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

Percentage Accurate: 95.4% → 98.5%

Time: 11.8s

Alternatives: 24

Speedup: 0.5×

• 36.0% 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: 95.4% 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: 98.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 60.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 66.7%

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

4. Final simplification 98.0%

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

Alternative 2: 35.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq -1.2 \cdot 10^{+307}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+298}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ t y) 2.0)) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 -1.2e+307)
     (* (- z) y)
     (if (<= t_1 1e+298) (+ a x) (* (- a) t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -1.2e+307) {
		tmp = -z * y;
	} else if (t_1 <= 1e+298) {
		tmp = a + x;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * ((t + y) - 2.0d0)) + ((x - (z * (y - 1.0d0))) - (a * (t - 1.0d0)))
    if (t_1 <= (-1.2d+307)) then
        tmp = -z * y
    else if (t_1 <= 1d+298) then
        tmp = a + x
    else
        tmp = -a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -1.2e+307) {
		tmp = -z * y;
	} else if (t_1 <= 1e+298) {
		tmp = a + x;
	} else {
		tmp = -a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= -1.2e+307:
		tmp = -z * y
	elif t_1 <= 1e+298:
		tmp = a + x
	else:
		tmp = -a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y - 1.0))) - Float64(a * Float64(t - 1.0))))
	tmp = 0.0
	if (t_1 <= -1.2e+307)
		tmp = Float64(Float64(-z) * y);
	elseif (t_1 <= 1e+298)
		tmp = Float64(a + x);
	else
		tmp = Float64(Float64(-a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= -1.2e+307)
		tmp = -z * y;
	elseif (t_1 <= 1e+298)
		tmp = a + x;
	else
		tmp = -a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1.2e+307], N[((-z) * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+298], N[(a + x), $MachinePrecision], N[((-a) * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 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)) < -1.20000000000000008e307

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 59.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 33.4%

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

   if -1.20000000000000008e307 < (+.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)) < 9.9999999999999996e297

   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

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 74.1

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 47.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 40.9%

       \[\leadsto x + a \]

   if 9.9999999999999996e297 < (+.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 69.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 54.2

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

   5. Applied rewrites 54.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 42.3%

      \[\leadsto \left(-a\right) \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -1.2 \cdot 10^{+307}:\\ \;\;\;\;\left(-z\right) \cdot y\\ \mathbf{elif}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 10^{+298}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 35.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right)\\ \mathbf{if}\;t\_1 \leq -1.2 \cdot 10^{+307}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+298}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (* b (- (+ t y) 2.0)) (- (- x (* z (- y 1.0))) (* a (- t 1.0))))))
   (if (<= t_1 -1.2e+307) (* b t) (if (<= t_1 1e+298) (+ a x) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -1.2e+307) {
		tmp = b * t;
	} else if (t_1 <= 1e+298) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * ((t + y) - 2.0d0)) + ((x - (z * (y - 1.0d0))) - (a * (t - 1.0d0)))
    if (t_1 <= (-1.2d+307)) then
        tmp = b * t
    else if (t_1 <= 1d+298) then
        tmp = a + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	double tmp;
	if (t_1 <= -1.2e+307) {
		tmp = b * t;
	} else if (t_1 <= 1e+298) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)))
	tmp = 0
	if t_1 <= -1.2e+307:
		tmp = b * t
	elif t_1 <= 1e+298:
		tmp = a + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) + Float64(Float64(x - Float64(z * Float64(y - 1.0))) - Float64(a * Float64(t - 1.0))))
	tmp = 0.0
	if (t_1 <= -1.2e+307)
		tmp = Float64(b * t);
	elseif (t_1 <= 1e+298)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * ((t + y) - 2.0)) + ((x - (z * (y - 1.0))) - (a * (t - 1.0)));
	tmp = 0.0;
	if (t_1 <= -1.2e+307)
		tmp = b * t;
	elseif (t_1 <= 1e+298)
		tmp = a + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(z * N[(y - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1.2e+307], N[(b * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+298], N[(a + x), $MachinePrecision], N[(b * t), $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)) < -1.20000000000000008e307 or 9.9999999999999996e297 < (+.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 84.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 49.9

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 27.2%

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

   if -1.20000000000000008e307 < (+.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)) < 9.9999999999999996e297

   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

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 74.1

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 47.8%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 40.9%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq -1.2 \cdot 10^{+307}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x - z \cdot \left(y - 1\right)\right) - a \cdot \left(t - 1\right)\right) \leq 10^{+298}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 20000000000000:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- b a) t (fma (- y 2.0) b (fma (- 1.0 y) z a)))))
   (if (<= a -2.7e+104)
     t_1
     (if (<= a 20000000000000.0)
       (fma (- 1.0 y) z (fma (- (+ t y) 2.0) b x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((b - a), t, fma((y - 2.0), b, fma((1.0 - y), z, a)));
	double tmp;
	if (a <= -2.7e+104) {
		tmp = t_1;
	} else if (a <= 20000000000000.0) {
		tmp = fma((1.0 - y), z, fma(((t + y) - 2.0), b, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(b - a), t, fma(Float64(y - 2.0), b, fma(Float64(1.0 - y), z, a)))
	tmp = 0.0
	if (a <= -2.7e+104)
		tmp = t_1;
	elseif (a <= 20000000000000.0)
		tmp = fma(Float64(1.0 - y), z, fma(Float64(Float64(t + y) - 2.0), b, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - a), $MachinePrecision] * t + N[(N[(y - 2.0), $MachinePrecision] * b + N[(N[(1.0 - y), $MachinePrecision] * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+104], t$95$1, If[LessEqual[a, 20000000000000.0], N[(N[(1.0 - y), $MachinePrecision] * z + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.69999999999999985e104 or 2e13 < a

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 92.9%

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

   if -2.69999999999999985e104 < a < 2e13

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 94.1

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

   5. Applied rewrites 94.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \mathbf{elif}\;a \leq 20000000000000:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b - a, t, \mathsf{fma}\left(y - 2, b, \mathsf{fma}\left(1 - y, z, a\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, x\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-92}:\\ \;\;\;\;\mathsf{fma}\left(t - 2, b, z\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a x)) (t_2 (* (- b z) y)))
   (if (<= y -8.5e+67)
     t_2
     (if (<= y -5.3e-265)
       t_1
       (if (<= y 4.2e-92) (fma (- t 2.0) b z) (if (<= y 8.2e+44) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, x);
	double t_2 = (b - z) * y;
	double tmp;
	if (y <= -8.5e+67) {
		tmp = t_2;
	} else if (y <= -5.3e-265) {
		tmp = t_1;
	} else if (y <= 4.2e-92) {
		tmp = fma((t - 2.0), b, z);
	} else if (y <= 8.2e+44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, x)
	t_2 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -8.5e+67)
		tmp = t_2;
	elseif (y <= -5.3e-265)
		tmp = t_1;
	elseif (y <= 4.2e-92)
		tmp = fma(Float64(t - 2.0), b, z);
	elseif (y <= 8.2e+44)
		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[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8.5e+67], t$95$2, If[LessEqual[y, -5.3e-265], t$95$1, If[LessEqual[y, 4.2e-92], N[(N[(t - 2.0), $MachinePrecision] * b + z), $MachinePrecision], If[LessEqual[y, 8.2e+44], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.50000000000000038e67 or 8.1999999999999993e44 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if -8.50000000000000038e67 < y < -5.3e-265 or 4.2e-92 < y < 8.1999999999999993e44

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 85.5

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 61.1%

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

   if -5.3e-265 < y < 4.2e-92

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 80.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 61.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 61.5%

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

Alternative 6: 88.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, t\_1\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -1.9e+32)
     (fma (- 1.0 y) z t_1)
     (if (<= b 1.02e+40)
       (fma (- 1.0 t) a (fma (- 1.0 y) z x))
       (fma (- 1.0 t) a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -1.9e+32) {
		tmp = fma((1.0 - y), z, t_1);
	} else if (b <= 1.02e+40) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = fma((1.0 - t), a, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -1.9e+32)
		tmp = fma(Float64(1.0 - y), z, t_1);
	elseif (b <= 1.02e+40)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = fma(Float64(1.0 - t), a, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -1.9e+32], N[(N[(1.0 - y), $MachinePrecision] * z + t$95$1), $MachinePrecision], If[LessEqual[b, 1.02e+40], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - t), $MachinePrecision] * a + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9000000000000002e32

   1. Initial program 86.6%

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

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if -1.9000000000000002e32 < b < 1.02e40

   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 b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 93.1%

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

   if 1.02e40 < b

   1. Initial program 90.6%

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

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 92.5

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

   5. Applied rewrites 92.5%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{if}\;b \leq -8.4 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 t) a (fma (- (+ t y) 2.0) b x))))
   (if (<= b -8.4e+27)
     t_1
     (if (<= b 1.02e+40) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - t), a, fma(((t + y) - 2.0), b, x));
	double tmp;
	if (b <= -8.4e+27) {
		tmp = t_1;
	} else if (b <= 1.02e+40) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - t), a, fma(Float64(Float64(t + y) - 2.0), b, x))
	tmp = 0.0
	if (b <= -8.4e+27)
		tmp = t_1;
	elseif (b <= 1.02e+40)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.4e+27], t$95$1, If[LessEqual[b, 1.02e+40], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.39999999999999978e27 or 1.02e40 < b

   1. Initial program 88.7%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 87.5

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

   5. Applied rewrites 87.5%

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

   if -8.39999999999999978e27 < b < 1.02e40

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 93.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - y, z, b \cdot \left(\left(t + y\right) - 2\right)\right)\\ \mathbf{if}\;b \leq -4.6 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 540000000:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 y) z (* b (- (+ t y) 2.0)))))
   (if (<= b -4.6e+48)
     t_1
     (if (<= b 540000000.0) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((1.0 - y), z, (b * ((t + y) - 2.0)));
	double tmp;
	if (b <= -4.6e+48) {
		tmp = t_1;
	} else if (b <= 540000000.0) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(1.0 - y), z, Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -4.6e+48)
		tmp = t_1;
	elseif (b <= 540000000.0)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 - y), $MachinePrecision] * z + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.6e+48], t$95$1, If[LessEqual[b, 540000000.0], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.6e48 or 5.4e8 < b

   1. Initial program 88.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 90.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 81.1%

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

   if -4.6e48 < b < 5.4e8

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 93.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, b \cdot \left(\left(t + y\right) - 2\right)\right)\\ \mathbf{elif}\;b \leq 540000000:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, b \cdot \left(\left(t + y\right) - 2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-303}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -5.4e+31)
     t_1
     (if (<= b -4.6e-303)
       (fma (- 1.0 t) a (+ z x))
       (if (<= b 1.16e+42) (+ (fma (- 1.0 y) z x) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -5.4e+31) {
		tmp = t_1;
	} else if (b <= -4.6e-303) {
		tmp = fma((1.0 - t), a, (z + x));
	} else if (b <= 1.16e+42) {
		tmp = fma((1.0 - y), z, x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -5.4e+31)
		tmp = t_1;
	elseif (b <= -4.6e-303)
		tmp = fma(Float64(1.0 - t), a, Float64(z + x));
	elseif (b <= 1.16e+42)
		tmp = Float64(fma(Float64(1.0 - y), z, x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -5.4e+31], t$95$1, If[LessEqual[b, -4.6e-303], N[(N[(1.0 - t), $MachinePrecision] * a + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.16e+42], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.39999999999999971e31 or 1.15999999999999995e42 < b

   1. Initial program 88.5%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 87.3

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 77.2%

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

   if -5.39999999999999971e31 < b < -4.59999999999999991e-303

   1. Initial program 96.9%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 77.8%

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

   if -4.59999999999999991e-303 < b < 1.15999999999999995e42

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 92.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 81.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-303}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, z + x\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) - 2\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;b \cdot t\_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, b, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ t y) 2.0)))
   (if (<= b -8.5e+123)
     (* b t_1)
     (if (<= b 1.2e+47) (fma (- 1.0 t) a (fma (- 1.0 y) z x)) (fma t_1 b x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) - 2.0;
	double tmp;
	if (b <= -8.5e+123) {
		tmp = b * t_1;
	} else if (b <= 1.2e+47) {
		tmp = fma((1.0 - t), a, fma((1.0 - y), z, x));
	} else {
		tmp = fma(t_1, b, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) - 2.0)
	tmp = 0.0
	if (b <= -8.5e+123)
		tmp = Float64(b * t_1);
	elseif (b <= 1.2e+47)
		tmp = fma(Float64(1.0 - t), a, fma(Float64(1.0 - y), z, x));
	else
		tmp = fma(t_1, b, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[b, -8.5e+123], N[(b * t$95$1), $MachinePrecision], If[LessEqual[b, 1.2e+47], N[(N[(1.0 - t), $MachinePrecision] * a + N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * b + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5e123

   1. Initial program 80.0%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 81.7

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

   5. Applied rewrites 81.7%

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

   if -8.5e123 < b < 1.20000000000000009e47

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 89.4%

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

   if 1.20000000000000009e47 < b

   1. Initial program 90.6%

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

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 92.5

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

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 79.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -1e+49)
     t_1
     (if (<= b 1.05e-280)
       (fma (- 1.0 t) a x)
       (if (<= b 1.25e+78) (fma (- 1.0 y) z x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1e+49) {
		tmp = t_1;
	} else if (b <= 1.05e-280) {
		tmp = fma((1.0 - t), a, x);
	} else if (b <= 1.25e+78) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -1e+49)
		tmp = t_1;
	elseif (b <= 1.05e-280)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (b <= 1.25e+78)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+49], t$95$1, If[LessEqual[b, 1.05e-280], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[b, 1.25e+78], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.99999999999999946e48 or 1.24999999999999996e78 < b

   1. Initial program 87.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 73.2

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

   5. Applied rewrites 73.2%

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

   if -9.99999999999999946e48 < b < 1.05e-280

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 66.3%

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

   if 1.05e-280 < b < 1.24999999999999996e78

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 73.9%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-280}:\\ \;\;\;\;\mathsf{fma}\left(1 - t, a, x\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.4e+32)
   (fma (- y 2.0) b x)
   (if (<= b 1.05e-280)
     (fma (- 1.0 t) a x)
     (if (<= b 1.25e+78) (fma (- 1.0 y) z x) (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 <= -4.4e+32) {
		tmp = fma((y - 2.0), b, x);
	} else if (b <= 1.05e-280) {
		tmp = fma((1.0 - t), a, x);
	} else if (b <= 1.25e+78) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = fma((y - 2.0), b, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.4e+32)
		tmp = fma(Float64(y - 2.0), b, x);
	elseif (b <= 1.05e-280)
		tmp = fma(Float64(1.0 - t), a, x);
	elseif (b <= 1.25e+78)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = fma(Float64(y - 2.0), b, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.4e+32], N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[b, 1.05e-280], N[(N[(1.0 - t), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[b, 1.25e+78], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.40000000000000002e32

   1. Initial program 86.6%

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

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 82.7

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 58.7%

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

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 54.6%

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

   if -4.40000000000000002e32 < b < 1.05e-280

   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 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 70.7

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

   5. Applied rewrites 70.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 66.8%

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

   if 1.05e-280 < b < 1.24999999999999996e78

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 73.9%

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

   if 1.24999999999999996e78 < b

   1. Initial program 90.0%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 92.1

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

   5. Applied rewrites 92.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.5%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 58.5%

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

Alternative 13: 41.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+122}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq -1.28 \cdot 10^{-231}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+70}:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+122)
   (* (- y 2.0) b)
   (if (<= b -1.28e-231)
     (fma (- t) a x)
     (if (<= b 1.28e+70) (* (- 1.0 y) z) (* (- t 2.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+122) {
		tmp = (y - 2.0) * b;
	} else if (b <= -1.28e-231) {
		tmp = fma(-t, a, x);
	} else if (b <= 1.28e+70) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e+122)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= -1.28e-231)
		tmp = fma(Float64(-t), a, x);
	elseif (b <= 1.28e+70)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e+122], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, -1.28e-231], N[((-t) * a + x), $MachinePrecision], If[LessEqual[b, 1.28e+70], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.1e122

   1. Initial program 80.0%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 81.7

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

   5. Applied rewrites 81.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.7%

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

   if -1.1e122 < b < -1.27999999999999995e-231

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 62.0%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 49.9%

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

   if -1.27999999999999995e-231 < b < 1.27999999999999994e70

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. metadata-eval N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-sub0 N/A

          \[\leadsto \color{blue}{\left(0 - \left(y - 1\right)\right)} \cdot z \]

      12. sub-neg N/A

          \[\leadsto \left(0 - \color{blue}{\left(y + \left(\mathsf{neg}\left(1\right)\right)\right)}\right) \cdot z \]

      13. metadata-eval N/A

          \[\leadsto \left(0 - \left(y + \color{blue}{-1}\right)\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(0 - \color{blue}{\left(-1 + y\right)}\right) \cdot z \]

      15. associate--r+ N/A

          \[\leadsto \color{blue}{\left(\left(0 - -1\right) - y\right)} \cdot z \]

      16. metadata-eval N/A

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

      17. lower--.f64 48.6

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

   5. Applied rewrites 48.6%

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

   if 1.27999999999999994e70 < b

   1. Initial program 90.4%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 75.0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 55.1%

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

Alternative 14: 72.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- (+ t y) 2.0) b x)))
   (if (<= b -3.8e+33)
     t_1
     (if (<= b 1.16e+42) (+ (fma (- 1.0 y) z x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((t + y) - 2.0), b, x);
	double tmp;
	if (b <= -3.8e+33) {
		tmp = t_1;
	} else if (b <= 1.16e+42) {
		tmp = fma((1.0 - y), z, x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(t + y) - 2.0), b, x)
	tmp = 0.0
	if (b <= -3.8e+33)
		tmp = t_1;
	elseif (b <= 1.16e+42)
		tmp = Float64(fma(Float64(1.0 - y), z, x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision] * b + x), $MachinePrecision]}, If[LessEqual[b, -3.8e+33], t$95$1, If[LessEqual[b, 1.16e+42], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.80000000000000002e33 or 1.15999999999999995e42 < b

   1. Initial program 88.5%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. distribute-lft-in N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. neg-mul-1 N/A

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

      13. sub-neg N/A

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

      14. lower--.f64 N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lower--.f64 N/A

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

      19. +-commutative N/A

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

      20. lower-+.f64 87.3

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 77.2%

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

   if -3.80000000000000002e33 < b < 1.15999999999999995e42

   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 b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 93.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 74.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.86 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -1.86e+80) t_1 (if (<= b 7e+78) (+ (fma (- 1.0 y) z x) a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.86e+80) {
		tmp = t_1;
	} else if (b <= 7e+78) {
		tmp = fma((1.0 - y), z, x) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -1.86e+80)
		tmp = t_1;
	elseif (b <= 7e+78)
		tmp = Float64(fma(Float64(1.0 - y), z, x) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.86e+80], t$95$1, If[LessEqual[b, 7e+78], N[(N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.8599999999999999e80 or 7.0000000000000003e78 < b

   1. Initial program 86.6%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -1.8599999999999999e80 < b < 7.0000000000000003e78

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0

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

      1. associate--r+ N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+r- N/A

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

      5. *-commutative N/A

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

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

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. lower--.f64 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. *-commutative N/A

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

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

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

      21. mul-1-neg N/A

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

      22. lower-fma.f64 N/A

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

   5. Applied rewrites 89.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 72.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.86 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right) + a\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, x\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 2, b, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.4e+27)
   (fma (- y 2.0) b x)
   (if (<= b 1.25e+78) (fma (- 1.0 y) z x) (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 <= -8.4e+27) {
		tmp = fma((y - 2.0), b, x);
	} else if (b <= 1.25e+78) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = fma((y - 2.0), b, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.4e+27)
		tmp = fma(Float64(y - 2.0), b, x);
	elseif (b <= 1.25e+78)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = fma(Float64(y - 2.0), b, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.4e+27], N[(N[(y - 2.0), $MachinePrecision] * b + x), $MachinePrecision], If[LessEqual[b, 1.25e+78], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.39999999999999978e27

   1. Initial program 87.1%

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

   3. Taylor expanded in 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. sub-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

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

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

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 83.3

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.0%

      \[\leadsto \mathsf{fma}\left(y - 2, \color{blue}{b}, x + a\right) \]

   9. Taylor expanded in a around 0

      \[\leadsto x + b \cdot \color{blue}{\left(y - 2\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 54.5%

       \[\leadsto \mathsf{fma}\left(y - 2, b, x\right) \]

   if -8.39999999999999978e27 < b < 1.24999999999999996e78

   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 b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) - z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)} - z \cdot \left(y - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x\right)} - z \cdot \left(y - 1\right) \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x - z \cdot \left(y - 1\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x - z \cdot \left(y - 1\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x - z \cdot \left(y - 1\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x - z \cdot \left(y - 1\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x - z \cdot \left(y - 1\right)\right)} \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x - z \cdot \left(y - 1\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x - z \cdot \left(y - 1\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x - z \cdot \left(y - 1\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x - z \cdot \left(y - 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x - z \cdot \left(y - 1\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x - z \cdot \left(y - 1\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x - z \cdot \left(y - 1\right)\right) \]

      16. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x - z \cdot \left(y - 1\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right) \cdot z}\right)\right) + x\right) \]

      20. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} + x\right) \]

      21. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \cdot z + x\right) \]

      22. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(-1 \cdot \left(y - 1\right), z, x\right)}\right) \]

   5. Applied rewrites 93.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.0%

      \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, x\right) \]

   if 1.24999999999999996e78 < b

   1. Initial program 90.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 92.1

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 60.5%

      \[\leadsto \mathsf{fma}\left(y - 2, \color{blue}{b}, x + a\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto a + b \cdot \color{blue}{\left(y - 2\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 58.5%

       \[\leadsto \mathsf{fma}\left(y - 2, b, a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 53.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - 2, b, a\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- y 2.0) b a)))
   (if (<= b -8.5e+104) t_1 (if (<= b 1.25e+78) (fma (- 1.0 y) z x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((y - 2.0), b, a);
	double tmp;
	if (b <= -8.5e+104) {
		tmp = t_1;
	} else if (b <= 1.25e+78) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(y - 2.0), b, a)
	tmp = 0.0
	if (b <= -8.5e+104)
		tmp = t_1;
	elseif (b <= 1.25e+78)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y - 2.0), $MachinePrecision] * b + a), $MachinePrecision]}, If[LessEqual[b, -8.5e+104], t$95$1, If[LessEqual[b, 1.25e+78], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.4999999999999999e104 or 1.24999999999999996e78 < b

   1. Initial program 85.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 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. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 90.4

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 90.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in t around 0

      \[\leadsto a + \color{blue}{\left(x + b \cdot \left(y - 2\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 62.0%

      \[\leadsto \mathsf{fma}\left(y - 2, \color{blue}{b}, x + a\right) \]

   9. Taylor expanded in x around 0

      \[\leadsto a + b \cdot \color{blue}{\left(y - 2\right)} \]
   10. Step-by-step derivation

   11. Applied rewrites 59.9%

       \[\leadsto \mathsf{fma}\left(y - 2, b, a\right) \]

   if -8.4999999999999999e104 < b < 1.24999999999999996e78

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) - z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)} - z \cdot \left(y - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x\right)} - z \cdot \left(y - 1\right) \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x - z \cdot \left(y - 1\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x - z \cdot \left(y - 1\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x - z \cdot \left(y - 1\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x - z \cdot \left(y - 1\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x - z \cdot \left(y - 1\right)\right)} \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x - z \cdot \left(y - 1\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x - z \cdot \left(y - 1\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x - z \cdot \left(y - 1\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x - z \cdot \left(y - 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x - z \cdot \left(y - 1\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x - z \cdot \left(y - 1\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x - z \cdot \left(y - 1\right)\right) \]

      16. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x - z \cdot \left(y - 1\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right) \cdot z}\right)\right) + x\right) \]

      20. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} + x\right) \]

      21. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \cdot z + x\right) \]

      22. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(-1 \cdot \left(y - 1\right), z, x\right)}\right) \]

   5. Applied rewrites 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.8%

      \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 52.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+122}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{+92}:\\ \;\;\;\;\mathsf{fma}\left(1 - y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+122)
   (* (- y 2.0) b)
   (if (<= b 1.16e+92) (fma (- 1.0 y) z x) (* (- t 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+122) {
		tmp = (y - 2.0) * b;
	} else if (b <= 1.16e+92) {
		tmp = fma((1.0 - y), z, x);
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+122)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= 1.16e+92)
		tmp = fma(Float64(1.0 - y), z, x);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+122], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 1.16e+92], N[(N[(1.0 - y), $MachinePrecision] * z + x), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e122

   1. Initial program 80.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 81.7

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 81.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 60.7%

      \[\leadsto \left(y - 2\right) \cdot b \]

   if -1.15e122 < b < 1.16000000000000006e92

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x - \left(a \cdot \left(t - 1\right) + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - a \cdot \left(t - 1\right)\right) - z \cdot \left(y - 1\right)} \]

      2. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)\right)} - z \cdot \left(y - 1\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x\right)} - z \cdot \left(y - 1\right) \]

      4. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x - z \cdot \left(y - 1\right)\right)} \]

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x - z \cdot \left(y - 1\right)\right) \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x - z \cdot \left(y - 1\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x - z \cdot \left(y - 1\right)\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x - z \cdot \left(y - 1\right)\right)} \]

      9. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x - z \cdot \left(y - 1\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x - z \cdot \left(y - 1\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x - z \cdot \left(y - 1\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x - z \cdot \left(y - 1\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x - z \cdot \left(y - 1\right)\right) \]

      14. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x - z \cdot \left(y - 1\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x - z \cdot \left(y - 1\right)\right) \]

      16. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x - z \cdot \left(y - 1\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \left(\mathsf{neg}\left(\color{blue}{\left(y - 1\right) \cdot z}\right)\right) + x\right) \]

      20. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\mathsf{neg}\left(\left(y - 1\right)\right)\right) \cdot z} + x\right) \]

      21. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} \cdot z + x\right) \]

      22. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(-1 \cdot \left(y - 1\right), z, x\right)}\right) \]

   5. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(1 - y, z, x\right)\right)} \]

   6. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{z \cdot \left(1 - y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.0%

      \[\leadsto \mathsf{fma}\left(1 - y, \color{blue}{z}, x\right) \]

   if 1.16000000000000006e92 < b

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 77.0

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 58.9%

      \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 51.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- b z) y)))
   (if (<= y -1.55e+67) t_1 (if (<= y 1.65e+16) (fma (- t) a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b - z) * y;
	double tmp;
	if (y <= -1.55e+67) {
		tmp = t_1;
	} else if (y <= 1.65e+16) {
		tmp = fma(-t, a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b - z) * y)
	tmp = 0.0
	if (y <= -1.55e+67)
		tmp = t_1;
	elseif (y <= 1.65e+16)
		tmp = fma(Float64(-t), a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.55e+67], t$95$1, If[LessEqual[y, 1.65e+16], N[((-t) * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999998e67 or 1.65e16 < y

   1. Initial program 91.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(b - z\right)} \]
   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 -1.54999999999999998e67 < y < 1.65e16

   1. Initial program 96.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 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. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 78.9

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.4%

      \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 42.8%

       \[\leadsto \mathsf{fma}\left(-t, a, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 44.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+122}:\\ \;\;\;\;\left(y - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+122)
   (* (- y 2.0) b)
   (if (<= b 1.9e+80) (fma (- t) a x) (* (- t 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+122) {
		tmp = (y - 2.0) * b;
	} else if (b <= 1.9e+80) {
		tmp = fma(-t, a, x);
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e+122)
		tmp = Float64(Float64(y - 2.0) * b);
	elseif (b <= 1.9e+80)
		tmp = fma(Float64(-t), a, x);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e+122], N[(N[(y - 2.0), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[b, 1.9e+80], N[((-t) * a + x), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1e122

   1. Initial program 80.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 81.7

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 81.7%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around 0

      \[\leadsto \left(y - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 60.7%

      \[\leadsto \left(y - 2\right) \cdot b \]

   if -1.1e122 < b < 1.89999999999999999e80

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 63.5

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto \mathsf{fma}\left(-t, a, x\right) \]

   if 1.89999999999999999e80 < b

   1. Initial program 89.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 75.5

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 75.5%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 57.7%

      \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 41.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+122}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+122)
   (* b y)
   (if (<= b 1.9e+80) (fma (- t) a x) (* (- t 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+122) {
		tmp = b * y;
	} else if (b <= 1.9e+80) {
		tmp = fma(-t, a, x);
	} else {
		tmp = (t - 2.0) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+122)
		tmp = Float64(b * y);
	elseif (b <= 1.9e+80)
		tmp = fma(Float64(-t), a, x);
	else
		tmp = Float64(Float64(t - 2.0) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+122], N[(b * y), $MachinePrecision], If[LessEqual[b, 1.9e+80], N[((-t) * a + x), $MachinePrecision], N[(N[(t - 2.0), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e122

   1. Initial program 80.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 87.7

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.1%

      \[\leadsto y \cdot \color{blue}{b} \]

   if -1.15e122 < b < 1.89999999999999999e80

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 63.5

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.6%

      \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 43.1%

       \[\leadsto \mathsf{fma}\left(-t, a, x\right) \]

   if 1.89999999999999999e80 < b

   1. Initial program 89.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 75.5

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 75.5%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(t - 2\right) \cdot b \]
   7. Step-by-step derivation

   8. Applied rewrites 57.7%

      \[\leadsto \left(t - 2\right) \cdot b \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+122}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 41.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, x\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.7:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (- t) a x)))
   (if (<= t -2.25e+21) t_1 (if (<= t 0.7) (+ a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(-t, a, x);
	double tmp;
	if (t <= -2.25e+21) {
		tmp = t_1;
	} else if (t <= 0.7) {
		tmp = a + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(-t), a, x)
	tmp = 0.0
	if (t <= -2.25e+21)
		tmp = t_1;
	elseif (t <= 0.7)
		tmp = Float64(a + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-t) * a + x), $MachinePrecision]}, If[LessEqual[t, -2.25e+21], t$95$1, If[LessEqual[t, 0.7], N[(a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.25e21 or 0.69999999999999996 < t

   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. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 75.1

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 75.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.1%

      \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]

   9. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot t, a, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 50.5%

       \[\leadsto \mathsf{fma}\left(-t, a, x\right) \]

   if -2.25e21 < t < 0.69999999999999996

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 70.7

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 70.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.6%

      \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 36.9%

       \[\leadsto x + a \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \mathbf{elif}\;t \leq 0.7:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 33.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+90}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e+122) (* b y) (if (<= b 2e+90) (+ a x) (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+122) {
		tmp = b * y;
	} else if (b <= 2e+90) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.2d+122)) then
        tmp = b * y
    else if (b <= 2d+90) then
        tmp = a + x
    else
        tmp = b * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.2e+122) {
		tmp = b * y;
	} else if (b <= 2e+90) {
		tmp = a + x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e+122:
		tmp = b * y
	elif b <= 2e+90:
		tmp = a + x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e+122)
		tmp = Float64(b * y);
	elseif (b <= 2e+90)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.2e+122)
		tmp = b * y;
	elseif (b <= 2e+90)
		tmp = a + x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e+122], N[(b * y), $MachinePrecision], If[LessEqual[b, 2e+90], N[(a + x), $MachinePrecision], N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2000000000000001e122

   1. Initial program 80.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 87.7

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in y around inf

      \[\leadsto b \cdot \color{blue}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 45.1%

      \[\leadsto y \cdot \color{blue}{b} \]

   if -1.2000000000000001e122 < b < 1.99999999999999993e90

   1. Initial program 98.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) - a \cdot \left(t - 1\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      9. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

      17. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

      18. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

      19. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

      20. lower-+.f64 63.8

          \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   5. Applied rewrites 63.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.9%

      \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]

   9. Taylor expanded in t around 0

      \[\leadsto a + x \]
   10. Step-by-step derivation

   11. Applied rewrites 35.5%

       \[\leadsto x + a \]

   if 1.99999999999999993e90 < b

   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 b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + y\right) - 2\right)} \cdot b \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

      5. lower-+.f64 77.0

         \[\leadsto \left(\color{blue}{\left(y + t\right)} - 2\right) \cdot b \]

   5. Applied rewrites 77.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 38.5%

      \[\leadsto t \cdot \color{blue}{b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+90}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 25.3% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ a + x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ a x))

C

double code(double x, double y, double z, double t, double a, double b) {
	return a + 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 = a + x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a + x;
}

Python

def code(x, y, z, t, a, b):
	return a + x

Julia

function code(x, y, z, t, a, b)
	return Float64(a + x)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a + x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a + x), $MachinePrecision]

Derivation

1. Initial program 94.1%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in 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. sub-neg N/A

      \[\leadsto \color{blue}{\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   3. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(t - 1\right) \cdot a}\right)\right) + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   4. distribute-lft-neg-in N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(t - 1\right)\right)\right) \cdot a} + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   5. mul-1-neg N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} \cdot a + \left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   6. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - 1\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right)} \]

   7. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(-1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(-1 \cdot \left(t + \color{blue}{-1}\right), a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   9. distribute-lft-in N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot t + -1 \cdot -1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(-1 \cdot t + \color{blue}{1}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   11. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 + -1 \cdot t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{fma}\left(1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   13. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   14. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{1 - t}, a, x + b \cdot \left(\left(t + y\right) - 2\right)\right) \]

   15. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + x}\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\left(\left(t + y\right) - 2\right) \cdot b} + x\right) \]

   17. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(1 - t, a, \color{blue}{\mathsf{fma}\left(\left(t + y\right) - 2, b, x\right)}\right) \]

   18. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(t + y\right) - 2}, b, x\right)\right) \]

   19. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

   20. lower-+.f64 72.7

       \[\leadsto \mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\color{blue}{\left(y + t\right)} - 2, b, x\right)\right) \]

5. Applied rewrites 72.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(1 - t, a, \mathsf{fma}\left(\left(y + t\right) - 2, b, x\right)\right)} \]

6. Taylor expanded in b around 0

   \[\leadsto x + \color{blue}{a \cdot \left(1 - t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 44.0%

   \[\leadsto \mathsf{fma}\left(1 - t, \color{blue}{a}, x\right) \]

9. Taylor expanded in t around 0

   \[\leadsto a + x \]
10. Step-by-step derivation

11. Applied rewrites 26.8%

    \[\leadsto x + a \]

12. Final simplification 26.8%

    \[\leadsto a + x \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024235 
(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)))