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

Percentage Accurate: 60.3% → 87.9%

Time: 9.2s

Alternatives: 12

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 60.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 10^{+252}\right):\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-y, b, \mathsf{fma}\left(a, t + y, z \cdot \left(y + x\right)\right)\right)}{t\_1}\\ \end{array} \end{array} \]

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_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+252)))
     (+ (- z b) a)
     (/ (fma (- y) b (fma a (+ t y) (* z (+ y x)))) t_1))))

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)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+252)) {
		tmp = (z - b) + a;
	} else {
		tmp = fma(-y, b, fma(a, (t + y), (z * (y + x)))) / t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+252))
		tmp = Float64(Float64(z - b) + a);
	else
		tmp = Float64(fma(Float64(-y), b, fma(a, Float64(t + y), Float64(z * Float64(y + x)))) / t_1);
	end
	return 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[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+252]], $MachinePrecision]], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], N[(N[((-y) * b + N[(a * N[(t + y), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

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 1.0000000000000001e252 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 9.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 81.2

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

   5. Applied rewrites 81.2%

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

   7. Applied rewrites 81.2%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e252

   1. Initial program 99.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 99.0

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 99.0

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.0

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

      15. lift-+.f64 N/A

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

      16. +-commutative N/A

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

      17. lower-+.f64 99.0

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

   4. Applied rewrites 99.0%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+252}\right):\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-y, b, \mathsf{fma}\left(a, t + y, z \cdot \left(y + x\right)\right)\right)}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := \left(z - b\right) + a\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+67}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, y, \mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)\right)}{y + x}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y)))
        (t_3 (+ (- z b) a)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 1e+67)
       (/ (fma (+ y x) z t_1) (+ (+ y x) t))
       (if (<= t_2 5e+153)
         (/ (fma a y (fma z x (* y (- z b)))) (+ y x))
         t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double t_3 = (z - b) + a;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= 1e+67) {
		tmp = fma((y + x), z, t_1) / ((y + x) + t);
	} else if (t_2 <= 5e+153) {
		tmp = fma(a, y, fma(z, x, (y * (z - b)))) / (y + x);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(Float64(z - b) + a)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= 1e+67)
		tmp = Float64(fma(Float64(y + x), z, t_1) / Float64(Float64(y + x) + t));
	elseif (t_2 <= 5e+153)
		tmp = Float64(fma(a, y, fma(z, x, Float64(y * Float64(z - b)))) / Float64(y + x));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, 1e+67], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+153], N[(N[(a * y + N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision], 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)) < -inf.0 or 5.00000000000000018e153 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 17.5%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 80.4

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

   5. Applied rewrites 80.4%

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

   7. Applied rewrites 80.4%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999983e66

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 81.4

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

   5. Applied rewrites 81.4%

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

   if 9.99999999999999983e66 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000018e153

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. distribute-rgt-in N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 89.6

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

   5. Applied rewrites 89.6%

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

Alternative 3: 66.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := \left(z - b\right) + a\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+195}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+67}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, y, \mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)\right)}{y + x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ (- z b) a)))
   (if (<= t_1 -2e+195)
     t_2
     (if (<= t_1 1e+67)
       (/ (fma a t (* z x)) (+ t x))
       (if (<= t_1 5e+153)
         (/ (fma a y (fma z x (* y (- z b)))) (+ y x))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = (z - b) + a;
	double tmp;
	if (t_1 <= -2e+195) {
		tmp = t_2;
	} else if (t_1 <= 1e+67) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (t_1 <= 5e+153) {
		tmp = fma(a, y, fma(z, x, (y * (z - b)))) / (y + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(Float64(z - b) + a)
	tmp = 0.0
	if (t_1 <= -2e+195)
		tmp = t_2;
	elseif (t_1 <= 1e+67)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (t_1 <= 5e+153)
		tmp = Float64(fma(a, y, fma(z, x, Float64(y * Float64(z - b)))) / Float64(y + 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[(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]}, Block[{t$95$2 = N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+195], t$95$2, If[LessEqual[t$95$1, 1e+67], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+153], N[(N[(a * y + N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $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)) < -1.99999999999999995e195 or 5.00000000000000018e153 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 23.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 80.2

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

   5. Applied rewrites 80.2%

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

   7. Applied rewrites 80.2%

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

   if -1.99999999999999995e195 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999983e66

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 66.6

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

   5. Applied rewrites 66.6%

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

   if 9.99999999999999983e66 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000018e153

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. associate--l+ N/A

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

      3. lower-fma.f64 N/A

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

      4. distribute-rgt-in N/A

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

      5. associate--l+ N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. *-commutative N/A

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

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

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

      10. lower-*.f64 N/A

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

      11. lower--.f64 N/A

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

      12. +-commutative N/A

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

      13. lower-+.f64 89.6

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

   5. Applied rewrites 89.6%

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

Alternative 4: 66.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := \left(z - b\right) + a\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+195}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-b, y, t\_1\right)}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (/ (- (+ (* (+ x y) z) t_1) (* y b)) (+ (+ x t) y)))
        (t_3 (+ (- z b) a)))
   (if (<= t_2 -2e+195)
     t_3
     (if (<= t_2 4e+42)
       (/ (fma a t (* z x)) (+ t x))
       (if (<= t_2 5e+153) (/ (fma (- b) y t_1) (+ (+ y x) t)) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + y) * a;
	double t_2 = ((((x + y) * z) + t_1) - (y * b)) / ((x + t) + y);
	double t_3 = (z - b) + a;
	double tmp;
	if (t_2 <= -2e+195) {
		tmp = t_3;
	} else if (t_2 <= 4e+42) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (t_2 <= 5e+153) {
		tmp = fma(-b, y, t_1) / ((y + x) + t);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_3 = Float64(Float64(z - b) + a)
	tmp = 0.0
	if (t_2 <= -2e+195)
		tmp = t_3;
	elseif (t_2 <= 4e+42)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (t_2 <= 5e+153)
		tmp = Float64(fma(Float64(-b), y, t_1) / Float64(Float64(y + x) + t));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + y), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+195], t$95$3, If[LessEqual[t$95$2, 4e+42], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+153], N[(N[((-b) * y + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], 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)) < -1.99999999999999995e195 or 5.00000000000000018e153 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 23.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 80.2

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

   5. Applied rewrites 80.2%

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

   7. Applied rewrites 80.2%

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

   if -1.99999999999999995e195 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.00000000000000018e42

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 66.0

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

   5. Applied rewrites 66.0%

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

   if 4.00000000000000018e42 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

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

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 83.3

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

   5. Applied rewrites 83.3%

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

Alternative 5: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+195} \lor \neg \left(t\_1 \leq 10^{+67}\right):\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))))
   (if (or (<= t_1 -2e+195) (not (<= t_1 1e+67)))
     (+ (- z b) a)
     (/ (fma a t (* z x)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double tmp;
	if ((t_1 <= -2e+195) || !(t_1 <= 1e+67)) {
		tmp = (z - b) + a;
	} else {
		tmp = fma(a, t, (z * x)) / (t + x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	tmp = 0.0
	if ((t_1 <= -2e+195) || !(t_1 <= 1e+67))
		tmp = Float64(Float64(z - b) + a);
	else
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -2e+195], N[Not[LessEqual[t$95$1, 1e+67]], $MachinePrecision]], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision]]]

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)) < -1.99999999999999995e195 or 9.99999999999999983e66 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 29.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 77.4

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

   5. Applied rewrites 77.4%

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

   7. Applied rewrites 77.5%

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

   if -1.99999999999999995e195 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999983e66

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 66.6

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

   5. Applied rewrites 66.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{+195} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 10^{+67}\right):\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{t + x} \cdot z\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-32}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+125}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;z - \frac{b - a}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.9e+149)
   (* (/ x (+ t x)) z)
   (if (<= x -3.8e-32)
     (+ z a)
     (if (<= x 2.3e+125) (+ (- z b) a) (- z (* (/ (- b a) x) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e+149) {
		tmp = (x / (t + x)) * z;
	} else if (x <= -3.8e-32) {
		tmp = z + a;
	} else if (x <= 2.3e+125) {
		tmp = (z - b) + a;
	} else {
		tmp = z - (((b - a) / x) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.9d+149)) then
        tmp = (x / (t + x)) * z
    else if (x <= (-3.8d-32)) then
        tmp = z + a
    else if (x <= 2.3d+125) then
        tmp = (z - b) + a
    else
        tmp = z - (((b - a) / x) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e+149) {
		tmp = (x / (t + x)) * z;
	} else if (x <= -3.8e-32) {
		tmp = z + a;
	} else if (x <= 2.3e+125) {
		tmp = (z - b) + a;
	} else {
		tmp = z - (((b - a) / x) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.9e+149:
		tmp = (x / (t + x)) * z
	elif x <= -3.8e-32:
		tmp = z + a
	elif x <= 2.3e+125:
		tmp = (z - b) + a
	else:
		tmp = z - (((b - a) / x) * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.9e+149)
		tmp = Float64(Float64(x / Float64(t + x)) * z);
	elseif (x <= -3.8e-32)
		tmp = Float64(z + a);
	elseif (x <= 2.3e+125)
		tmp = Float64(Float64(z - b) + a);
	else
		tmp = Float64(z - Float64(Float64(Float64(b - a) / x) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.9e+149)
		tmp = (x / (t + x)) * z;
	elseif (x <= -3.8e-32)
		tmp = z + a;
	elseif (x <= 2.3e+125)
		tmp = (z - b) + a;
	else
		tmp = z - (((b - a) / x) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.9e+149], N[(N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[x, -3.8e-32], N[(z + a), $MachinePrecision], If[LessEqual[x, 2.3e+125], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], N[(z - N[(N[(N[(b - a), $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.9000000000000002e149

   1. Initial program 55.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 70.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 70.7%

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

   if -2.9000000000000002e149 < x < -3.80000000000000008e-32

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 50.8

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

   5. Applied rewrites 50.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 8.9%

      \[\leadsto -b \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 62.3%

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

   if -3.80000000000000008e-32 < x < 2.30000000000000013e125

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 67.9

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

   5. Applied rewrites 67.9%

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

   7. Applied rewrites 68.0%

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

   if 2.30000000000000013e125 < x

   1. Initial program 56.3%

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

   3. Taylor expanded in x around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 60.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 76.7%

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

Alternative 7: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t + x} \cdot z\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-32}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+125}:\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x (+ t x)) z)))
   (if (<= x -2.9e+149)
     t_1
     (if (<= x -3.8e-32) (+ z a) (if (<= x 2e+125) (+ (- z b) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (t + x)) * z;
	double tmp;
	if (x <= -2.9e+149) {
		tmp = t_1;
	} else if (x <= -3.8e-32) {
		tmp = z + a;
	} else if (x <= 2e+125) {
		tmp = (z - b) + a;
	} 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 = (x / (t + x)) * z
    if (x <= (-2.9d+149)) then
        tmp = t_1
    else if (x <= (-3.8d-32)) then
        tmp = z + a
    else if (x <= 2d+125) then
        tmp = (z - b) + a
    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 = (x / (t + x)) * z;
	double tmp;
	if (x <= -2.9e+149) {
		tmp = t_1;
	} else if (x <= -3.8e-32) {
		tmp = z + a;
	} else if (x <= 2e+125) {
		tmp = (z - b) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (t + x)) * z
	tmp = 0
	if x <= -2.9e+149:
		tmp = t_1
	elif x <= -3.8e-32:
		tmp = z + a
	elif x <= 2e+125:
		tmp = (z - b) + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(t + x)) * z)
	tmp = 0.0
	if (x <= -2.9e+149)
		tmp = t_1;
	elseif (x <= -3.8e-32)
		tmp = Float64(z + a);
	elseif (x <= 2e+125)
		tmp = Float64(Float64(z - b) + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (t + x)) * z;
	tmp = 0.0;
	if (x <= -2.9e+149)
		tmp = t_1;
	elseif (x <= -3.8e-32)
		tmp = z + a;
	elseif (x <= 2e+125)
		tmp = (z - b) + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(t + x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -2.9e+149], t$95$1, If[LessEqual[x, -3.8e-32], N[(z + a), $MachinePrecision], If[LessEqual[x, 2e+125], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9000000000000002e149 or 1.9999999999999998e125 < x

   1. Initial program 56.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

   5. Applied rewrites 75.4%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 72.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 68.2%

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

   if -2.9000000000000002e149 < x < -3.80000000000000008e-32

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 50.8

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

   5. Applied rewrites 50.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 8.9%

      \[\leadsto -b \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 62.3%

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

   if -3.80000000000000008e-32 < x < 1.9999999999999998e125

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 67.9

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

   5. Applied rewrites 67.9%

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

   7. Applied rewrites 68.0%

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

Alternative 8: 59.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+185} \lor \neg \left(t \leq 4 \cdot 10^{+113}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, x, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.8e+185) (not (<= t 4e+113)))
   (fma (/ z t) x a)
   (+ (- z b) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.8e+185) || !(t <= 4e+113)) {
		tmp = fma((z / t), x, a);
	} else {
		tmp = (z - b) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.8e+185) || !(t <= 4e+113))
		tmp = fma(Float64(z / t), x, a);
	else
		tmp = Float64(Float64(z - b) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.8e+185], N[Not[LessEqual[t, 4e+113]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * x + a), $MachinePrecision], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7999999999999998e185 or 4e113 < t

   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 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 46.2

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

   5. Applied rewrites 46.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 58.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 58.4%

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

   if -3.7999999999999998e185 < t < 4e113

   1. Initial program 62.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 66.0

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

   5. Applied rewrites 66.0%

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

   7. Applied rewrites 66.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+185} \lor \neg \left(t \leq 4 \cdot 10^{+113}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, x, a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - b\right) + a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+15} \lor \neg \left(y \leq 3.4 \cdot 10^{-233}\right):\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+15) (not (<= y 3.4e-233))) (+ (- z b) a) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+15) || !(y <= 3.4e-233)) {
		tmp = (z - b) + a;
	} else {
		tmp = z + 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 ((y <= (-1.05d+15)) .or. (.not. (y <= 3.4d-233))) then
        tmp = (z - b) + a
    else
        tmp = z + 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 ((y <= -1.05e+15) || !(y <= 3.4e-233)) {
		tmp = (z - b) + a;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+15) or not (y <= 3.4e-233):
		tmp = (z - b) + a
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+15) || !(y <= 3.4e-233))
		tmp = Float64(Float64(z - b) + a);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e+15) || ~((y <= 3.4e-233)))
		tmp = (z - b) + a;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+15], N[Not[LessEqual[y, 3.4e-233]], $MachinePrecision]], N[(N[(z - b), $MachinePrecision] + a), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e15 or 3.4000000000000002e-233 < y

   1. Initial program 53.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 68.7

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

   5. Applied rewrites 68.7%

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

   7. Applied rewrites 68.7%

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

   if -1.05e15 < y < 3.4000000000000002e-233

   1. Initial program 79.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 38.8

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

   5. Applied rewrites 38.8%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 4.2%

      \[\leadsto -b \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 54.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+15} \lor \neg \left(y \leq 3.4 \cdot 10^{-233}\right):\\ \;\;\;\;\left(z - b\right) + a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.9% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.52 \cdot 10^{+91}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.52e+91) (- a b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.52e+91) {
		tmp = a - b;
	} else {
		tmp = z + 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 (b <= (-1.52d+91)) then
        tmp = a - b
    else
        tmp = z + 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 (b <= -1.52e+91) {
		tmp = a - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.52e+91:
		tmp = a - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.52e+91)
		tmp = Float64(a - b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.52e+91)
		tmp = a - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.52e+91], N[(a - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.52e91

   1. Initial program 50.3%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 45.5

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 43.1%

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

   if -1.52e91 < b

   1. Initial program 65.9%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 60.1

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

   5. Applied rewrites 60.1%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 9.2%

      \[\leadsto -b \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 59.6%

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

Alternative 11: 50.8% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+198}:\\ \;\;\;\;-b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (if (<= b -1e+198) (- b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e+198) {
		tmp = -b;
	} else {
		tmp = z + 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 (b <= (-1d+198)) then
        tmp = -b
    else
        tmp = z + 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 (b <= -1e+198) {
		tmp = -b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e+198:
		tmp = -b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e+198)
		tmp = Float64(-b);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1e+198)
		tmp = -b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e+198], (-b), N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.00000000000000002e198

   1. Initial program 43.4%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. lower-+.f64 47.2

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

   5. Applied rewrites 47.2%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 42.7%

      \[\leadsto -b \]

   if -1.00000000000000002e198 < b

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 58.6

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

   5. Applied rewrites 58.6%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 11.1%

      \[\leadsto -b \]

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 57.7%

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

Alternative 12: 13.8% 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 63.3%

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

3. Taylor expanded in y around inf

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

   1. lower--.f64 N/A

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

   2. lower-+.f64 57.7

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

5. Applied rewrites 57.7%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 13.6%

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

Developer Target 1: 81.5% 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 2024329 
(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)))