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

Percentage Accurate: 95.1% → 97.8%

Time: 12.2s

Alternatives: 24

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% 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 98.8%

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

Alternative 2: 43.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+306)))
     (* b t)
     (+ (+ a x) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+306)) {
		tmp = b * t;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+306)) {
		tmp = b * t;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+306):
		tmp = b * t
	else:
		tmp = (a + x) + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+306))
		tmp = Float64(b * t);
	else
		tmp = Float64(Float64(a + x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+306)))
		tmp = b * t;
	else
		tmp = (a + x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+306]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -inf.0 or 4.99999999999999993e306 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 88.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 75.1

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.1%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 22.1%

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

   if -inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 4.99999999999999993e306

   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 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 78.9%

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

   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 53.5%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 58.6%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 48.7%

       \[\leadsto \left(a + x\right) + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq -\infty \lor \neg \left(\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 35.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+306))) (* b t) (+ z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+306)) {
		tmp = b * t;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+306)) {
		tmp = b * t;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+306):
		tmp = b * t
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+306))
		tmp = Float64(b * t);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+306)))
		tmp = b * t;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+306]], $MachinePrecision]], N[(b * t), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -inf.0 or 4.99999999999999993e306 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b))

   1. Initial program 88.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 75.1

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.1%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 22.1%

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

   if -inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 4.99999999999999993e306

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 73.9

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

   5. Applied rewrites 73.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 48.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 37.3%

       \[\leadsto z + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq -\infty \lor \neg \left(\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;b \cdot t\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

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

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

      4. distribute-rgt-out-- N/A

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

      5. *-commutative N/A

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

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

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

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

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

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

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

      13. *-rgt-identity N/A

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

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

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

      15. associate-*l* N/A

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

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

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

      17. mul-1-neg N/A

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

      18. remove-double-neg N/A

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

      19. *-commutative N/A

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

   5. Applied rewrites 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in 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 72.7%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 72.7

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

   8. Applied rewrites 72.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 72.7%

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

Alternative 5: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x - \left(y - 1\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(t\_1, b, \mathsf{fma}\left(-z, y, z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= x -2.6e+181)
     (fma t_1 b (- x (* (- y 1.0) z)))
     (if (<= x 3.4e+53)
       (fma (- 1.0 t) a (fma t_1 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 t_1 = (t + y) - 2.0;
	double tmp;
	if (x <= -2.6e+181) {
		tmp = fma(t_1, b, (x - ((y - 1.0) * z)));
	} else if (x <= 3.4e+53) {
		tmp = fma((1.0 - t), a, fma(t_1, 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)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (x <= -2.6e+181)
		tmp = fma(t_1, b, Float64(x - Float64(Float64(y - 1.0) * z)));
	elseif (x <= 3.4e+53)
		tmp = fma(Float64(1.0 - t), a, fma(t_1, 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_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[x, -2.6e+181], N[(t$95$1 * b + N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+53], N[(N[(1.0 - t), $MachinePrecision] * a + N[(t$95$1 * 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 3 regimes

2. if x < -2.6e181

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 95.4

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

   5. Applied rewrites 95.4%

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

   if -2.6e181 < x < 3.39999999999999998e53

   1. Initial program 95.0%

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

   3. Taylor expanded in 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-rgt-out-- N/A

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

      3. *-commutative N/A

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

      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. associate-*l* N/A

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

      14. mul-1-neg 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

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

   5. Applied rewrites 95.3%

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

   if 3.39999999999999998e53 < x

   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 98.1%

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

   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 91.0%

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

Alternative 6: 71.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t - 2, b, z\right) + \left(a + x\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -2.45 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-259}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z\right) + x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- t 2.0) b z) (+ a x))) (t_2 (* (- b z) y)))
   (if (<= y -2.45e+42)
     t_2
     (if (<= y -1.45e-205)
       t_1
       (if (<= y 3.8e-259)
         (+ (fma (- 1.0 t) a z) x)
         (if (<= y 2.5e+110) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((t - 2.0), b, z) + (a + x);
	double t_2 = (b - z) * y;
	double tmp;
	if (y <= -2.45e+42) {
		tmp = t_2;
	} else if (y <= -1.45e-205) {
		tmp = t_1;
	} else if (y <= 3.8e-259) {
		tmp = fma((1.0 - t), a, z) + x;
	} else if (y <= 2.5e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(t - 2.0), b, z) + Float64(a + x))
	t_2 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -2.45e+42)
		tmp = t_2;
	elseif (y <= -1.45e-205)
		tmp = t_1;
	elseif (y <= 3.8e-259)
		tmp = Float64(fma(Float64(1.0 - t), a, z) + x);
	elseif (y <= 2.5e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + N[(a + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.45e+42], t$95$2, If[LessEqual[y, -1.45e-205], t$95$1, If[LessEqual[y, 3.8e-259], N[(N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 2.5e+110], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000001e42 or 2.49999999999999989e110 < 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 78.3

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

   5. Applied rewrites 78.3%

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

   if -2.4500000000000001e42 < y < -1.45000000000000009e-205 or 3.8e-259 < y < 2.49999999999999989e110

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 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 86.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.9%

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

   if -1.45000000000000009e-205 < y < 3.8e-259

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0

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

      1. 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 97.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.4%

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

Alternative 7: 54.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -3400000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-250}:\\ \;\;\;\;\mathsf{fma}\left(-2, b, x\right) + z\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-303}:\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-144}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -3400000000000.0)
     t_1
     (if (<= y -5.5e-250)
       (+ (fma -2.0 b x) z)
       (if (<= y 9.8e-303)
         (fma (- a) t a)
         (if (<= y 8.5e-144)
           (+ (+ a x) z)
           (if (<= y 2.9e+18) (- x (* a t)) 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 <= -3400000000000.0) {
		tmp = t_1;
	} else if (y <= -5.5e-250) {
		tmp = fma(-2.0, b, x) + z;
	} else if (y <= 9.8e-303) {
		tmp = fma(-a, t, a);
	} else if (y <= 8.5e-144) {
		tmp = (a + x) + z;
	} else if (y <= 2.9e+18) {
		tmp = x - (a * t);
	} 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 <= -3400000000000.0)
		tmp = t_1;
	elseif (y <= -5.5e-250)
		tmp = Float64(fma(-2.0, b, x) + z);
	elseif (y <= 9.8e-303)
		tmp = fma(Float64(-a), t, a);
	elseif (y <= 8.5e-144)
		tmp = Float64(Float64(a + x) + z);
	elseif (y <= 2.9e+18)
		tmp = Float64(x - Float64(a * t));
	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, -3400000000000.0], t$95$1, If[LessEqual[y, -5.5e-250], N[(N[(-2.0 * b + x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 9.8e-303], N[((-a) * t + a), $MachinePrecision], If[LessEqual[y, 8.5e-144], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 2.9e+18], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.4e12 or 2.9e18 < y

   1. Initial program 94.6%

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

   3. Taylor expanded in 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 71.2

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

   5. Applied rewrites 71.2%

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

   if -3.4e12 < y < -5.5e-250

   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 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 97.8%

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

   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 66.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 52.9%

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

   if -5.5e-250 < y < 9.8e-303

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 20.2%

      \[\leadsto 1 \cdot a \]

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 73.0%

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

   if 9.8e-303 < y < 8.49999999999999958e-144

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0

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

      1. 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 97.1%

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

   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 72.3%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 77.7%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 71.3%

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

   if 8.49999999999999958e-144 < y < 2.9e18

   1. Initial program 93.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   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 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 65.6

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

   8. Applied rewrites 65.6%

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

   9. Taylor expanded in t around inf

      \[\leadsto x - a \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 55.8%

       \[\leadsto x - a \cdot \color{blue}{t} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 8: 75.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - z, y, \mathsf{fma}\left(-2, b, x\right)\right) + z\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-194}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, \mathsf{fma}\left(1 - t, a, z\right)\right)\\ \mathbf{elif}\;y \leq 0.034:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right) + \left(a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (fma (- b z) y (fma -2.0 b x)) z)))
   (if (<= y -1.2e-37)
     t_1
     (if (<= y 6e-194)
       (fma (- t 2.0) b (fma (- 1.0 t) a z))
       (if (<= y 0.034) (+ (fma (- t 2.0) b z) (+ a x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - z), y, fma(-2.0, b, x)) + z;
	double tmp;
	if (y <= -1.2e-37) {
		tmp = t_1;
	} else if (y <= 6e-194) {
		tmp = fma((t - 2.0), b, fma((1.0 - t), a, z));
	} else if (y <= 0.034) {
		tmp = fma((t - 2.0), b, z) + (a + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(Float64(b - z), y, fma(-2.0, b, x)) + z)
	tmp = 0.0
	if (y <= -1.2e-37)
		tmp = t_1;
	elseif (y <= 6e-194)
		tmp = fma(Float64(t - 2.0), b, fma(Float64(1.0 - t), a, z));
	elseif (y <= 0.034)
		tmp = Float64(fma(Float64(t - 2.0), b, z) + Float64(a + x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b - z), $MachinePrecision] * y + N[(-2.0 * b + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[y, -1.2e-37], t$95$1, If[LessEqual[y, 6e-194], N[(N[(t - 2.0), $MachinePrecision] * b + N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.034], N[(N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision] + N[(a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999995e-37 or 0.034000000000000002 < y

   1. Initial program 95.1%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 82.1

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

   5. Applied rewrites 82.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 80.6%

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

   if -1.19999999999999995e-37 < y < 6e-194

   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 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 97.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 90.3%

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

   if 6e-194 < y < 0.034000000000000002

   1. Initial program 94.7%

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

   3. Taylor expanded in y around 0

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

      1. 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 94.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 87.1%

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

Alternative 9: 85.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+136} \lor \neg \left(b \leq 0.0042\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.8e+136) (not (<= b 0.0042)))
   (fma (- b a) t (+ (fma (- y 2.0) b x) a))
   (- x (fma a (- t 1.0) (* z (- y 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.8e+136) || !(b <= 0.0042)) {
		tmp = fma((b - a), t, (fma((y - 2.0), b, x) + a));
	} else {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.8e+136) || !(b <= 0.0042))
		tmp = fma(Float64(b - a), t, Float64(fma(Float64(y - 2.0), b, x) + a));
	else
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.8e+136], N[Not[LessEqual[b, 0.0042]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t + N[(N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.7999999999999998e136 or 0.00419999999999999974 < b

   1. Initial program 92.0%

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

   3. Taylor expanded in 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 97.0%

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

   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 91.2%

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

   if -8.7999999999999998e136 < b < 0.00419999999999999974

   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 100.0%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 93.1

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

   8. Applied rewrites 93.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+136} \lor \neg \left(b \leq 0.0042\right):\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, x\right) + a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\\ \mathbf{elif}\;b \leq 0.0042:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.8e+136)
   (+ (fma (- b z) y (fma (- t 2.0) b x)) z)
   (if (<= b 0.0042)
     (- x (fma a (- t 1.0) (* z (- y 1.0))))
     (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.8e+136) {
		tmp = fma((b - z), y, fma((t - 2.0), b, x)) + z;
	} else if (b <= 0.0042) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else {
		tmp = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.8e+136)
		tmp = Float64(fma(Float64(b - z), y, fma(Float64(t - 2.0), b, x)) + z);
	elseif (b <= 0.0042)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	else
		tmp = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.8e+136], N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[b, 0.0042], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.7999999999999998e136

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 92.8

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 96.4%

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

   if -8.7999999999999998e136 < b < 0.00419999999999999974

   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 100.0%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 93.1

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

   8. Applied rewrites 93.1%

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

   if 0.00419999999999999974 < b

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0

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

      1. 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-rgt-out-- N/A

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

      8. *-commutative N/A

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

      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. associate-*l* N/A

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

      19. mul-1-neg 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 86.3%

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

Alternative 11: 55.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -42000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-233}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-144}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -42000000000.0)
     t_1
     (if (<= y -2.3e-233)
       (fma (- t 2.0) b z)
       (if (<= y 8.5e-144)
         (+ (+ a x) z)
         (if (<= y 2.9e+18) (- x (* a t)) 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 <= -42000000000.0) {
		tmp = t_1;
	} else if (y <= -2.3e-233) {
		tmp = fma((t - 2.0), b, z);
	} else if (y <= 8.5e-144) {
		tmp = (a + x) + z;
	} else if (y <= 2.9e+18) {
		tmp = x - (a * t);
	} 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 <= -42000000000.0)
		tmp = t_1;
	elseif (y <= -2.3e-233)
		tmp = fma(Float64(t - 2.0), b, z);
	elseif (y <= 8.5e-144)
		tmp = Float64(Float64(a + x) + z);
	elseif (y <= 2.9e+18)
		tmp = Float64(x - Float64(a * t));
	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, -42000000000.0], t$95$1, If[LessEqual[y, -2.3e-233], N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision], If[LessEqual[y, 8.5e-144], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 2.9e+18], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2e10 or 2.9e18 < y

   1. Initial program 94.6%

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

   3. Taylor expanded in 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 71.2

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

   5. Applied rewrites 71.2%

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

   if -4.2e10 < y < -2.3000000000000002e-233

   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 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 97.7%

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

   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 65.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 52.3%

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

   if -2.3000000000000002e-233 < y < 8.49999999999999958e-144

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 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 95.8%

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

   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 63.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 69.5%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 62.9%

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

   if 8.49999999999999958e-144 < y < 2.9e18

   1. Initial program 93.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   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 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 65.6

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

   8. Applied rewrites 65.6%

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

   9. Taylor expanded in t around inf

      \[\leadsto x - a \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 55.8%

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

Alternative 12: 83.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+136}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(t - 2, b, x\right)\right) + z\\ \mathbf{elif}\;b \leq 0.0175:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.8e+136)
   (+ (fma (- b z) y (fma (- t 2.0) b x)) z)
   (if (<= b 0.0175)
     (- x (fma a (- t 1.0) (* z (- y 1.0))))
     (fma (- b a) t (fma (- y 2.0) b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.8e+136) {
		tmp = fma((b - z), y, fma((t - 2.0), b, x)) + z;
	} else if (b <= 0.0175) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else {
		tmp = fma((b - a), t, fma((y - 2.0), b, a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.8e+136)
		tmp = Float64(fma(Float64(b - z), y, fma(Float64(t - 2.0), b, x)) + z);
	elseif (b <= 0.0175)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	else
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.8e+136], N[(N[(N[(b - z), $MachinePrecision] * y + N[(N[(t - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[b, 0.0175], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.7999999999999998e136

   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 a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 92.8

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 96.4%

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

   if -8.7999999999999998e136 < b < 0.017500000000000002

   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 100.0%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 93.1

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

   8. Applied rewrites 93.1%

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

   if 0.017500000000000002 < b

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 97.2%

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

   6. Taylor expanded in 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 89.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 84.9%

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

Alternative 13: 81.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+180}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right)\\ \mathbf{elif}\;b \leq 0.0175:\\ \;\;\;\;x - \mathsf{fma}\left(a, t - 1, z \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.05e+180)
   (fma (- b a) t (* (- y 2.0) b))
   (if (<= b 0.0175)
     (- x (fma a (- t 1.0) (* z (- y 1.0))))
     (fma (- b a) t (fma (- y 2.0) b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.05e+180) {
		tmp = fma((b - a), t, ((y - 2.0) * b));
	} else if (b <= 0.0175) {
		tmp = x - fma(a, (t - 1.0), (z * (y - 1.0)));
	} else {
		tmp = fma((b - a), t, fma((y - 2.0), b, a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.05e+180)
		tmp = fma(Float64(b - a), t, Float64(Float64(y - 2.0) * b));
	elseif (b <= 0.0175)
		tmp = Float64(x - fma(a, Float64(t - 1.0), Float64(z * Float64(y - 1.0))));
	else
		tmp = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.05e+180], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.0175], N[(x - N[(a * N[(t - 1.0), $MachinePrecision] + N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.05e180

   1. Initial program 90.8%

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

   3. Taylor expanded in 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 b around inf

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

   8. Applied rewrites 91.7%

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

   if -2.05e180 < b < 0.017500000000000002

   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 100.0%

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

   6. Taylor expanded in b around 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 92.2

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

   8. Applied rewrites 92.2%

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

   if 0.017500000000000002 < b

   1. Initial program 91.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 97.2%

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

   6. Taylor expanded in 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 89.1%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 84.9%

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

Alternative 14: 75.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{+58}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(b - z, y, \mathsf{fma}\left(-2, b, x\right)\right) + z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \left(y - 2\right) \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.6e+58)
   (* (- b a) t)
   (if (<= t 2.45e+16)
     (+ (fma (- b z) y (fma -2.0 b x)) z)
     (fma (- b a) t (* (- y 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.6e+58) {
		tmp = (b - a) * t;
	} else if (t <= 2.45e+16) {
		tmp = fma((b - z), y, fma(-2.0, b, x)) + z;
	} else {
		tmp = fma((b - a), t, ((y - 2.0) * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.6e+58)
		tmp = Float64(Float64(b - a) * t);
	elseif (t <= 2.45e+16)
		tmp = Float64(fma(Float64(b - z), y, fma(-2.0, b, x)) + z);
	else
		tmp = fma(Float64(b - a), t, Float64(Float64(y - 2.0) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.6e+58], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 2.45e+16], N[(N[(N[(b - z), $MachinePrecision] * y + N[(-2.0 * b + x), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5999999999999999e58

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if -9.5999999999999999e58 < t < 2.45e16

   1. Initial program 97.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 84.5

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 85.2%

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

   if 2.45e16 < t

   1. Initial program 95.1%

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

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

   8. Applied rewrites 69.2%

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

Alternative 15: 96.5% 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 16: 55.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-144}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+18}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.2e+41)
     t_1
     (if (<= y 8.5e-144)
       (+ (+ a x) z)
       (if (<= y 2.9e+18) (- x (* a t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.2e+41) {
		tmp = t_1;
	} else if (y <= 8.5e-144) {
		tmp = (a + x) + z;
	} else if (y <= 2.9e+18) {
		tmp = x - (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-4.2d+41)) then
        tmp = t_1
    else if (y <= 8.5d-144) then
        tmp = (a + x) + z
    else if (y <= 2.9d+18) then
        tmp = x - (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.2e+41) {
		tmp = t_1;
	} else if (y <= 8.5e-144) {
		tmp = (a + x) + z;
	} else if (y <= 2.9e+18) {
		tmp = x - (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -4.2e+41:
		tmp = t_1
	elif y <= 8.5e-144:
		tmp = (a + x) + z
	elif y <= 2.9e+18:
		tmp = x - (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.2e+41)
		tmp = t_1;
	elseif (y <= 8.5e-144)
		tmp = Float64(Float64(a + x) + z);
	elseif (y <= 2.9e+18)
		tmp = Float64(x - Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -4.2e+41)
		tmp = t_1;
	elseif (y <= 8.5e-144)
		tmp = (a + x) + z;
	elseif (y <= 2.9e+18)
		tmp = x - (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.2e+41], t$95$1, If[LessEqual[y, 8.5e-144], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 2.9e+18], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1999999999999999e41 or 2.9e18 < y

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 72.4

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

   5. Applied rewrites 72.4%

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

   if -4.1999999999999999e41 < y < 8.49999999999999958e-144

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 95.1%

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

   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 61.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 63.1%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 51.2%

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

   if 8.49999999999999958e-144 < y < 2.9e18

   1. Initial program 93.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   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 0

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 65.6

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

   8. Applied rewrites 65.6%

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

   9. Taylor expanded in t around inf

      \[\leadsto x - a \cdot \color{blue}{t} \]
   10. Step-by-step derivation

   11. Applied rewrites 55.8%

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

Alternative 17: 55.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-144}:\\ \;\;\;\;\left(a + x\right) + z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+18}:\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -4.2e+41)
     t_1
     (if (<= y 1.7e-144)
       (+ (+ a x) z)
       (if (<= y 2.05e+18) (* (- b a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.2e+41) {
		tmp = t_1;
	} else if (y <= 1.7e-144) {
		tmp = (a + x) + z;
	} else if (y <= 2.05e+18) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b - z) * y
    if (y <= (-4.2d+41)) then
        tmp = t_1
    else if (y <= 1.7d-144) then
        tmp = (a + x) + z
    else if (y <= 2.05d+18) then
        tmp = (b - a) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -4.2e+41) {
		tmp = t_1;
	} else if (y <= 1.7e-144) {
		tmp = (a + x) + z;
	} else if (y <= 2.05e+18) {
		tmp = (b - a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b - z) * y
	tmp = 0
	if y <= -4.2e+41:
		tmp = t_1
	elif y <= 1.7e-144:
		tmp = (a + x) + z
	elif y <= 2.05e+18:
		tmp = (b - a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -4.2e+41)
		tmp = t_1;
	elseif (y <= 1.7e-144)
		tmp = Float64(Float64(a + x) + z);
	elseif (y <= 2.05e+18)
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b - z) * y;
	tmp = 0.0;
	if (y <= -4.2e+41)
		tmp = t_1;
	elseif (y <= 1.7e-144)
		tmp = (a + x) + z;
	elseif (y <= 2.05e+18)
		tmp = (b - a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.2e+41], t$95$1, If[LessEqual[y, 1.7e-144], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[y, 2.05e+18], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.1999999999999999e41 or 2.05e18 < y

   1. Initial program 94.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 72.4

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

   5. Applied rewrites 72.4%

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

   if -4.1999999999999999e41 < y < 1.70000000000000009e-144

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 95.1%

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

   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 61.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 63.1%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 51.2%

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

   if 1.70000000000000009e-144 < y < 2.05e18

   1. Initial program 93.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.2

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

   5. Applied rewrites 51.2%

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

Alternative 18: 66.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+42} \lor \neg \left(y \leq 1.6 \cdot 10^{+140}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.45e+42) (not (<= y 1.6e+140)))
   (* (- b z) y)
   (+ (fma (- 1.0 t) a z) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.45e+42) || !(y <= 1.6e+140)) {
		tmp = (b - z) * y;
	} else {
		tmp = fma((1.0 - t), a, z) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.45e+42) || !(y <= 1.6e+140))
		tmp = Float64(Float64(b - z) * y);
	else
		tmp = Float64(fma(Float64(1.0 - t), a, z) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.45e+42], N[Not[LessEqual[y, 1.6e+140]], $MachinePrecision]], N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(1.0 - t), $MachinePrecision] * a + z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000001e42 or 1.60000000000000005e140 < y

   1. Initial program 92.5%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   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 81.4

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

   5. Applied rewrites 81.4%

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

   if -2.4500000000000001e42 < y < 1.60000000000000005e140

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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 86.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 68.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+42} \lor \neg \left(y \leq 1.6 \cdot 10^{+140}\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 62.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+41} \lor \neg \left(y \leq 40000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e+41) (not (<= y 40000.0)))
   (* (- 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 <= -4.2e+41) || !(y <= 40000.0)) {
		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 <= -4.2e+41) || !(y <= 40000.0))
		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, -4.2e+41], N[Not[LessEqual[y, 40000.0]], $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 < -4.1999999999999999e41 or 4e4 < y

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 70.7

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

   5. Applied rewrites 70.7%

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

   if -4.1999999999999999e41 < y < 4e4

   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 94.5%

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

   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 61.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+41} \lor \neg \left(y \leq 40000\right):\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(-2, b, z\right) + x\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 61.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+78} \lor \neg \left(b \leq 0.0175\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y - 1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.4e+78) (not (<= b 0.0175)))
   (* (- (+ t y) 2.0) b)
   (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 <= -5.4e+78) || !(b <= 0.0175)) {
		tmp = ((t + y) - 2.0) * b;
	} else {
		tmp = fma(-z, (y - 1.0), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.4e+78) || !(b <= 0.0175))
		tmp = Float64(Float64(Float64(t + y) - 2.0) * b);
	else
		tmp = fma(Float64(-z), Float64(y - 1.0), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.4e+78], N[Not[LessEqual[b, 0.0175]], $MachinePrecision]], N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision], N[((-z) * N[(y - 1.0), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.40000000000000009e78 or 0.017500000000000002 < b

   1. Initial program 91.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 97.3%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   7. 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 70.8

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

   8. Applied rewrites 70.8%

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

   if -5.40000000000000009e78 < b < 0.017500000000000002

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 66.9

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.2%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+78} \lor \neg \left(b \leq 0.0175\right):\\ \;\;\;\;\left(\left(t + y\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-z, y - 1, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 57.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+55} \lor \neg \left(t \leq 2 \cdot 10^{+16}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.7e+55) (not (<= t 2e+16))) (* (- b a) t) (+ (+ a x) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.7e+55) || !(t <= 2e+16)) {
		tmp = (b - a) * t;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.7d+55)) .or. (.not. (t <= 2d+16))) then
        tmp = (b - a) * t
    else
        tmp = (a + x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.7e+55) || !(t <= 2e+16)) {
		tmp = (b - a) * t;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.7e+55) or not (t <= 2e+16):
		tmp = (b - a) * t
	else:
		tmp = (a + x) + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.7e+55) || !(t <= 2e+16))
		tmp = Float64(Float64(b - a) * t);
	else
		tmp = Float64(Float64(a + x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.7e+55) || ~((t <= 2e+16)))
		tmp = (b - a) * t;
	else
		tmp = (a + x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.7e+55], N[Not[LessEqual[t, 2e+16]], $MachinePrecision]], N[(N[(b - a), $MachinePrecision] * t), $MachinePrecision], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e55 or 2e16 < 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 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 66.7

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

   5. Applied rewrites 66.7%

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

   if -1.6999999999999999e55 < t < 2e16

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 56.5%

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

   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 42.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 54.7%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 43.7%

       \[\leadsto \left(a + x\right) + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+55} \lor \neg \left(t \leq 2 \cdot 10^{+16}\right):\\ \;\;\;\;\left(b - a\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 42.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+52} \lor \neg \left(a \leq 8 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.4e+52) (not (<= a 8e+45))) (fma (- a) t a) (* (- 1.0 y) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.4e+52) || !(a <= 8e+45)) {
		tmp = fma(-a, t, a);
	} else {
		tmp = (1.0 - y) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.4e+52) || !(a <= 8e+45))
		tmp = fma(Float64(-a), t, a);
	else
		tmp = Float64(Float64(1.0 - y) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.4e+52], N[Not[LessEqual[a, 8e+45]], $MachinePrecision]], N[((-a) * t + a), $MachinePrecision], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4e52 or 7.9999999999999994e45 < a

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 57.2

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

   5. Applied rewrites 57.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 18.8%

      \[\leadsto 1 \cdot a \]

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 57.2%

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

   if -3.4e52 < a < 7.9999999999999994e45

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.5

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

   5. Applied rewrites 41.5%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+52} \lor \neg \left(a \leq 8 \cdot 10^{+45}\right):\\ \;\;\;\;\mathsf{fma}\left(-a, t, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 41.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+146} \lor \neg \left(y \leq 6.8 \cdot 10^{+184}\right):\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e+146) (not (<= y 6.8e+184))) (* (- z) y) (+ (+ a x) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+146) || !(y <= 6.8e+184)) {
		tmp = -z * y;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d+146)) .or. (.not. (y <= 6.8d+184))) then
        tmp = -z * y
    else
        tmp = (a + x) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+146) || !(y <= 6.8e+184)) {
		tmp = -z * y;
	} else {
		tmp = (a + x) + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e+146) or not (y <= 6.8e+184):
		tmp = -z * y
	else:
		tmp = (a + x) + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e+146) || !(y <= 6.8e+184))
		tmp = Float64(Float64(-z) * y);
	else
		tmp = Float64(Float64(a + x) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e+146) || ~((y <= 6.8e+184)))
		tmp = -z * y;
	else
		tmp = (a + x) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e+146], N[Not[LessEqual[y, 6.8e+184]], $MachinePrecision]], N[((-z) * y), $MachinePrecision], N[(N[(a + x), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8999999999999999e146 or 6.8000000000000003e184 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower--.f64 85.7

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.8%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 55.8%

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

   if -1.8999999999999999e146 < y < 6.8000000000000003e184

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(t - 2\right)\right) - \left(-1 \cdot z + a \cdot \left(t - 1\right)\right)} \]
   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 81.9%

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

   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 54.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 51.4%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 42.4%

       \[\leadsto \left(a + x\right) + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+146} \lor \neg \left(y \leq 6.8 \cdot 10^{+184}\right):\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a + x\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.1% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ z + x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ z x))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = z + x
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return z + x

Julia

function code(x, y, z, t, a, b)
	return Float64(z + x)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + x), $MachinePrecision]

Derivation

1. Initial program 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 a around 0

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

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. *-commutative N/A

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

   4. lower-fma.f64 N/A

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

   5. lower--.f64 N/A

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

   6. lower-+.f64 N/A

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

   7. lower--.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower--.f64 74.3

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

5. Applied rewrites 74.3%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 44.3%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 24.6%

    \[\leadsto z + x \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024320 
(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)))