Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.0% → 89.7%

Time: 15.6s

Alternatives: 18

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: 66.0% 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: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-306}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_1\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 7000000:\\ \;\;\;\;\frac{t_1 + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2
         (+
          (* (/ y (- b y)) (/ x z))
          (-
           (/ t (- b y))
           (+ (/ a (- b y)) (* (/ (- t a) z) (/ y (pow (- b y) 2.0))))))))
   (if (<= z -1.55e+16)
     t_2
     (if (<= z -1.4e-306)
       (/ (fma x y t_1) (fma z (- b y) y))
       (if (<= z 8.5e-127)
         (+ x (/ t_1 y))
         (if (<= z 7000000.0) (/ (+ t_1 (* y x)) (- y (* z (- y b)))) t_2))))))

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 / (b - y)) * (x / z)) + ((t / (b - y)) - ((a / (b - y)) + (((t - a) / z) * (y / pow((b - y), 2.0)))));
	double tmp;
	if (z <= -1.55e+16) {
		tmp = t_2;
	} else if (z <= -1.4e-306) {
		tmp = fma(x, y, t_1) / fma(z, (b - y), y);
	} else if (z <= 8.5e-127) {
		tmp = x + (t_1 / y);
	} else if (z <= 7000000.0) {
		tmp = (t_1 + (y * x)) / (y - (z * (y - b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(Float64(t / Float64(b - y)) - Float64(Float64(a / Float64(b - y)) + Float64(Float64(Float64(t - a) / z) * Float64(y / (Float64(b - y) ^ 2.0))))))
	tmp = 0.0
	if (z <= -1.55e+16)
		tmp = t_2;
	elseif (z <= -1.4e-306)
		tmp = Float64(fma(x, y, t_1) / fma(z, Float64(b - y), y));
	elseif (z <= 8.5e-127)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 7000000.0)
		tmp = Float64(Float64(t_1 + Float64(y * x)) / Float64(y - Float64(z * Float64(y - b))));
	else
		tmp = t_2;
	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[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision] * N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+16], t$95$2, If[LessEqual[z, -1.4e-306], N[(N[(x * y + t$95$1), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-127], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7000000.0], N[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e16 or 7e6 < z

   1. Initial program 36.6%

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

   2. Taylor expanded in z around inf 66.3%

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

      1. associate--l+ 66.3%

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

      2. *-commutative 66.3%

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

      3. times-frac 75.3%

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

      4. +-commutative 75.3%

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

      5. times-frac 95.1%

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

   4. Simplified 95.1%

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

   if -1.55e16 < z < -1.4000000000000001e-306

   1. Initial program 90.4%

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

      1. fma-def 90.4%

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

      2. +-commutative 90.4%

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

      3. fma-def 90.5%

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

   3. Simplified 90.5%

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

   if -1.4000000000000001e-306 < z < 8.5e-127

   1. Initial program 79.0%

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

   2. Taylor expanded in b around inf 79.0%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-/l* 75.0%

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

      3. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in b around 0 89.8%

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

   if 8.5e-127 < z < 7e6

   1. Initial program 89.0%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-306}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 7000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)\right)\\ \end{array} \]

Alternative 2: 86.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2 + y \cdot x}{t_1}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-320}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot x}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + t_4\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ t_2 (* y x)) t_1))
        (t_4 (/ (- t a) (- b y))))
   (if (<= t_3 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_3 -5e-320)
       (/ (fma x y t_2) t_1)
       (if (<= t_3 0.0)
         (+
          (/ (+ (/ (* y x) (- b y)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
          t_4)
         (if (<= t_3 2e+162) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = z * (t - a);
	double t_3 = (t_2 + (y * x)) / t_1;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_3 <= -5e-320) {
		tmp = fma(x, y, t_2) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = ((((y * x) / (b - y)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) + t_4;
	} else if (t_3 <= 2e+162) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t_2 + Float64(y * x)) / t_1)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_3 <= -5e-320)
		tmp = Float64(fma(x, y, t_2) / t_1);
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(y * x) / Float64(b - y)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) + t_4);
	elseif (t_3 <= 2e+162)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-320], N[(N[(x * y + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(N[(y * x), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[t$95$3, 2e+162], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 36.0%

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

   2. Taylor expanded in y around -inf 53.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 53.6%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 53.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. mul-1-neg 53.6%

         \[\leadsto \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. distribute-neg-frac 53.6%

         \[\leadsto \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. cancel-sign-sub-inv 53.6%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{\left(t - a\right) \cdot z}{z - 1} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      6. associate-/l* 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{t - a}{\frac{z - 1}{z}}} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      7. metadata-eval 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{1} \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      8. *-lft-identity 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      9. associate-/l* 61.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}}{y} \]

   4. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}{y}} \]

   5. Taylor expanded in z around inf 73.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99994e-320

   1. Initial program 99.2%

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

      1. fma-def 99.2%

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

   3. Simplified 99.2%

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

   if -4.99994e-320 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 11.5%

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

   2. Taylor expanded in z around -inf 78.9%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + -1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z}\right) - \frac{a}{b - y}} \]
   3. Step-by-step derivation

      1. +-commutative 78.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right)} - \frac{a}{b - y} \]

      2. associate--l+ 78.9%

         \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y \cdot x}{b - y} - -1 \cdot \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{z} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

   4. Simplified 85.8%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y \cdot x}{b - y} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e162

   1. Initial program 99.5%

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

   if 1.9999999999999999e162 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 13.2%

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

   2. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -5 \cdot 10^{-320}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 0:\\ \;\;\;\;\frac{\frac{y \cdot x}{b - y} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+162}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 84.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t_2 + y \cdot x}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-320}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \mathbf{elif}\;t_3 \leq 0 \lor \neg \left(t_3 \leq 2 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ t_2 (* y x)) t_1)))
   (if (<= t_3 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_3 -5e-320)
       (/ (fma x y t_2) t_1)
       (if (or (<= t_3 0.0) (not (<= t_3 2e+162))) (/ (- t a) (- b y)) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = z * (t - a);
	double t_3 = (t_2 + (y * x)) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_3 <= -5e-320) {
		tmp = fma(x, y, t_2) / t_1;
	} else if ((t_3 <= 0.0) || !(t_3 <= 2e+162)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t_2 + Float64(y * x)) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_3 <= -5e-320)
		tmp = Float64(fma(x, y, t_2) / t_1);
	elseif ((t_3 <= 0.0) || !(t_3 <= 2e+162))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-320], N[(N[(x * y + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[Or[LessEqual[t$95$3, 0.0], N[Not[LessEqual[t$95$3, 2e+162]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 36.0%

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

   2. Taylor expanded in y around -inf 53.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 53.6%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 53.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. mul-1-neg 53.6%

         \[\leadsto \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. distribute-neg-frac 53.6%

         \[\leadsto \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. cancel-sign-sub-inv 53.6%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{\left(t - a\right) \cdot z}{z - 1} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      6. associate-/l* 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{t - a}{\frac{z - 1}{z}}} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      7. metadata-eval 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{1} \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      8. *-lft-identity 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      9. associate-/l* 61.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}}{y} \]

   4. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}{y}} \]

   5. Taylor expanded in z around inf 73.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99994e-320

   1. Initial program 99.2%

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

      1. fma-def 99.2%

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

   3. Simplified 99.2%

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

   if -4.99994e-320 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 1.9999999999999999e162 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.9%

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

   2. Taylor expanded in z around inf 68.8%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e162

   1. Initial program 99.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -5 \cdot 10^{-320}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 0 \lor \neg \left(\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \end{array} \]

Alternative 4: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t_1 + y \cdot x}{y - z \cdot \left(y - b\right)}\\ t_3 := \frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{if}\;z \leq -37000000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 47000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (+ t_1 (* y x)) (- y (* z (- y b)))))
        (t_3
         (+
          (* (/ y (- b y)) (/ x z))
          (-
           (/ t (- b y))
           (+ (/ a (- b y)) (* (/ (- t a) z) (/ y (pow (- b y) 2.0))))))))
   (if (<= z -37000000000000.0)
     t_3
     (if (<= z -2.6e-306)
       t_2
       (if (<= z 5.5e-127) (+ x (/ t_1 y)) (if (<= z 47000000.0) 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 = (t_1 + (y * x)) / (y - (z * (y - b)));
	double t_3 = ((y / (b - y)) * (x / z)) + ((t / (b - y)) - ((a / (b - y)) + (((t - a) / z) * (y / pow((b - y), 2.0)))));
	double tmp;
	if (z <= -37000000000000.0) {
		tmp = t_3;
	} else if (z <= -2.6e-306) {
		tmp = t_2;
	} else if (z <= 5.5e-127) {
		tmp = x + (t_1 / y);
	} else if (z <= 47000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t_1 + (y * x)) / (y - (z * (y - b)))
    t_3 = ((y / (b - y)) * (x / z)) + ((t / (b - y)) - ((a / (b - y)) + (((t - a) / z) * (y / ((b - y) ** 2.0d0)))))
    if (z <= (-37000000000000.0d0)) then
        tmp = t_3
    else if (z <= (-2.6d-306)) then
        tmp = t_2
    else if (z <= 5.5d-127) then
        tmp = x + (t_1 / y)
    else if (z <= 47000000.0d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t_1 + (y * x)) / (y - (z * (y - b)));
	double t_3 = ((y / (b - y)) * (x / z)) + ((t / (b - y)) - ((a / (b - y)) + (((t - a) / z) * (y / Math.pow((b - y), 2.0)))));
	double tmp;
	if (z <= -37000000000000.0) {
		tmp = t_3;
	} else if (z <= -2.6e-306) {
		tmp = t_2;
	} else if (z <= 5.5e-127) {
		tmp = x + (t_1 / y);
	} else if (z <= 47000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t_1 + (y * x)) / (y - (z * (y - b)))
	t_3 = ((y / (b - y)) * (x / z)) + ((t / (b - y)) - ((a / (b - y)) + (((t - a) / z) * (y / math.pow((b - y), 2.0)))))
	tmp = 0
	if z <= -37000000000000.0:
		tmp = t_3
	elif z <= -2.6e-306:
		tmp = t_2
	elif z <= 5.5e-127:
		tmp = x + (t_1 / y)
	elif z <= 47000000.0:
		tmp = 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(Float64(t_1 + Float64(y * x)) / Float64(y - Float64(z * Float64(y - b))))
	t_3 = Float64(Float64(Float64(y / Float64(b - y)) * Float64(x / z)) + Float64(Float64(t / Float64(b - y)) - Float64(Float64(a / Float64(b - y)) + Float64(Float64(Float64(t - a) / z) * Float64(y / (Float64(b - y) ^ 2.0))))))
	tmp = 0.0
	if (z <= -37000000000000.0)
		tmp = t_3;
	elseif (z <= -2.6e-306)
		tmp = t_2;
	elseif (z <= 5.5e-127)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 47000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t_1 + (y * x)) / (y - (z * (y - b)));
	t_3 = ((y / (b - y)) * (x / z)) + ((t / (b - y)) - ((a / (b - y)) + (((t - a) / z) * (y / ((b - y) ^ 2.0)))));
	tmp = 0.0;
	if (z <= -37000000000000.0)
		tmp = t_3;
	elseif (z <= -2.6e-306)
		tmp = t_2;
	elseif (z <= 5.5e-127)
		tmp = x + (t_1 / y);
	elseif (z <= 47000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = 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[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision] * N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -37000000000000.0], t$95$3, If[LessEqual[z, -2.6e-306], t$95$2, If[LessEqual[z, 5.5e-127], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 47000000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7e13 or 4.7e7 < z

   1. Initial program 37.2%

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

   2. Taylor expanded in z around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. *-commutative 66.6%

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

      3. times-frac 75.5%

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

      4. +-commutative 75.5%

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

      5. times-frac 95.2%

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

   4. Simplified 95.2%

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

   if -3.7e13 < z < -2.6e-306 or 5.50000000000000036e-127 < z < 4.7e7

   1. Initial program 89.9%

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

   if -2.6e-306 < z < 5.50000000000000036e-127

   1. Initial program 79.0%

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

   2. Taylor expanded in b around inf 79.0%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-/l* 75.0%

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

      3. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in b around 0 89.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -37000000000000:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-127}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 47000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{b - y} \cdot \frac{x}{z} + \left(\frac{t}{b - y} - \left(\frac{a}{b - y} + \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)\right)\\ \end{array} \]

Alternative 5: 84.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-320} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 2 \cdot 10^{+162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* y x)) (- y (* z (- y b))))))
   (if (<= t_1 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (or (<= t_1 -5e-320) (and (not (<= t_1 0.0)) (<= t_1 2e+162)))
       t_1
       (/ (- t a) (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -5e-320) || (!(t_1 <= 0.0) && (t_1 <= 2e+162))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if ((t_1 <= -5e-320) || (!(t_1 <= 0.0) && (t_1 <= 2e+162))) {
		tmp = t_1;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	elif (t_1 <= -5e-320) or (not (t_1 <= 0.0) and (t_1 <= 2e+162)):
		tmp = t_1
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y - Float64(z * Float64(y - b))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif ((t_1 <= -5e-320) || (!(t_1 <= 0.0) && (t_1 <= 2e+162)))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (t - a)) + (y * x)) / (y - (z * (y - b)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	elseif ((t_1 <= -5e-320) || (~((t_1 <= 0.0)) && (t_1 <= 2e+162)))
		tmp = t_1;
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-320], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 2e+162]]], t$95$1, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 36.0%

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

   2. Taylor expanded in y around -inf 53.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 53.6%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 53.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. mul-1-neg 53.6%

         \[\leadsto \color{blue}{\left(-\frac{x}{z - 1}\right)} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. distribute-neg-frac 53.6%

         \[\leadsto \color{blue}{\frac{-x}{z - 1}} - \frac{\frac{\left(t - a\right) \cdot z}{z - 1} - -1 \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. cancel-sign-sub-inv 53.6%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{\left(t - a\right) \cdot z}{z - 1} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      6. associate-/l* 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\color{blue}{\frac{t - a}{\frac{z - 1}{z}}} + \left(--1\right) \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      7. metadata-eval 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{1} \cdot \frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      8. *-lft-identity 61.5%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z \cdot \left(b \cdot x\right)}{{\left(z - 1\right)}^{2}}}}{y} \]

      9. associate-/l* 61.9%

         \[\leadsto \frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \color{blue}{\frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}}{y} \]

   4. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{-x}{z - 1} - \frac{\frac{t - a}{\frac{z - 1}{z}} + \frac{z}{\frac{{\left(z - 1\right)}^{2}}{b \cdot x}}}{y}} \]

   5. Taylor expanded in z around inf 73.6%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99994e-320 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.9999999999999999e162

   1. Initial program 99.3%

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

   if -4.99994e-320 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 1.9999999999999999e162 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.9%

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

   2. Taylor expanded in z around inf 68.8%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq -5 \cdot 10^{-320} \lor \neg \left(\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 0\right) \land \frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+162}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := x + \frac{t_1}{y}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{-46}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{+15}:\\ \;\;\;\;\frac{t_1}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (+ x (/ t_1 y))) (t_3 (/ (- t a) (- b y))))
   (if (<= z -3.15e-46)
     t_3
     (if (<= z -6.6e-84)
       t_2
       (if (<= z -3.4e-120)
         (/ (- t a) b)
         (if (<= z 5.2e-99)
           t_2
           (if (<= z 1e+15) (/ t_1 (- y (* z (- y b)))) 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 = x + (t_1 / y);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.15e-46) {
		tmp = t_3;
	} else if (z <= -6.6e-84) {
		tmp = t_2;
	} else if (z <= -3.4e-120) {
		tmp = (t - a) / b;
	} else if (z <= 5.2e-99) {
		tmp = t_2;
	} else if (z <= 1e+15) {
		tmp = t_1 / (y - (z * (y - b)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = x + (t_1 / y)
    t_3 = (t - a) / (b - y)
    if (z <= (-3.15d-46)) then
        tmp = t_3
    else if (z <= (-6.6d-84)) then
        tmp = t_2
    else if (z <= (-3.4d-120)) then
        tmp = (t - a) / b
    else if (z <= 5.2d-99) then
        tmp = t_2
    else if (z <= 1d+15) then
        tmp = t_1 / (y - (z * (y - b)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = x + (t_1 / y);
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.15e-46) {
		tmp = t_3;
	} else if (z <= -6.6e-84) {
		tmp = t_2;
	} else if (z <= -3.4e-120) {
		tmp = (t - a) / b;
	} else if (z <= 5.2e-99) {
		tmp = t_2;
	} else if (z <= 1e+15) {
		tmp = t_1 / (y - (z * (y - b)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = x + (t_1 / y)
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.15e-46:
		tmp = t_3
	elif z <= -6.6e-84:
		tmp = t_2
	elif z <= -3.4e-120:
		tmp = (t - a) / b
	elif z <= 5.2e-99:
		tmp = t_2
	elif z <= 1e+15:
		tmp = t_1 / (y - (z * (y - b)))
	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(x + Float64(t_1 / y))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.15e-46)
		tmp = t_3;
	elseif (z <= -6.6e-84)
		tmp = t_2;
	elseif (z <= -3.4e-120)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 5.2e-99)
		tmp = t_2;
	elseif (z <= 1e+15)
		tmp = Float64(t_1 / Float64(y - Float64(z * Float64(y - b))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = x + (t_1 / y);
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.15e-46)
		tmp = t_3;
	elseif (z <= -6.6e-84)
		tmp = t_2;
	elseif (z <= -3.4e-120)
		tmp = (t - a) / b;
	elseif (z <= 5.2e-99)
		tmp = t_2;
	elseif (z <= 1e+15)
		tmp = t_1 / (y - (z * (y - b)));
	else
		tmp = t_3;
	end
	tmp_2 = 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[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.15e-46], t$95$3, If[LessEqual[z, -6.6e-84], t$95$2, If[LessEqual[z, -3.4e-120], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 5.2e-99], t$95$2, If[LessEqual[z, 1e+15], N[(t$95$1 / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.15e-46 or 1e15 < z

   1. Initial program 40.3%

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

   2. Taylor expanded in z around inf 77.4%

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

   if -3.15e-46 < z < -6.59999999999999968e-84 or -3.4000000000000001e-120 < z < 5.2000000000000001e-99

   1. Initial program 85.0%

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

   2. Taylor expanded in b around inf 85.0%

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

   3. Taylor expanded in y around inf 72.0%

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

      1. associate--l+ 72.0%

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

      2. associate-/l* 71.1%

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

      3. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in b around 0 78.2%

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

   if -6.59999999999999968e-84 < z < -3.4000000000000001e-120

   1. Initial program 85.8%

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

   2. Taylor expanded in y around 0 72.3%

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

   if 5.2000000000000001e-99 < z < 1e15

   1. Initial program 90.5%

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

      1. fma-def 90.5%

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

      2. +-commutative 90.5%

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

      3. fma-def 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 70.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-46}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 10^{+15}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 81.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t_1 + y \cdot x}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -46000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (+ t_1 (* y x)) (+ y (* z b))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -46000.0)
     t_3
     (if (<= z -1.32e-306)
       t_2
       (if (<= z 3.2e-122) (+ x (/ t_1 y)) (if (<= z 3.3e+17) 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 = (t_1 + (y * x)) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -46000.0) {
		tmp = t_3;
	} else if (z <= -1.32e-306) {
		tmp = t_2;
	} else if (z <= 3.2e-122) {
		tmp = x + (t_1 / y);
	} else if (z <= 3.3e+17) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t_1 + (y * x)) / (y + (z * b))
    t_3 = (t - a) / (b - y)
    if (z <= (-46000.0d0)) then
        tmp = t_3
    else if (z <= (-1.32d-306)) then
        tmp = t_2
    else if (z <= 3.2d-122) then
        tmp = x + (t_1 / y)
    else if (z <= 3.3d+17) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t_1 + (y * x)) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -46000.0) {
		tmp = t_3;
	} else if (z <= -1.32e-306) {
		tmp = t_2;
	} else if (z <= 3.2e-122) {
		tmp = x + (t_1 / y);
	} else if (z <= 3.3e+17) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t_1 + (y * x)) / (y + (z * b))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -46000.0:
		tmp = t_3
	elif z <= -1.32e-306:
		tmp = t_2
	elif z <= 3.2e-122:
		tmp = x + (t_1 / y)
	elif z <= 3.3e+17:
		tmp = 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(Float64(t_1 + Float64(y * x)) / Float64(y + Float64(z * b)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -46000.0)
		tmp = t_3;
	elseif (z <= -1.32e-306)
		tmp = t_2;
	elseif (z <= 3.2e-122)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 3.3e+17)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t_1 + (y * x)) / (y + (z * b));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -46000.0)
		tmp = t_3;
	elseif (z <= -1.32e-306)
		tmp = t_2;
	elseif (z <= 3.2e-122)
		tmp = x + (t_1 / y);
	elseif (z <= 3.3e+17)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = 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[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -46000.0], t$95$3, If[LessEqual[z, -1.32e-306], t$95$2, If[LessEqual[z, 3.2e-122], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+17], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -46000 or 3.3e17 < z

   1. Initial program 38.9%

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

   2. Taylor expanded in z around inf 78.6%

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

   if -46000 < z < -1.32e-306 or 3.2000000000000002e-122 < z < 3.3e17

   1. Initial program 88.6%

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

   2. Taylor expanded in b around inf 88.4%

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

   if -1.32e-306 < z < 3.2000000000000002e-122

   1. Initial program 79.0%

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

   2. Taylor expanded in b around inf 79.0%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-/l* 75.0%

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

      3. associate-/l* 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in b around 0 89.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+17}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-303}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 13500000000000:\\ \;\;\;\;\frac{t_1}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -5.2e-31)
     t_2
     (if (<= z -8.2e-303)
       (/ (- (* y x) (* z a)) (+ y (* z b)))
       (if (<= z 4.7e-99)
         (+ x (/ t_1 y))
         (if (<= z 13500000000000.0) (/ t_1 (- y (* z (- y b)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.2e-31) {
		tmp = t_2;
	} else if (z <= -8.2e-303) {
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	} else if (z <= 4.7e-99) {
		tmp = x + (t_1 / y);
	} else if (z <= 13500000000000.0) {
		tmp = t_1 / (y - (z * (y - b)));
	} 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 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-5.2d-31)) then
        tmp = t_2
    else if (z <= (-8.2d-303)) then
        tmp = ((y * x) - (z * a)) / (y + (z * b))
    else if (z <= 4.7d-99) then
        tmp = x + (t_1 / y)
    else if (z <= 13500000000000.0d0) then
        tmp = t_1 / (y - (z * (y - b)))
    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 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.2e-31) {
		tmp = t_2;
	} else if (z <= -8.2e-303) {
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	} else if (z <= 4.7e-99) {
		tmp = x + (t_1 / y);
	} else if (z <= 13500000000000.0) {
		tmp = t_1 / (y - (z * (y - b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.2e-31:
		tmp = t_2
	elif z <= -8.2e-303:
		tmp = ((y * x) - (z * a)) / (y + (z * b))
	elif z <= 4.7e-99:
		tmp = x + (t_1 / y)
	elif z <= 13500000000000.0:
		tmp = t_1 / (y - (z * (y - b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.2e-31)
		tmp = t_2;
	elseif (z <= -8.2e-303)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / Float64(y + Float64(z * b)));
	elseif (z <= 4.7e-99)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 13500000000000.0)
		tmp = Float64(t_1 / Float64(y - Float64(z * Float64(y - b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.2e-31)
		tmp = t_2;
	elseif (z <= -8.2e-303)
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	elseif (z <= 4.7e-99)
		tmp = x + (t_1 / y);
	elseif (z <= 13500000000000.0)
		tmp = t_1 / (y - (z * (y - b)));
	else
		tmp = t_2;
	end
	tmp_2 = 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[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-31], t$95$2, If[LessEqual[z, -8.2e-303], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-99], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 13500000000000.0], N[(t$95$1 / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.19999999999999991e-31 or 1.35e13 < z

   1. Initial program 39.8%

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

   2. Taylor expanded in z around inf 77.2%

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

   if -5.19999999999999991e-31 < z < -8.20000000000000037e-303

   1. Initial program 90.8%

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

   2. Taylor expanded in t around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. mul-1-neg 74.7%

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

      3. unsub-neg 74.7%

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

      4. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   5. Taylor expanded in b around inf 74.7%

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

   if -8.20000000000000037e-303 < z < 4.69999999999999989e-99

   1. Initial program 79.6%

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

   2. Taylor expanded in b around inf 79.6%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. associate-/l* 72.2%

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

      3. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in b around 0 83.4%

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

   if 4.69999999999999989e-99 < z < 1.35e13

   1. Initial program 90.5%

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

      1. fma-def 90.5%

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

      2. +-commutative 90.5%

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

      3. fma-def 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 70.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-303}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 13500000000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 9: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot \left(t - a\right)}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z (- t a)) y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -4.2e-46)
     t_2
     (if (<= z -3.3e-84)
       t_1
       (if (<= z -3.4e-120) (/ (- t a) b) (if (<= z 5.2e-99) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * (t - a)) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.2e-46) {
		tmp = t_2;
	} else if (z <= -3.3e-84) {
		tmp = t_1;
	} else if (z <= -3.4e-120) {
		tmp = (t - a) / b;
	} else if (z <= 5.2e-99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z * (t - a)) / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-4.2d-46)) then
        tmp = t_2
    else if (z <= (-3.3d-84)) then
        tmp = t_1
    else if (z <= (-3.4d-120)) then
        tmp = (t - a) / b
    else if (z <= 5.2d-99) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * (t - a)) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.2e-46) {
		tmp = t_2;
	} else if (z <= -3.3e-84) {
		tmp = t_1;
	} else if (z <= -3.4e-120) {
		tmp = (t - a) / b;
	} else if (z <= 5.2e-99) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((z * (t - a)) / y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.2e-46:
		tmp = t_2
	elif z <= -3.3e-84:
		tmp = t_1
	elif z <= -3.4e-120:
		tmp = (t - a) / b
	elif z <= 5.2e-99:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(z * Float64(t - a)) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.2e-46)
		tmp = t_2;
	elseif (z <= -3.3e-84)
		tmp = t_1;
	elseif (z <= -3.4e-120)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 5.2e-99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((z * (t - a)) / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.2e-46)
		tmp = t_2;
	elseif (z <= -3.3e-84)
		tmp = t_1;
	elseif (z <= -3.4e-120)
		tmp = (t - a) / b;
	elseif (z <= 5.2e-99)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e-46], t$95$2, If[LessEqual[z, -3.3e-84], t$95$1, If[LessEqual[z, -3.4e-120], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 5.2e-99], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.19999999999999975e-46 or 5.2000000000000001e-99 < z

   1. Initial program 47.3%

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

   2. Taylor expanded in z around inf 73.6%

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

   if -4.19999999999999975e-46 < z < -3.29999999999999984e-84 or -3.4000000000000001e-120 < z < 5.2000000000000001e-99

   1. Initial program 85.0%

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

   2. Taylor expanded in b around inf 85.0%

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

   3. Taylor expanded in y around inf 72.0%

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

      1. associate--l+ 72.0%

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

      2. associate-/l* 71.1%

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

      3. associate-/l* 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in b around 0 78.2%

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

   if -3.29999999999999984e-84 < z < -3.4000000000000001e-120

   1. Initial program 85.8%

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

   2. Taylor expanded in y around 0 72.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 34.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= y -1.15e+38)
     x
     (if (<= y -3e-45)
       t_1
       (if (<= y -6.6e-62)
         (* t (/ z y))
         (if (<= y 8.2e-269) (/ t b) (if (<= y 2.2e-27) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (y <= -1.15e+38) {
		tmp = x;
	} else if (y <= -3e-45) {
		tmp = t_1;
	} else if (y <= -6.6e-62) {
		tmp = t * (z / y);
	} else if (y <= 8.2e-269) {
		tmp = t / b;
	} else if (y <= 2.2e-27) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (y <= (-1.15d+38)) then
        tmp = x
    else if (y <= (-3d-45)) then
        tmp = t_1
    else if (y <= (-6.6d-62)) then
        tmp = t * (z / y)
    else if (y <= 8.2d-269) then
        tmp = t / b
    else if (y <= 2.2d-27) then
        tmp = t_1
    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 t_1 = -a / b;
	double tmp;
	if (y <= -1.15e+38) {
		tmp = x;
	} else if (y <= -3e-45) {
		tmp = t_1;
	} else if (y <= -6.6e-62) {
		tmp = t * (z / y);
	} else if (y <= 8.2e-269) {
		tmp = t / b;
	} else if (y <= 2.2e-27) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if y <= -1.15e+38:
		tmp = x
	elif y <= -3e-45:
		tmp = t_1
	elif y <= -6.6e-62:
		tmp = t * (z / y)
	elif y <= 8.2e-269:
		tmp = t / b
	elif y <= 2.2e-27:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (y <= -1.15e+38)
		tmp = x;
	elseif (y <= -3e-45)
		tmp = t_1;
	elseif (y <= -6.6e-62)
		tmp = Float64(t * Float64(z / y));
	elseif (y <= 8.2e-269)
		tmp = Float64(t / b);
	elseif (y <= 2.2e-27)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (y <= -1.15e+38)
		tmp = x;
	elseif (y <= -3e-45)
		tmp = t_1;
	elseif (y <= -6.6e-62)
		tmp = t * (z / y);
	elseif (y <= 8.2e-269)
		tmp = t / b;
	elseif (y <= 2.2e-27)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[y, -1.15e+38], x, If[LessEqual[y, -3e-45], t$95$1, If[LessEqual[y, -6.6e-62], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-269], N[(t / b), $MachinePrecision], If[LessEqual[y, 2.2e-27], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1500000000000001e38 or 2.19999999999999987e-27 < y

   1. Initial program 51.9%

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

   2. Taylor expanded in z around 0 41.3%

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

   if -1.1500000000000001e38 < y < -3.00000000000000011e-45 or 8.2000000000000006e-269 < y < 2.19999999999999987e-27

   1. Initial program 72.1%

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

   2. Taylor expanded in t around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

      4. *-commutative 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y around 0 44.8%

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

      1. associate-*r/ 44.8%

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

      2. neg-mul-1 44.8%

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

   7. Simplified 44.8%

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

   if -3.00000000000000011e-45 < y < -6.60000000000000009e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 57.9%

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

      2. +-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. fma-def 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in z around 0 57.9%

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

   6. Taylor expanded in t around 0 57.9%

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

      1. associate-/l* 57.9%

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

      2. *-rgt-identity 57.9%

         \[\leadsto \frac{\color{blue}{t \cdot 1}}{\frac{y}{z}} \]

      3. associate-*r/ 57.3%

         \[\leadsto \color{blue}{t \cdot \frac{1}{\frac{y}{z}}} \]

      4. associate-/r/ 57.9%

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

      5. associate-*l/ 57.9%

         \[\leadsto t \cdot \color{blue}{\frac{1 \cdot z}{y}} \]

      6. associate-*r/ 57.9%

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

      7. *-lft-identity 57.9%

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

   8. Simplified 57.9%

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

   if -6.60000000000000009e-62 < y < 8.2000000000000006e-269

   1. Initial program 74.7%

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

   2. Taylor expanded in t around inf 44.3%

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

      1. associate-/l* 50.0%

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

      2. +-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. fma-def 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in b around inf 48.3%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-45}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 34.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= y -6.2e+38)
     (+ x (* z x))
     (if (<= y -3.8e-45)
       t_1
       (if (<= y -6.4e-62)
         (* t (/ z y))
         (if (<= y 6.5e-269) (/ t b) (if (<= y 1.1e-27) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (y <= -6.2e+38) {
		tmp = x + (z * x);
	} else if (y <= -3.8e-45) {
		tmp = t_1;
	} else if (y <= -6.4e-62) {
		tmp = t * (z / y);
	} else if (y <= 6.5e-269) {
		tmp = t / b;
	} else if (y <= 1.1e-27) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (y <= (-6.2d+38)) then
        tmp = x + (z * x)
    else if (y <= (-3.8d-45)) then
        tmp = t_1
    else if (y <= (-6.4d-62)) then
        tmp = t * (z / y)
    else if (y <= 6.5d-269) then
        tmp = t / b
    else if (y <= 1.1d-27) then
        tmp = t_1
    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 t_1 = -a / b;
	double tmp;
	if (y <= -6.2e+38) {
		tmp = x + (z * x);
	} else if (y <= -3.8e-45) {
		tmp = t_1;
	} else if (y <= -6.4e-62) {
		tmp = t * (z / y);
	} else if (y <= 6.5e-269) {
		tmp = t / b;
	} else if (y <= 1.1e-27) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if y <= -6.2e+38:
		tmp = x + (z * x)
	elif y <= -3.8e-45:
		tmp = t_1
	elif y <= -6.4e-62:
		tmp = t * (z / y)
	elif y <= 6.5e-269:
		tmp = t / b
	elif y <= 1.1e-27:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (y <= -6.2e+38)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= -3.8e-45)
		tmp = t_1;
	elseif (y <= -6.4e-62)
		tmp = Float64(t * Float64(z / y));
	elseif (y <= 6.5e-269)
		tmp = Float64(t / b);
	elseif (y <= 1.1e-27)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (y <= -6.2e+38)
		tmp = x + (z * x);
	elseif (y <= -3.8e-45)
		tmp = t_1;
	elseif (y <= -6.4e-62)
		tmp = t * (z / y);
	elseif (y <= 6.5e-269)
		tmp = t / b;
	elseif (y <= 1.1e-27)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[y, -6.2e+38], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e-45], t$95$1, If[LessEqual[y, -6.4e-62], N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-269], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.1e-27], t$95$1, x]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.20000000000000035e38

   1. Initial program 47.1%

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

   2. Taylor expanded in y around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in z around 0 44.3%

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

   if -6.20000000000000035e38 < y < -3.79999999999999997e-45 or 6.50000000000000006e-269 < y < 1.09999999999999993e-27

   1. Initial program 72.1%

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

   2. Taylor expanded in t around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

      4. *-commutative 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y around 0 44.8%

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

      1. associate-*r/ 44.8%

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

      2. neg-mul-1 44.8%

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

   7. Simplified 44.8%

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

   if -3.79999999999999997e-45 < y < -6.40000000000000043e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 57.9%

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

      2. +-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. fma-def 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in z around 0 57.9%

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

   6. Taylor expanded in t around 0 57.9%

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

      1. associate-/l* 57.9%

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

      2. *-rgt-identity 57.9%

         \[\leadsto \frac{\color{blue}{t \cdot 1}}{\frac{y}{z}} \]

      3. associate-*r/ 57.3%

         \[\leadsto \color{blue}{t \cdot \frac{1}{\frac{y}{z}}} \]

      4. associate-/r/ 57.9%

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

      5. associate-*l/ 57.9%

         \[\leadsto t \cdot \color{blue}{\frac{1 \cdot z}{y}} \]

      6. associate-*r/ 57.9%

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

      7. *-lft-identity 57.9%

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

   8. Simplified 57.9%

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

   if -6.40000000000000043e-62 < y < 6.50000000000000006e-269

   1. Initial program 74.7%

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

   2. Taylor expanded in t around inf 44.3%

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

      1. associate-/l* 50.0%

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

      2. +-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. fma-def 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in b around inf 48.3%

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

   if 1.09999999999999993e-27 < y

   1. Initial program 55.9%

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

   2. Taylor expanded in z around 0 39.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-45}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 42.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -5.5e+27)
     t_1
     (if (<= y 7e-269) (/ t (- b y)) (if (<= y 1.3e-27) (/ (- a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5.5e+27) {
		tmp = t_1;
	} else if (y <= 7e-269) {
		tmp = t / (b - y);
	} else if (y <= 1.3e-27) {
		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 = x / (1.0d0 - z)
    if (y <= (-5.5d+27)) then
        tmp = t_1
    else if (y <= 7d-269) then
        tmp = t / (b - y)
    else if (y <= 1.3d-27) 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 = x / (1.0 - z);
	double tmp;
	if (y <= -5.5e+27) {
		tmp = t_1;
	} else if (y <= 7e-269) {
		tmp = t / (b - y);
	} else if (y <= 1.3e-27) {
		tmp = -a / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -5.5e+27:
		tmp = t_1
	elif y <= 7e-269:
		tmp = t / (b - y)
	elif y <= 1.3e-27:
		tmp = -a / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5.5e+27)
		tmp = t_1;
	elseif (y <= 7e-269)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 1.3e-27)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5.5e+27)
		tmp = t_1;
	elseif (y <= 7e-269)
		tmp = t / (b - y);
	elseif (y <= 1.3e-27)
		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[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+27], t$95$1, If[LessEqual[y, 7e-269], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-27], N[((-a) / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999966e27 or 1.30000000000000009e-27 < y

   1. Initial program 51.5%

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

   2. Taylor expanded in y around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

   4. Simplified 56.3%

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

   if -5.49999999999999966e27 < y < 7.00000000000000038e-269

   1. Initial program 71.9%

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

   2. Taylor expanded in t around inf 39.5%

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

      1. associate-/l* 47.5%

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

      2. +-commutative 47.5%

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

      3. *-commutative 47.5%

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

      4. fma-def 47.5%

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

   4. Simplified 47.5%

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

   5. Taylor expanded in z around inf 45.6%

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

   if 7.00000000000000038e-269 < y < 1.30000000000000009e-27

   1. Initial program 79.2%

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

   2. Taylor expanded in t around 0 53.8%

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

      1. *-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. *-commutative 53.8%

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

   4. Simplified 53.8%

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

   5. Taylor expanded in y around 0 48.6%

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

      1. associate-*r/ 48.6%

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

      2. neg-mul-1 48.6%

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

   7. Simplified 48.6%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 13: 58.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+163} \lor \neg \left(y \leq 2.7 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.35e+163) (not (<= y 2.7e-27)))
   (/ x (- 1.0 z))
   (/ (- t a) (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.35e+163) || !(y <= 2.7e-27)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (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 ((y <= (-1.35d+163)) .or. (.not. (y <= 2.7d-27))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (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 ((y <= -1.35e+163) || !(y <= 2.7e-27)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.35e+163) or not (y <= 2.7e-27):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.35e+163) || !(y <= 2.7e-27))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.35e+163) || ~((y <= 2.7e-27)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.35e+163], N[Not[LessEqual[y, 2.7e-27]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e163 or 2.69999999999999989e-27 < y

   1. Initial program 51.6%

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

   2. Taylor expanded in y around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. mul-1-neg 62.0%

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

      3. unsub-neg 62.0%

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

   4. Simplified 62.0%

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

   if -1.35e163 < y < 2.69999999999999989e-27

   1. Initial program 69.3%

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

   2. Taylor expanded in z around inf 67.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+163} \lor \neg \left(y \leq 2.7 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 14: 34.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -20000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -20000.0)
   x
   (if (<= y 8.2e-269) (/ t b) (if (<= y 1.25e-27) (/ (- a) b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -20000.0) {
		tmp = x;
	} else if (y <= 8.2e-269) {
		tmp = t / b;
	} else if (y <= 1.25e-27) {
		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 (y <= (-20000.0d0)) then
        tmp = x
    else if (y <= 8.2d-269) then
        tmp = t / b
    else if (y <= 1.25d-27) 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 (y <= -20000.0) {
		tmp = x;
	} else if (y <= 8.2e-269) {
		tmp = t / b;
	} else if (y <= 1.25e-27) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -20000.0:
		tmp = x
	elif y <= 8.2e-269:
		tmp = t / b
	elif y <= 1.25e-27:
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -20000.0)
		tmp = x;
	elseif (y <= 8.2e-269)
		tmp = Float64(t / b);
	elseif (y <= 1.25e-27)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -20000.0)
		tmp = x;
	elseif (y <= 8.2e-269)
		tmp = t / b;
	elseif (y <= 1.25e-27)
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -20000.0], x, If[LessEqual[y, 8.2e-269], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.25e-27], N[((-a) / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e4 or 1.25e-27 < y

   1. Initial program 51.5%

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

   2. Taylor expanded in z around 0 40.0%

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

   if -2e4 < y < 8.2000000000000006e-269

   1. Initial program 73.0%

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

   2. Taylor expanded in t around inf 40.1%

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

      1. associate-/l* 48.6%

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

      2. +-commutative 48.6%

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

      3. *-commutative 48.6%

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

      4. fma-def 48.6%

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

   4. Simplified 48.6%

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

   5. Taylor expanded in b around inf 42.4%

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

   if 8.2000000000000006e-269 < y < 1.25e-27

   1. Initial program 79.2%

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

   2. Taylor expanded in t around 0 53.8%

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

      1. *-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. *-commutative 53.8%

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

   4. Simplified 53.8%

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

   5. Taylor expanded in y around 0 48.6%

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

      1. associate-*r/ 48.6%

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

      2. neg-mul-1 48.6%

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

   7. Simplified 48.6%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -20000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 36.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.2e+38)
   (+ x (* z x))
   (if (<= y 8.2e-269) (/ t (- b y)) (if (<= y 1.15e-27) (/ (- a) b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.2e+38) {
		tmp = x + (z * x);
	} else if (y <= 8.2e-269) {
		tmp = t / (b - y);
	} else if (y <= 1.15e-27) {
		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 (y <= (-6.2d+38)) then
        tmp = x + (z * x)
    else if (y <= 8.2d-269) then
        tmp = t / (b - y)
    else if (y <= 1.15d-27) 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 (y <= -6.2e+38) {
		tmp = x + (z * x);
	} else if (y <= 8.2e-269) {
		tmp = t / (b - y);
	} else if (y <= 1.15e-27) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.2e+38:
		tmp = x + (z * x)
	elif y <= 8.2e-269:
		tmp = t / (b - y)
	elif y <= 1.15e-27:
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.2e+38)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 8.2e-269)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 1.15e-27)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.2e+38)
		tmp = x + (z * x);
	elseif (y <= 8.2e-269)
		tmp = t / (b - y);
	elseif (y <= 1.15e-27)
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.2e+38], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-269], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-27], N[((-a) / b), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.20000000000000035e38

   1. Initial program 47.1%

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

   2. Taylor expanded in y around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

   4. Simplified 52.9%

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

   5. Taylor expanded in z around 0 44.3%

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

   if -6.20000000000000035e38 < y < 8.2000000000000006e-269

   1. Initial program 71.0%

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

   2. Taylor expanded in t around inf 39.0%

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

      1. associate-/l* 47.0%

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

      2. +-commutative 47.0%

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

      3. *-commutative 47.0%

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

      4. fma-def 47.0%

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

   4. Simplified 47.0%

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

   5. Taylor expanded in z around inf 45.1%

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

   if 8.2000000000000006e-269 < y < 1.15e-27

   1. Initial program 79.2%

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

   2. Taylor expanded in t around 0 53.8%

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

      1. *-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

      4. *-commutative 53.8%

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

   4. Simplified 53.8%

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

   5. Taylor expanded in y around 0 48.6%

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

      1. associate-*r/ 48.6%

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

      2. neg-mul-1 48.6%

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

   7. Simplified 48.6%

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

   if 1.15e-27 < y

   1. Initial program 55.9%

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

   2. Taylor expanded in z around 0 39.0%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-269}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 54.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+38} \lor \neg \left(y \leq 3.1 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+38) (not (<= y 3.1e-27))) (/ 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 <= -2.7e+38) || !(y <= 3.1e-27)) {
		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 <= (-2.7d+38)) .or. (.not. (y <= 3.1d-27))) 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 <= -2.7e+38) || !(y <= 3.1e-27)) {
		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 <= -2.7e+38) or not (y <= 3.1e-27):
		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 <= -2.7e+38) || !(y <= 3.1e-27))
		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 <= -2.7e+38) || ~((y <= 3.1e-27)))
		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, -2.7e+38], N[Not[LessEqual[y, 3.1e-27]], $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 < -2.69999999999999996e38 or 3.0999999999999998e-27 < y

   1. Initial program 51.9%

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

   2. Taylor expanded in y around inf 56.7%

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

      1. +-commutative 56.7%

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

      2. mul-1-neg 56.7%

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

      3. unsub-neg 56.7%

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

   4. Simplified 56.7%

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

   if -2.69999999999999996e38 < y < 3.0999999999999998e-27

   1. Initial program 74.0%

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

   2. Taylor expanded in y around 0 61.7%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+38} \lor \neg \left(y \leq 3.1 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 17: 34.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13500:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -13500.0) x (if (<= y 4.8e-108) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -13500.0) {
		tmp = x;
	} else if (y <= 4.8e-108) {
		tmp = t / 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 (y <= (-13500.0d0)) then
        tmp = x
    else if (y <= 4.8d-108) then
        tmp = t / 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 (y <= -13500.0) {
		tmp = x;
	} else if (y <= 4.8e-108) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -13500.0:
		tmp = x
	elif y <= 4.8e-108:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -13500.0)
		tmp = x;
	elseif (y <= 4.8e-108)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -13500.0)
		tmp = x;
	elseif (y <= 4.8e-108)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -13500.0], x, If[LessEqual[y, 4.8e-108], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -13500 or 4.80000000000000034e-108 < y

   1. Initial program 55.0%

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

   2. Taylor expanded in z around 0 37.6%

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

   if -13500 < y < 4.80000000000000034e-108

   1. Initial program 73.8%

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

   2. Taylor expanded in t around inf 38.6%

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

      1. associate-/l* 46.2%

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

      2. +-commutative 46.2%

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

      3. *-commutative 46.2%

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

      4. fma-def 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in b around inf 36.9%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13500:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 25.1% 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 62.8%

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

2. Taylor expanded in z around 0 24.1%

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

3. Final simplification 24.1%

   \[\leadsto x \]

Developer target: 73.4% 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 2023230 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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