Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.9% → 94.7%

Time: 32.5s

Alternatives: 16

Speedup: 1.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.9% 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: 94.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ t_3 := \sqrt[3]{\frac{z}{\frac{t_1}{t - a}}}\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{x \cdot y + t_4}{t_1}\\ t_6 := x + t_3 \cdot \left(t_3 \cdot t_3\right)\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_4\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_5 \leq 10^{+303}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (+
          (/ (- (/ x (/ (- b y) y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z)
          (/ (- t a) (- b y))))
        (t_3 (cbrt (/ z (/ t_1 (- t a)))))
        (t_4 (* z (- t a)))
        (t_5 (/ (+ (* x y) t_4) t_1))
        (t_6 (+ x (* t_3 (* t_3 t_3)))))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -1e-222)
       (/ (fma x y t_4) (fma z (- b y) y))
       (if (<= t_5 0.0)
         t_2
         (if (<= t_5 1e+303)
           (/ (+ (* x y) (- (* z t) (* z a))) t_1)
           (if (<= t_5 INFINITY) t_6 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((x / ((b - y) / y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y));
	double t_3 = cbrt((z / (t_1 / (t - a))));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double t_6 = x + (t_3 * (t_3 * t_3));
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -1e-222) {
		tmp = fma(x, y, t_4) / fma(z, (b - y), y);
	} else if (t_5 <= 0.0) {
		tmp = t_2;
	} else if (t_5 <= 1e+303) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_6;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	t_3 = cbrt(Float64(z / Float64(t_1 / Float64(t - a))))
	t_4 = Float64(z * Float64(t - a))
	t_5 = Float64(Float64(Float64(x * y) + t_4) / t_1)
	t_6 = Float64(x + Float64(t_3 * Float64(t_3 * t_3)))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -1e-222)
		tmp = Float64(fma(x, y, t_4) / fma(z, Float64(b - y), y));
	elseif (t_5 <= 0.0)
		tmp = t_2;
	elseif (t_5 <= 1e+303)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_5 <= Inf)
		tmp = t_6;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(z / N[(t$95$1 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(x + N[(t$95$3 * N[(t$95$3 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -1e-222], N[(N[(x * y + t$95$4), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 0.0], t$95$2, If[LessEqual[t$95$5, 1e+303], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$5, Infinity], t$95$6, t$95$2]]]]]]]]]]]

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 1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 32.6%

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

   2. Taylor expanded in x around 0 32.6%

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

      1. add-cube-cbrt 32.6%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(\sqrt[3]{\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}} \cdot \sqrt[3]{\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}}\right) \cdot \sqrt[3]{\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}}} \]

      2. associate-/l* 32.6%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(\sqrt[3]{\color{blue}{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}} \cdot \sqrt[3]{\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}}\right) \cdot \sqrt[3]{\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}} \]

      3. associate-/l* 32.6%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(\sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \sqrt[3]{\color{blue}{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}}\right) \cdot \sqrt[3]{\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}} \]

      4. associate-/l* 67.5%

         \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \left(\sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}} \]

   4. Applied egg-rr 67.5%

      \[\leadsto \frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \color{blue}{\left(\sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right) \cdot \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}} \]

   5. Taylor expanded in z around 0 88.8%

      \[\leadsto \color{blue}{x} + \left(\sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right) \cdot \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000005e-222

   1. Initial program 99.1%

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

      1. fma-def 99.2%

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

      2. +-commutative 99.2%

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

      3. fma-def 99.2%

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

   3. Simplified 99.2%

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

   if -1.00000000000000005e-222 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 13.6%

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

   2. Taylor expanded in z around -inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. mul-1-neg 63.6%

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

      3. distribute-lft-out-- 63.6%

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

      4. associate-/l* 72.6%

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

      5. associate-/l* 98.6%

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

      6. div-sub 98.6%

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

   4. Simplified 98.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e303

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.7%

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

   3. Applied egg-rr 99.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x + \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \left(\sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x + \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \left(\sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}} \cdot \sqrt[3]{\frac{z}{\frac{y + z \cdot \left(b - y\right)}{t - a}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \mathsf{fma}\left(z, b - y, y\right)\\ t_3 := \frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{x \cdot y + t_4}{t_1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_5 \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_4\right)}{t_2}\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_5 \leq 10^{+303}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;\frac{z}{\frac{t_2}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (fma z (- b y) y))
        (t_3
         (+
          (/ (- (/ x (/ (- b y) y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z)
          (/ (- t a) (- b y))))
        (t_4 (* z (- t a)))
        (t_5 (/ (+ (* x y) t_4) t_1)))
   (if (<= t_5 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_5 -1e-222)
       (/ (fma x y t_4) t_2)
       (if (<= t_5 0.0)
         t_3
         (if (<= t_5 1e+303)
           (/ (+ (* x y) (- (* z t) (* z a))) t_1)
           (if (<= t_5 INFINITY) (/ z (/ t_2 (- t a))) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = fma(z, (b - y), y);
	double t_3 = (((x / ((b - y) / y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_5 <= -1e-222) {
		tmp = fma(x, y, t_4) / t_2;
	} else if (t_5 <= 0.0) {
		tmp = t_3;
	} else if (t_5 <= 1e+303) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = z / (t_2 / (t - a));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = fma(z, Float64(b - y), y)
	t_3 = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	t_4 = Float64(z * Float64(t - a))
	t_5 = Float64(Float64(Float64(x * y) + t_4) / t_1)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_5 <= -1e-222)
		tmp = Float64(fma(x, y, t_4) / t_2);
	elseif (t_5 <= 0.0)
		tmp = t_3;
	elseif (t_5 <= 1e+303)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_5 <= Inf)
		tmp = Float64(z / Float64(t_2 / Float64(t - a)));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, -1e-222], N[(N[(x * y + t$95$4), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$5, 0.0], t$95$3, If[LessEqual[t$95$5, 1e+303], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$5, Infinity], N[(z / N[(t$95$2 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 27.8%

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

   2. Taylor expanded in y around -inf 47.7%

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

      1. distribute-lft-out 47.7%

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

      2. sub-neg 47.7%

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

      3. metadata-eval 47.7%

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

   4. Simplified 47.7%

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

   5. Taylor expanded in z around inf 73.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000005e-222

   1. Initial program 99.1%

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

      1. fma-def 99.2%

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

      2. +-commutative 99.2%

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

      3. fma-def 99.2%

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

   3. Simplified 99.2%

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

   if -1.00000000000000005e-222 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 13.6%

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

   2. Taylor expanded in z around -inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. mul-1-neg 63.6%

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

      3. distribute-lft-out-- 63.6%

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

      4. associate-/l* 72.6%

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

      5. associate-/l* 98.6%

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

      6. div-sub 98.6%

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

   4. Simplified 98.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e303

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.7%

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

   3. Applied egg-rr 99.7%

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

   if 1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 36.4%

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

   2. Taylor expanded in x around 0 35.1%

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

      1. associate-/l* 73.4%

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

      2. +-commutative 73.4%

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

      3. fma-def 73.4%

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

   4. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_3}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq 10^{+303}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{t_1}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (+
          (/ (- (/ x (/ (- b y) y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z)
          (/ (- t a) (- b y))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1)))
   (if (<= t_4 (- INFINITY))
     (- (/ (- a t) y) (/ x (+ z -1.0)))
     (if (<= t_4 -1e-222)
       (+ (/ (* x y) t_1) (/ t_3 t_1))
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 1e+303)
           (/ (+ (* x y) (- (* z t) (* z a))) t_1)
           (if (<= t_4 INFINITY) (/ z (/ (fma z (- b y) y) (- t a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((x / ((b - y) / y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else if (t_4 <= -1e-222) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 1e+303) {
		tmp = ((x * y) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = z / (fma(z, (b - y), y) / (t - a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z) + Float64(Float64(t - a) / Float64(b - y)))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	elseif (t_4 <= -1e-222)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 1e+303)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_4 <= Inf)
		tmp = Float64(z / Float64(fma(z, Float64(b - y), y) / Float64(t - a)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -1e-222], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 1e+303], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(z / N[(N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 27.8%

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

   2. Taylor expanded in y around -inf 47.7%

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

      1. distribute-lft-out 47.7%

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

      2. sub-neg 47.7%

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

      3. metadata-eval 47.7%

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

   4. Simplified 47.7%

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

   5. Taylor expanded in z around inf 73.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.00000000000000005e-222

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 99.2%

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

   if -1.00000000000000005e-222 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 13.6%

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

   2. Taylor expanded in z around -inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. mul-1-neg 63.6%

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

      3. distribute-lft-out-- 63.6%

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

      4. associate-/l* 72.6%

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

      5. associate-/l* 98.6%

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

      6. div-sub 98.6%

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

   4. Simplified 98.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e303

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.7%

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

   3. Applied egg-rr 99.7%

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

   if 1e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 36.4%

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

   2. Taylor expanded in x around 0 35.1%

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

      1. associate-/l* 73.4%

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

      2. +-commutative 73.4%

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

      3. fma-def 73.4%

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

   4. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-222}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+303}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{z}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{t - a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{t_2}{t_1}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + t_4\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-101}:\\ \;\;\;\;x + t_4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot y + t_2}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (/ t_2 t_1)))
   (if (<= z -3e+54)
     t_3
     (if (<= z 9.4e-291)
       (+ (/ (* x y) t_1) t_4)
       (if (<= z 1.18e-101)
         (+ x t_4)
         (if (<= z 4.6e+33) (/ (+ (* x y) t_2) t_1) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_2 / t_1;
	double tmp;
	if (z <= -3e+54) {
		tmp = t_3;
	} else if (z <= 9.4e-291) {
		tmp = ((x * y) / t_1) + t_4;
	} else if (z <= 1.18e-101) {
		tmp = x + t_4;
	} else if (z <= 4.6e+33) {
		tmp = ((x * y) + t_2) / t_1;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = z * (t - a)
    t_3 = (t - a) / (b - y)
    t_4 = t_2 / t_1
    if (z <= (-3d+54)) then
        tmp = t_3
    else if (z <= 9.4d-291) then
        tmp = ((x * y) / t_1) + t_4
    else if (z <= 1.18d-101) then
        tmp = x + t_4
    else if (z <= 4.6d+33) then
        tmp = ((x * y) + t_2) / t_1
    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 - y));
	double t_2 = z * (t - a);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_2 / t_1;
	double tmp;
	if (z <= -3e+54) {
		tmp = t_3;
	} else if (z <= 9.4e-291) {
		tmp = ((x * y) / t_1) + t_4;
	} else if (z <= 1.18e-101) {
		tmp = x + t_4;
	} else if (z <= 4.6e+33) {
		tmp = ((x * y) + t_2) / t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = (t - a) / (b - y)
	t_4 = t_2 / t_1
	tmp = 0
	if z <= -3e+54:
		tmp = t_3
	elif z <= 9.4e-291:
		tmp = ((x * y) / t_1) + t_4
	elif z <= 1.18e-101:
		tmp = x + t_4
	elif z <= 4.6e+33:
		tmp = ((x * y) + t_2) / t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(t_2 / t_1)
	tmp = 0.0
	if (z <= -3e+54)
		tmp = t_3;
	elseif (z <= 9.4e-291)
		tmp = Float64(Float64(Float64(x * y) / t_1) + t_4);
	elseif (z <= 1.18e-101)
		tmp = Float64(x + t_4);
	elseif (z <= 4.6e+33)
		tmp = Float64(Float64(Float64(x * y) + t_2) / t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (t - a) / (b - y);
	t_4 = t_2 / t_1;
	tmp = 0.0;
	if (z <= -3e+54)
		tmp = t_3;
	elseif (z <= 9.4e-291)
		tmp = ((x * y) / t_1) + t_4;
	elseif (z <= 1.18e-101)
		tmp = x + t_4;
	elseif (z <= 4.6e+33)
		tmp = ((x * y) + t_2) / t_1;
	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[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$1), $MachinePrecision]}, If[LessEqual[z, -3e+54], t$95$3, If[LessEqual[z, 9.4e-291], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + t$95$4), $MachinePrecision], If[LessEqual[z, 1.18e-101], N[(x + t$95$4), $MachinePrecision], If[LessEqual[z, 4.6e+33], N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9999999999999999e54 or 4.60000000000000021e33 < z

   1. Initial program 36.8%

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

   2. Taylor expanded in z around inf 83.7%

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

   if -2.9999999999999999e54 < z < 9.3999999999999997e-291

   1. Initial program 91.7%

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

   2. Taylor expanded in x around 0 91.8%

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

   if 9.3999999999999997e-291 < z < 1.1800000000000001e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

   if 1.1800000000000001e-101 < z < 4.60000000000000021e33

   1. Initial program 90.0%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x \cdot y + t_1}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.2:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-291}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 27.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+65} \lor \neg \left(z \leq 3.3 \cdot 10^{+121}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t + \left(\frac{1}{\frac{\frac{z}{y}}{x}} - a\right)}{b}\\ \end{array} \end{array} \]

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 -4.2)
     t_3
     (if (<= z 6.1e-291)
       t_2
       (if (<= z 3e-101)
         (+ x (/ t_1 (+ y (* z (- b y)))))
         (if (<= z 27.5)
           t_2
           (if (or (<= z 7.9e+65) (not (<= z 3.3e+121)))
             t_3
             (/ (+ t (- (/ 1.0 (/ (/ z y) x)) a)) b))))))))

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 <= -4.2) {
		tmp = t_3;
	} else if (z <= 6.1e-291) {
		tmp = t_2;
	} else if (z <= 3e-101) {
		tmp = x + (t_1 / (y + (z * (b - y))));
	} else if (z <= 27.5) {
		tmp = t_2;
	} else if ((z <= 7.9e+65) || !(z <= 3.3e+121)) {
		tmp = t_3;
	} else {
		tmp = (t + ((1.0 / ((z / y) / x)) - a)) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: 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 <= (-4.2d0)) then
        tmp = t_3
    else if (z <= 6.1d-291) then
        tmp = t_2
    else if (z <= 3d-101) then
        tmp = x + (t_1 / (y + (z * (b - y))))
    else if (z <= 27.5d0) then
        tmp = t_2
    else if ((z <= 7.9d+65) .or. (.not. (z <= 3.3d+121))) then
        tmp = t_3
    else
        tmp = (t + ((1.0d0 / ((z / y) / x)) - a)) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((x * y) + t_1) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.2) {
		tmp = t_3;
	} else if (z <= 6.1e-291) {
		tmp = t_2;
	} else if (z <= 3e-101) {
		tmp = x + (t_1 / (y + (z * (b - y))));
	} else if (z <= 27.5) {
		tmp = t_2;
	} else if ((z <= 7.9e+65) || !(z <= 3.3e+121)) {
		tmp = t_3;
	} else {
		tmp = (t + ((1.0 / ((z / y) / x)) - a)) / b;
	}
	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 <= -4.2:
		tmp = t_3
	elif z <= 6.1e-291:
		tmp = t_2
	elif z <= 3e-101:
		tmp = x + (t_1 / (y + (z * (b - y))))
	elif z <= 27.5:
		tmp = t_2
	elif (z <= 7.9e+65) or not (z <= 3.3e+121):
		tmp = t_3
	else:
		tmp = (t + ((1.0 / ((z / y) / x)) - a)) / b
	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 <= -4.2)
		tmp = t_3;
	elseif (z <= 6.1e-291)
		tmp = t_2;
	elseif (z <= 3e-101)
		tmp = Float64(x + Float64(t_1 / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 27.5)
		tmp = t_2;
	elseif ((z <= 7.9e+65) || !(z <= 3.3e+121))
		tmp = t_3;
	else
		tmp = Float64(Float64(t + Float64(Float64(1.0 / Float64(Float64(z / y) / x)) - a)) / b);
	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 <= -4.2)
		tmp = t_3;
	elseif (z <= 6.1e-291)
		tmp = t_2;
	elseif (z <= 3e-101)
		tmp = x + (t_1 / (y + (z * (b - y))));
	elseif (z <= 27.5)
		tmp = t_2;
	elseif ((z <= 7.9e+65) || ~((z <= 3.3e+121)))
		tmp = t_3;
	else
		tmp = (t + ((1.0 / ((z / y) / x)) - a)) / b;
	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, -4.2], t$95$3, If[LessEqual[z, 6.1e-291], t$95$2, If[LessEqual[z, 3e-101], N[(x + N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 27.5], t$95$2, If[Or[LessEqual[z, 7.9e+65], N[Not[LessEqual[z, 3.3e+121]], $MachinePrecision]], t$95$3, N[(N[(t + N[(N[(1.0 / N[(N[(z / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.20000000000000018 or 27.5 < z < 7.8999999999999998e65 or 3.29999999999999979e121 < z

   1. Initial program 41.5%

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

   2. Taylor expanded in z around inf 83.2%

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

   if -4.20000000000000018 < z < 6.1e-291 or 3.0000000000000003e-101 < z < 27.5

   1. Initial program 92.1%

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

   2. Taylor expanded in b around inf 89.7%

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

      1. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   if 6.1e-291 < z < 3.0000000000000003e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

   if 7.8999999999999998e65 < z < 3.29999999999999979e121

   1. Initial program 46.9%

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

   2. Taylor expanded in x around 0 46.9%

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

   3. Taylor expanded in b around inf 70.2%

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

      1. associate--l+ 70.2%

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

      2. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

      1. clear-num 78.8%

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

      2. inv-pow 78.8%

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

   7. Applied egg-rr 78.8%

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

      1. unpow-1 78.8%

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

   9. Simplified 78.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 27.5:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+65} \lor \neg \left(z \leq 3.3 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + \left(\frac{1}{\frac{\frac{z}{y}}{x}} - a\right)}{b}\\ \end{array} \]

Alternative 6: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + t_1}{t_2}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+55}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_1}{t_2}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* x y) t_1) t_2))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -3.4e+55)
     t_4
     (if (<= z 1.4e-290)
       t_3
       (if (<= z 1.18e-101) (+ x (/ t_1 t_2)) (if (<= z 7.5e+33) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + t_1) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.4e+55) {
		tmp = t_4;
	} else if (z <= 1.4e-290) {
		tmp = t_3;
	} else if (z <= 1.18e-101) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 7.5e+33) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = y + (z * (b - y))
    t_3 = ((x * y) + t_1) / t_2
    t_4 = (t - a) / (b - y)
    if (z <= (-3.4d+55)) then
        tmp = t_4
    else if (z <= 1.4d-290) then
        tmp = t_3
    else if (z <= 1.18d-101) then
        tmp = x + (t_1 / t_2)
    else if (z <= 7.5d+33) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + t_1) / t_2;
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.4e+55) {
		tmp = t_4;
	} else if (z <= 1.4e-290) {
		tmp = t_3;
	} else if (z <= 1.18e-101) {
		tmp = x + (t_1 / t_2);
	} else if (z <= 7.5e+33) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = y + (z * (b - y))
	t_3 = ((x * y) + t_1) / t_2
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.4e+55:
		tmp = t_4
	elif z <= 1.4e-290:
		tmp = t_3
	elif z <= 1.18e-101:
		tmp = x + (t_1 / t_2)
	elif z <= 7.5e+33:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(x * y) + t_1) / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.4e+55)
		tmp = t_4;
	elseif (z <= 1.4e-290)
		tmp = t_3;
	elseif (z <= 1.18e-101)
		tmp = Float64(x + Float64(t_1 / t_2));
	elseif (z <= 7.5e+33)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = y + (z * (b - y));
	t_3 = ((x * y) + t_1) / t_2;
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.4e+55)
		tmp = t_4;
	elseif (z <= 1.4e-290)
		tmp = t_3;
	elseif (z <= 1.18e-101)
		tmp = x + (t_1 / t_2);
	elseif (z <= 7.5e+33)
		tmp = t_3;
	else
		tmp = t_4;
	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[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+55], t$95$4, If[LessEqual[z, 1.4e-290], t$95$3, If[LessEqual[z, 1.18e-101], N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+33], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999998e55 or 7.50000000000000046e33 < z

   1. Initial program 36.8%

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

   2. Taylor expanded in z around inf 83.7%

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

   if -3.3999999999999998e55 < z < 1.39999999999999998e-290 or 1.1800000000000001e-101 < z < 7.50000000000000046e33

   1. Initial program 91.2%

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

   if 1.39999999999999998e-290 < z < 1.1800000000000001e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 67.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot t}{y}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+65} \lor \neg \left(z \leq 3.3 \cdot 10^{+121}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z t) y)))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ (+ t (- (/ x (/ z y)) a)) b)))
   (if (<= z -1.65e-24)
     t_2
     (if (<= z 1.12e-100)
       t_1
       (if (<= z 1.7e-32)
         t_3
         (if (<= z 1.8e-21)
           t_1
           (if (or (<= z 8e+65) (not (<= z 3.3e+121))) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * t) / y);
	double t_2 = (t - a) / (b - y);
	double t_3 = (t + ((x / (z / y)) - a)) / b;
	double tmp;
	if (z <= -1.65e-24) {
		tmp = t_2;
	} else if (z <= 1.12e-100) {
		tmp = t_1;
	} else if (z <= 1.7e-32) {
		tmp = t_3;
	} else if (z <= 1.8e-21) {
		tmp = t_1;
	} else if ((z <= 8e+65) || !(z <= 3.3e+121)) {
		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 = x + ((z * t) / y)
    t_2 = (t - a) / (b - y)
    t_3 = (t + ((x / (z / y)) - a)) / b
    if (z <= (-1.65d-24)) then
        tmp = t_2
    else if (z <= 1.12d-100) then
        tmp = t_1
    else if (z <= 1.7d-32) then
        tmp = t_3
    else if (z <= 1.8d-21) then
        tmp = t_1
    else if ((z <= 8d+65) .or. (.not. (z <= 3.3d+121))) 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 = x + ((z * t) / y);
	double t_2 = (t - a) / (b - y);
	double t_3 = (t + ((x / (z / y)) - a)) / b;
	double tmp;
	if (z <= -1.65e-24) {
		tmp = t_2;
	} else if (z <= 1.12e-100) {
		tmp = t_1;
	} else if (z <= 1.7e-32) {
		tmp = t_3;
	} else if (z <= 1.8e-21) {
		tmp = t_1;
	} else if ((z <= 8e+65) || !(z <= 3.3e+121)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((z * t) / y)
	t_2 = (t - a) / (b - y)
	t_3 = (t + ((x / (z / y)) - a)) / b
	tmp = 0
	if z <= -1.65e-24:
		tmp = t_2
	elif z <= 1.12e-100:
		tmp = t_1
	elif z <= 1.7e-32:
		tmp = t_3
	elif z <= 1.8e-21:
		tmp = t_1
	elif (z <= 8e+65) or not (z <= 3.3e+121):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(z * t) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(t + Float64(Float64(x / Float64(z / y)) - a)) / b)
	tmp = 0.0
	if (z <= -1.65e-24)
		tmp = t_2;
	elseif (z <= 1.12e-100)
		tmp = t_1;
	elseif (z <= 1.7e-32)
		tmp = t_3;
	elseif (z <= 1.8e-21)
		tmp = t_1;
	elseif ((z <= 8e+65) || !(z <= 3.3e+121))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((z * t) / y);
	t_2 = (t - a) / (b - y);
	t_3 = (t + ((x / (z / y)) - a)) / b;
	tmp = 0.0;
	if (z <= -1.65e-24)
		tmp = t_2;
	elseif (z <= 1.12e-100)
		tmp = t_1;
	elseif (z <= 1.7e-32)
		tmp = t_3;
	elseif (z <= 1.8e-21)
		tmp = t_1;
	elseif ((z <= 8e+65) || ~((z <= 3.3e+121)))
		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[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t + N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[z, -1.65e-24], t$95$2, If[LessEqual[z, 1.12e-100], t$95$1, If[LessEqual[z, 1.7e-32], t$95$3, If[LessEqual[z, 1.8e-21], t$95$1, If[Or[LessEqual[z, 8e+65], N[Not[LessEqual[z, 3.3e+121]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999992e-24 or 1.79999999999999995e-21 < z < 7.9999999999999999e65 or 3.29999999999999979e121 < z

   1. Initial program 46.9%

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

   2. Taylor expanded in z around inf 80.1%

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

   if -1.64999999999999992e-24 < z < 1.11999999999999996e-100 or 1.69999999999999989e-32 < z < 1.79999999999999995e-21

   1. Initial program 86.5%

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

   2. Taylor expanded in x around 0 86.5%

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

   3. Taylor expanded in z around 0 51.7%

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

      1. associate--r+ 51.7%

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

      2. div-sub 51.7%

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

      3. associate-/l* 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in t around inf 66.4%

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

   if 1.11999999999999996e-100 < z < 1.69999999999999989e-32 or 7.9999999999999999e65 < z < 3.29999999999999979e121

   1. Initial program 67.6%

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

   2. Taylor expanded in x around 0 67.6%

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

   3. Taylor expanded in b around inf 63.3%

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

      1. associate--l+ 63.3%

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

      2. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-24}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+65} \lor \neg \left(z \leq 3.3 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \end{array} \]

Alternative 8: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-57}:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{elif}\;y \leq 4500000000000:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+28}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= y -1.4e+31)
     t_1
     (if (<= y 3.4e-57)
       (/ (+ t (- (/ x (/ z y)) a)) b)
       (if (<= y 4500000000000.0)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= y 1.05e+28) (/ (- t a) (- b y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -1.4e+31) {
		tmp = t_1;
	} else if (y <= 3.4e-57) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} else if (y <= 4500000000000.0) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (y <= 1.05e+28) {
		tmp = (t - a) / (b - y);
	} 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 = ((a - t) / y) - (x / (z + (-1.0d0)))
    if (y <= (-1.4d+31)) then
        tmp = t_1
    else if (y <= 3.4d-57) then
        tmp = (t + ((x / (z / y)) - a)) / b
    else if (y <= 4500000000000.0d0) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (y <= 1.05d+28) then
        tmp = (t - a) / (b - y)
    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 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -1.4e+31) {
		tmp = t_1;
	} else if (y <= 3.4e-57) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} else if (y <= 4500000000000.0) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (y <= 1.05e+28) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if y <= -1.4e+31:
		tmp = t_1
	elif y <= 3.4e-57:
		tmp = (t + ((x / (z / y)) - a)) / b
	elif y <= 4500000000000.0:
		tmp = (x * y) / (y + (z * (b - y)))
	elif y <= 1.05e+28:
		tmp = (t - a) / (b - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (y <= -1.4e+31)
		tmp = t_1;
	elseif (y <= 3.4e-57)
		tmp = Float64(Float64(t + Float64(Float64(x / Float64(z / y)) - a)) / b);
	elseif (y <= 4500000000000.0)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (y <= 1.05e+28)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (y <= -1.4e+31)
		tmp = t_1;
	elseif (y <= 3.4e-57)
		tmp = (t + ((x / (z / y)) - a)) / b;
	elseif (y <= 4500000000000.0)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (y <= 1.05e+28)
		tmp = (t - a) / (b - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+31], t$95$1, If[LessEqual[y, 3.4e-57], N[(N[(t + N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4500000000000.0], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+28], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.40000000000000008e31 or 1.04999999999999995e28 < y

   1. Initial program 48.8%

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

   2. Taylor expanded in y around -inf 59.6%

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

      1. distribute-lft-out 59.6%

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

      2. sub-neg 59.6%

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

      3. metadata-eval 59.6%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in z around inf 67.5%

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

   if -1.40000000000000008e31 < y < 3.40000000000000016e-57

   1. Initial program 77.4%

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

   2. Taylor expanded in x around 0 77.5%

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

   3. Taylor expanded in b around inf 73.6%

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

      1. associate--l+ 73.6%

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

      2. associate-/l* 74.4%

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

   5. Simplified 74.4%

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

   if 3.40000000000000016e-57 < y < 4.5e12

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 74.5%

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

      1. *-commutative 74.5%

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

   4. Simplified 74.5%

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

   if 4.5e12 < y < 1.04999999999999995e28

   1. Initial program 23.4%

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

   2. Taylor expanded in z around inf 80.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-57}:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{elif}\;y \leq 4500000000000:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+28}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]

Alternative 9: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -880 \lor \neg \left(z \leq 1.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -880.0) (not (<= z 1.2e+14)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -880.0) || !(z <= 1.2e+14)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-880.0d0)) .or. (.not. (z <= 1.2d+14))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -880.0) || !(z <= 1.2e+14)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -880.0) or not (z <= 1.2e+14):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -880.0) || !(z <= 1.2e+14))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / Float64(y + Float64(z * Float64(b - y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -880.0) || ~((z <= 1.2e+14)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -880.0], N[Not[LessEqual[z, 1.2e+14]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -880 or 1.2e14 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -880 < z < 1.2e14

   1. Initial program 88.0%

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

   2. Taylor expanded in x around 0 88.0%

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

   3. Taylor expanded in z around 0 78.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -880 \lor \neg \left(z \leq 1.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 10: 42.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-262}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-242}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -3.5e-52)
     t_2
     (if (<= y -9e-262)
       (/ t b)
       (if (<= y 2.5e-284)
         t_1
         (if (<= y 8.8e-242) (/ t b) (if (<= y 1.35e-52) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e-52) {
		tmp = t_2;
	} else if (y <= -9e-262) {
		tmp = t / b;
	} else if (y <= 2.5e-284) {
		tmp = t_1;
	} else if (y <= 8.8e-242) {
		tmp = t / b;
	} else if (y <= 1.35e-52) {
		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 = -a / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-3.5d-52)) then
        tmp = t_2
    else if (y <= (-9d-262)) then
        tmp = t / b
    else if (y <= 2.5d-284) then
        tmp = t_1
    else if (y <= 8.8d-242) then
        tmp = t / b
    else if (y <= 1.35d-52) 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 = -a / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e-52) {
		tmp = t_2;
	} else if (y <= -9e-262) {
		tmp = t / b;
	} else if (y <= 2.5e-284) {
		tmp = t_1;
	} else if (y <= 8.8e-242) {
		tmp = t / b;
	} else if (y <= 1.35e-52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -3.5e-52:
		tmp = t_2
	elif y <= -9e-262:
		tmp = t / b
	elif y <= 2.5e-284:
		tmp = t_1
	elif y <= 8.8e-242:
		tmp = t / b
	elif y <= 1.35e-52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.5e-52)
		tmp = t_2;
	elseif (y <= -9e-262)
		tmp = Float64(t / b);
	elseif (y <= 2.5e-284)
		tmp = t_1;
	elseif (y <= 8.8e-242)
		tmp = Float64(t / b);
	elseif (y <= 1.35e-52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.5e-52)
		tmp = t_2;
	elseif (y <= -9e-262)
		tmp = t / b;
	elseif (y <= 2.5e-284)
		tmp = t_1;
	elseif (y <= 8.8e-242)
		tmp = t / b;
	elseif (y <= 1.35e-52)
		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[((-a) / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-52], t$95$2, If[LessEqual[y, -9e-262], N[(t / b), $MachinePrecision], If[LessEqual[y, 2.5e-284], t$95$1, If[LessEqual[y, 8.8e-242], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.35e-52], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5e-52 or 1.35000000000000005e-52 < y

   1. Initial program 56.9%

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

   2. Taylor expanded in y around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. unsub-neg 43.7%

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

   4. Simplified 43.7%

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

   if -3.5e-52 < y < -8.99999999999999997e-262 or 2.49999999999999987e-284 < y < 8.80000000000000006e-242

   1. Initial program 78.1%

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

   2. Taylor expanded in b around inf 58.6%

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

   3. Taylor expanded in t around inf 55.2%

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

   if -8.99999999999999997e-262 < y < 2.49999999999999987e-284 or 8.80000000000000006e-242 < y < 1.35000000000000005e-52

   1. Initial program 72.9%

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

   2. Taylor expanded in b around inf 54.0%

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

   3. Taylor expanded in a around inf 54.8%

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

      1. associate-*r/ 54.8%

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

      2. mul-1-neg 54.8%

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

   5. Simplified 54.8%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-262}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-242}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-52}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 11: 67.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-25} \lor \neg \left(z \leq 7 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-25) (not (<= z 7e-89)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-25) || !(z <= 7e-89)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.05d-25)) .or. (.not. (z <= 7d-89))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-25) || !(z <= 7e-89)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-25) or not (z <= 7e-89):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-25) || !(z <= 7e-89))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-25) || ~((z <= 7e-89)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-25], N[Not[LessEqual[z, 7e-89]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000001e-25 or 6.9999999999999994e-89 < z

   1. Initial program 50.8%

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

   2. Taylor expanded in z around inf 74.7%

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

   if -1.05000000000000001e-25 < z < 6.9999999999999994e-89

   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 x around 0 85.8%

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

   3. Taylor expanded in z around 0 49.3%

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

      1. associate--r+ 49.3%

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

      2. div-sub 49.3%

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

      3. associate-/l* 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in t around inf 62.9%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-25} \lor \neg \left(z \leq 7 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 12: 55.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-47} \lor \neg \left(y \leq 5.7 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.1e-47) (not (<= y 5.7e-49))) (/ 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 <= -3.1e-47) || !(y <= 5.7e-49)) {
		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 <= (-3.1d-47)) .or. (.not. (y <= 5.7d-49))) 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 <= -3.1e-47) || !(y <= 5.7e-49)) {
		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 <= -3.1e-47) or not (y <= 5.7e-49):
		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 <= -3.1e-47) || !(y <= 5.7e-49))
		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 <= -3.1e-47) || ~((y <= 5.7e-49)))
		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, -3.1e-47], N[Not[LessEqual[y, 5.7e-49]], $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 < -3.0999999999999998e-47 or 5.7000000000000003e-49 < y

   1. Initial program 56.9%

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

   2. Taylor expanded in y around inf 43.7%

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

      1. mul-1-neg 43.7%

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

      2. unsub-neg 43.7%

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

   4. Simplified 43.7%

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

   if -3.0999999999999998e-47 < y < 5.7000000000000003e-49

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0 71.9%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-47} \lor \neg \left(y \leq 5.7 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 13: 52.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.35e-49)
   (+ x (* z (/ t y)))
   (if (<= y 4.8e-49) (/ (- t a) b) (/ x (- 1.0 z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.35e-49) {
		tmp = x + (z * (t / y));
	} else if (y <= 4.8e-49) {
		tmp = (t - a) / b;
	} 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 (y <= (-2.35d-49)) then
        tmp = x + (z * (t / y))
    else if (y <= 4.8d-49) then
        tmp = (t - a) / b
    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 (y <= -2.35e-49) {
		tmp = x + (z * (t / y));
	} else if (y <= 4.8e-49) {
		tmp = (t - a) / b;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.35e-49:
		tmp = x + (z * (t / y))
	elif y <= 4.8e-49:
		tmp = (t - a) / b
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.35e-49)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (y <= 4.8e-49)
		tmp = Float64(Float64(t - a) / b);
	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 (y <= -2.35e-49)
		tmp = x + (z * (t / y));
	elseif (y <= 4.8e-49)
		tmp = (t - a) / b;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.35e-49], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-49], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.35000000000000011e-49

   1. Initial program 59.4%

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

   2. Taylor expanded in x around 0 59.4%

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

   3. Taylor expanded in z around 0 34.1%

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

      1. associate--r+ 34.1%

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

      2. div-sub 34.1%

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

      3. associate-/l* 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in t around inf 43.4%

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

   if -2.35000000000000011e-49 < y < 4.79999999999999985e-49

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0 71.9%

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

   if 4.79999999999999985e-49 < y

   1. Initial program 54.9%

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

   2. Taylor expanded in y around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unsub-neg 44.9%

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

   4. Simplified 44.9%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-49}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14: 36.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.8e-26) (/ t b) (if (<= z 2.8e-75) x (/ (- a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.8e-26) {
		tmp = t / b;
	} else if (z <= 2.8e-75) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.8d-26)) then
        tmp = t / b
    else if (z <= 2.8d-75) then
        tmp = x
    else
        tmp = -a / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.8e-26) {
		tmp = t / b;
	} else if (z <= 2.8e-75) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.8e-26:
		tmp = t / b
	elif z <= 2.8e-75:
		tmp = x
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.8e-26)
		tmp = Float64(t / b);
	elseif (z <= 2.8e-75)
		tmp = x;
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.8e-26)
		tmp = t / b;
	elseif (z <= 2.8e-75)
		tmp = x;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.8e-26], N[(t / b), $MachinePrecision], If[LessEqual[z, 2.8e-75], x, N[((-a) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000001e-26

   1. Initial program 47.0%

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

   2. Taylor expanded in b around inf 28.5%

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

   3. Taylor expanded in t around inf 35.2%

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

   if -2.8000000000000001e-26 < z < 2.79999999999999998e-75

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 49.8%

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

   if 2.79999999999999998e-75 < z

   1. Initial program 53.4%

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

   2. Taylor expanded in b around inf 34.7%

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

   3. Taylor expanded in a around inf 27.9%

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

      1. associate-*r/ 27.9%

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

      2. mul-1-neg 27.9%

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

   5. Simplified 27.9%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 15: 36.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.12e-26) (/ t b) (if (<= z 7e-89) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.12e-26) {
		tmp = t / b;
	} else if (z <= 7e-89) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.12d-26)) then
        tmp = t / b
    else if (z <= 7d-89) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.12e-26) {
		tmp = t / b;
	} else if (z <= 7e-89) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.12e-26:
		tmp = t / b
	elif z <= 7e-89:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.12e-26)
		tmp = Float64(t / b);
	elseif (z <= 7e-89)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.12e-26)
		tmp = t / b;
	elseif (z <= 7e-89)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.12e-26], N[(t / b), $MachinePrecision], If[LessEqual[z, 7e-89], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e-26 or 6.9999999999999994e-89 < z

   1. Initial program 50.8%

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

   2. Taylor expanded in b around inf 32.3%

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

   3. Taylor expanded in t around inf 30.4%

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

   if -1.12e-26 < z < 6.9999999999999994e-89

   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 z around 0 50.2%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16: 25.4% 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 64.6%

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

2. Taylor expanded in z around 0 22.9%

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

3. Final simplification 22.9%

   \[\leadsto x \]

Developer target: 72.7% 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 2023279 
(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)))))