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

Percentage Accurate: 95.3% → 98.5%

Time: 15.3s

Alternatives: 22

Speedup: 0.5×

• 35.4% 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: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + t\_1\right) + t\_2 \leq \infty:\\ \;\;\;\;t\_2 + \left(\left(x - \mathsf{fma}\left(z, y, 0 - z\right)\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(t, b - a, \mathsf{fma}\left(z, 1 - y, a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= (+ (+ (+ x (* z (- 1.0 y))) t_1) t_2) INFINITY)
     (+ t_2 (+ (- x (fma z y (- 0.0 z))) t_1))
     (fma b (+ y -2.0) (fma t (- b a) (fma z (- 1.0 y) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if ((((x + (z * (1.0 - y))) + t_1) + t_2) <= ((double) INFINITY)) {
		tmp = t_2 + ((x - fma(z, y, (0.0 - z))) + t_1);
	} else {
		tmp = fma(b, (y + -2.0), fma(t, (b - a), fma(z, (1.0 - y), a)));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], Infinity], N[(t$95$2 + N[(N[(x - N[(z * y + N[(0.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + -2.0), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. metadata-eval 100.0

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

   4. Applied egg-rr 100.0%

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

   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 x around 0

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

   5. Simplified 92.3%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \leq \infty:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \mathsf{fma}\left(z, y, 0 - z\right)\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(t, b - a, \mathsf{fma}\left(z, 1 - y, a\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.5% accurate, 0.5× speedup

Math

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

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
     (fma b (+ y -2.0) (fma t (- b a) (fma z (- 1.0 y) 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 = fma(b, (y + -2.0), fma(t, (b - a), fma(z, (1.0 - y), 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 = fma(b, Float64(y + -2.0), fma(t, Float64(b - a), fma(z, Float64(1.0 - y), a)));
	end
	return 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[(b * N[(y + -2.0), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 92.3%

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

4. Final simplification 99.6%

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

Alternative 3: 88.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-64}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, \mathsf{fma}\left(t, b - a, \mathsf{fma}\left(z, 1 - y, a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+15)
   (fma b (+ t (+ y -2.0)) (fma a (- 1.0 t) x))
   (if (<= b 3.4e-64)
     (fma a (- 1.0 t) (fma z (- 1.0 y) x))
     (fma b (+ y -2.0) (fma t (- b a) (fma z (- 1.0 y) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+15) {
		tmp = fma(b, (t + (y + -2.0)), fma(a, (1.0 - t), x));
	} else if (b <= 3.4e-64) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = fma(b, (y + -2.0), fma(t, (b - a), fma(z, (1.0 - y), a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+15)
		tmp = fma(b, Float64(t + Float64(y + -2.0)), fma(a, Float64(1.0 - t), x));
	elseif (b <= 3.4e-64)
		tmp = fma(a, Float64(1.0 - t), fma(z, Float64(1.0 - y), x));
	else
		tmp = fma(b, Float64(y + -2.0), fma(t, Float64(b - a), fma(z, Float64(1.0 - y), a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+15], N[(b * N[(t + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-64], N[(a * N[(1.0 - t), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(b * N[(y + -2.0), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e15

   1. Initial program 95.9%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. metadata-eval 95.9

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

      12. associate-+r+ N/A

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

      13. +-commutative N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. associate--l+ N/A

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

      16. +-lowering-+.f64 N/A

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

      17. sub-neg N/A

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

      18. +-lowering-+.f64 N/A

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

      19. metadata-eval N/A

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

      20. +-commutative N/A

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

   7. Simplified 92.4%

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

   if -1.15e15 < b < 3.40000000000000012e-64

   1. Initial program 99.2%

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

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. --lowering--.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. accelerator-lowering-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. Simplified 97.3%

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

   if 3.40000000000000012e-64 < b

   1. Initial program 86.5%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 91.7%

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

Alternative 4: 87.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, t + \left(y + -2\right), \mathsf{fma}\left(a, 1 - t, x\right)\right)\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (+ t (+ y -2.0)) (fma a (- 1.0 t) x))))
   (if (<= b -1.3e+17)
     t_1
     (if (<= b 8e-31) (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)), fma(a, (1.0 - t), x));
	double tmp;
	if (b <= -1.3e+17) {
		tmp = t_1;
	} else if (b <= 8e-31) {
		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)), fma(a, Float64(1.0 - t), x))
	tmp = 0.0
	if (b <= -1.3e+17)
		tmp = t_1;
	elseif (b <= 8e-31)
		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] + N[(a * N[(1.0 - t), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+17], t$95$1, If[LessEqual[b, 8e-31], 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 < -1.3e17 or 8.000000000000001e-31 < b

   1. Initial program 89.6%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. metadata-eval 89.6

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

   4. Applied egg-rr 89.6%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. metadata-eval N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. associate-+r+ N/A

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

      11. +-commutative N/A

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

      12. associate-+r+ N/A

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

      13. +-commutative N/A

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

      14. accelerator-lowering-fma.f64 N/A

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

      15. associate--l+ N/A

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

      16. +-lowering-+.f64 N/A

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

      17. sub-neg N/A

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

      18. +-lowering-+.f64 N/A

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

      19. metadata-eval N/A

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

      20. +-commutative N/A

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

   7. Simplified 85.6%

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

   if -1.3e17 < b < 8.000000000000001e-31

   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 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. accelerator-lowering-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. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. --lowering--.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. accelerator-lowering-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. Simplified 96.0%

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

Alternative 5: 87.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b, y + \left(t + -2\right), x\right)\right)\\ \mathbf{if}\;b \leq -1.22 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1.22e+16)
     t_1
     (if (<= b 2.4e-30) (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 <= -1.22e+16) {
		tmp = t_1;
	} else if (b <= 2.4e-30) {
		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 <= -1.22e+16)
		tmp = t_1;
	elseif (b <= 2.4e-30)
		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, -1.22e+16], t$95$1, If[LessEqual[b, 2.4e-30], 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 < -1.22e16 or 2.39999999999999985e-30 < b

   1. Initial program 89.6%

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

   3. Taylor expanded in 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. accelerator-lowering-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. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. metadata-eval N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. metadata-eval N/A

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

      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. --lowering--.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. accelerator-lowering-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. +-lowering-+.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. +-lowering-+.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 83.0

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

   5. Simplified 83.0%

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

   if -1.22e16 < b < 2.39999999999999985e-30

   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 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. accelerator-lowering-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. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. --lowering--.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. accelerator-lowering-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. Simplified 96.0%

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

Alternative 6: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot b\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t b))) (t_2 (* y (- b z))))
   (if (<= y -2.35e+92)
     t_2
     (if (<= y -3.2e-203)
       t_1
       (if (<= y 4.2e-298) (* a (- 1.0 t)) (if (<= y 1.7e+49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * b);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.35e+92) {
		tmp = t_2;
	} else if (y <= -3.2e-203) {
		tmp = t_1;
	} else if (y <= 4.2e-298) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.7e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * b)
    t_2 = y * (b - z)
    if (y <= (-2.35d+92)) then
        tmp = t_2
    else if (y <= (-3.2d-203)) then
        tmp = t_1
    else if (y <= 4.2d-298) then
        tmp = a * (1.0d0 - t)
    else if (y <= 1.7d+49) then
        tmp = t_1
    else
        tmp = t_2
    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 + (t * b);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.35e+92) {
		tmp = t_2;
	} else if (y <= -3.2e-203) {
		tmp = t_1;
	} else if (y <= 4.2e-298) {
		tmp = a * (1.0 - t);
	} else if (y <= 1.7e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * b)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -2.35e+92:
		tmp = t_2
	elif y <= -3.2e-203:
		tmp = t_1
	elif y <= 4.2e-298:
		tmp = a * (1.0 - t)
	elif y <= 1.7e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * b))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.35e+92)
		tmp = t_2;
	elseif (y <= -3.2e-203)
		tmp = t_1;
	elseif (y <= 4.2e-298)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 1.7e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * b);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.35e+92)
		tmp = t_2;
	elseif (y <= -3.2e-203)
		tmp = t_1;
	elseif (y <= 4.2e-298)
		tmp = a * (1.0 - t);
	elseif (y <= 1.7e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.35e+92], t$95$2, If[LessEqual[y, -3.2e-203], t$95$1, If[LessEqual[y, 4.2e-298], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.35e92 or 1.7e49 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 71.5

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

   5. Simplified 71.5%

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

   if -2.35e92 < y < -3.2e-203 or 4.2000000000000001e-298 < y < 1.7e49

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 55.1%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 45.2%

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

   if -3.2e-203 < y < 4.2000000000000001e-298

   1. Initial program 95.7%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 53.9

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

   5. Simplified 53.9%

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

Alternative 7: 72.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2400000000000:\\ \;\;\;\;a + \mathsf{fma}\left(t, b - a, \mathsf{fma}\left(b, -2, z\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+110}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -5.9e+115)
     t_1
     (if (<= y 2400000000000.0)
       (+ a (fma t (- b a) (fma b -2.0 z)))
       (if (<= y 4.8e+110) (+ x (* (- (+ y t) 2.0) b)) 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 <= -5.9e+115) {
		tmp = t_1;
	} else if (y <= 2400000000000.0) {
		tmp = a + fma(t, (b - a), fma(b, -2.0, z));
	} else if (y <= 4.8e+110) {
		tmp = x + (((y + t) - 2.0) * b);
	} 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 <= -5.9e+115)
		tmp = t_1;
	elseif (y <= 2400000000000.0)
		tmp = Float64(a + fma(t, Float64(b - a), fma(b, -2.0, z)));
	elseif (y <= 4.8e+110)
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	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, -5.9e+115], t$95$1, If[LessEqual[y, 2400000000000.0], N[(a + N[(t * N[(b - a), $MachinePrecision] + N[(b * -2.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+110], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8999999999999997e115 or 4.80000000000000025e110 < y

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 75.1

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

   5. Simplified 75.1%

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

   if -5.8999999999999997e115 < y < 2.4e12

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 77.0%

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

   6. Taylor expanded in y around 0

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

      1. +-lowering-+.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. accelerator-lowering-fma.f64 73.3

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

   8. Simplified 73.3%

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

   if 2.4e12 < y < 4.80000000000000025e110

   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 x around inf

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

   5. Simplified 70.9%

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

Alternative 8: 83.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.8 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+133}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, 1 - y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -9.8e+116)
     t_1
     (if (<= b 2.8e+133) (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 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -9.8e+116) {
		tmp = t_1;
	} else if (b <= 2.8e+133) {
		tmp = fma(a, (1.0 - t), fma(z, (1.0 - y), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -9.8e+116)
		tmp = t_1;
	elseif (b <= 2.8e+133)
		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[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.8e+116], t$95$1, If[LessEqual[b, 2.8e+133], 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 < -9.7999999999999996e116 or 2.80000000000000016e133 < 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 x around inf

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

   5. Simplified 86.4%

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

   if -9.7999999999999996e116 < b < 2.80000000000000016e133

   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 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. accelerator-lowering-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. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. --lowering--.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. accelerator-lowering-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. Simplified 88.6%

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

Alternative 9: 25.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-158}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e+105)
   (* y b)
   (if (<= y -2.85e-98)
     x
     (if (<= y 6.3e-158) z (if (<= y 4.5e+16) x (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+105) {
		tmp = y * b;
	} else if (y <= -2.85e-98) {
		tmp = x;
	} else if (y <= 6.3e-158) {
		tmp = z;
	} else if (y <= 4.5e+16) {
		tmp = x;
	} 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) :: tmp
    if (y <= (-2.2d+105)) then
        tmp = y * b
    else if (y <= (-2.85d-98)) then
        tmp = x
    else if (y <= 6.3d-158) then
        tmp = z
    else if (y <= 4.5d+16) then
        tmp = x
    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 tmp;
	if (y <= -2.2e+105) {
		tmp = y * b;
	} else if (y <= -2.85e-98) {
		tmp = x;
	} else if (y <= 6.3e-158) {
		tmp = z;
	} else if (y <= 4.5e+16) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e+105:
		tmp = y * b
	elif y <= -2.85e-98:
		tmp = x
	elif y <= 6.3e-158:
		tmp = z
	elif y <= 4.5e+16:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e+105)
		tmp = Float64(y * b);
	elseif (y <= -2.85e-98)
		tmp = x;
	elseif (y <= 6.3e-158)
		tmp = z;
	elseif (y <= 4.5e+16)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.2e+105)
		tmp = y * b;
	elseif (y <= -2.85e-98)
		tmp = x;
	elseif (y <= 6.3e-158)
		tmp = z;
	elseif (y <= 4.5e+16)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e+105], N[(y * b), $MachinePrecision], If[LessEqual[y, -2.85e-98], x, If[LessEqual[y, 6.3e-158], z, If[LessEqual[y, 4.5e+16], x, N[(y * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000007e105 or 4.5e16 < y

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 49.0%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 38.1

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

   8. Simplified 38.1%

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

   if -2.20000000000000007e105 < y < -2.8499999999999999e-98 or 6.30000000000000014e-158 < y < 4.5e16

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 29.7%

      \[\leadsto \color{blue}{x} \]

   if -2.8499999999999999e-98 < y < 6.30000000000000014e-158

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 34.5

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

   5. Simplified 34.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 34.5%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-158}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma b (+ y -2.0) x)))
   (if (<= b -7.5e+27)
     t_1
     (if (<= b 5.6e+140)
       (fma z (- 1.0 y) x)
       (if (<= b 5.5e+239) t_1 (* t (- b a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, (y + -2.0), x);
	double tmp;
	if (b <= -7.5e+27) {
		tmp = t_1;
	} else if (b <= 5.6e+140) {
		tmp = fma(z, (1.0 - y), x);
	} else if (b <= 5.5e+239) {
		tmp = t_1;
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(b, Float64(y + -2.0), x)
	tmp = 0.0
	if (b <= -7.5e+27)
		tmp = t_1;
	elseif (b <= 5.6e+140)
		tmp = fma(z, Float64(1.0 - y), x);
	elseif (b <= 5.5e+239)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[b, -7.5e+27], t$95$1, If[LessEqual[b, 5.6e+140], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[b, 5.5e+239], t$95$1, N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.5000000000000002e27 or 5.59999999999999966e140 < b < 5.5000000000000004e239

   1. Initial program 91.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 79.7%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 70.7

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

   8. Simplified 70.7%

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

   if -7.5000000000000002e27 < b < 5.59999999999999966e140

   1. Initial program 98.2%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. metadata-eval 98.3

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in b around 0

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

   7. Simplified 88.9%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 60.2

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

   10. Simplified 60.2%

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

   if 5.5000000000000004e239 < b

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 82.8

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

   5. Simplified 82.8%

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

Alternative 11: 51.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-95}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -3.4e+39)
     t_1
     (if (<= t 2.65e-95) (fma y b x) (if (<= t 5.5e+48) (* y (- b 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 <= -3.4e+39) {
		tmp = t_1;
	} else if (t <= 2.65e-95) {
		tmp = fma(y, b, x);
	} else if (t <= 5.5e+48) {
		tmp = y * (b - 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 <= -3.4e+39)
		tmp = t_1;
	elseif (t <= 2.65e-95)
		tmp = fma(y, b, x);
	elseif (t <= 5.5e+48)
		tmp = Float64(y * Float64(b - z));
	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, -3.4e+39], t$95$1, If[LessEqual[t, 2.65e-95], N[(y * b + x), $MachinePrecision], If[LessEqual[t, 5.5e+48], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3999999999999999e39 or 5.5000000000000002e48 < t

   1. Initial program 89.2%

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

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

      2. --lowering--.f64 62.0

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

   5. Simplified 62.0%

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

   if -3.3999999999999999e39 < t < 2.6499999999999999e-95

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 51.9%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 44.8%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 44.8

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

   10. Applied egg-rr 44.8%

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

   if 2.6499999999999999e-95 < t < 5.5000000000000002e48

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 52.0

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

   5. Simplified 52.0%

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

Alternative 12: 63.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-58}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -2.7e+32) t_1 (if (<= b 4.1e-58) (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 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -2.7e+32) {
		tmp = t_1;
	} else if (b <= 4.1e-58) {
		tmp = fma(z, (1.0 - y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -2.7e+32)
		tmp = t_1;
	elseif (b <= 4.1e-58)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+32], t$95$1, If[LessEqual[b, 4.1e-58], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.70000000000000013e32 or 4.10000000000000028e-58 < b

   1. Initial program 89.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 70.8%

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

   if -2.70000000000000013e32 < b < 4.10000000000000028e-58

   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. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. metadata-eval 99.3

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in b around 0

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

   7. Simplified 95.9%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 65.6

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

   10. Simplified 65.6%

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

Alternative 13: 25.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+239}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.2e+33)
   (* y b)
   (if (<= b 5.7e-36) x (if (<= b 4.2e+239) (* y b) (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.2e+33) {
		tmp = y * b;
	} else if (b <= 5.7e-36) {
		tmp = x;
	} else if (b <= 4.2e+239) {
		tmp = y * b;
	} 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 (b <= (-3.2d+33)) then
        tmp = y * b
    else if (b <= 5.7d-36) then
        tmp = x
    else if (b <= 4.2d+239) then
        tmp = y * b
    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 (b <= -3.2e+33) {
		tmp = y * b;
	} else if (b <= 5.7e-36) {
		tmp = x;
	} else if (b <= 4.2e+239) {
		tmp = y * b;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.2e+33:
		tmp = y * b
	elif b <= 5.7e-36:
		tmp = x
	elif b <= 4.2e+239:
		tmp = y * b
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.2e+33)
		tmp = Float64(y * b);
	elseif (b <= 5.7e-36)
		tmp = x;
	elseif (b <= 4.2e+239)
		tmp = Float64(y * b);
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.2e+33)
		tmp = y * b;
	elseif (b <= 5.7e-36)
		tmp = x;
	elseif (b <= 4.2e+239)
		tmp = y * b;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.2e+33], N[(y * b), $MachinePrecision], If[LessEqual[b, 5.7e-36], x, If[LessEqual[b, 4.2e+239], N[(y * b), $MachinePrecision], N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.20000000000000017e33 or 5.6999999999999999e-36 < b < 4.1999999999999998e239

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.1%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 41.4

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

   8. Simplified 41.4%

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

   if -3.20000000000000017e33 < b < 5.6999999999999999e-36

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 24.5%

      \[\leadsto \color{blue}{x} \]

   if 4.1999999999999998e239 < b

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 82.8

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

   5. Simplified 82.8%

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

   6. Taylor expanded in b around inf

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

   8. Simplified 73.8%

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

4. Final simplification 33.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+33}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+239}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+126}:\\ \;\;\;\;\mathsf{fma}\left(z, 1 - y, x\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(y + \left(t + -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+35)
   (fma b (+ y -2.0) x)
   (if (<= b 1.15e+126) (fma z (- 1.0 y) x) (* b (+ y (+ t -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+35) {
		tmp = fma(b, (y + -2.0), x);
	} else if (b <= 1.15e+126) {
		tmp = fma(z, (1.0 - y), x);
	} else {
		tmp = b * (y + (t + -2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+35)
		tmp = fma(b, Float64(y + -2.0), x);
	elseif (b <= 1.15e+126)
		tmp = fma(z, Float64(1.0 - y), x);
	else
		tmp = Float64(b * Float64(y + Float64(t + -2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+35], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[b, 1.15e+126], N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision], N[(b * N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9999999999999999e35

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 82.7%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 70.0

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

   8. Simplified 70.0%

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

   if -1.9999999999999999e35 < b < 1.15e126

   1. Initial program 98.3%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. distribute-lft-in N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. metadata-eval 98.3

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in b around 0

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

   7. Simplified 89.5%

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

   8. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 60.5

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

   10. Simplified 60.5%

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

   if 1.15e126 < b

   1. Initial program 78.4%

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

   3. Taylor expanded in b around inf

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

      1. *-lowering-*.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. +-lowering-+.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. +-lowering-+.f64 N/A

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

      7. metadata-eval 76.3

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

   5. Simplified 76.3%

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

Alternative 15: 50.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(b, y + -2, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -3.5e+108) t_1 (if (<= z 2e+108) (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 = z * (1.0 - y);
	double tmp;
	if (z <= -3.5e+108) {
		tmp = t_1;
	} else if (z <= 2e+108) {
		tmp = fma(b, (y + -2.0), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -3.5e+108)
		tmp = t_1;
	elseif (z <= 2e+108)
		tmp = 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[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+108], t$95$1, If[LessEqual[z, 2e+108], N[(b * N[(y + -2.0), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e108 or 2.0000000000000001e108 < z

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 70.3

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

   5. Simplified 70.3%

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

   if -3.5000000000000002e108 < z < 2.0000000000000001e108

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 59.6%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. sub-neg N/A

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

      4. +-lowering-+.f64 N/A

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

      5. metadata-eval 48.9

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

   8. Simplified 48.9%

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

Alternative 16: 45.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -3.8e+108) t_1 (if (<= z 1.26e+108) (fma y b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -3.8e+108) {
		tmp = t_1;
	} else if (z <= 1.26e+108) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -3.8e+108)
		tmp = t_1;
	elseif (z <= 1.26e+108)
		tmp = fma(y, b, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+108], t$95$1, If[LessEqual[z, 1.26e+108], N[(y * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000008e108 or 1.2600000000000001e108 < z

   1. Initial program 91.0%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 70.3

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

   5. Simplified 70.3%

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

   if -3.80000000000000008e108 < z < 1.2600000000000001e108

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 59.6%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 43.1%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 43.1

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

   10. Applied egg-rr 43.1%

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

Alternative 17: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.8e+39) t_1 (if (<= t 6e+20) (fma y b 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 <= -2.8e+39) {
		tmp = t_1;
	} else if (t <= 6e+20) {
		tmp = fma(y, b, 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 <= -2.8e+39)
		tmp = t_1;
	elseif (t <= 6e+20)
		tmp = fma(y, b, 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, -2.8e+39], t$95$1, If[LessEqual[t, 6e+20], N[(y * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000001e39 or 6e20 < t

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 60.7

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

   5. Simplified 60.7%

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

   if -2.80000000000000001e39 < t < 6e20

   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 x around inf

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

   5. Simplified 49.7%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 42.9%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 42.9

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

   10. Applied egg-rr 42.9%

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

Alternative 18: 44.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -6.8:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+62}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -6.8) t_1 (if (<= a 3.7e+62) (fma y b x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -6.8) {
		tmp = t_1;
	} else if (a <= 3.7e+62) {
		tmp = fma(y, b, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -6.8)
		tmp = t_1;
	elseif (a <= 3.7e+62)
		tmp = fma(y, b, 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]), $MachinePrecision]}, If[LessEqual[a, -6.8], t$95$1, If[LessEqual[a, 3.7e+62], N[(y * b + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.79999999999999982 or 3.70000000000000014e62 < a

   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 a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 53.2

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

   5. Simplified 53.2%

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

   if -6.79999999999999982 < a < 3.70000000000000014e62

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 63.0%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 45.4%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 45.4

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

   10. Applied egg-rr 45.4%

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

Alternative 19: 21.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.25e+42) x (if (<= x 5.4e+55) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.25e+42) {
		tmp = x;
	} else if (x <= 5.4e+55) {
		tmp = z;
	} else {
		tmp = x;
	}
	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 (x <= (-1.25d+42)) then
        tmp = x
    else if (x <= 5.4d+55) then
        tmp = z
    else
        tmp = x
    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 (x <= -1.25e+42) {
		tmp = x;
	} else if (x <= 5.4e+55) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.25e+42:
		tmp = x
	elif x <= 5.4e+55:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.25e+42)
		tmp = x;
	elseif (x <= 5.4e+55)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.25e+42)
		tmp = x;
	elseif (x <= 5.4e+55)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.25e+42], x, If[LessEqual[x, 5.4e+55], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000002e42 or 5.39999999999999954e55 < x

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 36.5%

      \[\leadsto \color{blue}{x} \]

   if -1.25000000000000002e42 < x < 5.39999999999999954e55

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 43.2

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

   5. Simplified 43.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 21.4%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 22.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+53}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.5e+42) x (if (<= x 1.7e+53) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.5e+42) {
		tmp = x;
	} else if (x <= 1.7e+53) {
		tmp = a;
	} else {
		tmp = x;
	}
	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 (x <= (-3.5d+42)) then
        tmp = x
    else if (x <= 1.7d+53) then
        tmp = a
    else
        tmp = x
    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 (x <= -3.5e+42) {
		tmp = x;
	} else if (x <= 1.7e+53) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.5e+42:
		tmp = x
	elif x <= 1.7e+53:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.5e+42)
		tmp = x;
	elseif (x <= 1.7e+53)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.5e+42)
		tmp = x;
	elseif (x <= 1.7e+53)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.5e+42], x, If[LessEqual[x, 1.7e+53], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.50000000000000023e42 or 1.69999999999999999e53 < x

   1. Initial program 93.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 36.8%

      \[\leadsto \color{blue}{x} \]

   if -3.50000000000000023e42 < x < 1.69999999999999999e53

   1. Initial program 95.7%

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

   3. Taylor expanded in a around inf

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

      1. sub-neg N/A

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

      2. neg-mul-1 N/A

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

      3. +-commutative N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 35.8

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

   5. Simplified 35.8%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{a} \]
   7. Step-by-step derivation

   8. Simplified 18.2%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 21: 32.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+153}:\\ \;\;\;\;\mathsf{fma}\left(y, b, x\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= z 5.5e+153) (fma y b x) z))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5.5e+153) {
		tmp = fma(y, b, x);
	} else {
		tmp = z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 5.5e+153)
		tmp = fma(y, b, x);
	else
		tmp = z;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 5.5e+153], N[(y * b + x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if z < 5.5000000000000003e153

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.0%

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

   6. Taylor expanded in y around inf

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

   8. Simplified 37.2%

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 37.2

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

   10. Applied egg-rr 37.2%

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

   if 5.5000000000000003e153 < z

   1. Initial program 87.5%

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

   3. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-lft-in N/A

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

      13. metadata-eval N/A

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

      14. neg-mul-1 N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 78.8

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

   5. Simplified 78.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{z} \]
   7. Step-by-step derivation

   8. Simplified 43.1%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 11.5% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 94.9%

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

3. Taylor expanded in a around inf

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

   1. sub-neg N/A

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

   2. neg-mul-1 N/A

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

   3. +-commutative N/A

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

   4. metadata-eval N/A

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

   5. distribute-lft-in N/A

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

   6. metadata-eval N/A

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

   7. sub-neg N/A

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

   8. *-lowering-*.f64 N/A

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

   9. mul-1-neg N/A

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

   10. sub-neg N/A

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

   11. metadata-eval N/A

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

   12. +-commutative N/A

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

   13. distribute-neg-in N/A

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

   14. metadata-eval N/A

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

   15. sub-neg N/A

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

   16. --lowering--.f64 28.4

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

5. Simplified 28.4%

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

6. Taylor expanded in t around 0

   \[\leadsto \color{blue}{a} \]
7. Step-by-step derivation

8. Simplified 12.0%

   \[\leadsto \color{blue}{a} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024195 
(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)))