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

Percentage Accurate: 95.3% → 97.8%

Time: 13.5s

Alternatives: 19

Speedup: 0.5×

• 35.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * (b - a)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 86.0

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

   5. Applied rewrites 86.0%

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

4. Final simplification 99.2%

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

Alternative 2: 44.4% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * (-a)), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + -2.0), $MachinePrecision]), $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)) < -inf.0

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 50.2%

      \[\leadsto t \cdot \left(-a\right) \]

   if -inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 9.99999999999999986e306

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.3%

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

   if 9.99999999999999986e306 < (+.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 72.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 53.0

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

   5. Applied rewrites 53.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 33.7%

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

4. Final simplification 47.7%

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

Alternative 3: 44.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * (-a)), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(y * b), $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)) < -inf.0

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 50.2%

      \[\leadsto t \cdot \left(-a\right) \]

   if -inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 9.99999999999999986e306

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.3%

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

   if 9.99999999999999986e306 < (+.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 72.0%

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

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 74.3

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 32.9%

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

4. Final simplification 47.6%

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

Alternative 4: 44.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * (-z)), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(y * b), $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)) < -inf.0

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. *-lft-identity N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

      8. lower--.f64 N/A

         \[\leadsto \color{blue}{z - y \cdot z} \]

      9. lower-*.f64 26.6

         \[\leadsto z - \color{blue}{y \cdot z} \]

   5. Applied rewrites 26.6%

      \[\leadsto \color{blue}{z - y \cdot z} \]

   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 26.2%

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

   if -inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < 9.99999999999999986e306

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.3%

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

   if 9.99999999999999986e306 < (+.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 72.0%

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

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 74.3

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 32.9%

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

4. Final simplification 44.1%

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

Alternative 5: 43.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y #s(literal 1 binary64)) z)) (*.f64 (-.f64 t #s(literal 1 binary64)) a)) (*.f64 (-.f64 (+.f64 y t) #s(literal 2 binary64)) b)) < -inf.0 or 9.99999999999999986e306 < (+.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 83.9%

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

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 75.5

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

   5. Applied rewrites 75.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 28.0%

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

   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)) < 9.99999999999999986e306

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.3%

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

4. Final simplification 43.4%

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

Alternative 6: 55.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x)) (t_2 (* t (- b a))))
   (if (<= t -1.7e+125)
     t_2
     (if (<= t -1.75e-23)
       t_1
       (if (<= t -7.5e-161)
         (* b (+ y -2.0))
         (if (<= t 4.2e-243)
           t_1
           (if (<= t 3.2e-37) (+ x (+ z a)) (if (<= t 5.4e+110) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1.7e+125) {
		tmp = t_2;
	} else if (t <= -1.75e-23) {
		tmp = t_1;
	} else if (t <= -7.5e-161) {
		tmp = b * (y + -2.0);
	} else if (t <= 4.2e-243) {
		tmp = t_1;
	} else if (t <= 3.2e-37) {
		tmp = x + (z + a);
	} else if (t <= 5.4e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1.7e+125)
		tmp = t_2;
	elseif (t <= -1.75e-23)
		tmp = t_1;
	elseif (t <= -7.5e-161)
		tmp = Float64(b * Float64(y + -2.0));
	elseif (t <= 4.2e-243)
		tmp = t_1;
	elseif (t <= 3.2e-37)
		tmp = Float64(x + Float64(z + a));
	elseif (t <= 5.4e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+125], t$95$2, If[LessEqual[t, -1.75e-23], t$95$1, If[LessEqual[t, -7.5e-161], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-243], t$95$1, If[LessEqual[t, 3.2e-37], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+110], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6999999999999999e125 or 5.40000000000000019e110 < t

   1. Initial program 87.6%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 79.6

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

   5. Applied rewrites 79.6%

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

   if -1.6999999999999999e125 < t < -1.74999999999999997e-23 or -7.49999999999999991e-161 < t < 4.2000000000000002e-243 or 3.1999999999999999e-37 < t < 5.40000000000000019e110

   1. Initial program 97.7%

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 79.0%

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

   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 62.3%

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

   if -1.74999999999999997e-23 < t < -7.49999999999999991e-161

   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 b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 54.8%

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

   if 4.2000000000000002e-243 < t < 3.1999999999999999e-37

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 71.8%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 61.3%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-243}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-37}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1e+165)
     t_1
     (if (<= t -7e+23)
       (fma a (- t) (+ x z))
       (if (<= t -8.4e-22)
         (fma a (- 1.0 t) (* y (- z)))
         (if (<= t -5.5e-239)
           (fma b (+ y -2.0) (+ x a))
           (if (<= t 5.4e+110) (+ a (fma z (- 1.0 y) x)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1e+165) {
		tmp = t_1;
	} else if (t <= -7e+23) {
		tmp = fma(a, -t, (x + z));
	} else if (t <= -8.4e-22) {
		tmp = fma(a, (1.0 - t), (y * -z));
	} else if (t <= -5.5e-239) {
		tmp = fma(b, (y + -2.0), (x + a));
	} else if (t <= 5.4e+110) {
		tmp = a + fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1e+165)
		tmp = t_1;
	elseif (t <= -7e+23)
		tmp = fma(a, Float64(-t), Float64(x + z));
	elseif (t <= -8.4e-22)
		tmp = fma(a, Float64(1.0 - t), Float64(y * Float64(-z)));
	elseif (t <= -5.5e-239)
		tmp = fma(b, Float64(y + -2.0), Float64(x + a));
	elseif (t <= 5.4e+110)
		tmp = Float64(a + fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+165], t$95$1, If[LessEqual[t, -7e+23], N[(a * (-t) + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.4e-22], N[(a * N[(1.0 - t), $MachinePrecision] + N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-239], N[(b * N[(y + -2.0), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+110], N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.99999999999999899e164 or 5.40000000000000019e110 < t

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   if -9.99999999999999899e164 < t < -7.0000000000000004e23

   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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 89.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 89.6%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 89.6%

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

   if -7.0000000000000004e23 < t < -8.40000000000000031e-22

   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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 91.5%

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

   if -8.40000000000000031e-22 < t < -5.49999999999999978e-239

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.5%

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

   if -5.49999999999999978e-239 < t < 5.40000000000000019e110

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 69.6%

      \[\leadsto a + \color{blue}{\mathsf{fma}\left(z, 1 - y, x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.35 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (fma z (- 1.0 y) x))) (t_2 (* t (- b a))))
   (if (<= t -1e+165)
     t_2
     (if (<= t -4.35e+18)
       (fma a (- t) (+ x z))
       (if (<= t -3.8e-23)
         t_1
         (if (<= t -5.5e-239)
           (fma b (+ y -2.0) (+ x a))
           (if (<= t 5.4e+110) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + fma(z, (1.0 - y), x);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -1e+165) {
		tmp = t_2;
	} else if (t <= -4.35e+18) {
		tmp = fma(a, -t, (x + z));
	} else if (t <= -3.8e-23) {
		tmp = t_1;
	} else if (t <= -5.5e-239) {
		tmp = fma(b, (y + -2.0), (x + a));
	} else if (t <= 5.4e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + fma(z, Float64(1.0 - y), x))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1e+165)
		tmp = t_2;
	elseif (t <= -4.35e+18)
		tmp = fma(a, Float64(-t), Float64(x + z));
	elseif (t <= -3.8e-23)
		tmp = t_1;
	elseif (t <= -5.5e-239)
		tmp = fma(b, Float64(y + -2.0), Float64(x + a));
	elseif (t <= 5.4e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+165], t$95$2, If[LessEqual[t, -4.35e+18], N[(a * (-t) + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-23], t$95$1, If[LessEqual[t, -5.5e-239], N[(b * N[(y + -2.0), $MachinePrecision] + N[(x + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+110], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.99999999999999899e164 or 5.40000000000000019e110 < t

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   if -9.99999999999999899e164 < t < -4.35e18

   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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 90.6%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 90.6%

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

   if -4.35e18 < t < -3.80000000000000011e-23 or -5.49999999999999978e-239 < t < 5.40000000000000019e110

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 92.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 71.3%

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

   if -3.80000000000000011e-23 < t < -5.49999999999999978e-239

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4.35 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-23}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-239}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x + a\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ t_2 := \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, t\_1\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+102}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, a + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x))
        (t_2 (fma b (+ y (+ t -2.0)) (fma a (- 1.0 t) x))))
   (if (<= t -4e+184)
     t_2
     (if (<= t -2.5e+18)
       (fma a (- 1.0 t) t_1)
       (if (<= t 2.5e+102) (fma b (+ y -2.0) (+ a t_1)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double t_2 = fma(b, (y + (t + -2.0)), fma(a, (1.0 - t), x));
	double tmp;
	if (t <= -4e+184) {
		tmp = t_2;
	} else if (t <= -2.5e+18) {
		tmp = fma(a, (1.0 - t), t_1);
	} else if (t <= 2.5e+102) {
		tmp = fma(b, (y + -2.0), (a + t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	t_2 = fma(b, Float64(y + Float64(t + -2.0)), fma(a, Float64(1.0 - t), x))
	tmp = 0.0
	if (t <= -4e+184)
		tmp = t_2;
	elseif (t <= -2.5e+18)
		tmp = fma(a, Float64(1.0 - t), t_1);
	elseif (t <= 2.5e+102)
		tmp = fma(b, Float64(y + -2.0), Float64(a + t_1));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+184], t$95$2, If[LessEqual[t, -2.5e+18], N[(a * N[(1.0 - t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 2.5e+102], N[(b * N[(y + -2.0), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000007e184 or 2.5e102 < t

   1. Initial program 86.4%

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

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

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. associate-+r- N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-rgt-neg-in N/A

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

      13. mul-1-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. metadata-eval N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 87.3

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

   5. Applied rewrites 87.3%

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

   if -4.00000000000000007e184 < t < -2.5e18

   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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 88.5%

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

   if -2.5e18 < t < 2.5e102

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 94.8%

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

Alternative 10: 54.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := x + \left(z + a\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.45 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (+ x (+ z a))) (t_3 (* t (- b a))))
   (if (<= t -3.45e+18)
     t_3
     (if (<= t -1.9e-70)
       t_1
       (if (<= t -9e-236)
         t_2
         (if (<= t 2.2e-196) t_1 (if (<= t 4.9e+64) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = x + (z + a);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -3.45e+18) {
		tmp = t_3;
	} else if (t <= -1.9e-70) {
		tmp = t_1;
	} else if (t <= -9e-236) {
		tmp = t_2;
	} else if (t <= 2.2e-196) {
		tmp = t_1;
	} else if (t <= 4.9e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (b - z)
    t_2 = x + (z + a)
    t_3 = t * (b - a)
    if (t <= (-3.45d+18)) then
        tmp = t_3
    else if (t <= (-1.9d-70)) then
        tmp = t_1
    else if (t <= (-9d-236)) then
        tmp = t_2
    else if (t <= 2.2d-196) then
        tmp = t_1
    else if (t <= 4.9d+64) then
        tmp = t_2
    else
        tmp = t_3
    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 = y * (b - z);
	double t_2 = x + (z + a);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -3.45e+18) {
		tmp = t_3;
	} else if (t <= -1.9e-70) {
		tmp = t_1;
	} else if (t <= -9e-236) {
		tmp = t_2;
	} else if (t <= 2.2e-196) {
		tmp = t_1;
	} else if (t <= 4.9e+64) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = x + (z + a)
	t_3 = t * (b - a)
	tmp = 0
	if t <= -3.45e+18:
		tmp = t_3
	elif t <= -1.9e-70:
		tmp = t_1
	elif t <= -9e-236:
		tmp = t_2
	elif t <= 2.2e-196:
		tmp = t_1
	elif t <= 4.9e+64:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(x + Float64(z + a))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.45e+18)
		tmp = t_3;
	elseif (t <= -1.9e-70)
		tmp = t_1;
	elseif (t <= -9e-236)
		tmp = t_2;
	elseif (t <= 2.2e-196)
		tmp = t_1;
	elseif (t <= 4.9e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = x + (z + a);
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.45e+18)
		tmp = t_3;
	elseif (t <= -1.9e-70)
		tmp = t_1;
	elseif (t <= -9e-236)
		tmp = t_2;
	elseif (t <= 2.2e-196)
		tmp = t_1;
	elseif (t <= 4.9e+64)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.45e+18], t$95$3, If[LessEqual[t, -1.9e-70], t$95$1, If[LessEqual[t, -9e-236], t$95$2, If[LessEqual[t, 2.2e-196], t$95$1, If[LessEqual[t, 4.9e+64], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.45e18 or 4.9000000000000003e64 < t

   1. Initial program 89.6%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 70.7

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

   5. Applied rewrites 70.7%

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

   if -3.45e18 < t < -1.8999999999999999e-70 or -8.99999999999999997e-236 < t < 2.20000000000000015e-196

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 61.1

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

   5. Applied rewrites 61.1%

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

   if -1.8999999999999999e-70 < t < -8.99999999999999997e-236 or 2.20000000000000015e-196 < t < 4.9000000000000003e64

   1. Initial program 97.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 55.4%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.45 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-236}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, x + z\right)\\ t_2 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+224}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) (+ x z))) (t_2 (* b (+ y (+ t -2.0)))))
   (if (<= b -6.5e+74)
     t_2
     (if (<= b -1.35e-25)
       t_1
       (if (<= b 1.32e-164)
         (+ a (fma z (- 1.0 y) x))
         (if (<= b 6.8e+224) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), (x + z));
	double t_2 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -6.5e+74) {
		tmp = t_2;
	} else if (b <= -1.35e-25) {
		tmp = t_1;
	} else if (b <= 1.32e-164) {
		tmp = a + fma(z, (1.0 - y), x);
	} else if (b <= 6.8e+224) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), Float64(x + z))
	t_2 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -6.5e+74)
		tmp = t_2;
	elseif (b <= -1.35e-25)
		tmp = t_1;
	elseif (b <= 1.32e-164)
		tmp = Float64(a + fma(z, Float64(1.0 - y), x));
	elseif (b <= 6.8e+224)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + N[(x + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.5e+74], t$95$2, If[LessEqual[b, -1.35e-25], t$95$1, If[LessEqual[b, 1.32e-164], N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+224], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.49999999999999962e74 or 6.8000000000000004e224 < b

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 80.1

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

   5. Applied rewrites 80.1%

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

   if -6.49999999999999962e74 < b < -1.35000000000000008e-25 or 1.3199999999999999e-164 < b < 6.8000000000000004e224

   1. Initial program 93.1%

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

   3. Taylor expanded in 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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 76.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.8%

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

   if -1.35000000000000008e-25 < b < 1.3199999999999999e-164

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 75.9%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x + z\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, -t, x + z\right)\\ t_2 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+199}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- t) (+ x z))) (t_2 (* b (+ y (+ t -2.0)))))
   (if (<= b -3.5e+71)
     t_2
     (if (<= b -1.35e-25)
       t_1
       (if (<= b 1.32e-164)
         (fma z (- 1.0 y) x)
         (if (<= b 2.1e+199) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, -t, (x + z));
	double t_2 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -3.5e+71) {
		tmp = t_2;
	} else if (b <= -1.35e-25) {
		tmp = t_1;
	} else if (b <= 1.32e-164) {
		tmp = fma(z, (1.0 - y), x);
	} else if (b <= 2.1e+199) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(-t), Float64(x + z))
	t_2 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -3.5e+71)
		tmp = t_2;
	elseif (b <= -1.35e-25)
		tmp = t_1;
	elseif (b <= 1.32e-164)
		tmp = fma(z, Float64(1.0 - y), x);
	elseif (b <= 2.1e+199)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * (-t) + N[(x + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+71], t$95$2, If[LessEqual[b, -1.35e-25], t$95$1, If[LessEqual[b, 1.32e-164], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[b, 2.1e+199], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4999999999999999e71 or 2.1e199 < b

   1. Initial program 89.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-+r- N/A

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

      4. lower-+.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval 78.4

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

   5. Applied rewrites 78.4%

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

   if -3.4999999999999999e71 < b < -1.35000000000000008e-25 or 1.3199999999999999e-164 < b < 2.1e199

   1. Initial program 92.8%

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

   3. Taylor expanded in 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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.7%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 58.5%

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

   if -1.35000000000000008e-25 < b < 1.3199999999999999e-164

   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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 94.2%

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

   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 64.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+199}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, t\_1\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, a + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- 1.0 y) x)))
   (if (<= t -2.5e+18)
     (fma a (- 1.0 t) t_1)
     (if (<= t 5.4e+110) (fma b (+ y -2.0) (+ a t_1)) (* t (- b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (1.0 - y), x);
	double tmp;
	if (t <= -2.5e+18) {
		tmp = fma(a, (1.0 - t), t_1);
	} else if (t <= 5.4e+110) {
		tmp = fma(b, (y + -2.0), (a + t_1));
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(1.0 - y), x)
	tmp = 0.0
	if (t <= -2.5e+18)
		tmp = fma(a, Float64(1.0 - t), t_1);
	elseif (t <= 5.4e+110)
		tmp = fma(b, Float64(y + -2.0), Float64(a + t_1));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.5e+18], N[(a * N[(1.0 - t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 5.4e+110], N[(b * N[(y + -2.0), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e18

   1. Initial program 91.4%

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

   3. Taylor expanded in 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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 74.8%

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

   if -2.5e18 < t < 5.40000000000000019e110

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. sub-neg N/A

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

      15. lower-+.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 94.2%

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

   if 5.40000000000000019e110 < t

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 89.1

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

   5. Applied rewrites 89.1%

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

Alternative 14: 66.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.35 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1e+165)
     t_1
     (if (<= t -4.35e+18)
       (fma a (- t) (+ x z))
       (if (<= t 5.4e+110) (+ a (fma z (- 1.0 y) x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -1e+165) {
		tmp = t_1;
	} else if (t <= -4.35e+18) {
		tmp = fma(a, -t, (x + z));
	} else if (t <= 5.4e+110) {
		tmp = a + fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -1e+165)
		tmp = t_1;
	elseif (t <= -4.35e+18)
		tmp = fma(a, Float64(-t), Float64(x + z));
	elseif (t <= 5.4e+110)
		tmp = Float64(a + fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+165], t$95$1, If[LessEqual[t, -4.35e+18], N[(a * (-t) + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+110], N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999899e164 or 5.40000000000000019e110 < t

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   if -9.99999999999999899e164 < t < -4.35e18

   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. distribute-rgt-neg-in N/A

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. sub-neg N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. distribute-lft-in N/A

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

      12. metadata-eval N/A

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

      13. neg-mul-1 N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. sub-neg N/A

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

      17. +-commutative N/A

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

      18. distribute-rgt-neg-in N/A

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

      19. mul-1-neg N/A

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

      20. lower-fma.f64 N/A

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 90.6%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 90.6%

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

   if -4.35e18 < t < 5.40000000000000019e110

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{\left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)} + x\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\color{blue}{a} + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

      12. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x - z \cdot \left(y - 1\right)\right)}\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(x - z \cdot \left(y - 1\right)\right)}\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right)\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 94.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + -2, a + \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

   6. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{\left(x + z \cdot \left(1 - y\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.0%

      \[\leadsto a + \color{blue}{\mathsf{fma}\left(z, 1 - y, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4.35 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x + z\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 78.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -7e+75)
     t_1
     (if (<= b 6.8e+224) (fma a (- 1.0 t) (fma z (- 1.0 y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -7e+75) {
		tmp = t_1;
	} else if (b <= 6.8e+224) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -7e+75)
		tmp = t_1;
	elseif (b <= 6.8e+224)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+75], t$95$1, If[LessEqual[b, 6.8e+224], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.9999999999999997e75 or 6.8000000000000004e224 < b

   1. Initial program 89.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right)} \]

      2. +-commutative N/A

         \[\leadsto b \cdot \left(\color{blue}{\left(y + t\right)} - 2\right) \]

      3. associate-+r- N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto b \cdot \color{blue}{\left(y + \left(t - 2\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      6. lower-+.f64 N/A

         \[\leadsto b \cdot \left(y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}\right) \]

      7. metadata-eval 80.1

         \[\leadsto b \cdot \left(y + \left(t + \color{blue}{-2}\right)\right) \]

   5. Applied rewrites 80.1%

      \[\leadsto \color{blue}{b \cdot \left(y + \left(t + -2\right)\right)} \]

   if -6.9999999999999997e75 < b < 6.8000000000000004e224

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 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. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x - z \cdot \left(y - 1\right)\right)} \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x - z \cdot \left(y - 1\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(-1 + t\right)}, x - z \cdot \left(y - 1\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot -1 + -1 \cdot t}, x - z \cdot \left(y - 1\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1} + -1 \cdot t, x - z \cdot \left(y - 1\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 84.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 56.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) x)))
   (if (<= a -3.5e+114) t_1 (if (<= a 1.2e+68) (fma z (- 1.0 y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(a, (1.0 - t), x);
	double tmp;
	if (a <= -3.5e+114) {
		tmp = t_1;
	} else if (a <= 1.2e+68) {
		tmp = fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(a, Float64(1.0 - t), x)
	tmp = 0.0
	if (a <= -3.5e+114)
		tmp = t_1;
	elseif (a <= 1.2e+68)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.5e+114], t$95$1, If[LessEqual[a, 1.2e+68], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5000000000000001e114 or 1.20000000000000004e68 < a

   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 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. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(\left(t + y\right) - 2\right) + x\right)} - a \cdot \left(t - 1\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(\left(t + y\right) - 2\right) + \left(x - a \cdot \left(t - 1\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, \left(t + y\right) - 2, x - a \cdot \left(t - 1\right)\right)} \]

      4. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{\left(y + t\right)} - 2, x - a \cdot \left(t - 1\right)\right) \]

      5. associate-+r- N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(t - 2\right)}, x - a \cdot \left(t - 1\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      8. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{\left(t + \left(\mathsf{neg}\left(2\right)\right)\right)}, x - a \cdot \left(t - 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, y + \left(t + \color{blue}{-2}\right), x - a \cdot \left(t - 1\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{x + \left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right)}\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{\left(\mathsf{neg}\left(a \cdot \left(t - 1\right)\right)\right) + x}\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + x\right) \]

      13. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + x\right) \]

      14. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x\right)}\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x\right)\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(-1 + t\right)}, x\right)\right) \]

      18. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{-1 \cdot -1 + -1 \cdot t}, x\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1} + -1 \cdot t, x\right)\right) \]

      20. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x\right)\right) \]

      21. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

      22. lower--.f64 86.6

          \[\leadsto \mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right)\right) \]

   5. Applied rewrites 86.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + \left(t + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)} \]

   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 75.0%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x\right) \]

   if -3.5000000000000001e114 < a < 1.20000000000000004e68

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in 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. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{a \cdot \left(\mathsf{neg}\left(\left(t - 1\right)\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t - 1\right)\right)} + \left(x - z \cdot \left(y - 1\right)\right) \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t - 1\right), x - z \cdot \left(y - 1\right)\right)} \]

      8. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(a, -1 \cdot \left(t + \color{blue}{-1}\right), x - z \cdot \left(y - 1\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, -1 \cdot \color{blue}{\left(-1 + t\right)}, x - z \cdot \left(y - 1\right)\right) \]

      11. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{-1 \cdot -1 + -1 \cdot t}, x - z \cdot \left(y - 1\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1} + -1 \cdot t, x - z \cdot \left(y - 1\right)\right) \]

      13. neg-mul-1 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}, x - z \cdot \left(y - 1\right)\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, x - z \cdot \left(y - 1\right)\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 59.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

   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 54.1%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{1 - y}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 54.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -6.8e+124) t_1 (if (<= t 4.9e+64) (+ x (+ z a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6.8e+124) {
		tmp = t_1;
	} else if (t <= 4.9e+64) {
		tmp = x + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-6.8d+124)) then
        tmp = t_1
    else if (t <= 4.9d+64) then
        tmp = x + (z + a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -6.8e+124) {
		tmp = t_1;
	} else if (t <= 4.9e+64) {
		tmp = x + (z + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -6.8e+124:
		tmp = t_1
	elif t <= 4.9e+64:
		tmp = x + (z + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -6.8e+124)
		tmp = t_1;
	elseif (t <= 4.9e+64)
		tmp = Float64(x + Float64(z + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -6.8e+124)
		tmp = t_1;
	elseif (t <= 4.9e+64)
		tmp = x + (z + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+124], t$95$1, If[LessEqual[t, 4.9e+64], N[(x + N[(z + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8e124 or 4.9000000000000003e64 < t

   1. Initial program 88.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

      2. lower--.f64 75.2

         \[\leadsto t \cdot \color{blue}{\left(b - a\right)} \]

   5. Applied rewrites 75.2%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -6.8e124 < t < 4.9000000000000003e64

   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 t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, y - 2, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{-2}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{x + \left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) + x}\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{\left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)} + x\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\color{blue}{a} + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

      12. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x - z \cdot \left(y - 1\right)\right)}\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(x - z \cdot \left(y - 1\right)\right)}\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right)\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 94.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + -2, a + \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto a + \color{blue}{\left(x + \left(z + -2 \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.5%

      \[\leadsto x + \color{blue}{\left(a + \mathsf{fma}\left(b, -2, z\right)\right)} \]

   9. Taylor expanded in b around 0

      \[\leadsto x + \left(a + z\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 47.0%

       \[\leadsto x + \left(a + z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+124}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+64}:\\ \;\;\;\;x + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+167}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+65}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.6e+167) (* t b) (if (<= t 1.6e+65) (+ z a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+167) {
		tmp = t * b;
	} else if (t <= 1.6e+65) {
		tmp = z + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.6d+167)) then
        tmp = t * b
    else if (t <= 1.6d+65) then
        tmp = z + a
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.6e+167) {
		tmp = t * b;
	} else if (t <= 1.6e+65) {
		tmp = z + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.6e+167:
		tmp = t * b
	elif t <= 1.6e+65:
		tmp = z + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.6e+167)
		tmp = Float64(t * b);
	elseif (t <= 1.6e+65)
		tmp = Float64(z + a);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.6e+167)
		tmp = t * b;
	elseif (t <= 1.6e+65)
		tmp = z + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.6e+167], N[(t * b), $MachinePrecision], If[LessEqual[t, 1.6e+65], N[(z + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.59999999999999987e167 or 1.60000000000000003e65 < t

   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 t around inf

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

      2. lower--.f64 76.2

         \[\leadsto t \cdot \color{blue}{\left(b - a\right)} \]

   5. Applied rewrites 76.2%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   6. Taylor expanded in b around inf

      \[\leadsto b \cdot \color{blue}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.6%

      \[\leadsto b \cdot \color{blue}{t} \]

   if -7.59999999999999987e167 < t < 1.60000000000000003e65

   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 t around 0

      \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

      2. associate--l+ N/A

         \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, y - 2, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

      4. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{-2}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{x + \left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) + x}\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{\left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)} + x\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\color{blue}{a} + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

      12. associate-+l+ N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      14. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x - z \cdot \left(y - 1\right)\right)}\right) \]

      15. lower-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(x - z \cdot \left(y - 1\right)\right)}\right) \]

      16. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

      17. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

      18. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right)\right) \]

      19. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right)\right) \]

      20. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

   5. Applied rewrites 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + -2, a + \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto a + \color{blue}{\left(x + \left(z + -2 \cdot b\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 55.2%

      \[\leadsto x + \color{blue}{\left(a + \mathsf{fma}\left(b, -2, z\right)\right)} \]

   9. Taylor expanded in x around 0

      \[\leadsto a + \left(z + \color{blue}{-2 \cdot b}\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 41.7%

       \[\leadsto \mathsf{fma}\left(b, -2, a + z\right) \]

   12. Taylor expanded in b around 0

       \[\leadsto a + z \]
   13. Step-by-step derivation

   14. Applied rewrites 32.6%

       \[\leadsto a + z \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+167}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+65}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 20.4% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ z + a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ z a))

C

double code(double x, double y, double z, double t, double a, double b) {
	return z + a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = z + a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return z + a;
}

Python

def code(x, y, z, t, a, b):
	return z + a

Julia

function code(x, y, z, t, a, b)
	return Float64(z + a)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = z + a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(z + a), $MachinePrecision]

Derivation

1. Initial program 94.5%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\left(x + b \cdot \left(y - 2\right)\right) - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\left(b \cdot \left(y - 2\right) + x\right)} - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right) \]

   2. associate--l+ N/A

      \[\leadsto \color{blue}{b \cdot \left(y - 2\right) + \left(x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, y - 2, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)} \]

   4. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

   5. lower-+.f64 N/A

      \[\leadsto \mathsf{fma}\left(b, \color{blue}{y + \left(\mathsf{neg}\left(2\right)\right)}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(b, y + \color{blue}{-2}, x - \left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right) \]

   7. sub-neg N/A

      \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{x + \left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

   8. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{\left(\mathsf{neg}\left(\left(-1 \cdot a + z \cdot \left(y - 1\right)\right)\right)\right) + x}\right) \]

   9. distribute-neg-in N/A

      \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{\left(\left(\mathsf{neg}\left(-1 \cdot a\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)} + x\right) \]

   10. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(a\right)\right)}\right)\right) + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

   11. remove-double-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, \left(\color{blue}{a} + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right) + x\right) \]

   12. associate-+l+ N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

   13. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

   14. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x - z \cdot \left(y - 1\right)\right)}\right) \]

   15. lower-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, \color{blue}{a + \left(x - z \cdot \left(y - 1\right)\right)}\right) \]

   16. sub-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(x + \left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right)\right)}\right) \]

   17. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\left(\left(\mathsf{neg}\left(z \cdot \left(y - 1\right)\right)\right) + x\right)}\right) \]

   18. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(\color{blue}{z \cdot \left(\mathsf{neg}\left(\left(y - 1\right)\right)\right)} + x\right)\right) \]

   19. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \left(z \cdot \color{blue}{\left(-1 \cdot \left(y - 1\right)\right)} + x\right)\right) \]

   20. lower-fma.f64 N/A

       \[\leadsto \mathsf{fma}\left(b, y + -2, a + \color{blue}{\mathsf{fma}\left(z, -1 \cdot \left(y - 1\right), x\right)}\right) \]

5. Applied rewrites 70.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(b, y + -2, a + \mathsf{fma}\left(z, 1 - y, x\right)\right)} \]

6. Taylor expanded in y around 0

   \[\leadsto a + \color{blue}{\left(x + \left(z + -2 \cdot b\right)\right)} \]
7. Step-by-step derivation

8. Applied rewrites 40.8%

   \[\leadsto x + \color{blue}{\left(a + \mathsf{fma}\left(b, -2, z\right)\right)} \]

9. Taylor expanded in x around 0

   \[\leadsto a + \left(z + \color{blue}{-2 \cdot b}\right) \]
10. Step-by-step derivation

11. Applied rewrites 28.6%

    \[\leadsto \mathsf{fma}\left(b, -2, a + z\right) \]

12. Taylor expanded in b around 0

    \[\leadsto a + z \]
13. Step-by-step derivation

14. Applied rewrites 22.7%

    \[\leadsto a + z \]

15. Final simplification 22.7%

    \[\leadsto z + a \]
16. Add Preprocessing

Reproduce

herbie shell --seed 2024222 
(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)))