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

Percentage Accurate: 95.3% → 98.0%

Time: 12.7s

Alternatives: 17

Speedup: 0.5×

• 36.1% 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: 98.0% 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 65.5

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

   5. Applied rewrites 65.5%

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

4. Final simplification 98.1%

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

Alternative 2: 34.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+302}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

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 -5e+302) (* t b) (if (<= t_1 2e+307) (+ x 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 <= -5e+302) {
		tmp = t * b;
	} else if (t_1 <= 2e+307) {
		tmp = x + a;
	} else {
		tmp = y * 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) :: t_1
    real(8) :: tmp
    t_1 = ((x + (z * (1.0d0 - y))) + (a * (1.0d0 - t))) + (((y + t) - 2.0d0) * b)
    if (t_1 <= (-5d+302)) then
        tmp = t * b
    else if (t_1 <= 2d+307) then
        tmp = x + a
    else
        tmp = y * 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 t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (((y + t) - 2.0) * b);
	double tmp;
	if (t_1 <= -5e+302) {
		tmp = t * b;
	} else if (t_1 <= 2e+307) {
		tmp = x + 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 <= -5e+302:
		tmp = t * b
	elif t_1 <= 2e+307:
		tmp = x + 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 <= -5e+302)
		tmp = Float64(t * b);
	elseif (t_1 <= 2e+307)
		tmp = Float64(x + 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 <= -5e+302)
		tmp = t * b;
	elseif (t_1 <= 2e+307)
		tmp = x + 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, -5e+302], N[(t * b), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(x + a), $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)) < -5e302

   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 52.7

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 21.6%

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

   if -5e302 < (+.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)) < 1.99999999999999997e307

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 52.9%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 42.6%

       \[\leadsto a + x \]

   if 1.99999999999999997e307 < (+.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 75.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 71.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 29.2%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq -5 \cdot 10^{+302}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq 2 \cdot 10^{+307}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, b - a, a + \mathsf{fma}\left(b, y + -2, x\right)\right)\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma t (- b a) (+ a (fma b (+ y -2.0) x)))))
   (if (<= b -2.3e+127)
     t_1
     (if (<= b 9.2e-63) (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 = fma(t, (b - a), (a + fma(b, (y + -2.0), x)));
	double tmp;
	if (b <= -2.3e+127) {
		tmp = t_1;
	} else if (b <= 9.2e-63) {
		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 = fma(t, Float64(b - a), Float64(a + fma(b, Float64(y + -2.0), x)))
	tmp = 0.0
	if (b <= -2.3e+127)
		tmp = t_1;
	elseif (b <= 9.2e-63)
		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[(t * N[(b - a), $MachinePrecision] + N[(a + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+127], t$95$1, If[LessEqual[b, 9.2e-63], 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 < -2.3000000000000002e127 or 9.2e-63 < b

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 90.5%

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

   if -2.3000000000000002e127 < b < 9.2e-63

   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 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. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative 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 92.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+127}:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, a + \mathsf{fma}\left(b, y + -2, x\right)\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-63}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, b - a, a + \mathsf{fma}\left(b, y + -2, x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, t + \left(y + -2\right), x\right)\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (+ t (+ y -2.0)) x)))
   (if (<= b -6.6e+148)
     t_1
     (if (<= b 2.65e+117) (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 = fma(b, (t + (y + -2.0)), x);
	double tmp;
	if (b <= -6.6e+148) {
		tmp = t_1;
	} else if (b <= 2.65e+117) {
		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 = fma(b, Float64(t + Float64(y + -2.0)), x)
	tmp = 0.0
	if (b <= -6.6e+148)
		tmp = t_1;
	elseif (b <= 2.65e+117)
		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[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[b, -6.6e+148], t$95$1, If[LessEqual[b, 2.65e+117], 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 < -6.60000000000000021e148 or 2.6500000000000001e117 < b

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 92.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 88.6%

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

   if -6.60000000000000021e148 < b < 2.6500000000000001e117

   1. Initial program 97.2%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative 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 87.1%

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

Alternative 5: 56.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-182}:\\ \;\;\;\;\mathsf{fma}\left(b, t + -2, x\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.8e+131)
     t_1
     (if (<= y -1.05e-182)
       (fma b (+ t -2.0) x)
       (if (<= y 3.1e+31) (fma a (- 1.0 t) x) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.8e+131) {
		tmp = t_1;
	} else if (y <= -1.05e-182) {
		tmp = fma(b, (t + -2.0), x);
	} else if (y <= 3.1e+31) {
		tmp = fma(a, (1.0 - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.8e+131)
		tmp = t_1;
	elseif (y <= -1.05e-182)
		tmp = fma(b, Float64(t + -2.0), x);
	elseif (y <= 3.1e+31)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+131], t$95$1, If[LessEqual[y, -1.05e-182], N[(b * N[(t + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 3.1e+31], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000016e131 or 3.1000000000000002e31 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in 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 72.9

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

   5. Applied rewrites 72.9%

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

   if -1.80000000000000016e131 < y < -1.05e-182

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 64.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 62.8%

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

   if -1.05e-182 < y < 3.1000000000000002e31

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 63.3%

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

Alternative 6: 72.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5000000:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a)))))
   (if (<= t -4.8e-7)
     t_1
     (if (<= t 5000000.0) (+ a (fma b (+ y -2.0) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double tmp;
	if (t <= -4.8e-7) {
		tmp = t_1;
	} else if (t <= 5000000.0) {
		tmp = a + fma(b, (y + -2.0), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	tmp = 0.0
	if (t <= -4.8e-7)
		tmp = t_1;
	elseif (t <= 5000000.0)
		tmp = Float64(a + fma(b, Float64(y + -2.0), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e-7], t$95$1, If[LessEqual[t, 5000000.0], N[(a + N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999957e-7 or 5e6 < t

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. sub-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 76.1

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.6%

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

   if -4.79999999999999957e-7 < t < 5e6

   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 z around 0

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.1%

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

Alternative 7: 60.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -6.8e+143) t_1 (if (<= y 3e+31) (+ x (* t (- b a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -6.8e+143) {
		tmp = t_1;
	} else if (y <= 3e+31) {
		tmp = x + (t * (b - 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 = y * (b - z)
    if (y <= (-6.8d+143)) then
        tmp = t_1
    else if (y <= 3d+31) then
        tmp = x + (t * (b - 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 = y * (b - z);
	double tmp;
	if (y <= -6.8e+143) {
		tmp = t_1;
	} else if (y <= 3e+31) {
		tmp = x + (t * (b - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -6.8e+143:
		tmp = t_1
	elif y <= 3e+31:
		tmp = x + (t * (b - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6.8e+143)
		tmp = t_1;
	elseif (y <= 3e+31)
		tmp = Float64(x + Float64(t * Float64(b - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -6.8e+143)
		tmp = t_1;
	elseif (y <= 3e+31)
		tmp = x + (t * (b - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+143], t$95$1, If[LessEqual[y, 3e+31], N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.79999999999999964e143 or 2.99999999999999989e31 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -6.79999999999999964e143 < y < 2.99999999999999989e31

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0

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

      1. associate--l+ N/A

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

      2. lower-+.f64 N/A

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

      3. sub-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

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

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

      11. mul-1-neg N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower-fma.f64 N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. distribute-lft-in N/A

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

      18. metadata-eval N/A

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

      19. +-commutative N/A

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

      20. neg-mul-1 N/A

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

      21. sub-neg N/A

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

      22. lower--.f64 93.7

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

   5. Applied rewrites 93.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 62.8%

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

Alternative 8: 57.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.8e+160) t_1 (if (<= y 3.1e+31) (fma a (- 1.0 t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.8e+160) {
		tmp = t_1;
	} else if (y <= 3.1e+31) {
		tmp = fma(a, (1.0 - t), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.8e+160)
		tmp = t_1;
	elseif (y <= 3.1e+31)
		tmp = fma(a, Float64(1.0 - t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+160], t$95$1, If[LessEqual[y, 3.1e+31], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000011e160 or 3.1000000000000002e31 < y

   1. Initial program 90.1%

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

   3. Taylor expanded in 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 76.4

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

   5. Applied rewrites 76.4%

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

   if -1.80000000000000011e160 < y < 3.1000000000000002e31

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 58.2%

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

Alternative 9: 50.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -1.7e+143) t_1 (if (<= y 1.46e+31) (fma a (- t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -1.7e+143) {
		tmp = t_1;
	} else if (y <= 1.46e+31) {
		tmp = fma(a, -t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.7e+143)
		tmp = t_1;
	elseif (y <= 1.46e+31)
		tmp = fma(a, Float64(-t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+143], t$95$1, If[LessEqual[y, 1.46e+31], N[(a * (-t) + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999991e143 or 1.46e31 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if -1.69999999999999991e143 < y < 1.46e31

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 58.5%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 48.2%

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

Alternative 10: 50.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -7.8e+34) t_1 (if (<= t 4.8e+20) (+ x 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 <= -7.8e+34) {
		tmp = t_1;
	} else if (t <= 4.8e+20) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-7.8d+34)) then
        tmp = t_1
    else if (t <= 4.8d+20) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -7.8e+34) {
		tmp = t_1;
	} else if (t <= 4.8e+20) {
		tmp = x + 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 <= -7.8e+34:
		tmp = t_1
	elif t <= 4.8e+20:
		tmp = x + 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 <= -7.8e+34)
		tmp = t_1;
	elseif (t <= 4.8e+20)
		tmp = Float64(x + 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 <= -7.8e+34)
		tmp = t_1;
	elseif (t <= 4.8e+20)
		tmp = x + 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, -7.8e+34], t$95$1, If[LessEqual[t, 4.8e+20], N[(x + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.80000000000000038e34 or 4.8e20 < t

   1. Initial program 90.4%

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

   3. Taylor expanded in 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 66.4

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

   5. Applied rewrites 66.4%

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

   if -7.80000000000000038e34 < t < 4.8e20

   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 z around 0

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 42.1%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 40.5%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+20}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.2e+112)
   (* b (+ t -2.0))
   (if (<= b 1.1e+117) (fma a (- t) x) (* b (+ y -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e+112) {
		tmp = b * (t + -2.0);
	} else if (b <= 1.1e+117) {
		tmp = fma(a, -t, x);
	} else {
		tmp = b * (y + -2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.2e+112)
		tmp = Float64(b * Float64(t + -2.0));
	elseif (b <= 1.1e+117)
		tmp = fma(a, Float64(-t), x);
	else
		tmp = Float64(b * Float64(y + -2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.2e+112], N[(b * N[(t + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e+117], N[(a * (-t) + x), $MachinePrecision], N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.19999999999999965e112

   1. Initial program 97.8%

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

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

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

      3. lower-+.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval 75.1

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.0%

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

   if -6.19999999999999965e112 < b < 1.10000000000000007e117

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 59.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 49.7%

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

   if 1.10000000000000007e117 < b

   1. Initial program 77.1%

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

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

      3. lower-+.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.3%

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

Alternative 12: 43.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + -2\right)\\ \mathbf{if}\;b \leq -4 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+117}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y -2.0))))
   (if (<= b -4e+182) t_1 (if (<= b 1.1e+117) (fma a (- t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y + -2.0);
	double tmp;
	if (b <= -4e+182) {
		tmp = t_1;
	} else if (b <= 1.1e+117) {
		tmp = fma(a, -t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y + -2.0))
	tmp = 0.0
	if (b <= -4e+182)
		tmp = t_1;
	elseif (b <= 1.1e+117)
		tmp = fma(a, Float64(-t), 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 + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4e+182], t$95$1, If[LessEqual[b, 1.1e+117], N[(a * (-t) + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.0000000000000003e182 or 1.10000000000000007e117 < b

   1. Initial program 87.3%

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

   3. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-+.f64 N/A

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

      4. sub-neg N/A

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

      5. lower-+.f64 N/A

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

      6. metadata-eval 77.5

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

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 52.9%

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

   if -4.0000000000000003e182 < b < 1.10000000000000007e117

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 69.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 57.7%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 48.7%

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

Alternative 13: 38.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= z -9.2e+128) t_1 (if (<= z 1.32e+185) (fma a (- t) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (z <= -9.2e+128) {
		tmp = t_1;
	} else if (z <= 1.32e+185) {
		tmp = fma(a, -t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (z <= -9.2e+128)
		tmp = t_1;
	elseif (z <= 1.32e+185)
		tmp = fma(a, Float64(-t), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[z, -9.2e+128], t$95$1, If[LessEqual[z, 1.32e+185], N[(a * (-t) + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999992e128 or 1.3199999999999999e185 < z

   1. Initial program 85.2%

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

   3. Taylor expanded in b around 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. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative 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 80.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.4%

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

   if -9.19999999999999992e128 < z < 1.3199999999999999e185

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 88.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 46.7%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(a, -t, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{+24}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -1.8e+33) t_1 (if (<= t 1e+24) (+ x a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.8e+33) {
		tmp = t_1;
	} else if (t <= 1e+24) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-1.8d+33)) then
        tmp = t_1
    else if (t <= 1d+24) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.8e+33) {
		tmp = t_1;
	} else if (t <= 1e+24) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -1.8e+33:
		tmp = t_1
	elif t <= 1e+24:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -1.8e+33)
		tmp = t_1;
	elseif (t <= 1e+24)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -1.8e+33)
		tmp = t_1;
	elseif (t <= 1e+24)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -1.8e+33], t$95$1, If[LessEqual[t, 1e+24], N[(x + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8000000000000001e33 or 9.9999999999999998e23 < t

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 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 65.8

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

   5. Applied rewrites 65.8%

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

   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 43.3%

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

   if -1.8000000000000001e33 < t < 9.9999999999999998e23

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 42.4%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 40.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 10^{+24}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 75000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- y))))
   (if (<= y -1.8e+131) t_1 (if (<= y 75000.0) (+ x a) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -1.8e+131) {
		tmp = t_1;
	} else if (y <= 75000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -y
    if (y <= (-1.8d+131)) then
        tmp = t_1
    else if (y <= 75000.0d0) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * -y;
	double tmp;
	if (y <= -1.8e+131) {
		tmp = t_1;
	} else if (y <= 75000.0) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * -y
	tmp = 0
	if y <= -1.8e+131:
		tmp = t_1
	elif y <= 75000.0:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -1.8e+131)
		tmp = t_1;
	elseif (y <= 75000.0)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * -y;
	tmp = 0.0;
	if (y <= -1.8e+131)
		tmp = t_1;
	elseif (y <= 75000.0)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.8e+131], t$95$1, If[LessEqual[y, 75000.0], N[(x + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000016e131 or 75000 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in 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. distribute-lft-in N/A

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

      11. metadata-eval N/A

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

      12. +-commutative 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 69.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.7%

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

   if -1.80000000000000016e131 < y < 75000

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 58.0%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 37.3%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 75000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+154}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+23}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -9.2e+154) (* t b) (if (<= t 4.3e+23) (+ x a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -9.2e+154) {
		tmp = t * b;
	} else if (t <= 4.3e+23) {
		tmp = x + 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 <= (-9.2d+154)) then
        tmp = t * b
    else if (t <= 4.3d+23) then
        tmp = x + 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 <= -9.2e+154) {
		tmp = t * b;
	} else if (t <= 4.3e+23) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -9.2e+154:
		tmp = t * b
	elif t <= 4.3e+23:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -9.2e+154)
		tmp = Float64(t * b);
	elseif (t <= 4.3e+23)
		tmp = Float64(x + 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 <= -9.2e+154)
		tmp = t * b;
	elseif (t <= 4.3e+23)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -9.2e+154], N[(t * b), $MachinePrecision], If[LessEqual[t, 4.3e+23], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.1999999999999999e154 or 4.2999999999999999e23 < 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 68.9

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

   5. Applied rewrites 68.9%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 33.5%

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

   if -9.1999999999999999e154 < t < 4.2999999999999999e23

   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 z around 0

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

   5. Applied rewrites 73.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 45.2%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 38.0%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+154}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+23}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.2% accurate, 9.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + 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 = x + a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + 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 z around 0

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

5. Applied rewrites 76.0%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 47.0%

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

9. Taylor expanded in t around 0

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

11. Applied rewrites 27.9%

    \[\leadsto a + x \]

12. Final simplification 27.9%

    \[\leadsto x + a \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024220 
(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)))