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

Percentage Accurate: 61.0% → 89.2%

Time: 10.6s

Alternatives: 17

Speedup: 0.4×

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: 61.0% 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: 89.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(y + x\right)\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{t\_1}, \frac{a}{t\_1} \cdot \left(t + y\right)\right)}{b} - \frac{y}{t\_1}\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (+ y x)))
        (t_2 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) (+ (+ t x) y))))
   (if (<= t_2 (- INFINITY))
     (- (+ a z) b)
     (if (<= t_2 2e+303)
       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 = t + (y + x);
	double t_2 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / ((t + x) + y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (a + z) - b;
	} else if (t_2 <= 2e+303) {
		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(t + Float64(y + x))
	t_2 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(Float64(t + x) + y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(a + z) - b);
	elseif (t_2 <= 2e+303)
		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[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], If[LessEqual[t$95$2, 2e+303], 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 6.8%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 72.8

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

   5. Applied rewrites 72.8%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e303

   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 2e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 4.1%

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

   3. Taylor expanded in 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. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

   5. Applied rewrites 77.6%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\mathsf{fma}\left(y + x, \frac{z}{t + \left(y + x\right)}, \frac{a}{t + \left(y + x\right)} \cdot \left(t + y\right)\right)}{b} - \frac{y}{t + \left(y + x\right)}\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{t\_1}\\ t_3 := \left(a + z\right) - b\\ t_4 := \frac{\mathsf{fma}\left(t, a, t\_3 \cdot y\right)}{t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+213}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-172}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 1000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) t_1))
        (t_3 (- (+ a z) b))
        (t_4 (/ (fma t a (* t_3 y)) t_1)))
   (if (<= t_2 -2e+213)
     t_3
     (if (<= t_2 -1e-172)
       t_4
       (if (<= t_2 1000000000.0)
         (/ (fma x z (* a t)) (+ t x))
         (if (<= t_2 2e+219) t_4 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + x) + y;
	double t_2 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / t_1;
	double t_3 = (a + z) - b;
	double t_4 = fma(t, a, (t_3 * y)) / t_1;
	double tmp;
	if (t_2 <= -2e+213) {
		tmp = t_3;
	} else if (t_2 <= -1e-172) {
		tmp = t_4;
	} else if (t_2 <= 1000000000.0) {
		tmp = fma(x, z, (a * t)) / (t + x);
	} else if (t_2 <= 2e+219) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + x) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	t_4 = Float64(fma(t, a, Float64(t_3 * y)) / t_1)
	tmp = 0.0
	if (t_2 <= -2e+213)
		tmp = t_3;
	elseif (t_2 <= -1e-172)
		tmp = t_4;
	elseif (t_2 <= 1000000000.0)
		tmp = Float64(fma(x, z, Float64(a * t)) / Float64(t + x));
	elseif (t_2 <= 2e+219)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * a + N[(t$95$3 * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+213], t$95$3, If[LessEqual[t$95$2, -1e-172], t$95$4, If[LessEqual[t$95$2, 1000000000.0], N[(N[(x * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+219], t$95$4, t$95$3]]]]]]]]

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)) < -1.99999999999999997e213 or 1.99999999999999993e219 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 15.3%

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

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

      3. lower-+.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if -1.99999999999999997e213 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -1e-172 or 1e9 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999993e219

   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. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. distribute-lft-in N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if -1e-172 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e9

   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. 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. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 81.3

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

   5. Applied rewrites 81.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -2 \cdot 10^{+213}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{-172}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, \left(\left(a + z\right) - b\right) \cdot y\right)}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 1000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, \left(\left(a + z\right) - b\right) \cdot y\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot y\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\left(a + z\right) \cdot y - b \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) t_1))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -1e-28)
       (/ (fma (+ y x) z (* a y)) t_1)
       (if (<= t_2 10000000000.0)
         (/ (fma x z (* a t)) (+ t x))
         (if (<= t_2 2e+219) (/ (- (* (+ a z) y) (* b y)) t_1) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + x) + y;
	double t_2 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1e-28) {
		tmp = fma((y + x), z, (a * y)) / t_1;
	} else if (t_2 <= 10000000000.0) {
		tmp = fma(x, z, (a * t)) / (t + x);
	} else if (t_2 <= 2e+219) {
		tmp = (((a + z) * y) - (b * y)) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + x) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1e-28)
		tmp = Float64(fma(Float64(y + x), z, Float64(a * y)) / t_1);
	elseif (t_2 <= 10000000000.0)
		tmp = Float64(fma(x, z, Float64(a * t)) / Float64(t + x));
	elseif (t_2 <= 2e+219)
		tmp = Float64(Float64(Float64(Float64(a + z) * y) - Float64(b * y)) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1e-28], N[(N[(N[(y + x), $MachinePrecision] * z + N[(a * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 10000000000.0], N[(N[(x * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+219], N[(N[(N[(N[(a + z), $MachinePrecision] * y), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 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 1.99999999999999993e219 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.8%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999971e-29

   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. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.9%

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

   if -9.99999999999999971e-29 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e10

   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. 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. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if 1e10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999993e219

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 66.6

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

   5. Applied rewrites 66.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{-28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot y\right)}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 10000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\left(a + z\right) \cdot y - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{t\_1}\\ t_3 := \left(a + z\right) - b\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot y\right)}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{t\_3 \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) t_1))
        (t_3 (- (+ a z) b)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -1e-28)
       (/ (fma (+ y x) z (* a y)) t_1)
       (if (<= t_2 10000000000.0)
         (/ (fma x z (* a t)) (+ t x))
         (if (<= t_2 2e+219) (/ (* t_3 y) t_1) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + x) + y;
	double t_2 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / t_1;
	double t_3 = (a + z) - b;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1e-28) {
		tmp = fma((y + x), z, (a * y)) / t_1;
	} else if (t_2 <= 10000000000.0) {
		tmp = fma(x, z, (a * t)) / (t + x);
	} else if (t_2 <= 2e+219) {
		tmp = (t_3 * y) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + x) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1e-28)
		tmp = Float64(fma(Float64(y + x), z, Float64(a * y)) / t_1);
	elseif (t_2 <= 10000000000.0)
		tmp = Float64(fma(x, z, Float64(a * t)) / Float64(t + x));
	elseif (t_2 <= 2e+219)
		tmp = Float64(Float64(t_3 * y) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1e-28], N[(N[(N[(y + x), $MachinePrecision] * z + N[(a * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 10000000000.0], N[(N[(x * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+219], N[(N[(t$95$3 * y), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 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 1.99999999999999993e219 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.8%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999971e-29

   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. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.9%

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

   if -9.99999999999999971e-29 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e10

   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. 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. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if 1e10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999993e219

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 66.5

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

   5. Applied rewrites 66.5%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{-28}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, a \cdot y\right)}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 10000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\left(\left(a + z\right) - b\right) \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{t\_1}\\ t_3 := \left(a + z\right) - b\\ t_4 := \frac{t\_3 \cdot y}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+192}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-28}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 10000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) t_1))
        (t_3 (- (+ a z) b))
        (t_4 (/ (* t_3 y) t_1)))
   (if (<= t_2 -1e+192)
     t_3
     (if (<= t_2 -1e-28)
       t_4
       (if (<= t_2 10000000000.0)
         (/ (fma x z (* a t)) (+ t x))
         (if (<= t_2 2e+219) t_4 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + x) + y;
	double t_2 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / t_1;
	double t_3 = (a + z) - b;
	double t_4 = (t_3 * y) / t_1;
	double tmp;
	if (t_2 <= -1e+192) {
		tmp = t_3;
	} else if (t_2 <= -1e-28) {
		tmp = t_4;
	} else if (t_2 <= 10000000000.0) {
		tmp = fma(x, z, (a * t)) / (t + x);
	} else if (t_2 <= 2e+219) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + x) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / t_1)
	t_3 = Float64(Float64(a + z) - b)
	t_4 = Float64(Float64(t_3 * y) / t_1)
	tmp = 0.0
	if (t_2 <= -1e+192)
		tmp = t_3;
	elseif (t_2 <= -1e-28)
		tmp = t_4;
	elseif (t_2 <= 10000000000.0)
		tmp = Float64(fma(x, z, Float64(a * t)) / Float64(t + x));
	elseif (t_2 <= 2e+219)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 * y), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+192], t$95$3, If[LessEqual[t$95$2, -1e-28], t$95$4, If[LessEqual[t$95$2, 10000000000.0], N[(N[(x * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+219], t$95$4, t$95$3]]]]]]]]

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)) < -1.00000000000000004e192 or 1.99999999999999993e219 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 16.8%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 75.1

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

   5. Applied rewrites 75.1%

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

   if -1.00000000000000004e192 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.99999999999999971e-29 or 1e10 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999993e219

   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. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if -9.99999999999999971e-29 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e10

   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. 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. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 77.8

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

   5. Applied rewrites 77.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{+192}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -1 \cdot 10^{-28}:\\ \;\;\;\;\frac{\left(\left(a + z\right) - b\right) \cdot y}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 10000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\left(\left(a + z\right) - b\right) \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + x\right) + y\\ t_2 := \left(a + z\right) - b\\ t_3 := \left(t + y\right) \cdot a\\ t_4 := \frac{\left(t\_3 + z \cdot \left(y + x\right)\right) - b \cdot y}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_3\right)}{t\_1}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, t\_2 \cdot y\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ t x) y))
        (t_2 (- (+ a z) b))
        (t_3 (* (+ t y) a))
        (t_4 (/ (- (+ t_3 (* z (+ y x))) (* b y)) t_1)))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 2e+21)
       (/ (fma (+ y x) z t_3) t_1)
       (if (<= t_4 2e+219) (/ (fma t a (* t_2 y)) t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + x) + y;
	double t_2 = (a + z) - b;
	double t_3 = (t + y) * a;
	double t_4 = ((t_3 + (z * (y + x))) - (b * y)) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= 2e+21) {
		tmp = fma((y + x), z, t_3) / t_1;
	} else if (t_4 <= 2e+219) {
		tmp = fma(t, a, (t_2 * y)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + x) + y)
	t_2 = Float64(Float64(a + z) - b)
	t_3 = Float64(Float64(t + y) * a)
	t_4 = Float64(Float64(Float64(t_3 + Float64(z * Float64(y + x))) - Float64(b * y)) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= 2e+21)
		tmp = Float64(fma(Float64(y + x), z, t_3) / t_1);
	elseif (t_4 <= 2e+219)
		tmp = Float64(fma(t, a, Float64(t_2 * y)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, 2e+21], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, 2e+219], N[(N[(t * a + N[(t$95$2 * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]]

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 or 1.99999999999999993e219 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.8%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e21

   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. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if 2e21 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999993e219

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. distribute-lft-in N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. *-commutative N/A

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

      6. *-commutative N/A

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

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

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

      8. distribute-lft-in N/A

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

      9. associate--l+ N/A

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

      10. lower-fma.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-+.f64 88.6

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

   5. Applied rewrites 88.6%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+21}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a, \left(\left(a + z\right) - b\right) \cdot y\right)}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) (+ (+ t x) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 2e+219) t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / ((t + x) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 2e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / ((t + x) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 2e+219) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / ((t + x) + y)
	t_2 = (a + z) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 2e+219:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 2e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / ((t + x) + y);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 2e+219)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 2e+219], 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 1.99999999999999993e219 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 8.8%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999993e219

   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 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -\infty:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+219}:\\ \;\;\;\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+85}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ t y) a) (* z (+ y x))) (* b y)) (+ (+ t x) y)))
        (t_2 (- (+ a z) b)))
   (if (<= t_1 -2e+89)
     t_2
     (if (<= t_1 2e+85) (/ (fma x z (* a t)) (+ t x)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((t + y) * a) + (z * (y + x))) - (b * y)) / ((t + x) + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (t_1 <= -2e+89) {
		tmp = t_2;
	} else if (t_1 <= 2e+85) {
		tmp = fma(x, z, (a * t)) / (t + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(t + y) * a) + Float64(z * Float64(y + x))) - Float64(b * y)) / Float64(Float64(t + x) + y))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (t_1 <= -2e+89)
		tmp = t_2;
	elseif (t_1 <= 2e+85)
		tmp = Float64(fma(x, z, Float64(a * t)) / Float64(t + x));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+89], t$95$2, If[LessEqual[t$95$1, 2e+85], N[(N[(x * z + N[(a * t), $MachinePrecision]), $MachinePrecision] / N[(t + x), $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)) < -1.99999999999999999e89 or 2e85 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 32.7%

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

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

      3. lower-+.f64 70.1

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

   5. Applied rewrites 70.1%

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

   if -1.99999999999999999e89 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 2e85

   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. 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. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 61.4

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

   5. Applied rewrites 61.4%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq -2 \cdot 10^{+89}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;\frac{\left(\left(t + y\right) \cdot a + z \cdot \left(y + x\right)\right) - b \cdot y}{\left(t + x\right) + y} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, a \cdot t\right)}{t + x}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{t + \left(y + x\right)} \cdot \left(t + y\right)\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-64}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ a (+ t (+ y x))) (+ t y))) (t_2 (- (+ a z) b)))
   (if (<= y -2.7e+41)
     t_2
     (if (<= y -9.5e-111)
       t_1
       (if (<= y 8.2e-64) (+ a z) (if (<= y 1.65e+58) 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 + x))) * (t + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -2.7e+41) {
		tmp = t_2;
	} else if (y <= -9.5e-111) {
		tmp = t_1;
	} else if (y <= 8.2e-64) {
		tmp = a + z;
	} else if (y <= 1.65e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a / (t + (y + x))) * (t + y)
    t_2 = (a + z) - b
    if (y <= (-2.7d+41)) then
        tmp = t_2
    else if (y <= (-9.5d-111)) then
        tmp = t_1
    else if (y <= 8.2d-64) then
        tmp = a + z
    else if (y <= 1.65d+58) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a / (t + (y + x))) * (t + y);
	double t_2 = (a + z) - b;
	double tmp;
	if (y <= -2.7e+41) {
		tmp = t_2;
	} else if (y <= -9.5e-111) {
		tmp = t_1;
	} else if (y <= 8.2e-64) {
		tmp = a + z;
	} else if (y <= 1.65e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a / (t + (y + x))) * (t + y)
	t_2 = (a + z) - b
	tmp = 0
	if y <= -2.7e+41:
		tmp = t_2
	elif y <= -9.5e-111:
		tmp = t_1
	elif y <= 8.2e-64:
		tmp = a + z
	elif y <= 1.65e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a / Float64(t + Float64(y + x))) * Float64(t + y))
	t_2 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -2.7e+41)
		tmp = t_2;
	elseif (y <= -9.5e-111)
		tmp = t_1;
	elseif (y <= 8.2e-64)
		tmp = Float64(a + z);
	elseif (y <= 1.65e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a / (t + (y + x))) * (t + y);
	t_2 = (a + z) - b;
	tmp = 0.0;
	if (y <= -2.7e+41)
		tmp = t_2;
	elseif (y <= -9.5e-111)
		tmp = t_1;
	elseif (y <= 8.2e-64)
		tmp = a + z;
	elseif (y <= 1.65e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a / N[(t + N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -2.7e+41], t$95$2, If[LessEqual[y, -9.5e-111], t$95$1, If[LessEqual[y, 8.2e-64], N[(a + z), $MachinePrecision], If[LessEqual[y, 1.65e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e41 or 1.64999999999999991e58 < y

   1. Initial program 39.7%

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

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

      3. lower-+.f64 79.2

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

   5. Applied rewrites 79.2%

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

   if -2.7e41 < y < -9.4999999999999995e-111 or 8.2000000000000001e-64 < y < 1.64999999999999991e58

   1. Initial program 85.5%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 56.6

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

   5. Applied rewrites 56.6%

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

   if -9.4999999999999995e-111 < y < 8.2000000000000001e-64

   1. Initial program 73.9%

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

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

      3. lower-+.f64 38.6

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

   5. Applied rewrites 38.6%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 53.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{a}{t + \left(y + x\right)} \cdot \left(t + y\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-64}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;\frac{a}{t + \left(y + x\right)} \cdot \left(t + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - \frac{x}{t + y} \cdot a\\ \mathbf{if}\;t \leq -5 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+172}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- a (* (/ x (+ t y)) a))))
   (if (<= t -5e+166) t_1 (if (<= t 1.12e+172) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a - ((x / (t + y)) * a);
	double tmp;
	if (t <= -5e+166) {
		tmp = t_1;
	} else if (t <= 1.12e+172) {
		tmp = (a + z) - 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 = a - ((x / (t + y)) * a)
    if (t <= (-5d+166)) then
        tmp = t_1
    else if (t <= 1.12d+172) then
        tmp = (a + z) - 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 = a - ((x / (t + y)) * a);
	double tmp;
	if (t <= -5e+166) {
		tmp = t_1;
	} else if (t <= 1.12e+172) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a - ((x / (t + y)) * a)
	tmp = 0
	if t <= -5e+166:
		tmp = t_1
	elif t <= 1.12e+172:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a - Float64(Float64(x / Float64(t + y)) * a))
	tmp = 0.0
	if (t <= -5e+166)
		tmp = t_1;
	elseif (t <= 1.12e+172)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a - ((x / (t + y)) * a);
	tmp = 0.0;
	if (t <= -5e+166)
		tmp = t_1;
	elseif (t <= 1.12e+172)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a - N[(N[(x / N[(t + y), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+166], t$95$1, If[LessEqual[t, 1.12e+172], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000002e166 or 1.12000000000000002e172 < t

   1. Initial program 50.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 58.9

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

   5. Applied rewrites 58.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 4.9%

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

   9. Taylor expanded in x around 0

      \[\leadsto a + \color{blue}{-1 \cdot \frac{a \cdot x}{t + y}} \]
   10. Step-by-step derivation

   11. Applied rewrites 70.2%

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

   if -5.0000000000000002e166 < t < 1.12000000000000002e172

   1. Initial program 66.2%

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

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

      3. lower-+.f64 58.4

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

   5. Applied rewrites 58.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+166}:\\ \;\;\;\;a - \frac{x}{t + y} \cdot a\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+172}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - \frac{x}{t + y} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+166}:\\ \;\;\;\;-1 \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+171}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5e+166)
   (* -1.0 (- a))
   (if (<= t 9e+171) (- (+ a z) b) (* (/ t (+ t x)) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+166) {
		tmp = -1.0 * -a;
	} else if (t <= 9e+171) {
		tmp = (a + z) - b;
	} else {
		tmp = (t / (t + x)) * a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5d+166)) then
        tmp = (-1.0d0) * -a
    else if (t <= 9d+171) then
        tmp = (a + z) - b
    else
        tmp = (t / (t + x)) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5e+166) {
		tmp = -1.0 * -a;
	} else if (t <= 9e+171) {
		tmp = (a + z) - b;
	} else {
		tmp = (t / (t + x)) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5e+166:
		tmp = -1.0 * -a
	elif t <= 9e+171:
		tmp = (a + z) - b
	else:
		tmp = (t / (t + x)) * a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5e+166)
		tmp = Float64(-1.0 * Float64(-a));
	elseif (t <= 9e+171)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(Float64(t / Float64(t + x)) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5e+166)
		tmp = -1.0 * -a;
	elseif (t <= 9e+171)
		tmp = (a + z) - b;
	else
		tmp = (t / (t + x)) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5e+166], N[(-1.0 * (-a)), $MachinePrecision], If[LessEqual[t, 9e+171], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.0000000000000002e166

   1. Initial program 49.1%

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

   3. Taylor expanded in 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. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

   5. Applied rewrites 64.0%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 88.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 66.7%

       \[\leadsto \left(-a\right) \cdot -1 \]

   if -5.0000000000000002e166 < t < 8.99999999999999937e171

   1. Initial program 66.2%

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

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

      3. lower-+.f64 58.4

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

   5. Applied rewrites 58.4%

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

   if 8.99999999999999937e171 < t

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 76.1

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

   5. Applied rewrites 76.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.8%

      \[\leadsto a \cdot \color{blue}{\frac{t}{x + t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+166}:\\ \;\;\;\;-1 \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+171}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t + x} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+171}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -1.0 (- a))))
   (if (<= t -5e+166) t_1 (if (<= t 9e+171) (- (+ a z) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -1.0 * -a;
	double tmp;
	if (t <= -5e+166) {
		tmp = t_1;
	} else if (t <= 9e+171) {
		tmp = (a + z) - 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 = (-1.0d0) * -a
    if (t <= (-5d+166)) then
        tmp = t_1
    else if (t <= 9d+171) then
        tmp = (a + z) - 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 = -1.0 * -a;
	double tmp;
	if (t <= -5e+166) {
		tmp = t_1;
	} else if (t <= 9e+171) {
		tmp = (a + z) - b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -1.0 * -a
	tmp = 0
	if t <= -5e+166:
		tmp = t_1
	elif t <= 9e+171:
		tmp = (a + z) - b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-1.0 * Float64(-a))
	tmp = 0.0
	if (t <= -5e+166)
		tmp = t_1;
	elseif (t <= 9e+171)
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -1.0 * -a;
	tmp = 0.0;
	if (t <= -5e+166)
		tmp = t_1;
	elseif (t <= 9e+171)
		tmp = (a + z) - b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-1.0 * (-a)), $MachinePrecision]}, If[LessEqual[t, -5e+166], t$95$1, If[LessEqual[t, 9e+171], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.0000000000000002e166 or 8.99999999999999937e171 < t

   1. Initial program 50.2%

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

   3. Taylor expanded in 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. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. lower--.f64 N/A

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in a around -inf

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

   8. Applied rewrites 87.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 70.1%

       \[\leadsto \left(-a\right) \cdot -1 \]

   if -5.0000000000000002e166 < t < 8.99999999999999937e171

   1. Initial program 66.2%

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

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

      3. lower-+.f64 58.4

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

   5. Applied rewrites 58.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+166}:\\ \;\;\;\;-1 \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+171}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(-a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+61}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -3.8e+45) t_1 (if (<= y 2.25e+61) (+ a z) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -3.8e+45) {
		tmp = t_1;
	} else if (y <= 2.25e+61) {
		tmp = a + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a + z) - b
    if (y <= (-3.8d+45)) then
        tmp = t_1
    else if (y <= 2.25d+61) then
        tmp = a + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + z) - b;
	double tmp;
	if (y <= -3.8e+45) {
		tmp = t_1;
	} else if (y <= 2.25e+61) {
		tmp = a + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + z) - b
	tmp = 0
	if y <= -3.8e+45:
		tmp = t_1
	elif y <= 2.25e+61:
		tmp = a + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + z) - b)
	tmp = 0.0
	if (y <= -3.8e+45)
		tmp = t_1;
	elseif (y <= 2.25e+61)
		tmp = Float64(a + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + z) - b;
	tmp = 0.0;
	if (y <= -3.8e+45)
		tmp = t_1;
	elseif (y <= 2.25e+61)
		tmp = a + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -3.8e+45], t$95$1, If[LessEqual[y, 2.25e+61], N[(a + z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000002e45 or 2.25e61 < y

   1. Initial program 39.7%

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

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

      3. lower-+.f64 79.2

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

   5. Applied rewrites 79.2%

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

   if -3.8000000000000002e45 < y < 2.25e61

   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 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. +-commutative N/A

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

      3. lower-+.f64 34.1

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

   5. Applied rewrites 34.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 46.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+61}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+230}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.65e+230) (- z b) (if (<= y 1.1e+113) (+ a z) (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.65e+230) {
		tmp = z - b;
	} else if (y <= 1.1e+113) {
		tmp = a + z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.65d+230)) then
        tmp = z - b
    else if (y <= 1.1d+113) then
        tmp = a + z
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.65e+230) {
		tmp = z - b;
	} else if (y <= 1.1e+113) {
		tmp = a + z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.65e+230:
		tmp = z - b
	elif y <= 1.1e+113:
		tmp = a + z
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.65e+230)
		tmp = Float64(z - b);
	elseif (y <= 1.1e+113)
		tmp = Float64(a + z);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.65e+230)
		tmp = z - b;
	elseif (y <= 1.1e+113)
		tmp = a + z;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.65e+230], N[(z - b), $MachinePrecision], If[LessEqual[y, 1.1e+113], N[(a + z), $MachinePrecision], N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65000000000000007e230

   1. Initial program 3.7%

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

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

      3. lower-+.f64 75.2

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 75.6%

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

   if -1.65000000000000007e230 < y < 1.10000000000000005e113

   1. Initial program 72.9%

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

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

      3. lower-+.f64 44.1

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

   5. Applied rewrites 44.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 50.0%

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

   if 1.10000000000000005e113 < y

   1. Initial program 34.7%

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

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

      3. lower-+.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 66.3%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+230}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+217}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.1e+217) (- a b) (if (<= y 1.1e+113) (+ a z) (- a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.1e+217) {
		tmp = a - b;
	} else if (y <= 1.1e+113) {
		tmp = a + z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.1d+217)) then
        tmp = a - b
    else if (y <= 1.1d+113) then
        tmp = a + z
    else
        tmp = a - b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.1e+217) {
		tmp = a - b;
	} else if (y <= 1.1e+113) {
		tmp = a + z;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.1e+217:
		tmp = a - b
	elif y <= 1.1e+113:
		tmp = a + z
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.1e+217)
		tmp = Float64(a - b);
	elseif (y <= 1.1e+113)
		tmp = Float64(a + z);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.1e+217)
		tmp = a - b;
	elseif (y <= 1.1e+113)
		tmp = a + z;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.1e+217], N[(a - b), $MachinePrecision], If[LessEqual[y, 1.1e+113], N[(a + z), $MachinePrecision], N[(a - b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e217 or 1.10000000000000005e113 < y

   1. Initial program 28.8%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 81.0

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

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 67.1%

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

   if -1.1e217 < y < 1.10000000000000005e113

   1. Initial program 72.7%

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

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

      3. lower-+.f64 43.8

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

   5. Applied rewrites 43.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 49.9%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+217}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+113}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+230}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= y -2.65e+230) (- b) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.65e+230) {
		tmp = -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 <= (-2.65d+230)) then
        tmp = -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 <= -2.65e+230) {
		tmp = -b;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.65e+230:
		tmp = -b
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.65e+230)
		tmp = Float64(-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 <= -2.65e+230)
		tmp = -b;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.65e+230], (-b), N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65000000000000017e230

   1. Initial program 3.7%

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

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

      3. lower-+.f64 75.2

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

   5. Applied rewrites 75.2%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 68.0%

      \[\leadsto -b \]

   if -2.65000000000000017e230 < y

   1. Initial program 66.0%

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

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

      3. lower-+.f64 51.0

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 50.8%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+230}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 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 62.8%

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

3. Taylor expanded in 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. +-commutative N/A

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

   3. lower-+.f64 52.2

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

5. Applied rewrites 52.2%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 14.7%

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

Developer Target 1: 81.8% 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 2024235 
(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)))