AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Percentage Accurate: 60.9% → 89.5%

Time: 6.3s

Alternatives: 13

Speedup: 1.4×

Specification

Math

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

FPCore

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

C

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

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) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{t\_1}, \frac{a}{t\_1} \cdot \left(t + y\right)\right)}{b} - \frac{y}{t\_1}\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t))
        (t_2 (/ (- (+ (* a (+ t y)) (* (+ y x) z)) (* b y)) (+ (+ t x) y))))
   (if (<= t_2 (- INFINITY))
     (fma (- z b) (/ y (+ t y)) a)
     (if (<= t_2 2e+306)
       t_2
       (*
        (- (/ (fma (+ y x) (/ z t_1) (* (/ a t_1) (+ t y))) b) (/ y t_1))
        b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = (((a * (t + y)) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma((z - b), (y / (t + y)), a);
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else {
		tmp = ((fma((y + x), (z / t_1), ((a / t_1) * (t + y))) / b) - (y / t_1)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(Float64(y + x) * z)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(fma(Float64(y + x), Float64(z / t_1), Float64(Float64(a / t_1) * Float64(t + y))) / b) - Float64(y / t_1)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[t$95$2, 2e+306], t$95$2, N[(N[(N[(N[(N[(y + x), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision] + N[(N[(a / t$95$1), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision] - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0

   1. Initial program 6.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 12.0

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

   5. Applied rewrites 12.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 19.7%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t + y}} \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 79.4%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z - b}{y + t}}, a\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 84.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.00000000000000003e306

   1. Initial program 99.7%

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

   if 2.00000000000000003e306 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.8%

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

   3. Taylor expanded in b around -inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

   5. Applied rewrites 76.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{elif}\;\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{\left(y + x\right) + t}, \frac{a}{\left(y + x\right) + t} \cdot \left(t + y\right)\right)}{b} - \frac{y}{\left(y + x\right) + t}\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+274}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* a (+ t y)) (* (+ y x) z)) (* b y)) (+ (+ t x) y)))
        (t_2 (fma (- z b) (/ y (+ t y)) a)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 4e+274) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((a * (t + y)) + ((y + x) * z)) - (b * y)) / ((t + x) + y);
	double t_2 = fma((z - b), (y / (t + y)), a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 4e+274) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(t + y)) + Float64(Float64(y + x) * z)) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = fma(Float64(z - b), Float64(y / Float64(t + y)), a)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 4e+274)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(a * N[(t + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 4e+274], t$95$1, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 3.99999999999999969e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 13.8

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

   5. Applied rewrites 13.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.0%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t + y}} \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 76.7%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z - b}{y + t}}, a\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 79.5%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 3.99999999999999969e274

   1. Initial program 99.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{elif}\;\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y} \leq 4 \cdot 10^{+274}:\\ \;\;\;\;\frac{\left(a \cdot \left(t + y\right) + \left(y + x\right) \cdot z\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{x} - \frac{z}{x}, t, z\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{\left(b - a\right) \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.45e+81)
   (fma (- (/ a x) (/ z x)) t z)
   (if (<= x 2.8e+53)
     (fma (- z b) (/ y (+ t y)) a)
     (- z (/ (* (- b a) y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.45e+81) {
		tmp = fma(((a / x) - (z / x)), t, z);
	} else if (x <= 2.8e+53) {
		tmp = fma((z - b), (y / (t + y)), a);
	} else {
		tmp = z - (((b - a) * y) / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.45e+81)
		tmp = fma(Float64(Float64(a / x) - Float64(z / x)), t, z);
	elseif (x <= 2.8e+53)
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) * y) / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.45e+81], N[(N[(N[(a / x), $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision] * t + z), $MachinePrecision], If[LessEqual[x, 2.8e+53], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.45000000000000011e81

   1. Initial program 47.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{a \cdot t + x \cdot z}{t + x}} \]

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 38.6

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

   5. Applied rewrites 38.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.7%

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

   if -2.45000000000000011e81 < x < 2.8e53

   1. Initial program 63.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 52.3

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

   5. Applied rewrites 52.3%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.4%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t + y}} \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 84.5%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z - b}{y + t}}, a\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 88.0%

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

   if 2.8e53 < x

   1. Initial program 69.7%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 62.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto z - \frac{y \cdot \left(b - a\right)}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 76.0%

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

Alternative 4: 70.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{z}{\left(y + x\right) + t} \cdot \left(y + x\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{\left(b - a\right) \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.5e+81)
   (* (/ z (+ (+ y x) t)) (+ y x))
   (if (<= x 2.8e+53)
     (fma (- z b) (/ y (+ t y)) a)
     (- z (/ (* (- b a) y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.5e+81) {
		tmp = (z / ((y + x) + t)) * (y + x);
	} else if (x <= 2.8e+53) {
		tmp = fma((z - b), (y / (t + y)), a);
	} else {
		tmp = z - (((b - a) * y) / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.5e+81)
		tmp = Float64(Float64(z / Float64(Float64(y + x) + t)) * Float64(y + x));
	elseif (x <= 2.8e+53)
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) * y) / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.5e+81], N[(N[(z / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+53], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4999999999999999e81

   1. Initial program 47.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 49.7

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

   5. Applied rewrites 49.7%

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

   if -2.4999999999999999e81 < x < 2.8e53

   1. Initial program 63.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 52.3

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

   5. Applied rewrites 52.3%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.4%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t + y}} \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 84.5%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z - b}{y + t}}, a\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 88.0%

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

   if 2.8e53 < x

   1. Initial program 69.7%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 62.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto z - \frac{y \cdot \left(b - a\right)}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 76.0%

      \[\leadsto z - \frac{\left(b - a\right) \cdot y}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{z}{\left(y + x\right) + t} \cdot \left(y + x\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{\left(b - a\right) \cdot y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+190}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(z - b, \frac{y}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{\left(b - a\right) \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9e+190)
   (- z (/ (* b y) x))
   (if (<= x 2.8e+53)
     (fma (- z b) (/ y (+ t y)) a)
     (- z (/ (* (- b a) y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9e+190) {
		tmp = z - ((b * y) / x);
	} else if (x <= 2.8e+53) {
		tmp = fma((z - b), (y / (t + y)), a);
	} else {
		tmp = z - (((b - a) * y) / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9e+190)
		tmp = Float64(z - Float64(Float64(b * y) / x));
	elseif (x <= 2.8e+53)
		tmp = fma(Float64(z - b), Float64(y / Float64(t + y)), a);
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) * y) / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9e+190], N[(z - N[(N[(b * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+53], N[(N[(z - b), $MachinePrecision] * N[(y / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.9999999999999999e190

   1. Initial program 39.0%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto z - \frac{b \cdot y}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.3%

      \[\leadsto z - \frac{b \cdot y}{x} \]

   if -8.9999999999999999e190 < x < 2.8e53

   1. Initial program 62.2%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 46.4

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

   5. Applied rewrites 46.4%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 23.0%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t + y}} \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 77.8%

       \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z - b}{y + t}}, a\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 80.8%

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

   if 2.8e53 < x

   1. Initial program 69.7%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 62.6%

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

   6. Taylor expanded in y around inf

      \[\leadsto z - \frac{y \cdot \left(b - a\right)}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 76.0%

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

Alternative 6: 70.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+190}:\\ \;\;\;\;z - \frac{b \cdot y}{x}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - b}{t + y}, a\right)\\ \mathbf{else}:\\ \;\;\;\;z - \frac{\left(b - a\right) \cdot y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9e+190)
   (- z (/ (* b y) x))
   (if (<= x 3.8e+47)
     (fma y (/ (- z b) (+ t y)) a)
     (- z (/ (* (- b a) y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9e+190) {
		tmp = z - ((b * y) / x);
	} else if (x <= 3.8e+47) {
		tmp = fma(y, ((z - b) / (t + y)), a);
	} else {
		tmp = z - (((b - a) * y) / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9e+190)
		tmp = Float64(z - Float64(Float64(b * y) / x));
	elseif (x <= 3.8e+47)
		tmp = fma(y, Float64(Float64(z - b) / Float64(t + y)), a);
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) * y) / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9e+190], N[(z - N[(N[(b * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+47], N[(y * N[(N[(z - b), $MachinePrecision] / N[(t + y), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.9999999999999999e190

   1. Initial program 39.0%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in b around inf

      \[\leadsto z - \frac{b \cdot y}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.3%

      \[\leadsto z - \frac{b \cdot y}{x} \]

   if -8.9999999999999999e190 < x < 3.8000000000000003e47

   1. Initial program 62.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 46.5

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

   5. Applied rewrites 46.5%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 78.0%

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

   if 3.8000000000000003e47 < x

   1. Initial program 69.1%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in y around inf

      \[\leadsto z - \frac{y \cdot \left(b - a\right)}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 75.3%

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

Alternative 7: 61.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z - b}{t}, a\right)\\ \mathbf{if}\;t \leq -2.26 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y (/ (- z b) t) a)))
   (if (<= t -2.26e+148) t_1 (if (<= t 1.2e+64) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, ((z - b) / t), a);
	double tmp;
	if (t <= -2.26e+148) {
		tmp = t_1;
	} else if (t <= 1.2e+64) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(z - b) / t), a)
	tmp = 0.0
	if (t <= -2.26e+148)
		tmp = t_1;
	elseif (t <= 1.2e+64)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(z - b), $MachinePrecision] / t), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[t, -2.26e+148], t$95$1, If[LessEqual[t, 1.2e+64], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2599999999999999e148 or 1.2e64 < t

   1. Initial program 51.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 39.3

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

   5. Applied rewrites 39.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 69.0%

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

   if -2.2599999999999999e148 < t < 1.2e64

   1. Initial program 67.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 63.6

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

   5. Applied rewrites 63.6%

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

Alternative 8: 58.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{t}, y, a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+64}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (/ z t) y a)))
   (if (<= t -2.1e+130) t_1 (if (<= t 1.2e+64) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((z / t), y, a);
	double tmp;
	if (t <= -2.1e+130) {
		tmp = t_1;
	} else if (t <= 1.2e+64) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(z / t), y, a)
	tmp = 0.0
	if (t <= -2.1e+130)
		tmp = t_1;
	elseif (t <= 1.2e+64)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] * y + a), $MachinePrecision]}, If[LessEqual[t, -2.1e+130], t$95$1, If[LessEqual[t, 1.2e+64], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0999999999999999e130 or 1.2e64 < t

   1. Initial program 54.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. *-commutative N/A

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

      7. distribute-lft-out-- N/A

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

      8. lower-*.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 41.0

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

   5. Applied rewrites 41.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t + y}} \]
   7. Step-by-step derivation

   8. Applied rewrites 19.2%

      \[\leadsto y \cdot \color{blue}{\frac{z}{t + y}} \]

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 67.9%

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

   12. Taylor expanded in z around inf

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

   14. Applied rewrites 61.3%

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

   if -2.0999999999999999e130 < t < 1.2e64

   1. Initial program 66.3%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 64.0

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

   5. Applied rewrites 64.0%

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

Alternative 9: 56.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+125}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.3e+125) (* 1.0 z) (if (<= x 2.4e+53) (- (+ a z) b) (* 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.3e+125) {
		tmp = 1.0 * z;
	} else if (x <= 2.4e+53) {
		tmp = (a + z) - b;
	} else {
		tmp = 1.0 * z;
	}
	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 <= (-1.3d+125)) then
        tmp = 1.0d0 * z
    else if (x <= 2.4d+53) then
        tmp = (a + z) - b
    else
        tmp = 1.0d0 * z
    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 <= -1.3e+125) {
		tmp = 1.0 * z;
	} else if (x <= 2.4e+53) {
		tmp = (a + z) - b;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.3e+125:
		tmp = 1.0 * z
	elif x <= 2.4e+53:
		tmp = (a + z) - b
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.3e+125)
		tmp = Float64(1.0 * z);
	elseif (x <= 2.4e+53)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.3e+125)
		tmp = 1.0 * z;
	elseif (x <= 2.4e+53)
		tmp = (a + z) - b;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.3e+125], N[(1.0 * z), $MachinePrecision], If[LessEqual[x, 2.4e+53], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.30000000000000002e125 or 2.4e53 < x

   1. Initial program 58.0%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 58.6%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 61.0%

       \[\leadsto 1 \cdot z \]

   if -1.30000000000000002e125 < x < 2.4e53

   1. Initial program 63.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 58.6

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

   5. Applied rewrites 58.6%

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

Alternative 10: 52.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{+191}:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+67}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.18e+191) (* 1.0 z) (if (<= x 1.9e+67) (+ a z) (* 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.18e+191) {
		tmp = 1.0 * z;
	} else if (x <= 1.9e+67) {
		tmp = a + z;
	} else {
		tmp = 1.0 * z;
	}
	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 <= (-1.18d+191)) then
        tmp = 1.0d0 * z
    else if (x <= 1.9d+67) then
        tmp = a + z
    else
        tmp = 1.0d0 * z
    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 <= -1.18e+191) {
		tmp = 1.0 * z;
	} else if (x <= 1.9e+67) {
		tmp = a + z;
	} else {
		tmp = 1.0 * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.18e+191:
		tmp = 1.0 * z
	elif x <= 1.9e+67:
		tmp = a + z
	else:
		tmp = 1.0 * z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.18e+191)
		tmp = Float64(1.0 * z);
	elseif (x <= 1.9e+67)
		tmp = Float64(a + z);
	else
		tmp = Float64(1.0 * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.18e+191)
		tmp = 1.0 * z;
	elseif (x <= 1.9e+67)
		tmp = a + z;
	else
		tmp = 1.0 * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.18e+191], N[(1.0 * z), $MachinePrecision], If[LessEqual[x, 1.9e+67], N[(a + z), $MachinePrecision], N[(1.0 * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.17999999999999994e191 or 1.9000000000000001e67 < x

   1. Initial program 59.3%

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

   3. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 61.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 66.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 67.5%

       \[\leadsto 1 \cdot z \]

   if -1.17999999999999994e191 < x < 1.9000000000000001e67

   1. Initial program 62.6%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 55.4

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

   5. Applied rewrites 55.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 42.8%

      \[\leadsto a - \color{blue}{b} \]

   9. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 52.7%

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

Alternative 11: 51.6% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+243}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.8e+243) (- a b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.8e+243) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	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 <= (-2.8d+243)) then
        tmp = a - b
    else
        tmp = a + z
    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 <= -2.8e+243) {
		tmp = a - b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.8e+243:
		tmp = a - b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.8e+243)
		tmp = Float64(a - b);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.8e+243)
		tmp = a - b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.8e+243], N[(a - b), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e243

   1. Initial program 29.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 88.5

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

   5. Applied rewrites 88.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 87.8%

      \[\leadsto a - \color{blue}{b} \]

   if -2.7999999999999999e243 < y

   1. Initial program 63.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 52.3

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

   5. Applied rewrites 52.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 31.5%

      \[\leadsto a - \color{blue}{b} \]

   9. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 53.1%

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

Alternative 12: 51.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.8 \cdot 10^{+223}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;-b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b 1.8e+223) (+ a z) (- b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.8e+223) {
		tmp = a + z;
	} else {
		tmp = -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 <= 1.8d+223) then
        tmp = a + z
    else
        tmp = -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 <= 1.8e+223) {
		tmp = a + z;
	} else {
		tmp = -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.8e+223:
		tmp = a + z
	else:
		tmp = -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.8e+223)
		tmp = Float64(a + z);
	else
		tmp = Float64(-b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.8e+223)
		tmp = a + z;
	else
		tmp = -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.8e+223], N[(a + z), $MachinePrecision], (-b)]

Derivation

1. Split input into 2 regimes

2. if b < 1.79999999999999996e223

   1. Initial program 64.1%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 54.6

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

   5. Applied rewrites 54.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 33.3%

      \[\leadsto a - \color{blue}{b} \]

   9. Taylor expanded in b around 0

      \[\leadsto a + \color{blue}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 55.1%

       \[\leadsto a + \color{blue}{z} \]

   if 1.79999999999999996e223 < b

   1. Initial program 28.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 42.6

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

   5. Applied rewrites 42.6%

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

   6. Taylor expanded in b around inf

      \[\leadsto -1 \cdot \color{blue}{b} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.7%

      \[\leadsto -b \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 13.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -b \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := (-b)

Derivation

1. Initial program 61.7%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

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

   2. lower-+.f64 53.8

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

5. Applied rewrites 53.8%

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

6. Taylor expanded in b around inf

   \[\leadsto -1 \cdot \color{blue}{b} \]
7. Step-by-step derivation

8. Applied rewrites 11.5%

   \[\leadsto -b \]
9. Add Preprocessing

Developer Target 1: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;t\_3 < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y))
        (t_2 (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))
        (t_3 (/ t_2 t_1))
        (t_4 (- (+ z a) b)))
   (if (< t_3 -3.5813117084150564e+153)
     t_4
     (if (< t_3 1.2285964308315609e+82) (/ 1.0 (/ t_1 t_2)) t_4))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + t) + y
    t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
    t_3 = t_2 / t_1
    t_4 = (z + a) - b
    if (t_3 < (-3.5813117084150564d+153)) then
        tmp = t_4
    else if (t_3 < 1.2285964308315609d+82) then
        tmp = 1.0d0 / (t_1 / t_2)
    else
        tmp = t_4
    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) + y;
	double t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	double t_3 = t_2 / t_1;
	double t_4 = (z + a) - b;
	double tmp;
	if (t_3 < -3.5813117084150564e+153) {
		tmp = t_4;
	} else if (t_3 < 1.2285964308315609e+82) {
		tmp = 1.0 / (t_1 / t_2);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b)
	t_3 = t_2 / t_1
	t_4 = (z + a) - b
	tmp = 0
	if t_3 < -3.5813117084150564e+153:
		tmp = t_4
	elif t_3 < 1.2285964308315609e+82:
		tmp = 1.0 / (t_1 / t_2)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = Float64(1.0 / Float64(t_1 / t_2));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	t_2 = (((x + y) * z) + ((t + y) * a)) - (y * b);
	t_3 = t_2 / t_1;
	t_4 = (z + a) - b;
	tmp = 0.0;
	if (t_3 < -3.5813117084150564e+153)
		tmp = t_4;
	elseif (t_3 < 1.2285964308315609e+82)
		tmp = 1.0 / (t_1 / t_2);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[Less[t$95$3, -3.5813117084150564e+153], t$95$4, If[Less[t$95$3, 1.2285964308315609e+82], N[(1.0 / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Reproduce

herbie shell --seed 2024332 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3581311708415056400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 12285964308315609000000000000000000000000000000000000000000000000000000000000000000) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b))))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))