Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.4% → 90.1%

Time: 17.9s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \left(\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_1\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + \frac{t\_1}{x \cdot t\_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3
         (-
          (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y)))
          (* y (/ (- t a) (* z (pow (- b y) 2.0)))))))
   (if (<= z -7e+79)
     t_3
     (if (<= z -3.8e-74)
       (/ (fma x y t_1) (fma z (- b y) y))
       (if (<= z 6.8e+42) (* x (+ (/ y t_2) (/ t_1 (* x t_2)))) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = (((x / z) * (y / (b - y))) + ((t - a) / (b - y))) - (y * ((t - a) / (z * pow((b - y), 2.0))));
	double tmp;
	if (z <= -7e+79) {
		tmp = t_3;
	} else if (z <= -3.8e-74) {
		tmp = fma(x, y, t_1) / fma(z, (b - y), y);
	} else if (z <= 6.8e+42) {
		tmp = x * ((y / t_2) + (t_1 / (x * t_2)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / Float64(z * (Float64(b - y) ^ 2.0)))))
	tmp = 0.0
	if (z <= -7e+79)
		tmp = t_3;
	elseif (z <= -3.8e-74)
		tmp = Float64(fma(x, y, t_1) / fma(z, Float64(b - y), y));
	elseif (z <= 6.8e+42)
		tmp = Float64(x * Float64(Float64(y / t_2) + Float64(t_1 / Float64(x * t_2))));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+79], t$95$3, If[LessEqual[z, -3.8e-74], N[(N[(x * y + t$95$1), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+42], N[(x * N[(N[(y / t$95$2), $MachinePrecision] + N[(t$95$1 / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999961e79 or 6.7999999999999995e42 < z

   1. Initial program 44.9%

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

      1. fma-define 44.9%

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

      2. +-commutative 44.9%

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

      3. fma-define 44.9%

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

   3. Simplified 44.9%

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

   5. Taylor expanded in z around inf 76.1%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
   6. Step-by-step derivation

      1. associate--r+ 76.1%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 76.1%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 76.1%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. times-frac 81.8%

         \[\leadsto \left(\color{blue}{\frac{x}{z} \cdot \frac{y}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. div-sub 81.8%

         \[\leadsto \left(\frac{x}{z} \cdot \frac{y}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. associate-/l* 95.1%

         \[\leadsto \left(\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   7. Simplified 95.1%

      \[\leadsto \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   if -6.99999999999999961e79 < z < -3.7999999999999996e-74

   1. Initial program 96.5%

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

      1. fma-define 96.5%

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

      2. +-commutative 96.5%

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

      3. fma-define 96.5%

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

   3. Simplified 96.5%

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

   if -3.7999999999999996e-74 < z < 6.7999999999999995e42

   1. Initial program 81.7%

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

      1. fma-define 81.7%

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

      2. +-commutative 81.7%

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

      3. fma-define 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in x around inf 94.1%

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

Alternative 2: 89.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \left(\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-69}:\\ \;\;\;\;\frac{z \cdot \left(t + \left(x \cdot \frac{y}{z} - a\right)\right)}{t\_1}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (-
          (+ (* (/ x z) (/ y (- b y))) (/ (- t a) (- b y)))
          (* y (/ (- t a) (* z (pow (- b y) 2.0)))))))
   (if (<= z -6e+79)
     t_2
     (if (<= z -1.4e-69)
       (/ (* z (+ t (- (* x (/ y z)) a))) t_1)
       (if (<= z 2.55e+44)
         (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((x / z) * (y / (b - y))) + ((t - a) / (b - y))) - (y * ((t - a) / (z * pow((b - y), 2.0))));
	double tmp;
	if (z <= -6e+79) {
		tmp = t_2;
	} else if (z <= -1.4e-69) {
		tmp = (z * (t + ((x * (y / z)) - a))) / t_1;
	} else if (z <= 2.55e+44) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (((x / z) * (y / (b - y))) + ((t - a) / (b - y))) - (y * ((t - a) / (z * ((b - y) ** 2.0d0))))
    if (z <= (-6d+79)) then
        tmp = t_2
    else if (z <= (-1.4d-69)) then
        tmp = (z * (t + ((x * (y / z)) - a))) / t_1
    else if (z <= 2.55d+44) then
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((x / z) * (y / (b - y))) + ((t - a) / (b - y))) - (y * ((t - a) / (z * Math.pow((b - y), 2.0))));
	double tmp;
	if (z <= -6e+79) {
		tmp = t_2;
	} else if (z <= -1.4e-69) {
		tmp = (z * (t + ((x * (y / z)) - a))) / t_1;
	} else if (z <= 2.55e+44) {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (((x / z) * (y / (b - y))) + ((t - a) / (b - y))) - (y * ((t - a) / (z * math.pow((b - y), 2.0))))
	tmp = 0
	if z <= -6e+79:
		tmp = t_2
	elif z <= -1.4e-69:
		tmp = (z * (t + ((x * (y / z)) - a))) / t_1
	elif z <= 2.55e+44:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / Float64(z * (Float64(b - y) ^ 2.0)))))
	tmp = 0.0
	if (z <= -6e+79)
		tmp = t_2;
	elseif (z <= -1.4e-69)
		tmp = Float64(Float64(z * Float64(t + Float64(Float64(x * Float64(y / z)) - a))) / t_1);
	elseif (z <= 2.55e+44)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (((x / z) * (y / (b - y))) + ((t - a) / (b - y))) - (y * ((t - a) / (z * ((b - y) ^ 2.0))));
	tmp = 0.0;
	if (z <= -6e+79)
		tmp = t_2;
	elseif (z <= -1.4e-69)
		tmp = (z * (t + ((x * (y / z)) - a))) / t_1;
	elseif (z <= 2.55e+44)
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+79], t$95$2, If[LessEqual[z, -1.4e-69], N[(N[(z * N[(t + N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.55e+44], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999948e79 or 2.55e44 < z

   1. Initial program 44.9%

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

      1. fma-define 44.9%

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

      2. +-commutative 44.9%

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

      3. fma-define 44.9%

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

   3. Simplified 44.9%

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

   5. Taylor expanded in z around inf 76.1%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
   6. Step-by-step derivation

      1. associate--r+ 76.1%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 76.1%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 76.1%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. times-frac 81.8%

         \[\leadsto \left(\color{blue}{\frac{x}{z} \cdot \frac{y}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. div-sub 81.8%

         \[\leadsto \left(\frac{x}{z} \cdot \frac{y}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. associate-/l* 95.1%

         \[\leadsto \left(\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   7. Simplified 95.1%

      \[\leadsto \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t - a}{b - y}\right) - y \cdot \frac{t - a}{z \cdot {\left(b - y\right)}^{2}}} \]

   if -5.99999999999999948e79 < z < -1.3999999999999999e-69

   1. Initial program 96.2%

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

      1. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in z around inf 96.1%

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

      1. associate--l+ 96.1%

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

      2. associate-/l* 96.3%

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

   7. Simplified 96.3%

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

   if -1.3999999999999999e-69 < z < 2.55e44

   1. Initial program 82.0%

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

      1. fma-define 82.0%

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

      2. +-commutative 82.0%

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

      3. fma-define 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 94.1%

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

Alternative 3: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+128} \lor \neg \left(z \leq 1.75 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -3.05e+128) (not (<= z 1.75e+72)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3.05e+128) || !(z <= 1.75e+72)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = y + (z * (b - y))
    if ((z <= (-3.05d+128)) .or. (.not. (z <= 1.75d+72))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -3.05e+128) || !(z <= 1.75e+72)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -3.05e+128) or not (z <= 1.75e+72):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -3.05e+128) || !(z <= 1.75e+72))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -3.05e+128) || ~((z <= 1.75e+72)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3.05e+128], N[Not[LessEqual[z, 1.75e+72]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0500000000000001e128 or 1.75000000000000005e72 < z

   1. Initial program 38.6%

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

      1. fma-define 38.6%

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

      2. +-commutative 38.6%

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

      3. fma-define 38.6%

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

   3. Simplified 38.6%

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

   5. Taylor expanded in z around inf 89.1%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -3.0500000000000001e128 < z < 1.75000000000000005e72

   1. Initial program 84.8%

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

      1. fma-define 84.8%

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

      2. +-commutative 84.8%

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

      3. fma-define 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around inf 91.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+128} \lor \neg \left(z \leq 1.75 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+58} \lor \neg \left(z \leq 1.9 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{z \cdot \left(t - a\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -4.4e+58) (not (<= z 1.9e+114)))
     (/ (- t a) (- b y))
     (+ (/ (* x y) t_1) (/ (* z (- t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -4.4e+58) || !(z <= 1.9e+114)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) / t_1) + ((z * (t - a)) / 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 = y + (z * (b - y))
    if ((z <= (-4.4d+58)) .or. (.not. (z <= 1.9d+114))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) / t_1) + ((z * (t - a)) / 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -4.4e+58) || !(z <= 1.9e+114)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -4.4e+58) or not (z <= 1.9e+114):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) / t_1) + ((z * (t - a)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -4.4e+58) || !(z <= 1.9e+114))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(Float64(z * Float64(t - a)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -4.4e+58) || ~((z <= 1.9e+114)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) / t_1) + ((z * (t - a)) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -4.4e+58], N[Not[LessEqual[z, 1.9e+114]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000001e58 or 1.9e114 < z

   1. Initial program 39.8%

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

      1. fma-define 39.8%

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

      2. +-commutative 39.8%

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

      3. fma-define 39.8%

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

   3. Simplified 39.8%

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

   5. Taylor expanded in z around inf 92.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -4.4000000000000001e58 < z < 1.9e114

   1. Initial program 84.1%

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

      1. fma-define 84.1%

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

      2. +-commutative 84.1%

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

      3. fma-define 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in x around 0 84.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+58} \lor \neg \left(z \leq 1.9 \cdot 10^{+114}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+52} \lor \neg \left(z \leq 2.5 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.1e+52) (not (<= z 2.5e+112)))
   (/ (- t a) (- b y))
   (/ (- (* x y) (* z (- a t))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e+52) || !(z <= 2.5e+112)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - 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 ((z <= (-1.1d+52)) .or. (.not. (z <= 2.5d+112))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - 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 ((z <= -1.1e+52) || !(z <= 2.5e+112)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.1e+52) or not (z <= 2.5e+112):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.1e+52) || !(z <= 2.5e+112))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.1e+52) || ~((z <= 2.5e+112)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) - (z * (a - t))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.1e+52], N[Not[LessEqual[z, 2.5e+112]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e52 or 2.5e112 < z

   1. Initial program 39.8%

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

      1. fma-define 39.8%

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

      2. +-commutative 39.8%

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

      3. fma-define 39.8%

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

   3. Simplified 39.8%

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

   5. Taylor expanded in z around inf 92.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.1e52 < z < 2.5e112

   1. Initial program 84.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+52} \lor \neg \left(z \leq 2.5 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+129} \lor \neg \left(z \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1e-69)
     t_1
     (if (<= z 3.7e-86)
       x
       (if (or (<= z 5.5e+129) (not (<= z 2e+267))) (/ a (- b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1e-69) {
		tmp = t_1;
	} else if (z <= 3.7e-86) {
		tmp = x;
	} else if ((z <= 5.5e+129) || !(z <= 2e+267)) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-1d-69)) then
        tmp = t_1
    else if (z <= 3.7d-86) then
        tmp = x
    else if ((z <= 5.5d+129) .or. (.not. (z <= 2d+267))) then
        tmp = a / -b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1e-69) {
		tmp = t_1;
	} else if (z <= 3.7e-86) {
		tmp = x;
	} else if ((z <= 5.5e+129) || !(z <= 2e+267)) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -1e-69:
		tmp = t_1
	elif z <= 3.7e-86:
		tmp = x
	elif (z <= 5.5e+129) or not (z <= 2e+267):
		tmp = a / -b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1e-69)
		tmp = t_1;
	elseif (z <= 3.7e-86)
		tmp = x;
	elseif ((z <= 5.5e+129) || !(z <= 2e+267))
		tmp = Float64(a / Float64(-b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -1e-69)
		tmp = t_1;
	elseif (z <= 3.7e-86)
		tmp = x;
	elseif ((z <= 5.5e+129) || ~((z <= 2e+267)))
		tmp = a / -b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-69], t$95$1, If[LessEqual[z, 3.7e-86], x, If[Or[LessEqual[z, 5.5e+129], N[Not[LessEqual[z, 2e+267]], $MachinePrecision]], N[(a / (-b)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999996e-70 or 5.49999999999999984e129 < z < 1.9999999999999999e267

   1. Initial program 55.9%

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

      1. fma-define 55.9%

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

   3. Simplified 55.9%

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

   5. Taylor expanded in t around inf 42.7%

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

      1. associate-+r+ 42.7%

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

      2. mul-1-neg 42.7%

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

      3. unsub-neg 42.7%

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

      4. associate-/l* 38.6%

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

      5. associate-/l* 38.6%

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

   7. Simplified 38.6%

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

   8. Taylor expanded in z around inf 75.6%

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

   9. Taylor expanded in t around inf 47.9%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -9.9999999999999996e-70 < z < 3.6999999999999998e-86

   1. Initial program 81.4%

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

      1. fma-define 81.5%

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

      2. +-commutative 81.5%

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

      3. fma-define 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in z around 0 59.0%

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

   if 3.6999999999999998e-86 < z < 5.49999999999999984e129 or 1.9999999999999999e267 < z

   1. Initial program 67.9%

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

      1. fma-define 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in t around inf 55.8%

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

      1. associate-+r+ 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. associate-/l* 52.9%

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

      5. associate-/l* 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in a around inf 33.7%

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

      1. associate-*r* 33.7%

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

      2. neg-mul-1 33.7%

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

   10. Simplified 33.7%

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

   11. Taylor expanded in y around 0 43.2%

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

       1. associate-*r/ 43.2%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. mul-1-neg 43.2%

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

   13. Simplified 43.2%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-69}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+129} \lor \neg \left(z \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1850000 \lor \neg \left(z \leq 78000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1850000.0) (not (<= z 78000.0)))
   (/ (- t a) (- b y))
   (/ (- (* x y) (* z (- a t))) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1850000.0) || !(z <= 78000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1850000.0d0)) .or. (.not. (z <= 78000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) - (z * (a - t))) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1850000.0) || !(z <= 78000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1850000.0) or not (z <= 78000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1850000.0) || !(z <= 78000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(a - t))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1850000.0) || ~((z <= 78000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) - (z * (a - t))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1850000.0], N[Not[LessEqual[z, 78000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85e6 or 78000 < z

   1. Initial program 52.1%

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

      1. fma-define 52.1%

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

      2. +-commutative 52.1%

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

      3. fma-define 52.1%

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

   3. Simplified 52.1%

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

   5. Taylor expanded in z around inf 83.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.85e6 < z < 78000

   1. Initial program 83.8%

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

   3. Taylor expanded in b around inf 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850000 \lor \neg \left(z \leq 78000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(a - t\right)}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+14}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4e+14)
   (/ a (- y b))
   (if (<= z -4.1e-57)
     (/ t (- b y))
     (if (<= z 7.6e-80) (+ x (/ (* z t) y)) (/ (- t a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4e+14) {
		tmp = a / (y - b);
	} else if (z <= -4.1e-57) {
		tmp = t / (b - y);
	} else if (z <= 7.6e-80) {
		tmp = x + ((z * t) / y);
	} else {
		tmp = (t - 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 <= (-4d+14)) then
        tmp = a / (y - b)
    else if (z <= (-4.1d-57)) then
        tmp = t / (b - y)
    else if (z <= 7.6d-80) then
        tmp = x + ((z * t) / y)
    else
        tmp = (t - 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 <= -4e+14) {
		tmp = a / (y - b);
	} else if (z <= -4.1e-57) {
		tmp = t / (b - y);
	} else if (z <= 7.6e-80) {
		tmp = x + ((z * t) / y);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4e+14:
		tmp = a / (y - b)
	elif z <= -4.1e-57:
		tmp = t / (b - y)
	elif z <= 7.6e-80:
		tmp = x + ((z * t) / y)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4e+14)
		tmp = Float64(a / Float64(y - b));
	elseif (z <= -4.1e-57)
		tmp = Float64(t / Float64(b - y));
	elseif (z <= 7.6e-80)
		tmp = Float64(x + Float64(Float64(z * t) / y));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4e+14)
		tmp = a / (y - b);
	elseif (z <= -4.1e-57)
		tmp = t / (b - y);
	elseif (z <= 7.6e-80)
		tmp = x + ((z * t) / y);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4e+14], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-57], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-80], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4e14

   1. Initial program 53.1%

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

      1. fma-define 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in t around inf 35.5%

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

      1. associate-+r+ 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. associate-/l* 31.8%

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

      5. associate-/l* 31.9%

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

   7. Simplified 31.9%

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

   8. Taylor expanded in z around inf 76.2%

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

   9. Taylor expanded in t around 0 53.6%

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

       1. associate-*r/ 53.6%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b - y}} \]

       2. mul-1-neg 53.6%

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

   11. Simplified 53.6%

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

   if -4e14 < z < -4.1000000000000001e-57

   1. Initial program 99.7%

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

      1. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 82.2%

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

      1. associate-+r+ 82.2%

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

      2. mul-1-neg 82.2%

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

      3. unsub-neg 82.2%

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

      4. associate-/l* 82.2%

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

      5. associate-/l* 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in z around inf 63.2%

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

   9. Taylor expanded in t around inf 63.0%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -4.1000000000000001e-57 < z < 7.59999999999999933e-80

   1. Initial program 83.1%

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

      1. fma-define 83.1%

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

      2. +-commutative 83.1%

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

      3. fma-define 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around 0 52.4%

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

   6. Taylor expanded in t around inf 71.5%

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

      1. *-commutative 71.5%

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

   8. Simplified 71.5%

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

   if 7.59999999999999933e-80 < z

   1. Initial program 56.8%

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

      1. fma-define 56.8%

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

      2. +-commutative 56.8%

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

      3. fma-define 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around 0 55.2%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+14}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.25e+14)
   (/ a (- y b))
   (if (<= z -1.55e-56)
     (/ t (- b y))
     (if (<= z 7.5e-80) (+ x (* z (/ t y))) (/ (- t a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.25e+14) {
		tmp = a / (y - b);
	} else if (z <= -1.55e-56) {
		tmp = t / (b - y);
	} else if (z <= 7.5e-80) {
		tmp = x + (z * (t / y));
	} else {
		tmp = (t - 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 <= (-1.25d+14)) then
        tmp = a / (y - b)
    else if (z <= (-1.55d-56)) then
        tmp = t / (b - y)
    else if (z <= 7.5d-80) then
        tmp = x + (z * (t / y))
    else
        tmp = (t - 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 <= -1.25e+14) {
		tmp = a / (y - b);
	} else if (z <= -1.55e-56) {
		tmp = t / (b - y);
	} else if (z <= 7.5e-80) {
		tmp = x + (z * (t / y));
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.25e+14:
		tmp = a / (y - b)
	elif z <= -1.55e-56:
		tmp = t / (b - y)
	elif z <= 7.5e-80:
		tmp = x + (z * (t / y))
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.25e+14)
		tmp = Float64(a / Float64(y - b));
	elseif (z <= -1.55e-56)
		tmp = Float64(t / Float64(b - y));
	elseif (z <= 7.5e-80)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.25e+14)
		tmp = a / (y - b);
	elseif (z <= -1.55e-56)
		tmp = t / (b - y);
	elseif (z <= 7.5e-80)
		tmp = x + (z * (t / y));
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.25e+14], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-56], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-80], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25e14

   1. Initial program 53.1%

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

      1. fma-define 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in t around inf 35.5%

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

      1. associate-+r+ 35.5%

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

      2. mul-1-neg 35.5%

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

      3. unsub-neg 35.5%

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

      4. associate-/l* 31.8%

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

      5. associate-/l* 31.9%

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

   7. Simplified 31.9%

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

   8. Taylor expanded in z around inf 76.2%

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

   9. Taylor expanded in t around 0 53.6%

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

       1. associate-*r/ 53.6%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b - y}} \]

       2. mul-1-neg 53.6%

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

   11. Simplified 53.6%

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

   if -1.25e14 < z < -1.54999999999999994e-56

   1. Initial program 99.7%

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

      1. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 82.2%

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

      1. associate-+r+ 82.2%

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

      2. mul-1-neg 82.2%

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

      3. unsub-neg 82.2%

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

      4. associate-/l* 82.2%

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

      5. associate-/l* 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in z around inf 63.2%

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

   9. Taylor expanded in t around inf 63.0%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -1.54999999999999994e-56 < z < 7.49999999999999999e-80

   1. Initial program 83.1%

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

      1. fma-define 83.1%

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

      2. +-commutative 83.1%

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

      3. fma-define 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around 0 52.4%

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

   6. Taylor expanded in t around inf 65.6%

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

   if 7.49999999999999999e-80 < z

   1. Initial program 56.8%

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

      1. fma-define 56.8%

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

      2. +-commutative 56.8%

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

      3. fma-define 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in y around 0 55.2%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+14}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+267}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -4.2e-70)
     t_1
     (if (<= z 6e+41) (/ x (- 1.0 z)) (if (<= z 1.02e+267) t_1 (/ a (- b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -4.2e-70) {
		tmp = t_1;
	} else if (z <= 6e+41) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.02e+267) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-4.2d-70)) then
        tmp = t_1
    else if (z <= 6d+41) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.02d+267) then
        tmp = t_1
    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 t_1 = t / (b - y);
	double tmp;
	if (z <= -4.2e-70) {
		tmp = t_1;
	} else if (z <= 6e+41) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.02e+267) {
		tmp = t_1;
	} else {
		tmp = a / -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -4.2e-70:
		tmp = t_1
	elif z <= 6e+41:
		tmp = x / (1.0 - z)
	elif z <= 1.02e+267:
		tmp = t_1
	else:
		tmp = a / -b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -4.2e-70)
		tmp = t_1;
	elseif (z <= 6e+41)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.02e+267)
		tmp = t_1;
	else
		tmp = Float64(a / Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -4.2e-70)
		tmp = t_1;
	elseif (z <= 6e+41)
		tmp = x / (1.0 - z);
	elseif (z <= 1.02e+267)
		tmp = t_1;
	else
		tmp = a / -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-70], t$95$1, If[LessEqual[z, 6e+41], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+267], t$95$1, N[(a / (-b)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000002e-70 or 5.9999999999999997e41 < z < 1.02000000000000001e267

   1. Initial program 60.7%

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

      1. fma-define 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in t around inf 48.3%

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

      1. associate-+r+ 48.3%

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

      2. mul-1-neg 48.3%

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

      3. unsub-neg 48.3%

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

      4. associate-/l* 43.2%

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

      5. associate-/l* 43.3%

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

   7. Simplified 43.3%

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

   8. Taylor expanded in z around inf 72.9%

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

   9. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{\frac{t}{b - y}} \]

   if -4.2000000000000002e-70 < z < 5.9999999999999997e41

   1. Initial program 81.9%

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

      1. fma-define 81.9%

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

      2. +-commutative 81.9%

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

      3. fma-define 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in y around inf 52.9%

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 52.9%

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

      2. unsub-neg 52.9%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if 1.02000000000000001e267 < z

   1. Initial program 20.9%

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

      1. fma-define 20.9%

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

   3. Simplified 20.9%

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

   5. Taylor expanded in t around inf 13.9%

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

      1. associate-+r+ 13.9%

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

      2. mul-1-neg 13.9%

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

      3. unsub-neg 13.9%

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

      4. associate-/l* 13.9%

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

      5. associate-/l* 13.9%

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

   7. Simplified 13.9%

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

   8. Taylor expanded in a around inf 14.9%

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

      1. associate-*r* 14.9%

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

      2. neg-mul-1 14.9%

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

   10. Simplified 14.9%

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

   11. Taylor expanded in y around 0 64.1%

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

       1. associate-*r/ 64.1%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. mul-1-neg 64.1%

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

   13. Simplified 64.1%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+267}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-52} \lor \neg \left(z \leq 7.6 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.1e-52) (not (<= z 7.6e-80)))
   (/ (- t a) (- b y))
   (+ x (* z (/ (- t a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.1e-52) || !(z <= 7.6e-80)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / 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 ((z <= (-5.1d-52)) .or. (.not. (z <= 7.6d-80))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * ((t - a) / 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 ((z <= -5.1e-52) || !(z <= 7.6e-80)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.1e-52) or not (z <= 7.6e-80):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.1e-52) || !(z <= 7.6e-80))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.1e-52) || ~((z <= 7.6e-80)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.1e-52], N[Not[LessEqual[z, 7.6e-80]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.09999999999999989e-52 or 7.59999999999999933e-80 < z

   1. Initial program 58.2%

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

      1. fma-define 58.2%

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

      2. +-commutative 58.2%

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

      3. fma-define 58.2%

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

   3. Simplified 58.2%

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

   5. Taylor expanded in z around inf 77.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -5.09999999999999989e-52 < z < 7.59999999999999933e-80

   1. Initial program 83.2%

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

      1. fma-define 83.3%

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

      2. +-commutative 83.3%

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

      3. fma-define 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around 0 52.8%

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

   6. Taylor expanded in x around 0 72.3%

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

      1. div-sub 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-52} \lor \neg \left(z \leq 7.6 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-57} \lor \neg \left(z \leq 8.4 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.8e-57) (not (<= z 8.4e-81)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.8e-57) || !(z <= 8.4e-81)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / 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 ((z <= (-7.8d-57)) .or. (.not. (z <= 8.4d-81))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * t) / 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 ((z <= -7.8e-57) || !(z <= 8.4e-81)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.8e-57) or not (z <= 8.4e-81):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.8e-57) || !(z <= 8.4e-81))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.8e-57) || ~((z <= 8.4e-81)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.8e-57], N[Not[LessEqual[z, 8.4e-81]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000013e-57 or 8.3999999999999997e-81 < z

   1. Initial program 58.5%

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

      1. fma-define 58.5%

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

      2. +-commutative 58.5%

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

      3. fma-define 58.5%

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

   3. Simplified 58.5%

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

   5. Taylor expanded in z around inf 77.4%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -7.80000000000000013e-57 < z < 8.3999999999999997e-81

   1. Initial program 83.1%

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

      1. fma-define 83.1%

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

      2. +-commutative 83.1%

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

      3. fma-define 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around 0 52.4%

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

   6. Taylor expanded in t around inf 71.5%

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

      1. *-commutative 71.5%

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

   8. Simplified 71.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-57} \lor \neg \left(z \leq 8.4 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-27} \lor \neg \left(y \leq 9 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e-27) (not (<= y 9e+40))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e-27) || !(y <= 9e+40)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.5d-27)) .or. (.not. (y <= 9d+40))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e-27) || !(y <= 9e+40)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.5e-27) or not (y <= 9e+40):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e-27) || !(y <= 9e+40))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.5e-27) || ~((y <= 9e+40)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e-27], N[Not[LessEqual[y, 9e+40]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000001e-27 or 9.00000000000000064e40 < y

   1. Initial program 55.6%

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

      1. fma-define 55.6%

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

      2. +-commutative 55.6%

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

      3. fma-define 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in y around inf 55.0%

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.0%

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

      2. unsub-neg 55.0%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   7. Simplified 55.0%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -1.5000000000000001e-27 < y < 9.00000000000000064e40

   1. Initial program 78.5%

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

      1. fma-define 78.5%

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

      2. +-commutative 78.5%

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

      3. fma-define 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in y around 0 55.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-27} \lor \neg \left(y \leq 9 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-69} \lor \neg \left(z \leq 1.05 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-69) (not (<= z 1.05e-86))) (/ a (- b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-69) || !(z <= 1.05e-86)) {
		tmp = a / -b;
	} else {
		tmp = 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 ((z <= (-1.05d-69)) .or. (.not. (z <= 1.05d-86))) then
        tmp = a / -b
    else
        tmp = 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 ((z <= -1.05e-69) || !(z <= 1.05e-86)) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-69) or not (z <= 1.05e-86):
		tmp = a / -b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-69) || !(z <= 1.05e-86))
		tmp = Float64(a / Float64(-b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-69) || ~((z <= 1.05e-86)))
		tmp = a / -b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-69], N[Not[LessEqual[z, 1.05e-86]], $MachinePrecision]], N[(a / (-b)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-69 or 1.05e-86 < z

   1. Initial program 60.8%

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

      1. fma-define 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in t around inf 48.1%

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

      1. associate-+r+ 48.1%

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

      2. mul-1-neg 48.1%

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

      3. unsub-neg 48.1%

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

      4. associate-/l* 44.5%

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

      5. associate-/l* 44.4%

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

   7. Simplified 44.4%

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

   8. Taylor expanded in a around inf 30.0%

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

      1. associate-*r* 30.0%

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

      2. neg-mul-1 30.0%

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

   10. Simplified 30.0%

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

   11. Taylor expanded in y around 0 31.4%

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

       1. associate-*r/ 31.4%

          \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

       2. mul-1-neg 31.4%

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

   13. Simplified 31.4%

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

   if -1.05e-69 < z < 1.05e-86

   1. Initial program 81.4%

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

      1. fma-define 81.5%

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

      2. +-commutative 81.5%

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

      3. fma-define 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in z around 0 59.0%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-69} \lor \neg \left(z \leq 1.05 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.9% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 68.2%

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

   1. fma-define 68.2%

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

   2. +-commutative 68.2%

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

   3. fma-define 68.2%

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

3. Simplified 68.2%

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

5. Taylor expanded in z around 0 25.4%

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

Developer Target 1: 73.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

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