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

Percentage Accurate: 61.6% → 93.1%

Time: 9.7s

Alternatives: 13

Speedup: 0.9×

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: 61.6% 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: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + t\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{y}{t\_2}\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{-45} \lor \neg \left(z \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{-b}{z}, t\_3, \frac{x}{t\_2}\right) + \mathsf{fma}\left(a, \frac{t\_3 + \frac{t}{t\_2}}{z}, t\_3\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{t\_1} + \frac{y}{t\_1}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ y x) t)) (t_2 (+ (+ x t) y)) (t_3 (/ y t_2)))
   (if (or (<= z -2.45e-45) (not (<= z 8e-37)))
     (*
      (+ (fma (/ (- b) z) t_3 (/ x t_2)) (fma a (/ (+ t_3 (/ t t_2)) z) t_3))
      z)
     (fma (+ (/ t t_1) (/ y t_1)) a (/ (fma z x (* y (- z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y + x) + t;
	double t_2 = (x + t) + y;
	double t_3 = y / t_2;
	double tmp;
	if ((z <= -2.45e-45) || !(z <= 8e-37)) {
		tmp = (fma((-b / z), t_3, (x / t_2)) + fma(a, ((t_3 + (t / t_2)) / z), t_3)) * z;
	} else {
		tmp = fma(((t / t_1) + (y / t_1)), a, (fma(z, x, (y * (z - b))) / t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y + x) + t)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(y / t_2)
	tmp = 0.0
	if ((z <= -2.45e-45) || !(z <= 8e-37))
		tmp = Float64(Float64(fma(Float64(Float64(-b) / z), t_3, Float64(x / t_2)) + fma(a, Float64(Float64(t_3 + Float64(t / t_2)) / z), t_3)) * z);
	else
		tmp = fma(Float64(Float64(t / t_1) + Float64(y / t_1)), a, Float64(fma(z, x, Float64(y * Float64(z - b))) / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(y / t$95$2), $MachinePrecision]}, If[Or[LessEqual[z, -2.45e-45], N[Not[LessEqual[z, 8e-37]], $MachinePrecision]], N[(N[(N[(N[((-b) / z), $MachinePrecision] * t$95$3 + N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(t$95$3 + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision] * a + N[(N[(z * x + N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4499999999999999e-45 or 8.00000000000000053e-37 < z

   1. Initial program 47.5%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 99.8%

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

   if -2.4499999999999999e-45 < z < 8.00000000000000053e-37

   1. Initial program 70.0%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 87.4%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-45} \lor \neg \left(z \leq 8 \cdot 10^{-37}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{-b}{z}, \frac{y}{\left(x + t\right) + y}, \frac{x}{\left(x + t\right) + y}\right) + \mathsf{fma}\left(a, \frac{\frac{y}{\left(x + t\right) + y} + \frac{t}{\left(x + t\right) + y}}{z}, \frac{y}{\left(x + t\right) + y}\right)\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{\left(y + x\right) + t} + \frac{y}{\left(y + x\right) + t}, a, \frac{\mathsf{fma}\left(z, x, y \cdot \left(z - b\right)\right)}{\left(y + x\right) + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + y\right) \cdot a\\ t_2 := \left(x + t\right) + y\\ t_3 := \frac{\left(\left(x + y\right) \cdot z + t\_1\right) - y \cdot b}{t\_2}\\ t_4 := \left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{+163}:\\ \;\;\;\;\frac{t\_1 - y \cdot b}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, t\_1\right)}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t y) a))
        (t_2 (+ (+ x t) y))
        (t_3 (/ (- (+ (* (+ x y) z) t_1) (* y b)) t_2))
        (t_4 (- (+ z a) (* y (/ b (+ (+ t x) y))))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -1e+163)
       (/ (- t_1 (* y b)) t_2)
       (if (<= t_3 5e+45) (/ (fma (+ y x) z t_1) (+ (+ y x) t)) t_4)))))

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 + t) + y;
	double t_3 = ((((x + y) * z) + t_1) - (y * b)) / t_2;
	double t_4 = (z + a) - (y * (b / ((t + x) + y)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -1e+163) {
		tmp = (t_1 - (y * b)) / t_2;
	} else if (t_3 <= 5e+45) {
		tmp = fma((y + x), z, t_1) / ((y + x) + t);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + y) * a)
	t_2 = Float64(Float64(x + t) + y)
	t_3 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + t_1) - Float64(y * b)) / t_2)
	t_4 = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -1e+163)
		tmp = Float64(Float64(t_1 - Float64(y * b)) / t_2);
	elseif (t_3 <= 5e+45)
		tmp = Float64(fma(Float64(y + x), z, t_1) / Float64(Float64(y + x) + t));
	else
		tmp = t_4;
	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[(x + t), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -1e+163], N[(N[(t$95$1 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$3, 5e+45], N[(N[(N[(y + x), $MachinePrecision] * z + t$95$1), $MachinePrecision] / N[(N[(y + x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]

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 5e45 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 23.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

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

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 28.9%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 80.3

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

   7. Applied rewrites 80.3%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -9.9999999999999994e162

   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 z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -9.9999999999999994e162 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5e45

   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

      \[\leadsto \color{blue}{\frac{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}{t + \left(x + y\right)}} \]
   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 79.4

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

   5. Applied rewrites 79.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -1 \cdot 10^{+163}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot a - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y + x, z, \left(t + y\right) \cdot a\right)}{\left(y + x\right) + t}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+235}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- INFINITY)) (not (<= t_1 5e+235)))
     (- (+ z a) (* y (/ b (+ (+ t x) y))))
     t_1)))

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 <= -((double) INFINITY)) || !(t_1 <= 5e+235)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static 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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+235)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+235):
		tmp = (z + a) - (y * (b / ((t + x) + y)))
	else:
		tmp = t_1
	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 <= Float64(-Inf)) || !(t_1 <= 5e+235))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+235)))
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	else
		tmp = t_1;
	end
	tmp_2 = 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, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+235]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

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 5.00000000000000027e235 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 6.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

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

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 13.9%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000027e235

   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 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+235}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-132} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \end{array} \]

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-132) (not (<= t_1 5e+45)))
     (- (+ z a) (* y (/ b (+ (+ t x) y))))
     (/ (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-132) || !(t_1 <= 5e+45)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} 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-132) || !(t_1 <= 5e+45))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	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-132], N[Not[LessEqual[t$95$1, 5e+45]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)) < -2e-132 or 5e45 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 49.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

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

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.2

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

   7. Applied rewrites 77.2%

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

   if -2e-132 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5e45

   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. 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 75.8

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

   5. Applied rewrites 75.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -2 \cdot 10^{-132} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-33} \lor \neg \left(y \leq 690\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{x + t}, x \cdot \frac{z}{x + t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e-33) (not (<= y 690.0)))
   (- (+ z a) (* y (/ b (+ (+ t x) y))))
   (fma a (/ t (+ x t)) (* x (/ z (+ x t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e-33) || !(y <= 690.0)) {
		tmp = (z + a) - (y * (b / ((t + x) + y)));
	} else {
		tmp = fma(a, (t / (x + t)), (x * (z / (x + t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e-33) || !(y <= 690.0))
		tmp = Float64(Float64(z + a) - Float64(y * Float64(b / Float64(Float64(t + x) + y))));
	else
		tmp = fma(a, Float64(t / Float64(x + t)), Float64(x * Float64(z / Float64(x + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e-33], N[Not[LessEqual[y, 690.0]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - N[(y * N[(b / N[(N[(t + x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(t / N[(x + t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z / N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0000000000000001e-33 or 690 < y

   1. Initial program 43.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

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

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 50.2%

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

   5. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 86.2

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

   7. Applied rewrites 86.2%

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

   if -1.0000000000000001e-33 < y < 690

   1. Initial program 70.7%

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

   3. Taylor expanded in a around 0

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

      1. associate--l+ N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 86.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-33} \lor \neg \left(y \leq 690\right):\\ \;\;\;\;\left(z + a\right) - y \cdot \frac{b}{\left(t + x\right) + y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{t}{x + t}, x \cdot \frac{z}{x + t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-208}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;y \leq 23000000:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ a z) b)))
   (if (<= y -1e-33)
     t_1
     (if (<= y -4e-211)
       (* a (/ t (+ t x)))
       (if (<= y 1.7e-208)
         (/ (fma a t (* z x)) (+ t x))
         (if (<= y 23000000.0) (+ z a) 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 <= -1e-33) {
		tmp = t_1;
	} else if (y <= -4e-211) {
		tmp = a * (t / (t + x));
	} else if (y <= 1.7e-208) {
		tmp = fma(a, t, (z * x)) / (t + x);
	} else if (y <= 23000000.0) {
		tmp = z + a;
	} 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 <= -1e-33)
		tmp = t_1;
	elseif (y <= -4e-211)
		tmp = Float64(a * Float64(t / Float64(t + x)));
	elseif (y <= 1.7e-208)
		tmp = Float64(fma(a, t, Float64(z * x)) / Float64(t + x));
	elseif (y <= 23000000.0)
		tmp = Float64(z + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[y, -1e-33], t$95$1, If[LessEqual[y, -4e-211], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-208], N[(N[(a * t + N[(z * x), $MachinePrecision]), $MachinePrecision] / N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 23000000.0], N[(z + a), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0000000000000001e-33 or 2.3e7 < y

   1. Initial program 43.6%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -1.0000000000000001e-33 < y < -4.00000000000000034e-211

   1. Initial program 63.7%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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. 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 50.8

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

   5. Applied rewrites 50.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 62.3%

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

   if -4.00000000000000034e-211 < y < 1.7e-208

   1. Initial program 86.5%

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

   3. Taylor expanded in y around 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 75.5

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

   5. Applied rewrites 75.5%

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

   if 1.7e-208 < y < 2.3e7

   1. Initial program 60.7%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{a \cdot \left(t + y\right) + z \cdot \left(x + y\right)}{t + \left(x + y\right)}} \]
   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 45.1

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

   5. Applied rewrites 45.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 55.8%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-208}:\\ \;\;\;\;\frac{\mathsf{fma}\left(a, t, z \cdot x\right)}{t + x}\\ \mathbf{elif}\;y \leq 23000000:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-33} \lor \neg \left(y \leq 8.6 \cdot 10^{-15}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e-33) (not (<= y 8.6e-15)))
   (- (+ a z) b)
   (* a (/ t (+ t x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e-33) || !(y <= 8.6e-15)) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (t + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1d-33)) .or. (.not. (y <= 8.6d-15))) then
        tmp = (a + z) - b
    else
        tmp = a * (t / (t + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e-33) || !(y <= 8.6e-15)) {
		tmp = (a + z) - b;
	} else {
		tmp = a * (t / (t + x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1e-33) or not (y <= 8.6e-15):
		tmp = (a + z) - b
	else:
		tmp = a * (t / (t + x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e-33) || !(y <= 8.6e-15))
		tmp = Float64(Float64(a + z) - b);
	else
		tmp = Float64(a * Float64(t / Float64(t + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1e-33) || ~((y <= 8.6e-15)))
		tmp = (a + z) - b;
	else
		tmp = a * (t / (t + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e-33], N[Not[LessEqual[y, 8.6e-15]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(a * N[(t / N[(t + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0000000000000001e-33 or 8.5999999999999993e-15 < y

   1. Initial program 44.2%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 75.3

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

   5. Applied rewrites 75.3%

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

   if -1.0000000000000001e-33 < y < 8.5999999999999993e-15

   1. Initial program 70.3%

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

   3. Taylor expanded in y around 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 57.3

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

   5. Applied rewrites 57.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 53.4%

      \[\leadsto a \cdot \color{blue}{\frac{t}{t + x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-33} \lor \neg \left(y \leq 8.6 \cdot 10^{-15}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{t + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-13} \lor \neg \left(y \leq 23000000\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e-13) (not (<= y 23000000.0))) (- (+ a z) b) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e-13) || !(y <= 23000000.0)) {
		tmp = (a + z) - 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 ((y <= (-1.3d-13)) .or. (.not. (y <= 23000000.0d0))) then
        tmp = (a + z) - 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 ((y <= -1.3e-13) || !(y <= 23000000.0)) {
		tmp = (a + z) - b;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e-13) or not (y <= 23000000.0):
		tmp = (a + z) - b
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e-13) || !(y <= 23000000.0))
		tmp = Float64(Float64(a + z) - 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 ((y <= -1.3e-13) || ~((y <= 23000000.0)))
		tmp = (a + z) - b;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e-13], N[Not[LessEqual[y, 23000000.0]], $MachinePrecision]], N[(N[(a + z), $MachinePrecision] - b), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e-13 or 2.3e7 < y

   1. Initial program 42.1%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 76.8

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

   5. Applied rewrites 76.8%

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

   if -1.3e-13 < y < 2.3e7

   1. Initial program 70.6%

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

   3. Taylor expanded in 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 57.2

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

   5. Applied rewrites 57.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 52.8%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-13} \lor \neg \left(y \leq 23000000\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+194} \lor \neg \left(t \leq 9.8 \cdot 10^{+204}\right):\\ \;\;\;\;a \cdot 1\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.9e+194) (not (<= t 9.8e+204))) (* a 1.0) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.9e+194) || !(t <= 9.8e+204)) {
		tmp = a * 1.0;
	} 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 ((t <= (-2.9d+194)) .or. (.not. (t <= 9.8d+204))) then
        tmp = a * 1.0d0
    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 ((t <= -2.9e+194) || !(t <= 9.8e+204)) {
		tmp = a * 1.0;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.9e+194) or not (t <= 9.8e+204):
		tmp = a * 1.0
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.9e+194) || !(t <= 9.8e+204))
		tmp = Float64(a * 1.0);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.9e+194) || ~((t <= 9.8e+204)))
		tmp = a * 1.0;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.9e+194], N[Not[LessEqual[t, 9.8e+204]], $MachinePrecision]], N[(a * 1.0), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000001e194 or 9.7999999999999995e204 < t

   1. Initial program 37.4%

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

   3. Taylor expanded in y around 0

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

      1. 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 31.9

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

   5. Applied rewrites 31.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 67.7%

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

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 65.8%

       \[\leadsto a \cdot 1 \]

   if -2.9000000000000001e194 < t < 9.7999999999999995e204

   1. Initial program 61.5%

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

   3. Taylor expanded in 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 45.3

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

   5. Applied rewrites 45.3%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 57.3%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+194} \lor \neg \left(t \leq 9.8 \cdot 10^{+204}\right):\\ \;\;\;\;a \cdot 1\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-152} \lor \neg \left(x \leq -6.6 \cdot 10^{-295}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -1.7e-152) (not (<= x -6.6e-295))) (+ z a) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -1.7e-152) || !(x <= -6.6e-295)) {
		tmp = z + a;
	} 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 ((x <= (-1.7d-152)) .or. (.not. (x <= (-6.6d-295)))) then
        tmp = z + a
    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 ((x <= -1.7e-152) || !(x <= -6.6e-295)) {
		tmp = z + a;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -1.7e-152) or not (x <= -6.6e-295):
		tmp = z + a
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -1.7e-152) || !(x <= -6.6e-295))
		tmp = Float64(z + a);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -1.7e-152) || ~((x <= -6.6e-295)))
		tmp = z + a;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -1.7e-152], N[Not[LessEqual[x, -6.6e-295]], $MachinePrecision]], N[(z + a), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999992e-152 or -6.5999999999999997e-295 < x

   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 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 43.5

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

   5. Applied rewrites 43.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 56.9%

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

   if -1.69999999999999992e-152 < x < -6.5999999999999997e-295

   1. Initial program 63.1%

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

   3. Taylor expanded in y around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 62.7

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

   5. Applied rewrites 62.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 68.2%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-152} \lor \neg \left(x \leq -6.6 \cdot 10^{-295}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+57} \lor \neg \left(z \leq 3.8 \cdot 10^{+85}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.12e+57) (not (<= z 3.8e+85))) (- z b) (- a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.12e+57) || !(z <= 3.8e+85)) {
		tmp = z - b;
	} 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 ((z <= (-1.12d+57)) .or. (.not. (z <= 3.8d+85))) then
        tmp = z - b
    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 ((z <= -1.12e+57) || !(z <= 3.8e+85)) {
		tmp = z - b;
	} else {
		tmp = a - b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.12e+57) or not (z <= 3.8e+85):
		tmp = z - b
	else:
		tmp = a - b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.12e+57) || !(z <= 3.8e+85))
		tmp = Float64(z - b);
	else
		tmp = Float64(a - b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.12e+57) || ~((z <= 3.8e+85)))
		tmp = z - b;
	else
		tmp = a - b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.12e+57], N[Not[LessEqual[z, 3.8e+85]], $MachinePrecision]], N[(z - b), $MachinePrecision], N[(a - b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12000000000000003e57 or 3.79999999999999992e85 < z

   1. Initial program 33.8%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 56.7

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

   5. Applied rewrites 56.7%

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

   6. Taylor expanded in b around inf

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

   8. Applied rewrites 10.6%

      \[\leadsto -b \]

   9. Taylor expanded in a around 0

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

   11. Applied rewrites 57.7%

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

   if -1.12000000000000003e57 < z < 3.79999999999999992e85

   1. Initial program 70.5%

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   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 53.5

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

   5. Applied rewrites 53.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 49.5%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+57} \lor \neg \left(z \leq 3.8 \cdot 10^{+85}\right):\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.9% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.9%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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 54.7

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

5. Applied rewrites 54.7%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 39.5%

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

9. Final simplification 39.5%

   \[\leadsto a - b \]
10. Add Preprocessing

Alternative 13: 13.4% 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 56.9%

   \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
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 54.7

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

5. Applied rewrites 54.7%

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

6. Taylor expanded in b around inf

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

8. Applied rewrites 13.0%

   \[\leadsto -b \]

9. Final simplification 13.0%

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

Developer Target 1: 82.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024298 
(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)))