 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 51.0

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

   5. Applied rewrites 51.0%

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

   if 2.6e-253 < b < 1.39999999999999999e113

   1. Initial program 98.7%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 75.7%

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

   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 48.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 44.3%

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

   if 1.39999999999999999e113 < b

   1. Initial program 88.9%

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

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 60.7%

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

   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 24.6%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 51.3%

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

Alternative 15: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.92 \cdot 10^{+46}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-167}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+113}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.92e+46)
   (* (- y 2.0) b)
   (if (<= b -6.2e-167)
     (* (- y) z)
     (if (<= b 1.4e+113) (+ (+ z x) a) (* (- t 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.92e+46) {
		tmp = (y - 2.0) * b;
	} else if (b <= -6.2e-167) {
		tmp = -y * z;
	} else if (b <= 1.4e+113) {
		tmp = (z + x) + a;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.92d+46)) then
        tmp = (y - 2.0d0) * b
    else if (b <= (-6.2d-167)) then
        tmp = -y * z
    else if (b <= 1.4d+113) then
        tmp = (z + x) + a
    else
        tmp = (t - 2.0d0) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.92e+46) {
		tmp = (y - 2.0) * b;
	} else if (b <= -6.2e-167) {
		tmp = -y * z;
	} else if (b <= 1.4e+113) {
		tmp = (z + x) + a;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.92e+46:
		tmp = (y - 2.0) * b
	elif b <= -6.2e-167:
		tmp = -y * z
	elif b <= 1.4e+113:
		tmp = (z + x) + a
	else:
		tmp = (t - 2.0) * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.92e+46)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= -6.2e-167)
		tmp = Float64(Float64(-y) * z);
	elseif (b <= 1.4e+113)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.92e+46)
		tmp = (y - 2.0) * b;
	elseif (b <= -6.2e-167)
		tmp = -y * z;
	elseif (b <= 1.4e+113)
		tmp = (z + x) + a;
	else
		tmp = (t - 2.0) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.92e+46], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -6.2e-167], N[((-y) * z), $MachinePrecision], If[LessEqual[b, 1.4e+113], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.91999999999999992e46

   1. Initial program 94.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. associate--l+ N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. associate--l+ N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 91.2%

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

   9. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   10. 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 84.2

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

   11. Applied rewrites 84.2%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 61.8%

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

   if -1.91999999999999992e46 < b < -6.2e-167

   1. Initial program 97.3%

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

   3. Taylor expanded in 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 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.7%

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

   if -6.2e-167 < b < 1.39999999999999999e113

   1. Initial program 98.3%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 73.4%

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

   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 46.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 43.2%

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

   if 1.39999999999999999e113 < b

   1. Initial program 88.9%

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

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 60.7%

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

   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 24.6%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 51.3%

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

Alternative 16: 41.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-167}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+113}:\\ \;\;\;\;\left(z + x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 2.0) b)))
   (if (<= b -2.45e+80)
     t_1
     (if (<= b -6.2e-167)
       (* (- y) z)
       (if (<= b 1.4e+113) (+ (+ z x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 2.0) * b;
	double tmp;
	if (b <= -2.45e+80) {
		tmp = t_1;
	} else if (b <= -6.2e-167) {
		tmp = -y * z;
	} else if (b <= 1.4e+113) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - 2.0d0) * b
    if (b <= (-2.45d+80)) then
        tmp = t_1
    else if (b <= (-6.2d-167)) then
        tmp = -y * z
    else if (b <= 1.4d+113) then
        tmp = (z + x) + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 2.0) * b;
	double tmp;
	if (b <= -2.45e+80) {
		tmp = t_1;
	} else if (b <= -6.2e-167) {
		tmp = -y * z;
	} else if (b <= 1.4e+113) {
		tmp = (z + x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 2.0) * b
	tmp = 0
	if b <= -2.45e+80:
		tmp = t_1
	elif b <= -6.2e-167:
		tmp = -y * z
	elif b <= 1.4e+113:
		tmp = (z + x) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 2.0) * b)
	tmp = 0.0
	if (b <= -2.45e+80)
		tmp = t_1;
	elseif (b <= -6.2e-167)
		tmp = Float64(Float64(-y) * z);
	elseif (b <= 1.4e+113)
		tmp = Float64(Float64(z + x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 2.0) * b;
	tmp = 0.0;
	if (b <= -2.45e+80)
		tmp = t_1;
	elseif (b <= -6.2e-167)
		tmp = -y * z;
	elseif (b <= 1.4e+113)
		tmp = (z + x) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -2.45e+80], t$95$1, If[LessEqual[b, -6.2e-167], N[((-y) * z), $MachinePrecision], If[LessEqual[b, 1.4e+113], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4499999999999998e80 or 1.39999999999999999e113 < b

   1. Initial program 91.8%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 62.0%

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

   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 31.2%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 51.5%

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

   if -2.4499999999999998e80 < b < -6.2e-167

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 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 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 45.9%

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

   if -6.2e-167 < b < 1.39999999999999999e113

   1. Initial program 98.3%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 73.4%

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

   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 46.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 43.2%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 66.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 1.26 \cdot 10^{+42}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e+34) (not (<= y 1.26e+42)))
   (* (- 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 <= -3.6e+34) || !(y <= 1.26e+42)) {
		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 <= -3.6e+34) || !(y <= 1.26e+42))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(fma(Float64(t - 2.0), b, z) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e+34], N[Not[LessEqual[y, 1.26e+42]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e34 or 1.26e42 < 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 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 75.0

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

   5. Applied rewrites 75.0%

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

   if -3.6e34 < y < 1.26e42

   1. Initial program 98.5%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower-+.f64 N/A

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

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

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

      10. *-commutative N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-fma.f64 N/A

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

      14. lower--.f64 N/A

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

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

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

      16. *-commutative N/A

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

      17. metadata-eval N/A

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

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

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

      19. +-commutative N/A

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

   5. Applied rewrites 93.6%

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

   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 71.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 1.26 \cdot 10^{+42}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 400000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e+34) (not (<= y 400000.0)))
   (* (- b z) y)
   (+ (+ (fma -2.0 b z) x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+34) || !(y <= 400000.0)) {
		tmp = (b - z) * y;
	} else {
		tmp = (fma(-2.0, b, z) + x) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.6e+34) || !(y <= 400000.0))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(Float64(fma(-2.0, b, z) + x) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e+34], N[Not[LessEqual[y, 400000.0]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(-2.0 * b + z), $MachinePrecision] + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e34 or 4e5 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 72.1

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

   5. Applied rewrites 72.1%

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

   if -3.6e34 < y < 4e5

   1. Initial program 98.4%

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

   3. Taylor expanded in 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. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. associate--r- N/A

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

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(t - 2\right) \cdot b} + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{1} \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{z}\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{t - 2}, b, z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      15. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t - a \cdot 1\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{1 \cdot a}\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right)\right) \]

      18. fp-cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t + -1 \cdot a\right)}\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(-1 \cdot a + a \cdot t\right)}\right) \]

   5. Applied rewrites 96.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)} \]

   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 60.9%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, z\right) + x\right) + \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 400000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 56.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 400000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.6e+34) (not (<= y 400000.0))) (* (- b z) y) (+ (+ z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+34) || !(y <= 400000.0)) {
		tmp = (b - z) * y;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.6d+34)) .or. (.not. (y <= 400000.0d0))) then
        tmp = (b - z) * y
    else
        tmp = (z + x) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.6e+34) || !(y <= 400000.0)) {
		tmp = (b - z) * y;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.6e+34) or not (y <= 400000.0):
		tmp = (b - z) * y
	else:
		tmp = (z + x) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.6e+34) || !(y <= 400000.0))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(Float64(z + x) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.6e+34) || ~((y <= 400000.0)))
		tmp = (b - z) * y;
	else
		tmp = (z + x) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.6e+34], N[Not[LessEqual[y, 400000.0]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e34 or 4e5 < y

   1. Initial program 93.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

      3. lower--.f64 72.1

         \[\leadsto \color{blue}{\left(b - z\right)} \cdot y \]

   5. Applied rewrites 72.1%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -3.6e34 < y < 4e5

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) + x} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - \color{blue}{\left(-1 \cdot z - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)}\right) + x \]

      4. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} + x \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(t - 2\right) \cdot b} + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{1} \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{z}\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{t - 2}, b, z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      15. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t - a \cdot 1\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{1 \cdot a}\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right)\right) \]

      18. fp-cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t + -1 \cdot a\right)}\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(-1 \cdot a + a \cdot t\right)}\right) \]

   5. Applied rewrites 96.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)} \]

   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 60.9%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, z\right) + x\right) + \color{blue}{a} \]

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 44.9%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 400000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+36} \lor \neg \left(y \leq 23500000\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e+36) (not (<= y 23500000.0))) (* (- y) z) (+ (+ z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+36) || !(y <= 23500000.0)) {
		tmp = -y * z;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d+36)) .or. (.not. (y <= 23500000.0d0))) then
        tmp = -y * z
    else
        tmp = (z + x) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+36) || !(y <= 23500000.0)) {
		tmp = -y * z;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e+36) or not (y <= 23500000.0):
		tmp = -y * z
	else:
		tmp = (z + x) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e+36) || !(y <= 23500000.0))
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(Float64(z + x) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e+36) || ~((y <= 23500000.0)))
		tmp = -y * z;
	else
		tmp = (z + x) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e+36], N[Not[LessEqual[y, 23500000.0]], $MachinePrecision]], N[((-y) * z), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000012e36 or 2.35e7 < y

   1. Initial program 92.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 46.1

         \[\leadsto \color{blue}{\left(1 - y\right)} \cdot z \]

   5. Applied rewrites 46.1%

      \[\leadsto \color{blue}{\left(1 - y\right) \cdot z} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 45.6%

      \[\leadsto \left(-y\right) \cdot z \]

   if -1.90000000000000012e36 < y < 2.35e7

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) + x} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - \color{blue}{\left(-1 \cdot z - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)}\right) + x \]

      4. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} + x \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(t - 2\right) \cdot b} + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{1} \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{z}\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{t - 2}, b, z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      15. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t - a \cdot 1\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{1 \cdot a}\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right)\right) \]

      18. fp-cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t + -1 \cdot a\right)}\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(-1 \cdot a + a \cdot t\right)}\right) \]

   5. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)} \]

   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 60.5%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, z\right) + x\right) + \color{blue}{a} \]

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 44.6%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+36} \lor \neg \left(y \leq 23500000\right):\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 42.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+35} \lor \neg \left(y \leq 4.8 \cdot 10^{+38}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.42e+35) (not (<= y 4.8e+38))) (* b y) (+ (+ z x) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.42e+35) || !(y <= 4.8e+38)) {
		tmp = b * y;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.42d+35)) .or. (.not. (y <= 4.8d+38))) then
        tmp = b * y
    else
        tmp = (z + x) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.42e+35) || !(y <= 4.8e+38)) {
		tmp = b * y;
	} else {
		tmp = (z + x) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.42e+35) or not (y <= 4.8e+38):
		tmp = b * y
	else:
		tmp = (z + x) + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.42e+35) || !(y <= 4.8e+38))
		tmp = Float64(b * y);
	else
		tmp = Float64(Float64(z + x) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.42e+35) || ~((y <= 4.8e+38)))
		tmp = b * y;
	else
		tmp = (z + x) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.42e+35], N[Not[LessEqual[y, 4.8e+38]], $MachinePrecision]], N[(b * y), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.41999999999999991e35 or 4.80000000000000035e38 < 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 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. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right)} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right) + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - a\right) \cdot t + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + x\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - a\right) \cdot t + \left(\color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - a}, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\mathsf{fma}\left(y - 2, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(\color{blue}{y - 2}, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

   5. Applied rewrites 96.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot t + -1 \cdot \left(y - 2\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.6%

      \[\leadsto \left(-\left(\left(t + y\right) - 2\right)\right) \cdot \color{blue}{\left(-b\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 37.1%

       \[\leadsto b \cdot y \]

   if -1.41999999999999991e35 < y < 4.80000000000000035e38

   1. Initial program 98.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. associate--l+ N/A

         \[\leadsto \color{blue}{x + \left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)\right) + x} \]

      3. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - \color{blue}{\left(-1 \cdot z - \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)}\right) + x \]

      4. associate--r- N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} + x \]

      5. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(\left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right) + x\right)} \]

      6. +-commutative N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x + \left(\mathsf{neg}\left(a\right)\right) \cdot \left(t - 1\right)\right)} \]

      7. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \color{blue}{\left(x - a \cdot \left(t - 1\right)\right)} \]

      8. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) - -1 \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      9. fp-cancel-sub-sign-inv N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(t - 2\right) + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\color{blue}{\left(t - 2\right) \cdot b} + \left(\mathsf{neg}\left(-1\right)\right) \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{1} \cdot z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      12. *-lft-identity N/A

          \[\leadsto \left(\left(t - 2\right) \cdot b + \color{blue}{z}\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right)} + \left(x - a \cdot \left(t - 1\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{t - 2}, b, z\right) + \left(x - a \cdot \left(t - 1\right)\right) \]

      15. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t - a \cdot 1\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{1 \cdot a}\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \left(a \cdot t - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot a\right)\right) \]

      18. fp-cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(a \cdot t + -1 \cdot a\right)}\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(t - 2, b, z\right) + \left(x - \color{blue}{\left(-1 \cdot a + a \cdot t\right)}\right) \]

   5. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - 2, b, z\right) + \mathsf{fma}\left(1 - t, a, x\right)} \]

   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 58.9%

      \[\leadsto \left(\mathsf{fma}\left(-2, b, z\right) + x\right) + \color{blue}{a} \]

   9. Taylor expanded in b around 0

      \[\leadsto \left(x + z\right) + a \]
   10. Step-by-step derivation

   11. Applied rewrites 43.8%

       \[\leadsto \left(z + x\right) + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+35} \lor \neg \left(y \leq 4.8 \cdot 10^{+38}\right):\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 27.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+41} \lor \neg \left(t \leq 2.1 \cdot 10^{+60}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.75e+41) (not (<= t 2.1e+60))) (* b t) (* b y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.75e+41) || !(t <= 2.1e+60)) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.75d+41)) .or. (.not. (t <= 2.1d+60))) then
        tmp = b * t
    else
        tmp = b * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.75e+41) || !(t <= 2.1e+60)) {
		tmp = b * t;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.75e+41) or not (t <= 2.1e+60):
		tmp = b * t
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.75e+41) || !(t <= 2.1e+60))
		tmp = Float64(b * t);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.75e+41) || ~((t <= 2.1e+60)))
		tmp = b * t;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.75e+41], N[Not[LessEqual[t, 2.1e+60]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(b * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e41 or 2.1000000000000001e60 < t

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right)} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right) + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - a\right) \cdot t + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + x\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - a\right) \cdot t + \left(\color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - a}, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\mathsf{fma}\left(y - 2, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(\color{blue}{y - 2}, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

   5. Applied rewrites 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\right)} \]

   6. Taylor expanded in b around -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot t + -1 \cdot \left(y - 2\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.8%

      \[\leadsto \left(-\left(\left(t + y\right) - 2\right)\right) \cdot \color{blue}{\left(-b\right)} \]

   9. Taylor expanded in t around inf

      \[\leadsto b \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 44.7%

       \[\leadsto b \cdot t \]

   if -1.75e41 < t < 2.1000000000000001e60

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right)} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      4. associate-+l+ N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right) + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(b - a\right) \cdot t} + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      6. associate--l+ N/A

         \[\leadsto \left(b - a\right) \cdot t + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + x\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      7. +-commutative N/A

         \[\leadsto \left(b - a\right) \cdot t + \left(\color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{b - a}, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      11. associate--l+ N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

      13. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\mathsf{fma}\left(y - 2, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(\color{blue}{y - 2}, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

   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 -inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot t + -1 \cdot \left(y - 2\right)\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 38.3%

      \[\leadsto \left(-\left(\left(t + y\right) - 2\right)\right) \cdot \color{blue}{\left(-b\right)} \]

   9. Taylor expanded in y around inf

      \[\leadsto b \cdot y \]
   10. Step-by-step derivation

   11. Applied rewrites 23.0%

       \[\leadsto b \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+41} \lor \neg \left(t \leq 2.1 \cdot 10^{+60}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 17.6% 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 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. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

   2. associate--l+ N/A

      \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + b \cdot \left(y - 2\right)\right)} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

   4. associate-+l+ N/A

      \[\leadsto \color{blue}{t \cdot \left(b - a\right) + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)} \]

   5. *-commutative N/A

      \[\leadsto \color{blue}{\left(b - a\right) \cdot t} + \left(b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

   6. associate--l+ N/A

      \[\leadsto \left(b - a\right) \cdot t + \color{blue}{\left(\left(b \cdot \left(y - 2\right) + x\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

   7. +-commutative N/A

      \[\leadsto \left(b - a\right) \cdot t + \left(\color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

   9. lower--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{b - a}, t, \left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

   10. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

   11. associate--l+ N/A

       \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\left(y - 2\right) \cdot b} + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

   13. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(b - a, t, \color{blue}{\mathsf{fma}\left(y - 2, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)}\right) \]

   14. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(\color{blue}{y - 2}, b, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) \]

5. Applied rewrites 98.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x - \mathsf{fma}\left(y - 1, z, -a\right)\right)\right)} \]

6. Taylor expanded in b around -inf

   \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(-1 \cdot t + -1 \cdot \left(y - 2\right)\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 42.6%

   \[\leadsto \left(-\left(\left(t + y\right) - 2\right)\right) \cdot \color{blue}{\left(-b\right)} \]

9. Taylor expanded in t around inf

   \[\leadsto b \cdot t \]
10. Step-by-step derivation

11. Applied rewrites 18.5%

    \[\leadsto b \cdot t \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024329 
(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)))