Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.1% → 98.1%

Time: 20.8s

Alternatives: 22

Speedup: 1.3×

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: 66.1% 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: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {\left(b - y\right)}^{2}\\ t_2 := \mathsf{fma}\left(z, b - y, y\right)\\ t_3 := y - z \cdot \left(y - b\right)\\ t_4 := \frac{x \cdot y}{t_3} + \left(\frac{z \cdot t}{t_3} - \frac{z \cdot a}{t_3}\right)\\ t_5 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t_3}\\ t_6 := \frac{y}{\frac{t_2}{x}} + \frac{t - a}{\frac{t_2}{z}}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -1 \cdot 10^{-221}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} - \left(\left(\frac{a}{b - y} + \frac{t - a}{t_1} \cdot \frac{y}{z}\right) - \frac{t}{b - y}\right)\\ \mathbf{elif}\;t_5 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{t_1}{y}}}{z} + \frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow (- b y) 2.0))
        (t_2 (fma z (- b y) y))
        (t_3 (- y (* z (- y b))))
        (t_4 (+ (/ (* x y) t_3) (- (/ (* z t) t_3) (/ (* z a) t_3))))
        (t_5 (/ (+ (* x y) (* z (- t a))) t_3))
        (t_6 (+ (/ y (/ t_2 x)) (/ (- t a) (/ t_2 z)))))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -1e-221)
       t_4
       (if (<= t_5 2e-281)
         (-
          (/ (/ (* x y) z) (- b y))
          (- (+ (/ a (- b y)) (* (/ (- t a) t_1) (/ y z))) (/ t (- b y))))
         (if (<= t_5 2e+306)
           t_4
           (if (<= t_5 INFINITY)
             t_6
             (+
              (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ t_1 y))) z)
              (/ (- t a) (- b y))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow((b - y), 2.0);
	double t_2 = fma(z, (b - y), y);
	double t_3 = y - (z * (y - b));
	double t_4 = ((x * y) / t_3) + (((z * t) / t_3) - ((z * a) / t_3));
	double t_5 = ((x * y) + (z * (t - a))) / t_3;
	double t_6 = (y / (t_2 / x)) + ((t - a) / (t_2 / z));
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -1e-221) {
		tmp = t_4;
	} else if (t_5 <= 2e-281) {
		tmp = (((x * y) / z) / (b - y)) - (((a / (b - y)) + (((t - a) / t_1) * (y / z))) - (t / (b - y)));
	} else if (t_5 <= 2e+306) {
		tmp = t_4;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_6;
	} else {
		tmp = (((y / ((b - y) / x)) + ((a - t) / (t_1 / y))) / z) + ((t - a) / (b - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b - y) ^ 2.0
	t_2 = fma(z, Float64(b - y), y)
	t_3 = Float64(y - Float64(z * Float64(y - b)))
	t_4 = Float64(Float64(Float64(x * y) / t_3) + Float64(Float64(Float64(z * t) / t_3) - Float64(Float64(z * a) / t_3)))
	t_5 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_3)
	t_6 = Float64(Float64(y / Float64(t_2 / x)) + Float64(Float64(t - a) / Float64(t_2 / z)))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -1e-221)
		tmp = t_4;
	elseif (t_5 <= 2e-281)
		tmp = Float64(Float64(Float64(Float64(x * y) / z) / Float64(b - y)) - Float64(Float64(Float64(a / Float64(b - y)) + Float64(Float64(Float64(t - a) / t_1) * Float64(y / z))) - Float64(t / Float64(b - y))));
	elseif (t_5 <= 2e+306)
		tmp = t_4;
	elseif (t_5 <= Inf)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64(t_1 / y))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$3), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(N[(y / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -1e-221], t$95$4, If[LessEqual[t$95$5, 2e-281], N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+306], t$95$4, If[LessEqual[t$95$5, Infinity], t$95$6, N[(N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

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 or 2.00000000000000003e306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 25.5%

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

   2. Taylor expanded in x around 0 25.5%

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

      1. associate-/l* 61.5%

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

      2. +-commutative 61.5%

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

      3. *-commutative 61.5%

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

      4. fma-udef 61.5%

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

      5. associate-/l* 99.8%

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

      6. +-commutative 99.8%

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

      7. *-commutative 99.8%

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

      8. fma-udef 99.8%

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

   4. Simplified 99.8%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000002e-221 or 2e-281 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.5%

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

   2. Taylor expanded in a around inf 99.6%

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

   if -1.00000000000000002e-221 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e-281

   1. Initial program 41.3%

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

   2. Taylor expanded in z around inf 69.9%

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

      1. associate--l+ 69.9%

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

      2. associate-/r* 95.2%

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

      3. +-commutative 95.2%

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

      4. *-commutative 95.2%

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

      5. times-frac 99.6%

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

   4. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 38.2%

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

      1. +-commutative 38.2%

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

      2. associate--l+ 38.2%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}} + \frac{t - a}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq -1 \cdot 10^{-221}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)} + \left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} - \left(\left(\frac{a}{b - y} + \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\right) - \frac{t}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)} + \left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}} + \frac{t - a}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ t_3 := \frac{x \cdot y}{t_1} + \left(\frac{z \cdot t}{t_1} - \frac{z \cdot a}{t_1}\right)\\ \mathbf{if}\;z \leq -38000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-195}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-234}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2
         (+
          (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)
          (/ (- t a) (- b y))))
        (t_3 (+ (/ (* x y) t_1) (- (/ (* z t) t_1) (/ (* z a) t_1)))))
   (if (<= z -38000000000.0)
     t_2
     (if (<= z -1.5e-195)
       t_3
       (if (<= z 2.35e-234)
         (- (/ (* z (- t a)) y) (/ x (+ z -1.0)))
         (if (<= z 15.0) t_3 t_2))))))

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 = (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	double t_3 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1));
	double tmp;
	if (z <= -38000000000.0) {
		tmp = t_2;
	} else if (z <= -1.5e-195) {
		tmp = t_3;
	} else if (z <= 2.35e-234) {
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0));
	} else if (z <= 15.0) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y - (z * (y - b))
    t_2 = (((y / ((b - y) / x)) + ((a - t) / (((b - y) ** 2.0d0) / y))) / z) + ((t - a) / (b - y))
    t_3 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1))
    if (z <= (-38000000000.0d0)) then
        tmp = t_2
    else if (z <= (-1.5d-195)) then
        tmp = t_3
    else if (z <= 2.35d-234) then
        tmp = ((z * (t - a)) / y) - (x / (z + (-1.0d0)))
    else if (z <= 15.0d0) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (z * (y - b));
	double t_2 = (((y / ((b - y) / x)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y));
	double t_3 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1));
	double tmp;
	if (z <= -38000000000.0) {
		tmp = t_2;
	} else if (z <= -1.5e-195) {
		tmp = t_3;
	} else if (z <= 2.35e-234) {
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0));
	} else if (z <= 15.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = (((y / ((b - y) / x)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z) + ((t - a) / (b - y))
	t_3 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1))
	tmp = 0
	if z <= -38000000000.0:
		tmp = t_2
	elif z <= -1.5e-195:
		tmp = t_3
	elif z <= 2.35e-234:
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0))
	elif z <= 15.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(z * Float64(y - b)))
	t_2 = Float64(Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	t_3 = Float64(Float64(Float64(x * y) / t_1) + Float64(Float64(Float64(z * t) / t_1) - Float64(Float64(z * a) / t_1)))
	tmp = 0.0
	if (z <= -38000000000.0)
		tmp = t_2;
	elseif (z <= -1.5e-195)
		tmp = t_3;
	elseif (z <= 2.35e-234)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) / y) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 15.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = (((y / ((b - y) / x)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z) + ((t - a) / (b - y));
	t_3 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1));
	tmp = 0.0;
	if (z <= -38000000000.0)
		tmp = t_2;
	elseif (z <= -1.5e-195)
		tmp = t_3;
	elseif (z <= 2.35e-234)
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0));
	elseif (z <= 15.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -38000000000.0], t$95$2, If[LessEqual[z, -1.5e-195], t$95$3, If[LessEqual[z, 2.35e-234], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 15.0], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e10 or 15 < z

   1. Initial program 36.5%

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

   2. Taylor expanded in z around -inf 68.0%

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

      1. +-commutative 68.0%

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

      2. associate--l+ 68.0%

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

   4. Simplified 96.5%

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

   if -3.8e10 < z < -1.5e-195 or 2.35e-234 < z < 15

   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 a around inf 90.8%

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

   if -1.5e-195 < z < 2.35e-234

   1. Initial program 76.8%

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

   2. Taylor expanded in y around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. mul-1-neg 80.0%

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

      4. distribute-neg-frac 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. associate-/l* 80.0%

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

      7. metadata-eval 80.0%

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

      8. *-lft-identity 80.0%

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

      9. associate-/l* 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate-/l* 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in b around 0 91.2%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{z \cdot \left(a - t\right)}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38000000000:\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)} + \left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-234}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)} + \left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \left(y - b\right)\\ t_2 := \frac{x \cdot y}{t_1} + \left(\frac{z \cdot t}{t_1} - \frac{z \cdot a}{t_1}\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-231}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* z (- y b))))
        (t_2 (+ (/ (* x y) t_1) (- (/ (* z t) t_1) (/ (* z a) t_1))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2.55e+16)
     t_3
     (if (<= z -2.6e-197)
       t_2
       (if (<= z 1.05e-231)
         (- (/ (* z (- t a)) y) (/ x (+ z -1.0)))
         (if (<= z 15.0) t_2 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 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.55e+16) {
		tmp = t_3;
	} else if (z <= -2.6e-197) {
		tmp = t_2;
	} else if (z <= 1.05e-231) {
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0));
	} else if (z <= 15.0) {
		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 = y - (z * (y - b))
    t_2 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1))
    t_3 = (t - a) / (b - y)
    if (z <= (-2.55d+16)) then
        tmp = t_3
    else if (z <= (-2.6d-197)) then
        tmp = t_2
    else if (z <= 1.05d-231) then
        tmp = ((z * (t - a)) / y) - (x / (z + (-1.0d0)))
    else if (z <= 15.0d0) 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 = y - (z * (y - b));
	double t_2 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.55e+16) {
		tmp = t_3;
	} else if (z <= -2.6e-197) {
		tmp = t_2;
	} else if (z <= 1.05e-231) {
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0));
	} else if (z <= 15.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (z * (y - b))
	t_2 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.55e+16:
		tmp = t_3
	elif z <= -2.6e-197:
		tmp = t_2
	elif z <= 1.05e-231:
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0))
	elif z <= 15.0:
		tmp = t_2
	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(Float64(Float64(x * y) / t_1) + Float64(Float64(Float64(z * t) / t_1) - Float64(Float64(z * a) / t_1)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.55e+16)
		tmp = t_3;
	elseif (z <= -2.6e-197)
		tmp = t_2;
	elseif (z <= 1.05e-231)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) / y) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 15.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (z * (y - b));
	t_2 = ((x * y) / t_1) + (((z * t) / t_1) - ((z * a) / t_1));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.55e+16)
		tmp = t_3;
	elseif (z <= -2.6e-197)
		tmp = t_2;
	elseif (z <= 1.05e-231)
		tmp = ((z * (t - a)) / y) - (x / (z + -1.0));
	elseif (z <= 15.0)
		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[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+16], t$95$3, If[LessEqual[z, -2.6e-197], t$95$2, If[LessEqual[z, 1.05e-231], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 15.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55e16 or 15 < z

   1. Initial program 36.7%

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

   2. Taylor expanded in z around inf 81.3%

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

   if -2.55e16 < z < -2.6000000000000001e-197 or 1.04999999999999995e-231 < z < 15

   1. Initial program 89.8%

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

   2. Taylor expanded in a around inf 89.8%

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

   if -2.6000000000000001e-197 < z < 1.04999999999999995e-231

   1. Initial program 76.8%

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

   2. Taylor expanded in y around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. mul-1-neg 80.0%

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

      4. distribute-neg-frac 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. associate-/l* 80.0%

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

      7. metadata-eval 80.0%

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

      8. *-lft-identity 80.0%

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

      9. associate-/l* 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate-/l* 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in b around 0 91.2%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{z \cdot \left(a - t\right)}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-197}:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)} + \left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-231}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;\frac{x \cdot y}{y - z \cdot \left(y - b\right)} + \left(\frac{z \cdot t}{y - z \cdot \left(y - b\right)} - \frac{z \cdot a}{y - z \cdot \left(y - b\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot b\\ t_2 := \frac{z \cdot \left(t - a\right)}{t_1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.82:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-293}:\\ \;\;\;\;\frac{t}{\frac{y}{z}} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x \cdot y}{t_1}\\ \mathbf{elif}\;z \leq 0.465:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z b)))
        (t_2 (/ (* z (- t a)) t_1))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -0.82)
     t_3
     (if (<= z -5.8e-161)
       t_2
       (if (<= z 1.72e-293)
         (- (/ t (/ y z)) (/ x (+ z -1.0)))
         (if (<= z 5.3e-114)
           (- x (* z (- (/ a y) x)))
           (if (<= z 4.5e-93)
             t_2
             (if (<= z 2.2e-61)
               (/ (* x y) t_1)
               (if (<= z 0.465)
                 (- (/ (- x) (+ z -1.0)) (/ a (/ y z)))
                 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * b);
	double t_2 = (z * (t - a)) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.82) {
		tmp = t_3;
	} else if (z <= -5.8e-161) {
		tmp = t_2;
	} else if (z <= 1.72e-293) {
		tmp = (t / (y / z)) - (x / (z + -1.0));
	} else if (z <= 5.3e-114) {
		tmp = x - (z * ((a / y) - x));
	} else if (z <= 4.5e-93) {
		tmp = t_2;
	} else if (z <= 2.2e-61) {
		tmp = (x * y) / t_1;
	} else if (z <= 0.465) {
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	} 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 = y + (z * b)
    t_2 = (z * (t - a)) / t_1
    t_3 = (t - a) / (b - y)
    if (z <= (-0.82d0)) then
        tmp = t_3
    else if (z <= (-5.8d-161)) then
        tmp = t_2
    else if (z <= 1.72d-293) then
        tmp = (t / (y / z)) - (x / (z + (-1.0d0)))
    else if (z <= 5.3d-114) then
        tmp = x - (z * ((a / y) - x))
    else if (z <= 4.5d-93) then
        tmp = t_2
    else if (z <= 2.2d-61) then
        tmp = (x * y) / t_1
    else if (z <= 0.465d0) then
        tmp = (-x / (z + (-1.0d0))) - (a / (y / z))
    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 = y + (z * b);
	double t_2 = (z * (t - a)) / t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.82) {
		tmp = t_3;
	} else if (z <= -5.8e-161) {
		tmp = t_2;
	} else if (z <= 1.72e-293) {
		tmp = (t / (y / z)) - (x / (z + -1.0));
	} else if (z <= 5.3e-114) {
		tmp = x - (z * ((a / y) - x));
	} else if (z <= 4.5e-93) {
		tmp = t_2;
	} else if (z <= 2.2e-61) {
		tmp = (x * y) / t_1;
	} else if (z <= 0.465) {
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * b)
	t_2 = (z * (t - a)) / t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.82:
		tmp = t_3
	elif z <= -5.8e-161:
		tmp = t_2
	elif z <= 1.72e-293:
		tmp = (t / (y / z)) - (x / (z + -1.0))
	elif z <= 5.3e-114:
		tmp = x - (z * ((a / y) - x))
	elif z <= 4.5e-93:
		tmp = t_2
	elif z <= 2.2e-61:
		tmp = (x * y) / t_1
	elif z <= 0.465:
		tmp = (-x / (z + -1.0)) - (a / (y / z))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * b))
	t_2 = Float64(Float64(z * Float64(t - a)) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.82)
		tmp = t_3;
	elseif (z <= -5.8e-161)
		tmp = t_2;
	elseif (z <= 1.72e-293)
		tmp = Float64(Float64(t / Float64(y / z)) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 5.3e-114)
		tmp = Float64(x - Float64(z * Float64(Float64(a / y) - x)));
	elseif (z <= 4.5e-93)
		tmp = t_2;
	elseif (z <= 2.2e-61)
		tmp = Float64(Float64(x * y) / t_1);
	elseif (z <= 0.465)
		tmp = Float64(Float64(Float64(-x) / Float64(z + -1.0)) - Float64(a / Float64(y / z)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * b);
	t_2 = (z * (t - a)) / t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.82)
		tmp = t_3;
	elseif (z <= -5.8e-161)
		tmp = t_2;
	elseif (z <= 1.72e-293)
		tmp = (t / (y / z)) - (x / (z + -1.0));
	elseif (z <= 5.3e-114)
		tmp = x - (z * ((a / y) - x));
	elseif (z <= 4.5e-93)
		tmp = t_2;
	elseif (z <= 2.2e-61)
		tmp = (x * y) / t_1;
	elseif (z <= 0.465)
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.82], t$95$3, If[LessEqual[z, -5.8e-161], t$95$2, If[LessEqual[z, 1.72e-293], N[(N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-114], N[(x - N[(z * N[(N[(a / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-93], t$95$2, If[LessEqual[z, 2.2e-61], N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 0.465], N[(N[((-x) / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(a / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -0.819999999999999951 or 0.465000000000000024 < z

   1. Initial program 38.4%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -0.819999999999999951 < z < -5.8e-161 or 5.29999999999999973e-114 < z < 4.5000000000000002e-93

   1. Initial program 88.4%

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

   2. Taylor expanded in x around 0 71.0%

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

   3. Taylor expanded in b around inf 69.8%

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

   if -5.8e-161 < z < 1.72000000000000008e-293

   1. Initial program 84.4%

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

   2. Taylor expanded in y around -inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

      3. mul-1-neg 78.4%

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

      4. distribute-neg-frac 78.4%

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

      5. cancel-sign-sub-inv 78.4%

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

      6. associate-/l* 78.4%

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

      7. metadata-eval 78.4%

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

      8. *-lft-identity 78.4%

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

      9. associate-/l* 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in z around 0 78.4%

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

      1. associate-/l* 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in t around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. associate-/l* 75.7%

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

      3. distribute-neg-frac 75.7%

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

   10. Simplified 75.7%

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

   if 1.72000000000000008e-293 < z < 5.29999999999999973e-114

   1. Initial program 78.6%

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

   2. Taylor expanded in y around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

      3. mul-1-neg 74.2%

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

      4. distribute-neg-frac 74.2%

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

      5. cancel-sign-sub-inv 74.2%

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

      6. associate-/l* 74.3%

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

      7. metadata-eval 74.3%

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

      8. *-lft-identity 74.3%

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

      9. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

      1. div-inv 74.4%

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

      2. +-commutative 74.4%

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

      3. associate-/r/ 74.4%

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

      4. sub-neg 74.4%

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

      5. metadata-eval 74.4%

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

      6. associate-/r/ 74.2%

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

      7. sub-neg 74.2%

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

      8. metadata-eval 74.2%

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

   6. Applied egg-rr 74.2%

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

   7. Taylor expanded in a around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. times-frac 69.1%

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

      3. distribute-rgt-neg-in 69.1%

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

      4. sub-neg 69.1%

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

      5. metadata-eval 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in z around 0 71.8%

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

   if 4.5000000000000002e-93 < z < 2.20000000000000009e-61

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 63.8%

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

      1. associate-/l* 51.9%

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

      2. +-commutative 51.9%

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

      3. *-commutative 51.9%

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

      4. fma-udef 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in x around 0 63.8%

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

   6. Taylor expanded in b around inf 63.8%

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

   if 2.20000000000000009e-61 < z < 0.465000000000000024

   1. Initial program 92.0%

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

   2. Taylor expanded in y around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. unsub-neg 67.7%

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

      3. mul-1-neg 67.7%

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

      4. distribute-neg-frac 67.7%

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

      5. cancel-sign-sub-inv 67.7%

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

      6. associate-/l* 67.7%

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

      7. metadata-eval 67.7%

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

      8. *-lft-identity 67.7%

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

      9. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around 0 67.7%

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

      1. associate-/l* 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in a around inf 72.3%

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

      1. associate-/l* 72.4%

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

   10. Simplified 72.4%

       \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{a}{\frac{y}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.82:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{-293}:\\ \;\;\;\;\frac{t}{\frac{y}{z}} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.465:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 69.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := y + z \cdot b\\ \mathbf{if}\;z \leq -1150:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{t_1}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-293}:\\ \;\;\;\;\frac{t}{\frac{y}{z}} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{elif}\;z \leq 10^{-92}:\\ \;\;\;\;\frac{t_1}{t_3}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-61}:\\ \;\;\;\;\frac{x \cdot y}{t_3}\\ \mathbf{elif}\;z \leq 0.29:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))) (t_3 (+ y (* z b))))
   (if (<= z -1150.0)
     t_2
     (if (<= z -5.8e-161)
       (/ t_1 (- y (* z (- y b))))
       (if (<= z 1.75e-293)
         (- (/ t (/ y z)) (/ x (+ z -1.0)))
         (if (<= z 6.4e-114)
           (- x (* z (- (/ a y) x)))
           (if (<= z 1e-92)
             (/ t_1 t_3)
             (if (<= z 3e-61)
               (/ (* x y) t_3)
               (if (<= z 0.29)
                 (- (/ (- x) (+ z -1.0)) (/ a (/ y z)))
                 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 t_3 = y + (z * b);
	double tmp;
	if (z <= -1150.0) {
		tmp = t_2;
	} else if (z <= -5.8e-161) {
		tmp = t_1 / (y - (z * (y - b)));
	} else if (z <= 1.75e-293) {
		tmp = (t / (y / z)) - (x / (z + -1.0));
	} else if (z <= 6.4e-114) {
		tmp = x - (z * ((a / y) - x));
	} else if (z <= 1e-92) {
		tmp = t_1 / t_3;
	} else if (z <= 3e-61) {
		tmp = (x * y) / t_3;
	} else if (z <= 0.29) {
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    t_3 = y + (z * b)
    if (z <= (-1150.0d0)) then
        tmp = t_2
    else if (z <= (-5.8d-161)) then
        tmp = t_1 / (y - (z * (y - b)))
    else if (z <= 1.75d-293) then
        tmp = (t / (y / z)) - (x / (z + (-1.0d0)))
    else if (z <= 6.4d-114) then
        tmp = x - (z * ((a / y) - x))
    else if (z <= 1d-92) then
        tmp = t_1 / t_3
    else if (z <= 3d-61) then
        tmp = (x * y) / t_3
    else if (z <= 0.29d0) then
        tmp = (-x / (z + (-1.0d0))) - (a / (y / z))
    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 t_3 = y + (z * b);
	double tmp;
	if (z <= -1150.0) {
		tmp = t_2;
	} else if (z <= -5.8e-161) {
		tmp = t_1 / (y - (z * (y - b)));
	} else if (z <= 1.75e-293) {
		tmp = (t / (y / z)) - (x / (z + -1.0));
	} else if (z <= 6.4e-114) {
		tmp = x - (z * ((a / y) - x));
	} else if (z <= 1e-92) {
		tmp = t_1 / t_3;
	} else if (z <= 3e-61) {
		tmp = (x * y) / t_3;
	} else if (z <= 0.29) {
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	} 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)
	t_3 = y + (z * b)
	tmp = 0
	if z <= -1150.0:
		tmp = t_2
	elif z <= -5.8e-161:
		tmp = t_1 / (y - (z * (y - b)))
	elif z <= 1.75e-293:
		tmp = (t / (y / z)) - (x / (z + -1.0))
	elif z <= 6.4e-114:
		tmp = x - (z * ((a / y) - x))
	elif z <= 1e-92:
		tmp = t_1 / t_3
	elif z <= 3e-61:
		tmp = (x * y) / t_3
	elif z <= 0.29:
		tmp = (-x / (z + -1.0)) - (a / (y / z))
	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))
	t_3 = Float64(y + Float64(z * b))
	tmp = 0.0
	if (z <= -1150.0)
		tmp = t_2;
	elseif (z <= -5.8e-161)
		tmp = Float64(t_1 / Float64(y - Float64(z * Float64(y - b))));
	elseif (z <= 1.75e-293)
		tmp = Float64(Float64(t / Float64(y / z)) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 6.4e-114)
		tmp = Float64(x - Float64(z * Float64(Float64(a / y) - x)));
	elseif (z <= 1e-92)
		tmp = Float64(t_1 / t_3);
	elseif (z <= 3e-61)
		tmp = Float64(Float64(x * y) / t_3);
	elseif (z <= 0.29)
		tmp = Float64(Float64(Float64(-x) / Float64(z + -1.0)) - Float64(a / Float64(y / z)));
	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);
	t_3 = y + (z * b);
	tmp = 0.0;
	if (z <= -1150.0)
		tmp = t_2;
	elseif (z <= -5.8e-161)
		tmp = t_1 / (y - (z * (y - b)));
	elseif (z <= 1.75e-293)
		tmp = (t / (y / z)) - (x / (z + -1.0));
	elseif (z <= 6.4e-114)
		tmp = x - (z * ((a / y) - x));
	elseif (z <= 1e-92)
		tmp = t_1 / t_3;
	elseif (z <= 3e-61)
		tmp = (x * y) / t_3;
	elseif (z <= 0.29)
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	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]}, Block[{t$95$3 = N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1150.0], t$95$2, If[LessEqual[z, -5.8e-161], N[(t$95$1 / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e-293], N[(N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-114], N[(x - N[(z * N[(N[(a / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-92], N[(t$95$1 / t$95$3), $MachinePrecision], If[LessEqual[z, 3e-61], N[(N[(x * y), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[z, 0.29], N[(N[((-x) / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(a / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1150 or 0.28999999999999998 < z

   1. Initial program 38.4%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -1150 < z < -5.8e-161

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 67.1%

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

   if -5.8e-161 < z < 1.7500000000000001e-293

   1. Initial program 84.4%

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

   2. Taylor expanded in y around -inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

      3. mul-1-neg 78.4%

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

      4. distribute-neg-frac 78.4%

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

      5. cancel-sign-sub-inv 78.4%

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

      6. associate-/l* 78.4%

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

      7. metadata-eval 78.4%

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

      8. *-lft-identity 78.4%

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

      9. associate-/l* 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in z around 0 78.4%

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

      1. associate-/l* 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in t around inf 78.6%

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

      1. mul-1-neg 78.6%

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

      2. associate-/l* 75.7%

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

      3. distribute-neg-frac 75.7%

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

   10. Simplified 75.7%

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

   if 1.7500000000000001e-293 < z < 6.4000000000000003e-114

   1. Initial program 78.6%

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

   2. Taylor expanded in y around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

      3. mul-1-neg 74.2%

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

      4. distribute-neg-frac 74.2%

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

      5. cancel-sign-sub-inv 74.2%

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

      6. associate-/l* 74.3%

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

      7. metadata-eval 74.3%

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

      8. *-lft-identity 74.3%

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

      9. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

      1. div-inv 74.4%

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

      2. +-commutative 74.4%

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

      3. associate-/r/ 74.4%

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

      4. sub-neg 74.4%

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

      5. metadata-eval 74.4%

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

      6. associate-/r/ 74.2%

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

      7. sub-neg 74.2%

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

      8. metadata-eval 74.2%

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

   6. Applied egg-rr 74.2%

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

   7. Taylor expanded in a around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. times-frac 69.1%

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

      3. distribute-rgt-neg-in 69.1%

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

      4. sub-neg 69.1%

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

      5. metadata-eval 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in z around 0 71.8%

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

   if 6.4000000000000003e-114 < z < 9.99999999999999988e-93

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in b around inf 85.9%

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

   if 9.99999999999999988e-93 < z < 3.00000000000000012e-61

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 63.8%

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

      1. associate-/l* 51.9%

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

      2. +-commutative 51.9%

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

      3. *-commutative 51.9%

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

      4. fma-udef 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in x around 0 63.8%

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

   6. Taylor expanded in b around inf 63.8%

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

   if 3.00000000000000012e-61 < z < 0.28999999999999998

   1. Initial program 92.0%

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

   2. Taylor expanded in y around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. unsub-neg 67.7%

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

      3. mul-1-neg 67.7%

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

      4. distribute-neg-frac 67.7%

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

      5. cancel-sign-sub-inv 67.7%

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

      6. associate-/l* 67.7%

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

      7. metadata-eval 67.7%

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

      8. *-lft-identity 67.7%

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

      9. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around 0 67.7%

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

      1. associate-/l* 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in a around inf 72.3%

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

      1. associate-/l* 72.4%

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

   10. Simplified 72.4%

       \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{a}{\frac{y}{z}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1150:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-293}:\\ \;\;\;\;\frac{t}{\frac{y}{z}} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{elif}\;z \leq 10^{-92}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-61}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.29:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x \cdot y + t_1}{y - z \cdot \left(y - b\right)}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-225}:\\ \;\;\;\;\frac{t_1}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (+ (* x y) t_1) (- y (* z (- y b)))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -2.3e+16)
     t_3
     (if (<= z -8.5e-198)
       t_2
       (if (<= z 6.2e-225)
         (- (/ t_1 y) (/ x (+ z -1.0)))
         (if (<= z 15.0) 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 = ((x * y) + t_1) / (y - (z * (y - b)));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.3e+16) {
		tmp = t_3;
	} else if (z <= -8.5e-198) {
		tmp = t_2;
	} else if (z <= 6.2e-225) {
		tmp = (t_1 / y) - (x / (z + -1.0));
	} else if (z <= 15.0) {
		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 = ((x * y) + t_1) / (y - (z * (y - b)))
    t_3 = (t - a) / (b - y)
    if (z <= (-2.3d+16)) then
        tmp = t_3
    else if (z <= (-8.5d-198)) then
        tmp = t_2
    else if (z <= 6.2d-225) then
        tmp = (t_1 / y) - (x / (z + (-1.0d0)))
    else if (z <= 15.0d0) 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 = ((x * y) + t_1) / (y - (z * (y - b)));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.3e+16) {
		tmp = t_3;
	} else if (z <= -8.5e-198) {
		tmp = t_2;
	} else if (z <= 6.2e-225) {
		tmp = (t_1 / y) - (x / (z + -1.0));
	} else if (z <= 15.0) {
		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 = ((x * y) + t_1) / (y - (z * (y - b)))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.3e+16:
		tmp = t_3
	elif z <= -8.5e-198:
		tmp = t_2
	elif z <= 6.2e-225:
		tmp = (t_1 / y) - (x / (z + -1.0))
	elif z <= 15.0:
		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(Float64(x * y) + t_1) / Float64(y - Float64(z * Float64(y - b))))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.3e+16)
		tmp = t_3;
	elseif (z <= -8.5e-198)
		tmp = t_2;
	elseif (z <= 6.2e-225)
		tmp = Float64(Float64(t_1 / y) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 15.0)
		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 = ((x * y) + t_1) / (y - (z * (y - b)));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.3e+16)
		tmp = t_3;
	elseif (z <= -8.5e-198)
		tmp = t_2;
	elseif (z <= 6.2e-225)
		tmp = (t_1 / y) - (x / (z + -1.0));
	elseif (z <= 15.0)
		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[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+16], t$95$3, If[LessEqual[z, -8.5e-198], t$95$2, If[LessEqual[z, 6.2e-225], N[(N[(t$95$1 / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 15.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e16 or 15 < z

   1. Initial program 36.7%

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

   2. Taylor expanded in z around inf 81.3%

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

   if -2.3e16 < z < -8.4999999999999994e-198 or 6.19999999999999993e-225 < z < 15

   1. Initial program 89.8%

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

   if -8.4999999999999994e-198 < z < 6.19999999999999993e-225

   1. Initial program 76.8%

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

   2. Taylor expanded in y around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. mul-1-neg 80.0%

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

      4. distribute-neg-frac 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. associate-/l* 80.0%

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

      7. metadata-eval 80.0%

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

      8. *-lft-identity 80.0%

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

      9. associate-/l* 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate-/l* 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in b around 0 91.2%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{z \cdot \left(a - t\right)}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+16}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-225}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 66.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ t_2 := x - z \cdot \left(\frac{a}{y} - x\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{\frac{y - z \cdot \left(y - b\right)}{x}}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.202:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z (- t a)) (+ y (* z b))))
        (t_2 (- x (* z (- (/ a y) x))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -0.88)
     t_3
     (if (<= z -4.6e-156)
       t_1
       (if (<= z -8e-264)
         (/ y (/ (- y (* z (- y b))) x))
         (if (<= z -5.3e-297)
           (* (- t a) (/ z y))
           (if (<= z 8.2e-114)
             t_2
             (if (<= z 5.8e-93) t_1 (if (<= z 0.202) 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)) / (y + (z * b));
	double t_2 = x - (z * ((a / y) - x));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.88) {
		tmp = t_3;
	} else if (z <= -4.6e-156) {
		tmp = t_1;
	} else if (z <= -8e-264) {
		tmp = y / ((y - (z * (y - b))) / x);
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 8.2e-114) {
		tmp = t_2;
	} else if (z <= 5.8e-93) {
		tmp = t_1;
	} else if (z <= 0.202) {
		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)) / (y + (z * b))
    t_2 = x - (z * ((a / y) - x))
    t_3 = (t - a) / (b - y)
    if (z <= (-0.88d0)) then
        tmp = t_3
    else if (z <= (-4.6d-156)) then
        tmp = t_1
    else if (z <= (-8d-264)) then
        tmp = y / ((y - (z * (y - b))) / x)
    else if (z <= (-5.3d-297)) then
        tmp = (t - a) * (z / y)
    else if (z <= 8.2d-114) then
        tmp = t_2
    else if (z <= 5.8d-93) then
        tmp = t_1
    else if (z <= 0.202d0) 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)) / (y + (z * b));
	double t_2 = x - (z * ((a / y) - x));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.88) {
		tmp = t_3;
	} else if (z <= -4.6e-156) {
		tmp = t_1;
	} else if (z <= -8e-264) {
		tmp = y / ((y - (z * (y - b))) / x);
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 8.2e-114) {
		tmp = t_2;
	} else if (z <= 5.8e-93) {
		tmp = t_1;
	} else if (z <= 0.202) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (t - a)) / (y + (z * b))
	t_2 = x - (z * ((a / y) - x))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.88:
		tmp = t_3
	elif z <= -4.6e-156:
		tmp = t_1
	elif z <= -8e-264:
		tmp = y / ((y - (z * (y - b))) / x)
	elif z <= -5.3e-297:
		tmp = (t - a) * (z / y)
	elif z <= 8.2e-114:
		tmp = t_2
	elif z <= 5.8e-93:
		tmp = t_1
	elif z <= 0.202:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)))
	t_2 = Float64(x - Float64(z * Float64(Float64(a / y) - x)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.88)
		tmp = t_3;
	elseif (z <= -4.6e-156)
		tmp = t_1;
	elseif (z <= -8e-264)
		tmp = Float64(y / Float64(Float64(y - Float64(z * Float64(y - b))) / x));
	elseif (z <= -5.3e-297)
		tmp = Float64(Float64(t - a) * Float64(z / y));
	elseif (z <= 8.2e-114)
		tmp = t_2;
	elseif (z <= 5.8e-93)
		tmp = t_1;
	elseif (z <= 0.202)
		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)) / (y + (z * b));
	t_2 = x - (z * ((a / y) - x));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.88)
		tmp = t_3;
	elseif (z <= -4.6e-156)
		tmp = t_1;
	elseif (z <= -8e-264)
		tmp = y / ((y - (z * (y - b))) / x);
	elseif (z <= -5.3e-297)
		tmp = (t - a) * (z / y);
	elseif (z <= 8.2e-114)
		tmp = t_2;
	elseif (z <= 5.8e-93)
		tmp = t_1;
	elseif (z <= 0.202)
		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[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * N[(N[(a / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.88], t$95$3, If[LessEqual[z, -4.6e-156], t$95$1, If[LessEqual[z, -8e-264], N[(y / N[(N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-297], N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-114], t$95$2, If[LessEqual[z, 5.8e-93], t$95$1, If[LessEqual[z, 0.202], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.880000000000000004 or 0.20200000000000001 < z

   1. Initial program 38.4%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -0.880000000000000004 < z < -4.5999999999999999e-156 or 8.1999999999999993e-114 < z < 5.7999999999999997e-93

   1. Initial program 88.1%

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

   2. Taylor expanded in x around 0 73.1%

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

   3. Taylor expanded in b around inf 71.8%

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

   if -4.5999999999999999e-156 < z < -8.0000000000000001e-264

   1. Initial program 82.0%

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

   2. Taylor expanded in x around inf 59.0%

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

      1. associate-/l* 67.4%

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

      2. +-commutative 67.4%

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

      3. *-commutative 67.4%

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

      4. fma-udef 67.4%

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

   4. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}} \]
   5. Step-by-step derivation

      1. fma-udef 67.4%

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

   6. Applied egg-rr 67.4%

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

   if -8.0000000000000001e-264 < z < -5.30000000000000019e-297

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.8%

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

   3. Taylor expanded in b around inf 85.8%

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

   4. Taylor expanded in z around 0 85.8%

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

      1. div-inv 85.6%

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

      2. *-commutative 85.6%

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

   6. Applied egg-rr 85.6%

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

      1. associate-*r/ 85.8%

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

      2. *-rgt-identity 85.8%

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

      3. *-commutative 85.8%

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

      4. associate-*r/ 86.2%

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

   8. Simplified 86.2%

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

   if -5.30000000000000019e-297 < z < 8.1999999999999993e-114 or 5.7999999999999997e-93 < z < 0.20200000000000001

   1. Initial program 83.9%

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

   2. Taylor expanded in y around -inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. mul-1-neg 72.1%

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

      4. distribute-neg-frac 72.1%

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

      5. cancel-sign-sub-inv 72.1%

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

      6. associate-/l* 72.2%

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

      7. metadata-eval 72.2%

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

      8. *-lft-identity 72.2%

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

      9. associate-/l* 72.2%

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

   4. Simplified 72.2%

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

      1. div-inv 72.2%

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

      2. +-commutative 72.2%

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

      3. associate-/r/ 72.2%

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

      4. sub-neg 72.2%

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

      5. metadata-eval 72.2%

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

      6. associate-/r/ 72.1%

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

      7. sub-neg 72.1%

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

      8. metadata-eval 72.1%

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

   6. Applied egg-rr 72.1%

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

   7. Taylor expanded in a around inf 72.9%

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

      1. mul-1-neg 72.9%

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

      2. times-frac 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

      4. sub-neg 71.5%

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

      5. metadata-eval 71.5%

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

   9. Simplified 71.5%

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

   10. Taylor expanded in z around 0 67.7%

       \[\leadsto \color{blue}{\left(x - \frac{a}{y}\right) \cdot z + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-156}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{\frac{y - z \cdot \left(y - b\right)}{x}}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 0.202:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x \cdot y + t_1}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -350000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{t_1}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 1.9:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (+ (* x y) t_1) (+ y (* z b))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -350000000000.0)
     t_3
     (if (<= z -3.8e-195)
       t_2
       (if (<= z 6.5e-233)
         (- (/ t_1 y) (/ x (+ z -1.0)))
         (if (<= z 1.9) 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 = ((x * y) + t_1) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -350000000000.0) {
		tmp = t_3;
	} else if (z <= -3.8e-195) {
		tmp = t_2;
	} else if (z <= 6.5e-233) {
		tmp = (t_1 / y) - (x / (z + -1.0));
	} else if (z <= 1.9) {
		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 = ((x * y) + t_1) / (y + (z * b))
    t_3 = (t - a) / (b - y)
    if (z <= (-350000000000.0d0)) then
        tmp = t_3
    else if (z <= (-3.8d-195)) then
        tmp = t_2
    else if (z <= 6.5d-233) then
        tmp = (t_1 / y) - (x / (z + (-1.0d0)))
    else if (z <= 1.9d0) 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 = ((x * y) + t_1) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -350000000000.0) {
		tmp = t_3;
	} else if (z <= -3.8e-195) {
		tmp = t_2;
	} else if (z <= 6.5e-233) {
		tmp = (t_1 / y) - (x / (z + -1.0));
	} else if (z <= 1.9) {
		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 = ((x * y) + t_1) / (y + (z * b))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -350000000000.0:
		tmp = t_3
	elif z <= -3.8e-195:
		tmp = t_2
	elif z <= 6.5e-233:
		tmp = (t_1 / y) - (x / (z + -1.0))
	elif z <= 1.9:
		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(Float64(x * y) + t_1) / Float64(y + Float64(z * b)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -350000000000.0)
		tmp = t_3;
	elseif (z <= -3.8e-195)
		tmp = t_2;
	elseif (z <= 6.5e-233)
		tmp = Float64(Float64(t_1 / y) - Float64(x / Float64(z + -1.0)));
	elseif (z <= 1.9)
		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 = ((x * y) + t_1) / (y + (z * b));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -350000000000.0)
		tmp = t_3;
	elseif (z <= -3.8e-195)
		tmp = t_2;
	elseif (z <= 6.5e-233)
		tmp = (t_1 / y) - (x / (z + -1.0));
	elseif (z <= 1.9)
		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[(N[(x * y), $MachinePrecision] + t$95$1), $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, -350000000000.0], t$95$3, If[LessEqual[z, -3.8e-195], t$95$2, If[LessEqual[z, 6.5e-233], N[(N[(t$95$1 / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e11 or 1.8999999999999999 < z

   1. Initial program 36.7%

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

   2. Taylor expanded in z around inf 81.3%

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

   if -3.5e11 < z < -3.80000000000000013e-195 or 6.49999999999999989e-233 < z < 1.8999999999999999

   1. Initial program 89.8%

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

   2. Taylor expanded in b around inf 86.1%

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

   if -3.80000000000000013e-195 < z < 6.49999999999999989e-233

   1. Initial program 76.8%

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

   2. Taylor expanded in y around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. mul-1-neg 80.0%

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

      4. distribute-neg-frac 80.0%

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

      5. cancel-sign-sub-inv 80.0%

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

      6. associate-/l* 80.0%

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

      7. metadata-eval 80.0%

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

      8. *-lft-identity 80.0%

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

      9. associate-/l* 80.0%

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

   4. Simplified 80.0%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate-/l* 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in b around 0 91.2%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{z \cdot \left(a - t\right)}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000000:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 1.9:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 9: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.82:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{\frac{y - z \cdot \left(y - b\right)}{x}}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -0.82)
     t_1
     (if (<= z -3.5e-157)
       (/ (* z (- t a)) (+ y (* z b)))
       (if (<= z -8e-264)
         (/ y (/ (- y (* z (- y b))) x))
         (if (<= z -5.3e-297)
           (* (- t a) (/ z y))
           (if (<= z 0.6) (- (/ (- x) (+ z -1.0)) (/ a (/ y z))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.82) {
		tmp = t_1;
	} else if (z <= -3.5e-157) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else if (z <= -8e-264) {
		tmp = y / ((y - (z * (y - b))) / x);
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 0.6) {
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-0.82d0)) then
        tmp = t_1
    else if (z <= (-3.5d-157)) then
        tmp = (z * (t - a)) / (y + (z * b))
    else if (z <= (-8d-264)) then
        tmp = y / ((y - (z * (y - b))) / x)
    else if (z <= (-5.3d-297)) then
        tmp = (t - a) * (z / y)
    else if (z <= 0.6d0) then
        tmp = (-x / (z + (-1.0d0))) - (a / (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.82) {
		tmp = t_1;
	} else if (z <= -3.5e-157) {
		tmp = (z * (t - a)) / (y + (z * b));
	} else if (z <= -8e-264) {
		tmp = y / ((y - (z * (y - b))) / x);
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 0.6) {
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.82:
		tmp = t_1
	elif z <= -3.5e-157:
		tmp = (z * (t - a)) / (y + (z * b))
	elif z <= -8e-264:
		tmp = y / ((y - (z * (y - b))) / x)
	elif z <= -5.3e-297:
		tmp = (t - a) * (z / y)
	elif z <= 0.6:
		tmp = (-x / (z + -1.0)) - (a / (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.82)
		tmp = t_1;
	elseif (z <= -3.5e-157)
		tmp = Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * b)));
	elseif (z <= -8e-264)
		tmp = Float64(y / Float64(Float64(y - Float64(z * Float64(y - b))) / x));
	elseif (z <= -5.3e-297)
		tmp = Float64(Float64(t - a) * Float64(z / y));
	elseif (z <= 0.6)
		tmp = Float64(Float64(Float64(-x) / Float64(z + -1.0)) - Float64(a / Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.82)
		tmp = t_1;
	elseif (z <= -3.5e-157)
		tmp = (z * (t - a)) / (y + (z * b));
	elseif (z <= -8e-264)
		tmp = y / ((y - (z * (y - b))) / x);
	elseif (z <= -5.3e-297)
		tmp = (t - a) * (z / y);
	elseif (z <= 0.6)
		tmp = (-x / (z + -1.0)) - (a / (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.82], t$95$1, If[LessEqual[z, -3.5e-157], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8e-264], N[(y / N[(N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-297], N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(N[((-x) / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(a / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.819999999999999951 or 0.599999999999999978 < z

   1. Initial program 38.4%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -0.819999999999999951 < z < -3.5000000000000002e-157

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 69.6%

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

   3. Taylor expanded in b around inf 68.1%

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

   if -3.5000000000000002e-157 < z < -8.0000000000000001e-264

   1. Initial program 82.0%

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

   2. Taylor expanded in x around inf 59.0%

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

      1. associate-/l* 67.4%

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

      2. +-commutative 67.4%

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

      3. *-commutative 67.4%

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

      4. fma-udef 67.4%

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

   4. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}} \]
   5. Step-by-step derivation

      1. fma-udef 67.4%

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

   6. Applied egg-rr 67.4%

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

   if -8.0000000000000001e-264 < z < -5.30000000000000019e-297

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.8%

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

   3. Taylor expanded in b around inf 85.8%

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

   4. Taylor expanded in z around 0 85.8%

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

      1. div-inv 85.6%

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

      2. *-commutative 85.6%

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

   6. Applied egg-rr 85.6%

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

      1. associate-*r/ 85.8%

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

      2. *-rgt-identity 85.8%

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

      3. *-commutative 85.8%

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

      4. associate-*r/ 86.2%

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

   8. Simplified 86.2%

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

   if -5.30000000000000019e-297 < z < 0.599999999999999978

   1. Initial program 84.1%

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

   2. Taylor expanded in y around -inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. mul-1-neg 72.1%

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

      4. distribute-neg-frac 72.1%

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

      5. cancel-sign-sub-inv 72.1%

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

      6. associate-/l* 72.1%

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

      7. metadata-eval 72.1%

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

      8. *-lft-identity 72.1%

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

      9. associate-/l* 72.1%

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

   4. Simplified 72.1%

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

   5. Taylor expanded in z around 0 72.1%

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

      1. associate-/l* 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in a around inf 70.2%

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

      1. associate-/l* 67.6%

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

   10. Simplified 67.6%

       \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{a}{\frac{y}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.82:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{\frac{y - z \cdot \left(y - b\right)}{x}}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{a}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y - z \cdot \left(y - b\right)\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1300:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-157}:\\ \;\;\;\;\frac{t_1}{t_2}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-199}:\\ \;\;\;\;\frac{y}{\frac{t_2}{x}}\\ \mathbf{elif}\;z \leq 0.37:\\ \;\;\;\;\frac{t_1}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (- y (* z (- y b))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -1300.0)
     t_3
     (if (<= z -1.7e-157)
       (/ t_1 t_2)
       (if (<= z -1e-199)
         (/ y (/ t_2 x))
         (if (<= z 0.37) (- (/ t_1 y) (/ x (+ z -1.0))) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y - (z * (y - b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1300.0) {
		tmp = t_3;
	} else if (z <= -1.7e-157) {
		tmp = t_1 / t_2;
	} else if (z <= -1e-199) {
		tmp = y / (t_2 / x);
	} else if (z <= 0.37) {
		tmp = (t_1 / y) - (x / (z + -1.0));
	} 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 = y - (z * (y - b))
    t_3 = (t - a) / (b - y)
    if (z <= (-1300.0d0)) then
        tmp = t_3
    else if (z <= (-1.7d-157)) then
        tmp = t_1 / t_2
    else if (z <= (-1d-199)) then
        tmp = y / (t_2 / x)
    else if (z <= 0.37d0) then
        tmp = (t_1 / y) - (x / (z + (-1.0d0)))
    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 = y - (z * (y - b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1300.0) {
		tmp = t_3;
	} else if (z <= -1.7e-157) {
		tmp = t_1 / t_2;
	} else if (z <= -1e-199) {
		tmp = y / (t_2 / x);
	} else if (z <= 0.37) {
		tmp = (t_1 / y) - (x / (z + -1.0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y - (z * (y - b))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -1300.0:
		tmp = t_3
	elif z <= -1.7e-157:
		tmp = t_1 / t_2
	elif z <= -1e-199:
		tmp = y / (t_2 / x)
	elif z <= 0.37:
		tmp = (t_1 / y) - (x / (z + -1.0))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y - Float64(z * Float64(y - b)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1300.0)
		tmp = t_3;
	elseif (z <= -1.7e-157)
		tmp = Float64(t_1 / t_2);
	elseif (z <= -1e-199)
		tmp = Float64(y / Float64(t_2 / x));
	elseif (z <= 0.37)
		tmp = Float64(Float64(t_1 / y) - Float64(x / Float64(z + -1.0)));
	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 = y - (z * (y - b));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1300.0)
		tmp = t_3;
	elseif (z <= -1.7e-157)
		tmp = t_1 / t_2;
	elseif (z <= -1e-199)
		tmp = y / (t_2 / x);
	elseif (z <= 0.37)
		tmp = (t_1 / y) - (x / (z + -1.0));
	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[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1300.0], t$95$3, If[LessEqual[z, -1.7e-157], N[(t$95$1 / t$95$2), $MachinePrecision], If[LessEqual[z, -1e-199], N[(y / N[(t$95$2 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.37], N[(N[(t$95$1 / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1300 or 0.37 < z

   1. Initial program 38.4%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -1300 < z < -1.69999999999999989e-157

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 69.6%

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

   if -1.69999999999999989e-157 < z < -9.99999999999999982e-200

   1. Initial program 72.7%

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

   2. Taylor expanded in x around inf 58.6%

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

      1. associate-/l* 85.2%

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

      2. +-commutative 85.2%

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

      3. *-commutative 85.2%

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

      4. fma-udef 85.2%

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

   4. Simplified 85.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}} \]
   5. Step-by-step derivation

      1. fma-udef 85.2%

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

   6. Applied egg-rr 85.2%

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

   if -9.99999999999999982e-200 < z < 0.37

   1. Initial program 85.7%

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

   2. Taylor expanded in y around -inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. unsub-neg 74.2%

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

      3. mul-1-neg 74.2%

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

      4. distribute-neg-frac 74.2%

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

      5. cancel-sign-sub-inv 74.2%

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

      6. associate-/l* 74.3%

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

      7. metadata-eval 74.3%

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

      8. *-lft-identity 74.3%

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

      9. associate-/l* 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 69.6%

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

      2. mul-1-neg 69.6%

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

      3. unsub-neg 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in b around 0 80.2%

      \[\leadsto \frac{-x}{z - 1} - \color{blue}{\frac{z \cdot \left(a - t\right)}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-157}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y - z \cdot \left(y - b\right)}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-199}:\\ \;\;\;\;\frac{y}{\frac{y - z \cdot \left(y - b\right)}{x}}\\ \mathbf{elif}\;z \leq 0.37:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 11: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{\frac{y - z \cdot \left(y - b\right)}{x}}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 0.048:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.25e-120)
     t_1
     (if (<= z -8e-264)
       (/ y (/ (- y (* z (- y b))) x))
       (if (<= z -5.3e-297)
         (* (- t a) (/ z y))
         (if (<= z 0.048) (- x (* z (- (/ a y) x))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.25e-120) {
		tmp = t_1;
	} else if (z <= -8e-264) {
		tmp = y / ((y - (z * (y - b))) / x);
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 0.048) {
		tmp = x - (z * ((a / y) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.25d-120)) then
        tmp = t_1
    else if (z <= (-8d-264)) then
        tmp = y / ((y - (z * (y - b))) / x)
    else if (z <= (-5.3d-297)) then
        tmp = (t - a) * (z / y)
    else if (z <= 0.048d0) then
        tmp = x - (z * ((a / y) - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.25e-120) {
		tmp = t_1;
	} else if (z <= -8e-264) {
		tmp = y / ((y - (z * (y - b))) / x);
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 0.048) {
		tmp = x - (z * ((a / y) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.25e-120:
		tmp = t_1
	elif z <= -8e-264:
		tmp = y / ((y - (z * (y - b))) / x)
	elif z <= -5.3e-297:
		tmp = (t - a) * (z / y)
	elif z <= 0.048:
		tmp = x - (z * ((a / y) - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.25e-120)
		tmp = t_1;
	elseif (z <= -8e-264)
		tmp = Float64(y / Float64(Float64(y - Float64(z * Float64(y - b))) / x));
	elseif (z <= -5.3e-297)
		tmp = Float64(Float64(t - a) * Float64(z / y));
	elseif (z <= 0.048)
		tmp = Float64(x - Float64(z * Float64(Float64(a / y) - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.25e-120)
		tmp = t_1;
	elseif (z <= -8e-264)
		tmp = y / ((y - (z * (y - b))) / x);
	elseif (z <= -5.3e-297)
		tmp = (t - a) * (z / y);
	elseif (z <= 0.048)
		tmp = x - (z * ((a / y) - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e-120], t$95$1, If[LessEqual[z, -8e-264], N[(y / N[(N[(y - N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.3e-297], N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.048], N[(x - N[(z * N[(N[(a / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25000000000000002e-120 or 0.048000000000000001 < z

   1. Initial program 44.8%

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

   2. Taylor expanded in z around inf 76.1%

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

   if -1.25000000000000002e-120 < z < -8.0000000000000001e-264

   1. Initial program 83.2%

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

   2. Taylor expanded in x around inf 52.1%

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

      1. associate-/l* 61.7%

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

      2. +-commutative 61.7%

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

      3. *-commutative 61.7%

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

      4. fma-udef 61.7%

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

   4. Simplified 61.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}}} \]
   5. Step-by-step derivation

      1. fma-udef 61.7%

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

   6. Applied egg-rr 61.7%

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

   if -8.0000000000000001e-264 < z < -5.30000000000000019e-297

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.8%

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

   3. Taylor expanded in b around inf 85.8%

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

   4. Taylor expanded in z around 0 85.8%

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

      1. div-inv 85.6%

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

      2. *-commutative 85.6%

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

   6. Applied egg-rr 85.6%

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

      1. associate-*r/ 85.8%

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

      2. *-rgt-identity 85.8%

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

      3. *-commutative 85.8%

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

      4. associate-*r/ 86.2%

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

   8. Simplified 86.2%

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

   if -5.30000000000000019e-297 < z < 0.048000000000000001

   1. Initial program 84.1%

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

   2. Taylor expanded in y around -inf 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. mul-1-neg 72.1%

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

      4. distribute-neg-frac 72.1%

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

      5. cancel-sign-sub-inv 72.1%

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

      6. associate-/l* 72.1%

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

      7. metadata-eval 72.1%

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

      8. *-lft-identity 72.1%

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

      9. associate-/l* 72.1%

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

   4. Simplified 72.1%

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

      1. div-inv 72.1%

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

      2. +-commutative 72.1%

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

      3. associate-/r/ 72.1%

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

      4. sub-neg 72.1%

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

      5. metadata-eval 72.1%

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

      6. associate-/r/ 72.1%

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

      7. sub-neg 72.1%

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

      8. metadata-eval 72.1%

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

   6. Applied egg-rr 72.1%

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

   7. Taylor expanded in a around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. times-frac 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. sub-neg 68.9%

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

      5. metadata-eval 68.9%

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

   9. Simplified 68.9%

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

   10. Taylor expanded in z around 0 63.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-120}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{\frac{y - z \cdot \left(y - b\right)}{x}}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 0.048:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 52.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -130000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;\frac{-z \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.3e+96)
     t_2
     (if (<= y -130000000.0)
       t_1
       (if (<= y -2.65e-32)
         t_2
         (if (<= y -1.05e-73)
           (/ (- (* z a)) y)
           (if (<= y 1.7e-55) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.3e+96) {
		tmp = t_2;
	} else if (y <= -130000000.0) {
		tmp = t_1;
	} else if (y <= -2.65e-32) {
		tmp = t_2;
	} else if (y <= -1.05e-73) {
		tmp = -(z * a) / y;
	} else if (y <= 1.7e-55) {
		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 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.3d+96)) then
        tmp = t_2
    else if (y <= (-130000000.0d0)) then
        tmp = t_1
    else if (y <= (-2.65d-32)) then
        tmp = t_2
    else if (y <= (-1.05d-73)) then
        tmp = -(z * a) / y
    else if (y <= 1.7d-55) 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 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.3e+96) {
		tmp = t_2;
	} else if (y <= -130000000.0) {
		tmp = t_1;
	} else if (y <= -2.65e-32) {
		tmp = t_2;
	} else if (y <= -1.05e-73) {
		tmp = -(z * a) / y;
	} else if (y <= 1.7e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.3e+96:
		tmp = t_2
	elif y <= -130000000.0:
		tmp = t_1
	elif y <= -2.65e-32:
		tmp = t_2
	elif y <= -1.05e-73:
		tmp = -(z * a) / y
	elif y <= 1.7e-55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.3e+96)
		tmp = t_2;
	elseif (y <= -130000000.0)
		tmp = t_1;
	elseif (y <= -2.65e-32)
		tmp = t_2;
	elseif (y <= -1.05e-73)
		tmp = Float64(Float64(-Float64(z * a)) / y);
	elseif (y <= 1.7e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.3e+96)
		tmp = t_2;
	elseif (y <= -130000000.0)
		tmp = t_1;
	elseif (y <= -2.65e-32)
		tmp = t_2;
	elseif (y <= -1.05e-73)
		tmp = -(z * a) / y;
	elseif (y <= 1.7e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+96], t$95$2, If[LessEqual[y, -130000000.0], t$95$1, If[LessEqual[y, -2.65e-32], t$95$2, If[LessEqual[y, -1.05e-73], N[((-N[(z * a), $MachinePrecision]) / y), $MachinePrecision], If[LessEqual[y, 1.7e-55], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000015e96 or -1.3e8 < y < -2.65e-32 or 1.69999999999999986e-55 < y

   1. Initial program 47.2%

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

   2. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

   if -2.30000000000000015e96 < y < -1.3e8 or -1.0499999999999999e-73 < y < 1.69999999999999986e-55

   1. Initial program 73.9%

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

   2. Taylor expanded in y around 0 55.4%

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

   if -2.65e-32 < y < -1.0499999999999999e-73

   1. Initial program 83.8%

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

   2. Taylor expanded in x around 0 75.6%

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

   3. Taylor expanded in b around inf 58.5%

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

   4. Taylor expanded in z around 0 51.5%

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

   5. Taylor expanded in t around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. associate-*r* 45.3%

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

      3. mul-1-neg 45.3%

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

   7. Simplified 45.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -130000000:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;\frac{-z \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 13: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -850000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-74}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.8e+96)
     t_2
     (if (<= y -850000.0)
       t_1
       (if (<= y -7.5e-31)
         t_2
         (if (<= y -3.15e-74)
           (* (- t a) (/ z y))
           (if (<= y 4.6e-55) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e+96) {
		tmp = t_2;
	} else if (y <= -850000.0) {
		tmp = t_1;
	} else if (y <= -7.5e-31) {
		tmp = t_2;
	} else if (y <= -3.15e-74) {
		tmp = (t - a) * (z / y);
	} else if (y <= 4.6e-55) {
		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 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.8d+96)) then
        tmp = t_2
    else if (y <= (-850000.0d0)) then
        tmp = t_1
    else if (y <= (-7.5d-31)) then
        tmp = t_2
    else if (y <= (-3.15d-74)) then
        tmp = (t - a) * (z / y)
    else if (y <= 4.6d-55) 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 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.8e+96) {
		tmp = t_2;
	} else if (y <= -850000.0) {
		tmp = t_1;
	} else if (y <= -7.5e-31) {
		tmp = t_2;
	} else if (y <= -3.15e-74) {
		tmp = (t - a) * (z / y);
	} else if (y <= 4.6e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.8e+96:
		tmp = t_2
	elif y <= -850000.0:
		tmp = t_1
	elif y <= -7.5e-31:
		tmp = t_2
	elif y <= -3.15e-74:
		tmp = (t - a) * (z / y)
	elif y <= 4.6e-55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.8e+96)
		tmp = t_2;
	elseif (y <= -850000.0)
		tmp = t_1;
	elseif (y <= -7.5e-31)
		tmp = t_2;
	elseif (y <= -3.15e-74)
		tmp = Float64(Float64(t - a) * Float64(z / y));
	elseif (y <= 4.6e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.8e+96)
		tmp = t_2;
	elseif (y <= -850000.0)
		tmp = t_1;
	elseif (y <= -7.5e-31)
		tmp = t_2;
	elseif (y <= -3.15e-74)
		tmp = (t - a) * (z / y);
	elseif (y <= 4.6e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+96], t$95$2, If[LessEqual[y, -850000.0], t$95$1, If[LessEqual[y, -7.5e-31], t$95$2, If[LessEqual[y, -3.15e-74], N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-55], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e96 or -8.5e5 < y < -7.49999999999999975e-31 or 4.60000000000000023e-55 < y

   1. Initial program 47.2%

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

   2. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

   if -2.8e96 < y < -8.5e5 or -3.15000000000000001e-74 < y < 4.60000000000000023e-55

   1. Initial program 73.9%

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

   2. Taylor expanded in y around 0 55.4%

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

   if -7.49999999999999975e-31 < y < -3.15000000000000001e-74

   1. Initial program 83.8%

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

   2. Taylor expanded in x around 0 75.6%

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

   3. Taylor expanded in b around inf 58.5%

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

   4. Taylor expanded in z around 0 51.5%

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

      1. div-inv 51.3%

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

      2. *-commutative 51.3%

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

   6. Applied egg-rr 51.3%

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

      1. associate-*r/ 51.5%

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

      2. *-rgt-identity 51.5%

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

      3. *-commutative 51.5%

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

      4. associate-*r/ 51.3%

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

   8. Simplified 51.3%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -850000:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-74}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.3e+96)
     t_2
     (if (<= y -2000000.0)
       t_1
       (if (<= y -1.12e-29)
         t_2
         (if (<= y -1.05e-73)
           (/ (* z (- t a)) y)
           (if (<= y 1.7e-55) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.3e+96) {
		tmp = t_2;
	} else if (y <= -2000000.0) {
		tmp = t_1;
	} else if (y <= -1.12e-29) {
		tmp = t_2;
	} else if (y <= -1.05e-73) {
		tmp = (z * (t - a)) / y;
	} else if (y <= 1.7e-55) {
		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 = (t - a) / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.3d+96)) then
        tmp = t_2
    else if (y <= (-2000000.0d0)) then
        tmp = t_1
    else if (y <= (-1.12d-29)) then
        tmp = t_2
    else if (y <= (-1.05d-73)) then
        tmp = (z * (t - a)) / y
    else if (y <= 1.7d-55) 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 = (t - a) / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.3e+96) {
		tmp = t_2;
	} else if (y <= -2000000.0) {
		tmp = t_1;
	} else if (y <= -1.12e-29) {
		tmp = t_2;
	} else if (y <= -1.05e-73) {
		tmp = (z * (t - a)) / y;
	} else if (y <= 1.7e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.3e+96:
		tmp = t_2
	elif y <= -2000000.0:
		tmp = t_1
	elif y <= -1.12e-29:
		tmp = t_2
	elif y <= -1.05e-73:
		tmp = (z * (t - a)) / y
	elif y <= 1.7e-55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.3e+96)
		tmp = t_2;
	elseif (y <= -2000000.0)
		tmp = t_1;
	elseif (y <= -1.12e-29)
		tmp = t_2;
	elseif (y <= -1.05e-73)
		tmp = Float64(Float64(z * Float64(t - a)) / y);
	elseif (y <= 1.7e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.3e+96)
		tmp = t_2;
	elseif (y <= -2000000.0)
		tmp = t_1;
	elseif (y <= -1.12e-29)
		tmp = t_2;
	elseif (y <= -1.05e-73)
		tmp = (z * (t - a)) / y;
	elseif (y <= 1.7e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+96], t$95$2, If[LessEqual[y, -2000000.0], t$95$1, If[LessEqual[y, -1.12e-29], t$95$2, If[LessEqual[y, -1.05e-73], N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.7e-55], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000015e96 or -2e6 < y < -1.11999999999999995e-29 or 1.69999999999999986e-55 < y

   1. Initial program 47.2%

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

   2. Taylor expanded in y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

   if -2.30000000000000015e96 < y < -2e6 or -1.0499999999999999e-73 < y < 1.69999999999999986e-55

   1. Initial program 73.9%

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

   2. Taylor expanded in y around 0 55.4%

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

   if -1.11999999999999995e-29 < y < -1.0499999999999999e-73

   1. Initial program 83.8%

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

   2. Taylor expanded in x around 0 75.6%

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

   3. Taylor expanded in b around inf 58.5%

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

   4. Taylor expanded in z around 0 51.5%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2000000:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 15: 63.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 0.135:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.6e-117)
     t_1
     (if (<= z -8e-264)
       x
       (if (<= z -5.3e-297)
         (* (- t a) (/ z y))
         (if (<= z 0.135) (/ x (- 1.0 z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e-117) {
		tmp = t_1;
	} else if (z <= -8e-264) {
		tmp = x;
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 0.135) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.6d-117)) then
        tmp = t_1
    else if (z <= (-8d-264)) then
        tmp = x
    else if (z <= (-5.3d-297)) then
        tmp = (t - a) * (z / y)
    else if (z <= 0.135d0) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.6e-117) {
		tmp = t_1;
	} else if (z <= -8e-264) {
		tmp = x;
	} else if (z <= -5.3e-297) {
		tmp = (t - a) * (z / y);
	} else if (z <= 0.135) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.6e-117:
		tmp = t_1
	elif z <= -8e-264:
		tmp = x
	elif z <= -5.3e-297:
		tmp = (t - a) * (z / y)
	elif z <= 0.135:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.6e-117)
		tmp = t_1;
	elseif (z <= -8e-264)
		tmp = x;
	elseif (z <= -5.3e-297)
		tmp = Float64(Float64(t - a) * Float64(z / y));
	elseif (z <= 0.135)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.6e-117)
		tmp = t_1;
	elseif (z <= -8e-264)
		tmp = x;
	elseif (z <= -5.3e-297)
		tmp = (t - a) * (z / y);
	elseif (z <= 0.135)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-117], t$95$1, If[LessEqual[z, -8e-264], x, If[LessEqual[z, -5.3e-297], N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.135], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.59999999999999983e-117 or 0.13500000000000001 < z

   1. Initial program 44.8%

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

   2. Taylor expanded in z around inf 76.1%

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

   if -2.59999999999999983e-117 < z < -8.0000000000000001e-264

   1. Initial program 83.2%

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

   2. Taylor expanded in z around 0 51.3%

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

   if -8.0000000000000001e-264 < z < -5.30000000000000019e-297

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.8%

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

   3. Taylor expanded in b around inf 85.8%

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

   4. Taylor expanded in z around 0 85.8%

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

      1. div-inv 85.6%

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

      2. *-commutative 85.6%

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

   6. Applied egg-rr 85.6%

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

      1. associate-*r/ 85.8%

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

      2. *-rgt-identity 85.8%

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

      3. *-commutative 85.8%

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

      4. associate-*r/ 86.2%

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

   8. Simplified 86.2%

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

   if -5.30000000000000019e-297 < z < 0.13500000000000001

   1. Initial program 84.1%

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

   2. Taylor expanded in y around inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

   4. Simplified 52.2%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-117}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-264}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-297}:\\ \;\;\;\;\left(t - a\right) \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 0.135:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 16: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-111} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e-111) (not (<= z 0.048)))
   (/ (- t a) (- b y))
   (- x (* z (- (/ a y) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-111) || !(z <= 0.048)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (z * ((a / y) - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-8.5d-111)) .or. (.not. (z <= 0.048d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - (z * ((a / y) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e-111) || !(z <= 0.048)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - (z * ((a / y) - x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e-111) or not (z <= 0.048):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - (z * ((a / y) - x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e-111) || !(z <= 0.048))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(z * Float64(Float64(a / y) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e-111) || ~((z <= 0.048)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - (z * ((a / y) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e-111], N[Not[LessEqual[z, 0.048]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(N[(a / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000003e-111 or 0.048000000000000001 < z

   1. Initial program 43.3%

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

   2. Taylor expanded in z around inf 77.4%

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

   if -8.5000000000000003e-111 < z < 0.048000000000000001

   1. Initial program 85.4%

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

   2. Taylor expanded in y around -inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. mul-1-neg 73.1%

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

      4. distribute-neg-frac 73.1%

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

      5. cancel-sign-sub-inv 73.1%

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

      6. associate-/l* 73.1%

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

      7. metadata-eval 73.1%

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

      8. *-lft-identity 73.1%

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

      9. associate-/l* 73.1%

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

   4. Simplified 73.1%

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

      1. div-inv 73.1%

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

      2. +-commutative 73.1%

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

      3. associate-/r/ 73.1%

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

      4. sub-neg 73.1%

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

      5. metadata-eval 73.1%

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

      6. associate-/r/ 73.1%

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

      7. sub-neg 73.1%

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

      8. metadata-eval 73.1%

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

   6. Applied egg-rr 73.1%

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

   7. Taylor expanded in a around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. times-frac 63.3%

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

      3. distribute-rgt-neg-in 63.3%

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

      4. sub-neg 63.3%

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

      5. metadata-eval 63.3%

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

   9. Simplified 63.3%

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

   10. Taylor expanded in z around 0 58.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-111} \lor \neg \left(z \leq 0.048\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(\frac{a}{y} - x\right)\\ \end{array} \]

Alternative 17: 53.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+100} \lor \neg \left(y \leq 1.35 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e+100) (not (<= y 1.35e-55))) (/ 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 <= -5e+100) || !(y <= 1.35e-55)) {
		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 <= (-5d+100)) .or. (.not. (y <= 1.35d-55))) 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 <= -5e+100) || !(y <= 1.35e-55)) {
		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 <= -5e+100) or not (y <= 1.35e-55):
		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 <= -5e+100) || !(y <= 1.35e-55))
		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 <= -5e+100) || ~((y <= 1.35e-55)))
		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, -5e+100], N[Not[LessEqual[y, 1.35e-55]], $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 < -4.9999999999999999e100 or 1.35000000000000002e-55 < y

   1. Initial program 44.5%

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

   2. Taylor expanded in y around inf 53.5%

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

      1. +-commutative 53.5%

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

      2. mul-1-neg 53.5%

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

      3. unsub-neg 53.5%

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

   4. Simplified 53.5%

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

   if -4.9999999999999999e100 < y < 1.35000000000000002e-55

   1. Initial program 75.9%

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

   2. Taylor expanded in y around 0 50.6%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+100} \lor \neg \left(y \leq 1.35 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18: 34.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.4e+32) (/ a y) (if (<= z 1.0) (+ x (* x z)) (- (/ x z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e+32) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x + (x * z);
	} else {
		tmp = -(x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-4.4d+32)) then
        tmp = a / y
    else if (z <= 1.0d0) then
        tmp = x + (x * z)
    else
        tmp = -(x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e+32) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x + (x * z);
	} else {
		tmp = -(x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.4e+32:
		tmp = a / y
	elif z <= 1.0:
		tmp = x + (x * z)
	else:
		tmp = -(x / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.4e+32)
		tmp = Float64(a / y);
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(-Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.4e+32)
		tmp = a / y;
	elseif (z <= 1.0)
		tmp = x + (x * z);
	else
		tmp = -(x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.4e+32], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], (-N[(x / z), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000002e32

   1. Initial program 39.5%

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

   2. Taylor expanded in y around -inf 25.9%

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

      1. mul-1-neg 25.9%

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

      2. unsub-neg 25.9%

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

      3. mul-1-neg 25.9%

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

      4. distribute-neg-frac 25.9%

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

      5. cancel-sign-sub-inv 25.9%

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

      6. associate-/l* 40.6%

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

      7. metadata-eval 40.6%

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

      8. *-lft-identity 40.6%

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

      9. associate-/l* 51.5%

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

   4. Simplified 51.5%

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

      1. div-inv 51.4%

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

      2. +-commutative 51.4%

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

      3. associate-/r/ 51.4%

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

      4. sub-neg 51.4%

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

      5. metadata-eval 51.4%

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

      6. associate-/r/ 49.4%

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

      7. sub-neg 49.4%

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

      8. metadata-eval 49.4%

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

   6. Applied egg-rr 49.4%

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

   7. Taylor expanded in a around inf 21.2%

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

      1. mul-1-neg 21.2%

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

      2. times-frac 31.1%

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

      3. distribute-rgt-neg-in 31.1%

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

      4. sub-neg 31.1%

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

      5. metadata-eval 31.1%

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

   9. Simplified 31.1%

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

   10. Taylor expanded in z around inf 23.1%

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

   if -4.40000000000000002e32 < z < 1

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in z around 0 41.0%

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

   if 1 < z

   1. Initial program 34.4%

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

   2. Taylor expanded in y around inf 20.4%

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

      1. +-commutative 20.4%

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

      2. mul-1-neg 20.4%

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

      3. unsub-neg 20.4%

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

   4. Simplified 20.4%

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

   5. Taylor expanded in z around inf 20.4%

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

      1. associate-*r/ 20.4%

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

      2. mul-1-neg 20.4%

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

   7. Simplified 20.4%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z}\\ \end{array} \]

Alternative 19: 33.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+44) (/ a y) (if (<= z 1.0) x (- (/ x z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+44) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -(x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.15d+44)) then
        tmp = a / y
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = -(x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+44) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -(x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e+44:
		tmp = a / y
	elif z <= 1.0:
		tmp = x
	else:
		tmp = -(x / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+44)
		tmp = Float64(a / y);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(-Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e+44)
		tmp = a / y;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = -(x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+44], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.0], x, (-N[(x / z), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000002e44

   1. Initial program 37.5%

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

   2. Taylor expanded in y around -inf 25.0%

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

      1. mul-1-neg 25.0%

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

      2. unsub-neg 25.0%

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

      3. mul-1-neg 25.0%

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

      4. distribute-neg-frac 25.0%

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

      5. cancel-sign-sub-inv 25.0%

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

      6. associate-/l* 40.2%

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

      7. metadata-eval 40.2%

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

      8. *-lft-identity 40.2%

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

      9. associate-/l* 51.5%

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

   4. Simplified 51.5%

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

      1. div-inv 51.4%

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

      2. +-commutative 51.4%

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

      3. associate-/r/ 51.4%

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

      4. sub-neg 51.4%

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

      5. metadata-eval 51.4%

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

      6. associate-/r/ 49.3%

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

      7. sub-neg 49.3%

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

      8. metadata-eval 49.3%

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

   6. Applied egg-rr 49.3%

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

   7. Taylor expanded in a around inf 21.6%

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

      1. mul-1-neg 21.6%

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

      2. times-frac 31.8%

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

      3. distribute-rgt-neg-in 31.8%

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

      4. sub-neg 31.8%

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

      5. metadata-eval 31.8%

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

   9. Simplified 31.8%

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

   10. Taylor expanded in z around inf 23.7%

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

   if -1.15000000000000002e44 < z < 1

   1. Initial program 84.0%

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

   2. Taylor expanded in z around 0 40.4%

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

   if 1 < z

   1. Initial program 34.4%

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

   2. Taylor expanded in y around inf 20.4%

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

      1. +-commutative 20.4%

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

      2. mul-1-neg 20.4%

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

      3. unsub-neg 20.4%

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

   4. Simplified 20.4%

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

   5. Taylor expanded in z around inf 20.4%

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

      1. associate-*r/ 20.4%

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

      2. mul-1-neg 20.4%

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

   7. Simplified 20.4%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\frac{x}{z}\\ \end{array} \]

Alternative 20: 34.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+44) (/ a y) (if (<= z 1.0) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+44) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.15d+44)) then
        tmp = a / y
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+44) {
		tmp = a / y;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e+44:
		tmp = a / y
	elif z <= 1.0:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+44)
		tmp = Float64(a / y);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e+44)
		tmp = a / y;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+44], N[(a / y), $MachinePrecision], If[LessEqual[z, 1.0], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000002e44 or 1 < z

   1. Initial program 35.9%

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

   2. Taylor expanded in y around -inf 25.1%

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

      1. mul-1-neg 25.1%

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

      2. unsub-neg 25.1%

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

      3. mul-1-neg 25.1%

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

      4. distribute-neg-frac 25.1%

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

      5. cancel-sign-sub-inv 25.1%

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

      6. associate-/l* 41.1%

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

      7. metadata-eval 41.1%

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

      8. *-lft-identity 41.1%

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

      9. associate-/l* 51.6%

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

   4. Simplified 51.6%

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

      1. div-inv 51.5%

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

      2. +-commutative 51.5%

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

      3. associate-/r/ 51.5%

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

      4. sub-neg 51.5%

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

      5. metadata-eval 51.5%

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

      6. associate-/r/ 50.3%

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

      7. sub-neg 50.3%

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

      8. metadata-eval 50.3%

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

   6. Applied egg-rr 50.3%

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

   7. Taylor expanded in a around inf 21.6%

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

      1. mul-1-neg 21.6%

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

      2. times-frac 30.3%

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

      3. distribute-rgt-neg-in 30.3%

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

      4. sub-neg 30.3%

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

      5. metadata-eval 30.3%

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

   9. Simplified 30.3%

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

   10. Taylor expanded in z around inf 18.0%

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

   if -1.15000000000000002e44 < z < 1

   1. Initial program 84.0%

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

   2. Taylor expanded in z around 0 40.4%

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

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+44}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 21: 35.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+57}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+57) (/ a y) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+57) {
		tmp = a / y;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.15d+57)) then
        tmp = a / y
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+57) {
		tmp = a / y;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.15e+57:
		tmp = a / y
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+57)
		tmp = Float64(a / y);
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.15e+57)
		tmp = a / y;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+57], N[(a / y), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e57

   1. Initial program 36.9%

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

   2. Taylor expanded in y around -inf 24.1%

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

      1. mul-1-neg 24.1%

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

      2. unsub-neg 24.1%

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

      3. mul-1-neg 24.1%

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

      4. distribute-neg-frac 24.1%

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

      5. cancel-sign-sub-inv 24.1%

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

      6. associate-/l* 39.8%

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

      7. metadata-eval 39.8%

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

      8. *-lft-identity 39.8%

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

      9. associate-/l* 51.5%

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

   4. Simplified 51.5%

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

      1. div-inv 51.4%

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

      2. +-commutative 51.4%

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

      3. associate-/r/ 51.4%

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

      4. sub-neg 51.4%

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

      5. metadata-eval 51.4%

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

      6. associate-/r/ 49.2%

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

      7. sub-neg 49.2%

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

      8. metadata-eval 49.2%

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

   6. Applied egg-rr 49.2%

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

   7. Taylor expanded in a around inf 20.5%

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

      1. mul-1-neg 20.5%

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

      2. times-frac 31.1%

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

      3. distribute-rgt-neg-in 31.1%

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

      4. sub-neg 31.1%

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

      5. metadata-eval 31.1%

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

   9. Simplified 31.1%

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

   10. Taylor expanded in z around inf 24.4%

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

   if -1.1499999999999999e57 < z

   1. Initial program 68.1%

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

   2. Taylor expanded in y around inf 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

   4. Simplified 36.6%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+57}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 22: 26.0% 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 61.4%

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

2. Taylor expanded in z around 0 22.8%

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

3. Final simplification 22.8%

   \[\leadsto x \]

Developer target: 73.3% 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 2023268 
(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)))))