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

Percentage Accurate: 60.1% → 87.5%

Time: 14.5s

Alternatives: 14

Speedup: 1.2×

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: 60.1% 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: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t\_3 + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, \mathsf{fma}\left(y, a - b, t\_3\right)\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (- (+ z a) b))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 2e+221) (/ (fma a t (fma y (- a b) t_3)) t_1) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= 2e+221) {
		tmp = fma(a, t, fma(y, (a - b), t_3)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= 2e+221)
		tmp = Float64(fma(a, t, fma(y, Float64(a - b), t_3)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, 2e+221], N[(N[(a * t + N[(y * N[(a - b), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], 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 2.0000000000000001e221 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 73.8

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

   5. Simplified 73.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e221

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0

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

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

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

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

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

      3. --lowering--.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 99.7

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

   8. Simplified 99.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, \mathsf{fma}\left(y, a - b, z \cdot \left(x + y\right)\right)\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t\_3 + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, a - b, t\_3\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (- (+ z a) b))
        (t_3 (* z (+ x y)))
        (t_4 (/ (- (+ t_3 (* (+ y t) a)) (* y b)) t_1)))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 2e+221) (/ (fma y (- a b) t_3) t_1) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (z + a) - b;
	double t_3 = z * (x + y);
	double t_4 = ((t_3 + ((y + t) * a)) - (y * b)) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= 2e+221) {
		tmp = fma(y, (a - b), t_3) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(z + a) - b)
	t_3 = Float64(z * Float64(x + y))
	t_4 = Float64(Float64(Float64(t_3 + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= 2e+221)
		tmp = Float64(fma(y, Float64(a - b), t_3) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, 2e+221], N[(N[(y * N[(a - b), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], 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 2.0000000000000001e221 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 73.8

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

   5. Simplified 73.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e221

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0

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

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

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

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

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

      3. --lowering--.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 99.7

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

   8. Simplified 99.7%

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

   9. Taylor expanded in t around 0

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

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

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

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

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

       3. *-commutative N/A

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

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

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

       5. +-commutative N/A

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

       6. +-lowering-+.f64 78.9

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

   11. Simplified 78.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, a - b, z \cdot \left(x + y\right)\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t\_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, z - b, x \cdot z\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (+ x t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_1))
        (t_3 (- (+ z a) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 2e+221) (/ (fma y (- z b) (* x z)) t_1) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (x + t);
	double t_2 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_1;
	double t_3 = (z + a) - b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 2e+221) {
		tmp = fma(y, (z - b), (x * z)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_1)
	t_3 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 2e+221)
		tmp = Float64(fma(y, Float64(z - b), Float64(x * z)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 2e+221], N[(N[(y * N[(z - b), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]

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 2.0000000000000001e221 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 73.8

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

   5. Simplified 73.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e221

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

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

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 64.4

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

   8. Simplified 64.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, z - b, x \cdot z\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+267}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, y \cdot t\_2\right)}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) (+ y (+ x t))))
        (t_2 (- (+ z a) b)))
   (if (<= t_1 -1e+267)
     t_2
     (if (<= t_1 2e+221) (/ (fma a t (* y t_2)) (+ y t)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / (y + (x + t));
	double t_2 = (z + a) - b;
	double tmp;
	if (t_1 <= -1e+267) {
		tmp = t_2;
	} else if (t_1 <= 2e+221) {
		tmp = fma(a, t, (y * t_2)) / (y + t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / Float64(y + Float64(x + t)))
	t_2 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (t_1 <= -1e+267)
		tmp = t_2;
	elseif (t_1 <= 2e+221)
		tmp = Float64(fma(a, t, Float64(y * t_2)) / Float64(y + t));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+267], t$95$2, If[LessEqual[t$95$1, 2e+221], N[(N[(a * t + N[(y * t$95$2), $MachinePrecision]), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision], 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)) < -9.9999999999999997e266 or 2.0000000000000001e221 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 11.2%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 72.7

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

   5. Simplified 72.7%

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

   if -9.9999999999999997e266 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2.0000000000000001e221

   1. Initial program 99.6%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. /-lowering-/.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. distribute-lft-in N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

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

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

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

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

      12. --lowering--.f64 N/A

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

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

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

      14. +-lowering-+.f64 61.7

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

   5. Simplified 61.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -1 \cdot 10^{+267}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+221}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, y \cdot \left(\left(z + a\right) - b\right)\right)}{y + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{x + t}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-44}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.45e-122)
     t_1
     (if (<= y 2.1e-165)
       (/ (fma a t (* x z)) (+ x t))
       (if (<= y 2.05e-44) (/ (- (* x z) (* y b)) (+ y (+ x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.45e-122) {
		tmp = t_1;
	} else if (y <= 2.1e-165) {
		tmp = fma(a, t, (x * z)) / (x + t);
	} else if (y <= 2.05e-44) {
		tmp = ((x * z) - (y * b)) / (y + (x + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.45e-122)
		tmp = t_1;
	elseif (y <= 2.1e-165)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(x + t));
	elseif (y <= 2.05e-44)
		tmp = Float64(Float64(Float64(x * z) - Float64(y * b)) / Float64(y + Float64(x + t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.45e-122], t$95$1, If[LessEqual[y, 2.1e-165], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-44], N[(N[(N[(x * z), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e-122 or 2.04999999999999996e-44 < y

   1. Initial program 46.4%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 68.3

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

   5. Simplified 68.3%

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

   if -1.4500000000000001e-122 < y < 2.09999999999999995e-165

   1. Initial program 78.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. /-lowering-/.f64 N/A

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

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

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

      5. +-lowering-+.f64 64.5

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

   5. Simplified 64.5%

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

   if 2.09999999999999995e-165 < y < 2.04999999999999996e-44

   1. Initial program 83.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 68.1

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

   5. Simplified 68.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-122}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{x + t}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-44}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ z a) b)))
   (if (<= y -1.5e-122)
     t_1
     (if (<= y 1.65e-43) (/ (fma a t (* x z)) (+ x t)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + a) - b;
	double tmp;
	if (y <= -1.5e-122) {
		tmp = t_1;
	} else if (y <= 1.65e-43) {
		tmp = fma(a, t, (x * z)) / (x + t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + a) - b)
	tmp = 0.0
	if (y <= -1.5e-122)
		tmp = t_1;
	elseif (y <= 1.65e-43)
		tmp = Float64(fma(a, t, Float64(x * z)) / Float64(x + t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1.5e-122], t$95$1, If[LessEqual[y, 1.65e-43], N[(N[(a * t + N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000002e-122 or 1.65000000000000008e-43 < y

   1. Initial program 46.4%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 68.3

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

   5. Simplified 68.3%

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

   if -1.50000000000000002e-122 < y < 1.65000000000000008e-43

   1. Initial program 79.9%

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

   3. Taylor expanded in y around 0

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

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

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

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

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

      5. +-lowering-+.f64 60.1

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

   5. Simplified 60.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-122}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-43}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, x \cdot z\right)}{x + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (/ (+ x y) (+ t (+ x y))))))
   (if (<= x -2.3e+17) t_1 (if (<= x 1.1e+151) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (t + (x + y)));
	double tmp;
	if (x <= -2.3e+17) {
		tmp = t_1;
	} else if (x <= 1.1e+151) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x + y) / (t + (x + y)))
    if (x <= (-2.3d+17)) then
        tmp = t_1
    else if (x <= 1.1d+151) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * ((x + y) / (t + (x + y)));
	double tmp;
	if (x <= -2.3e+17) {
		tmp = t_1;
	} else if (x <= 1.1e+151) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * ((x + y) / (t + (x + y)))
	tmp = 0
	if x <= -2.3e+17:
		tmp = t_1
	elif x <= 1.1e+151:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(Float64(x + y) / Float64(t + Float64(x + y))))
	tmp = 0.0
	if (x <= -2.3e+17)
		tmp = t_1;
	elseif (x <= 1.1e+151)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * ((x + y) / (t + (x + y)));
	tmp = 0.0;
	if (x <= -2.3e+17)
		tmp = t_1;
	elseif (x <= 1.1e+151)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(N[(x + y), $MachinePrecision] / N[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+17], t$95$1, If[LessEqual[x, 1.1e+151], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e17 or 1.10000000000000003e151 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 28.9

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

   5. Simplified 28.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

      7. /-lowering-/.f64 N/A

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

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

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

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

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

      10. +-lowering-+.f64 62.5

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

   7. Applied egg-rr 62.5%

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

   if -2.3e17 < x < 1.10000000000000003e151

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 65.6

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

   5. Simplified 65.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot \frac{1}{x + t}\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* x (/ 1.0 (+ x t))))))
   (if (<= x -2.1e+17) t_1 (if (<= x 1.15e+151) (- (+ z a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x * (1.0 / (x + t)));
	double tmp;
	if (x <= -2.1e+17) {
		tmp = t_1;
	} else if (x <= 1.15e+151) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * (1.0d0 / (x + t)))
    if (x <= (-2.1d+17)) then
        tmp = t_1
    else if (x <= 1.15d+151) then
        tmp = (z + a) - b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (x * (1.0 / (x + t)));
	double tmp;
	if (x <= -2.1e+17) {
		tmp = t_1;
	} else if (x <= 1.15e+151) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (x * (1.0 / (x + t)))
	tmp = 0
	if x <= -2.1e+17:
		tmp = t_1
	elif x <= 1.15e+151:
		tmp = (z + a) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(x * Float64(1.0 / Float64(x + t))))
	tmp = 0.0
	if (x <= -2.1e+17)
		tmp = t_1;
	elseif (x <= 1.15e+151)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (x * (1.0 / (x + t)));
	tmp = 0.0;
	if (x <= -2.1e+17)
		tmp = t_1;
	elseif (x <= 1.15e+151)
		tmp = (z + a) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(x * N[(1.0 / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+17], t$95$1, If[LessEqual[x, 1.15e+151], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e17 or 1.15e151 < x

   1. Initial program 53.3%

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

   3. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 28.9

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

   5. Simplified 28.9%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-lowering-+.f64 29.0

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

   8. Simplified 29.0%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

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

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

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

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

      6. +-commutative N/A

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

      7. /-lowering-/.f64 N/A

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

      8. +-lowering-+.f64 60.9

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

   10. Applied egg-rr 60.9%

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

   if -2.1e17 < x < 1.15e151

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 65.6

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

   5. Simplified 65.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(x \cdot \frac{1}{x + t}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+151}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \frac{1}{x + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+192}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.3e+17) (* x (/ z (+ x t))) (if (<= x 7e+192) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.3e+17) {
		tmp = x * (z / (x + t));
	} else if (x <= 7e+192) {
		tmp = (z + a) - b;
	} else {
		tmp = 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 <= (-2.3d+17)) then
        tmp = x * (z / (x + t))
    else if (x <= 7d+192) then
        tmp = (z + a) - b
    else
        tmp = 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 <= -2.3e+17) {
		tmp = x * (z / (x + t));
	} else if (x <= 7e+192) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.3e+17:
		tmp = x * (z / (x + t))
	elif x <= 7e+192:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.3e+17)
		tmp = Float64(x * Float64(z / Float64(x + t)));
	elseif (x <= 7e+192)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.3e+17)
		tmp = x * (z / (x + t));
	elseif (x <= 7e+192)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.3e+17], N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+192], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3e17

   1. Initial program 53.6%

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

   3. Taylor expanded in z around inf

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

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

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 27.5

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

   5. Simplified 27.5%

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

   6. Taylor expanded in y around 0

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

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

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

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

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

      3. +-lowering-+.f64 27.6

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

   8. Simplified 27.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. +-commutative N/A

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

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

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

      6. +-lowering-+.f64 53.7

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

   10. Applied egg-rr 53.7%

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

   if -2.3e17 < x < 6.99999999999999965e192

   1. Initial program 60.9%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 64.7

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

   5. Simplified 64.7%

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

   if 6.99999999999999965e192 < x

   1. Initial program 55.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 77.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+192}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+109}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+194}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.8e+109) z (if (<= x 5.1e+194) (- (+ z a) b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.8e+109) {
		tmp = z;
	} else if (x <= 5.1e+194) {
		tmp = (z + a) - b;
	} else {
		tmp = 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 <= (-2.8d+109)) then
        tmp = z
    else if (x <= 5.1d+194) then
        tmp = (z + a) - b
    else
        tmp = 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 <= -2.8e+109) {
		tmp = z;
	} else if (x <= 5.1e+194) {
		tmp = (z + a) - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.8e+109:
		tmp = z
	elif x <= 5.1e+194:
		tmp = (z + a) - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.8e+109)
		tmp = z;
	elseif (x <= 5.1e+194)
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.8e+109)
		tmp = z;
	elseif (x <= 5.1e+194)
		tmp = (z + a) - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.8e+109], z, If[LessEqual[x, 5.1e+194], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000002e109 or 5.1000000000000002e194 < x

   1. Initial program 48.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.4%

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

   if -2.8000000000000002e109 < x < 5.1000000000000002e194

   1. Initial program 62.0%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 62.5

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

   5. Simplified 62.5%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+109}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{+194}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+77}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.2e-107) (- z b) (if (<= z 7.6e+77) (- a b) (- z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.2e-107) {
		tmp = z - b;
	} else if (z <= 7.6e+77) {
		tmp = a - b;
	} else {
		tmp = z - 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 (z <= (-2.2d-107)) then
        tmp = z - b
    else if (z <= 7.6d+77) then
        tmp = a - b
    else
        tmp = z - 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 (z <= -2.2e-107) {
		tmp = z - b;
	} else if (z <= 7.6e+77) {
		tmp = a - b;
	} else {
		tmp = z - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.2e-107:
		tmp = z - b
	elif z <= 7.6e+77:
		tmp = a - b
	else:
		tmp = z - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.2e-107)
		tmp = Float64(z - b);
	elseif (z <= 7.6e+77)
		tmp = Float64(a - b);
	else
		tmp = Float64(z - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.2e-107)
		tmp = z - b;
	elseif (z <= 7.6e+77)
		tmp = a - b;
	else
		tmp = z - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.2e-107], N[(z - b), $MachinePrecision], If[LessEqual[z, 7.6e+77], N[(a - b), $MachinePrecision], N[(z - b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000012e-107 or 7.6000000000000002e77 < z

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 57.4

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

   5. Simplified 57.4%

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

   6. Taylor expanded in a around 0

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

      1. --lowering--.f64 55.2

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

   8. Simplified 55.2%

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

   if -2.20000000000000012e-107 < z < 7.6000000000000002e77

   1. Initial program 70.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 55.5

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

   5. Simplified 55.5%

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

   6. Taylor expanded in z around 0

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

      1. --lowering--.f64 52.6

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

   8. Simplified 52.6%

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

Alternative 12: 47.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-17}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+90}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.02e-17) z (if (<= x 1.35e+90) (- a b) z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.02e-17) {
		tmp = z;
	} else if (x <= 1.35e+90) {
		tmp = a - b;
	} else {
		tmp = 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 <= (-1.02d-17)) then
        tmp = z
    else if (x <= 1.35d+90) then
        tmp = a - b
    else
        tmp = 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 <= -1.02e-17) {
		tmp = z;
	} else if (x <= 1.35e+90) {
		tmp = a - b;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.02e-17:
		tmp = z
	elif x <= 1.35e+90:
		tmp = a - b
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.02e-17)
		tmp = z;
	elseif (x <= 1.35e+90)
		tmp = Float64(a - b);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.02e-17)
		tmp = z;
	elseif (x <= 1.35e+90)
		tmp = a - b;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.02e-17], z, If[LessEqual[x, 1.35e+90], N[(a - b), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999997e-17 or 1.35e90 < x

   1. Initial program 54.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 51.4%

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

   if -1.01999999999999997e-17 < x < 1.35e90

   1. Initial program 62.1%

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

   3. Taylor expanded in y around inf

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

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

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

      2. +-lowering-+.f64 66.3

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

   5. Simplified 66.3%

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

   6. Taylor expanded in z around 0

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

      1. --lowering--.f64 54.4

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

   8. Simplified 54.4%

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

Alternative 13: 45.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+19}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8e+19) z (if (<= z 2.65e-25) a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e+19) {
		tmp = z;
	} else if (z <= 2.65e-25) {
		tmp = a;
	} else {
		tmp = 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 (z <= (-8d+19)) then
        tmp = z
    else if (z <= 2.65d-25) then
        tmp = a
    else
        tmp = 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 (z <= -8e+19) {
		tmp = z;
	} else if (z <= 2.65e-25) {
		tmp = a;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8e+19:
		tmp = z
	elif z <= 2.65e-25:
		tmp = a
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8e+19)
		tmp = z;
	elseif (z <= 2.65e-25)
		tmp = a;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8e+19)
		tmp = z;
	elseif (z <= 2.65e-25)
		tmp = a;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8e+19], z, If[LessEqual[z, 2.65e-25], a, z]]

Derivation

1. Split input into 2 regimes

2. if z < -8e19 or 2.6499999999999998e-25 < z

   1. Initial program 49.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 48.3%

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

   if -8e19 < z < 2.6499999999999998e-25

   1. Initial program 69.5%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 45.2%

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

Alternative 14: 33.2% accurate, 45.0× 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 58.8%

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

3. Taylor expanded in t around inf

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

5. Simplified 28.7%

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

Developer Target 1: 82.0% 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 2024198 
(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)))