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

Percentage Accurate: 95.3% → 97.9%

Time: 13.4s

Alternatives: 12

Speedup: 0.5×

• 35.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% 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: 97.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)) (t_2 (+ x (* z (- 1.0 y)))))
   (if (<= (+ (+ t_2 (* a (- 1.0 t))) t_1) INFINITY)
     (+ t_1 (- t_2 (fma t a (- a))))
     (* t (- b a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (((t_2 + (a * (1.0 - t))) + t_1) <= ((double) INFINITY)) {
		tmp = t_1 + (t_2 - fma(t, a, -a));
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (Float64(Float64(t_2 + Float64(a * Float64(1.0 - t))) + t_1) <= Inf)
		tmp = Float64(t_1 + Float64(t_2 - fma(t, a, Float64(-a))));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(t$95$1 + N[(t$95$2 - N[(t * a + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 100.0

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

   4. Applied rewrites 100.0%

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

   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 66.7

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

   5. Applied rewrites 66.7%

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

4. Final simplification 99.2%

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

Alternative 2: 97.9% 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 66.7

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

   5. Applied rewrites 66.7%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
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 3: 87.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + -2\right), x\right)\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-67}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma a (- 1.0 t) (fma b (+ y (+ t -2.0)) x))))
   (if (<= b -3.8e+40)
     t_1
     (if (<= b 5.1e-67) (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(a, (1.0 - t), fma(b, (y + (t + -2.0)), x));
	double tmp;
	if (b <= -3.8e+40) {
		tmp = t_1;
	} else if (b <= 5.1e-67) {
		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(a, Float64(1.0 - t), fma(b, Float64(y + Float64(t + -2.0)), x))
	tmp = 0.0
	if (b <= -3.8e+40)
		tmp = t_1;
	elseif (b <= 5.1e-67)
		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[(a * N[(1.0 - t), $MachinePrecision] + N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e+40], t$95$1, If[LessEqual[b, 5.1e-67], 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 < -3.80000000000000004e40 or 5.09999999999999982e-67 < b

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 90.2

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

   5. Applied rewrites 90.2%

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

   if -3.80000000000000004e40 < b < 5.09999999999999982e-67

   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. 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 94.5%

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

Alternative 4: 83.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, y + \left(t + -2\right), x\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (+ y (+ t -2.0)) x)))
   (if (<= b -8.5e+121)
     t_1
     (if (<= b 7e+72) (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, (y + (t + -2.0)), x);
	double tmp;
	if (b <= -8.5e+121) {
		tmp = t_1;
	} else if (b <= 7e+72) {
		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(y + Float64(t + -2.0)), x)
	tmp = 0.0
	if (b <= -8.5e+121)
		tmp = t_1;
	elseif (b <= 7e+72)
		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] + x), $MachinePrecision]}, If[LessEqual[b, -8.5e+121], t$95$1, If[LessEqual[b, 7e+72], 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 < -8.5e121 or 7.0000000000000002e72 < b

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 96.2

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

   5. Applied rewrites 96.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 93.2%

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

   if -8.5e121 < b < 7.0000000000000002e72

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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 88.1%

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

Alternative 5: 43.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10000000000000:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -1.1e+76)
     t_1
     (if (<= t 10000000000000.0)
       (+ a (+ x z))
       (if (<= t 6.5e+144) t_1 (* t b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -1.1e+76) {
		tmp = t_1;
	} else if (t <= 10000000000000.0) {
		tmp = a + (x + z);
	} else if (t <= 6.5e+144) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * -a
    if (t <= (-1.1d+76)) then
        tmp = t_1
    else if (t <= 10000000000000.0d0) then
        tmp = a + (x + z)
    else if (t <= 6.5d+144) then
        tmp = t_1
    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 t_1 = t * -a;
	double tmp;
	if (t <= -1.1e+76) {
		tmp = t_1;
	} else if (t <= 10000000000000.0) {
		tmp = a + (x + z);
	} else if (t <= 6.5e+144) {
		tmp = t_1;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -1.1e+76:
		tmp = t_1
	elif t <= 10000000000000.0:
		tmp = a + (x + z)
	elif t <= 6.5e+144:
		tmp = t_1
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -1.1e+76)
		tmp = t_1;
	elseif (t <= 10000000000000.0)
		tmp = Float64(a + Float64(x + z));
	elseif (t <= 6.5e+144)
		tmp = t_1;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -1.1e+76)
		tmp = t_1;
	elseif (t <= 10000000000000.0)
		tmp = a + (x + z);
	elseif (t <= 6.5e+144)
		tmp = t_1;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -1.1e+76], t$95$1, If[LessEqual[t, 10000000000000.0], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+144], t$95$1, N[(t * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1e76 or 1e13 < t < 6.50000000000000007e144

   1. Initial program 93.2%

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

   3. Taylor expanded in t around 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 74.0

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

   5. Applied rewrites 74.0%

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

   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 53.4%

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

   if -1.1e76 < t < 1e13

   1. Initial program 99.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 77.0%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 74.2%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 54.8%

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

   if 6.50000000000000007e144 < t

   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 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 63.1%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 10000000000000:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+14}:\\ \;\;\;\;a + \mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.5e+124)
     t_1
     (if (<= t 2.2e+14) (+ 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 <= -1.5e+124) {
		tmp = t_1;
	} else if (t <= 2.2e+14) {
		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 <= -1.5e+124)
		tmp = t_1;
	elseif (t <= 2.2e+14)
		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, -1.5e+124], t$95$1, If[LessEqual[t, 2.2e+14], N[(a + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e124 or 2.2e14 < t

   1. Initial program 95.0%

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

   3. Taylor expanded in 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 79.7

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

   5. Applied rewrites 79.7%

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

   if -1.5e124 < t < 2.2e14

   1. Initial program 99.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 77.0%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 73.1%

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

Alternative 7: 66.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4400000000000:\\ \;\;\;\;a + \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.9e+76)
     t_1
     (if (<= t 4400000000000.0) (+ 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 = t * (b - a);
	double tmp;
	if (t <= -3.9e+76) {
		tmp = t_1;
	} else if (t <= 4400000000000.0) {
		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(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.9e+76)
		tmp = t_1;
	elseif (t <= 4400000000000.0)
		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[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+76], t$95$1, If[LessEqual[t, 4400000000000.0], 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 < -3.89999999999999989e76 or 4.4e12 < t

   1. Initial program 95.3%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if -3.89999999999999989e76 < t < 4.4e12

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 67.3%

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

Alternative 8: 61.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(y + \left(t + -2\right)\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (+ y (+ t -2.0)))))
   (if (<= b -1.45e+97) t_1 (if (<= b 2.55e+66) (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 = b * (y + (t + -2.0));
	double tmp;
	if (b <= -1.45e+97) {
		tmp = t_1;
	} else if (b <= 2.55e+66) {
		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(b * Float64(y + Float64(t + -2.0)))
	tmp = 0.0
	if (b <= -1.45e+97)
		tmp = t_1;
	elseif (b <= 2.55e+66)
		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[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e+97], t$95$1, If[LessEqual[b, 2.55e+66], N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.44999999999999994e97 or 2.55000000000000004e66 < b

   1. Initial program 93.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   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. +-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 83.7

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

   5. Applied rewrites 83.7%

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

   if -1.44999999999999994e97 < b < 2.55000000000000004e66

   1. Initial program 99.4%

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

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 72.2

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

   5. Applied rewrites 72.2%

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

   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 60.5%

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

Alternative 9: 57.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8000000000000:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.5e+24) t_1 (if (<= t 8000000000000.0) (+ a (+ x z)) 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 <= -3.5e+24) {
		tmp = t_1;
	} else if (t <= 8000000000000.0) {
		tmp = a + (x + z);
	} 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 <= (-3.5d+24)) then
        tmp = t_1
    else if (t <= 8000000000000.0d0) then
        tmp = a + (x + z)
    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 <= -3.5e+24) {
		tmp = t_1;
	} else if (t <= 8000000000000.0) {
		tmp = a + (x + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -3.5e+24:
		tmp = t_1
	elif t <= 8000000000000.0:
		tmp = a + (x + z)
	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 <= -3.5e+24)
		tmp = t_1;
	elseif (t <= 8000000000000.0)
		tmp = Float64(a + Float64(x + z));
	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 <= -3.5e+24)
		tmp = t_1;
	elseif (t <= 8000000000000.0)
		tmp = a + (x + z);
	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, -3.5e+24], t$95$1, If[LessEqual[t, 8000000000000.0], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5000000000000002e24 or 8e12 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in 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 74.8

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

   5. Applied rewrites 74.8%

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

   if -3.5000000000000002e24 < t < 8e12

   1. Initial program 99.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 77.9%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 75.5%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 57.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 8000000000000:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+30}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 41000000000000:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.5e+30)
   (* t b)
   (if (<= t 41000000000000.0) (+ a (+ x z)) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.5e+30) {
		tmp = t * b;
	} else if (t <= 41000000000000.0) {
		tmp = a + (x + z);
	} 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 <= (-7.5d+30)) then
        tmp = t * b
    else if (t <= 41000000000000.0d0) then
        tmp = a + (x + z)
    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 <= -7.5e+30) {
		tmp = t * b;
	} else if (t <= 41000000000000.0) {
		tmp = a + (x + z);
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.5e+30:
		tmp = t * b
	elif t <= 41000000000000.0:
		tmp = a + (x + z)
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.5e+30)
		tmp = Float64(t * b);
	elseif (t <= 41000000000000.0)
		tmp = Float64(a + Float64(x + z));
	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 <= -7.5e+30)
		tmp = t * b;
	elseif (t <= 41000000000000.0)
		tmp = a + (x + z);
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.5e+30], N[(t * b), $MachinePrecision], If[LessEqual[t, 41000000000000.0], N[(a + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999973e30 or 4.1e13 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in 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 74.8

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 40.5%

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

   if -7.49999999999999973e30 < t < 4.1e13

   1. Initial program 99.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 99.3

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

   4. Applied rewrites 99.3%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 77.9%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 75.5%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 57.2%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+30}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 41000000000000:\\ \;\;\;\;a + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 41000000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+29) (* t b) (if (<= t 41000000000000.0) (+ x a) (* t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+29) {
		tmp = t * b;
	} else if (t <= 41000000000000.0) {
		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 <= (-7.2d+29)) then
        tmp = t * b
    else if (t <= 41000000000000.0d0) 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 <= -7.2e+29) {
		tmp = t * b;
	} else if (t <= 41000000000000.0) {
		tmp = x + a;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+29:
		tmp = t * b
	elif t <= 41000000000000.0:
		tmp = x + a
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+29)
		tmp = Float64(t * b);
	elseif (t <= 41000000000000.0)
		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 <= -7.2e+29)
		tmp = t * b;
	elseif (t <= 41000000000000.0)
		tmp = x + a;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+29], N[(t * b), $MachinePrecision], If[LessEqual[t, 41000000000000.0], N[(x + a), $MachinePrecision], N[(t * b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.19999999999999952e29 or 4.1e13 < t

   1. Initial program 95.8%

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

   3. Taylor expanded in 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 74.8

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

   5. Applied rewrites 74.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 40.5%

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

   if -7.19999999999999952e29 < t < 4.1e13

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

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

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-in N/A

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

      9. metadata-eval N/A

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

      10. +-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. +-commutative N/A

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

      17. associate-+r- N/A

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

      18. lower-+.f64 N/A

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

      19. sub-neg N/A

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

      20. lower-+.f64 N/A

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

      21. metadata-eval 72.0

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

   5. Applied rewrites 72.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 47.0%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 44.7%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 41000000000000:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 25.3% 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 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

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

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

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

   4. mul-1-neg N/A

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

   5. lower-fma.f64 N/A

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

   6. sub-neg N/A

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

   7. metadata-eval N/A

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

   8. distribute-lft-in N/A

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

   9. metadata-eval N/A

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

   10. +-commutative N/A

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

   11. neg-mul-1 N/A

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

   12. sub-neg N/A

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

   13. lower--.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-fma.f64 N/A

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

   16. +-commutative N/A

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

   17. associate-+r- N/A

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

   18. lower-+.f64 N/A

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

   19. sub-neg N/A

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

   20. lower-+.f64 N/A

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

   21. metadata-eval 79.0

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

5. Applied rewrites 79.0%

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

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 48.4%

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

9. Taylor expanded in t around 0

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

11. Applied rewrites 27.7%

    \[\leadsto a + x \]

12. Final simplification 27.7%

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

Reproduce

herbie shell --seed 2024219 
(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)))