Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 91.9%

Time: 19.7s

Alternatives: 17

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.5% 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: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{t\_1}\\ t_5 := x \cdot \left(\frac{y}{t\_1} + \frac{t\_3}{x \cdot t\_1}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-275}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{+294}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_3\right)}{t\_1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (+
          (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z)
          (/ (- t a) (- b y))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (* x (+ (/ y t_1) (/ t_3 (* x t_1))))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -4e-275)
       t_4
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 4e+294)
           (/ (fma x y t_3) t_1)
           (if (<= t_4 INFINITY) t_5 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 * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z) + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -4e-275) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 4e+294) {
		tmp = fma(x, y, t_3) / t_1;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / 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)
	t_5 = Float64(x * Float64(Float64(y / t_1) + Float64(t_3 / Float64(x * t_1))))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -4e-275)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 4e+294)
		tmp = Float64(fma(x, y, t_3) / t_1);
	elseif (t_4 <= Inf)
		tmp = t_5;
	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[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $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]}, Block[{t$95$5 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$3 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -4e-275], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 4e+294], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, 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 4.00000000000000027e294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 70.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999974e-275

   1. Initial program 99.5%

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

   if -3.99999999999999974e-275 < (/.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 10.3%

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

   3. Taylor expanded in z around -inf 56.1%

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

      1. associate--l+ 56.1%

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

      2. mul-1-neg 56.1%

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

      3. distribute-lft-out-- 56.1%

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

      4. associate-/l* 65.6%

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

      5. associate-/l* 98.4%

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

      6. div-sub 98.4%

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

   5. Simplified 98.4%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.00000000000000027e294

   1. Initial program 99.6%

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

      1. fma-define 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-275}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{+294}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{t\_1}\\ t_5 := x \cdot \left(\frac{y}{t\_1} + \frac{t\_3}{x \cdot t\_1}\right)\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-275}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{+294}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_3\right)}{t\_1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (-
          (+ (/ (- t a) (- b y)) (* (/ y z) (/ x (- b y))))
          (* (/ (- t a) (pow (- b y) 2.0)) (/ y z))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (* x (+ (/ y t_1) (/ t_3 (* x t_1))))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -4e-275)
       t_4
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 4e+294)
           (/ (fma x y t_3) t_1)
           (if (<= t_4 INFINITY) t_5 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 = (((t - a) / (b - y)) + ((y / z) * (x / (b - y)))) - (((t - a) / pow((b - y), 2.0)) * (y / z));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = x * ((y / t_1) + (t_3 / (x * t_1)));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -4e-275) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 4e+294) {
		tmp = fma(x, y, t_3) / t_1;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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(t - a) / Float64(b - y)) + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) - Float64(Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)) * Float64(y / z)))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(x * Float64(Float64(y / t_1) + Float64(t_3 / Float64(x * t_1))))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -4e-275)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 4e+294)
		tmp = Float64(fma(x, y, t_3) / t_1);
	elseif (t_4 <= Inf)
		tmp = t_5;
	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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(y / z), $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]}, Block[{t$95$5 = N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$3 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -4e-275], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 4e+294], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$5, 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 4.00000000000000027e294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 24.4%

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

   3. Taylor expanded in x around inf 70.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999974e-275

   1. Initial program 99.5%

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

   if -3.99999999999999974e-275 < (/.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 10.3%

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

   3. Taylor expanded in z around inf 49.7%

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

      1. associate--r+ 49.7%

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

      2. +-commutative 49.7%

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

      3. associate--l+ 49.7%

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

      4. *-commutative 49.7%

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

      5. times-frac 63.0%

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

      6. div-sub 63.0%

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

      7. times-frac 95.7%

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

   5. Simplified 95.7%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.00000000000000027e294

   1. Initial program 99.6%

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

      1. fma-define 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-275}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{+294}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) - \frac{t - a}{{\left(b - y\right)}^{2}} \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{t\_2}{x \cdot t\_1} + 1\right)\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-278} \lor \neg \left(t\_3 \leq 0\right) \land t\_3 \leq 10^{+308}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1)))
   (if (<= t_3 (- INFINITY))
     (* x (+ (/ t_2 (* x t_1)) 1.0))
     (if (or (<= t_3 -2e-278) (and (not (<= t_3 0.0)) (<= t_3 1e+308)))
       t_3
       (/ (- t a) (- b y))))))

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 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x * ((t_2 / (x * t_1)) + 1.0);
	} else if ((t_3 <= -2e-278) || (!(t_3 <= 0.0) && (t_3 <= 1e+308))) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((t_2 / (x * t_1)) + 1.0);
	} else if ((t_3 <= -2e-278) || (!(t_3 <= 0.0) && (t_3 <= 1e+308))) {
		tmp = t_3;
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) + t_2) / t_1
	tmp = 0
	if t_3 <= -math.inf:
		tmp = x * ((t_2 / (x * t_1)) + 1.0)
	elif (t_3 <= -2e-278) or (not (t_3 <= 0.0) and (t_3 <= 1e+308)):
		tmp = t_3
	else:
		tmp = (t - a) / (b - y)
	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(Float64(x * y) + t_2) / t_1)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(t_2 / Float64(x * t_1)) + 1.0));
	elseif ((t_3 <= -2e-278) || (!(t_3 <= 0.0) && (t_3 <= 1e+308)))
		tmp = t_3;
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / t_1;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = x * ((t_2 / (x * t_1)) + 1.0);
	elseif ((t_3 <= -2e-278) || (~((t_3 <= 0.0)) && (t_3 <= 1e+308)))
		tmp = t_3;
	else
		tmp = (t - a) / (b - y);
	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[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x * N[(N[(t$95$2 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$3, -2e-278], And[N[Not[LessEqual[t$95$3, 0.0]], $MachinePrecision], LessEqual[t$95$3, 1e+308]]], t$95$3, N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 24.1%

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

   3. Taylor expanded in x around inf 68.4%

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

   4. Taylor expanded in z around 0 63.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.99999999999999988e-278 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1e308

   1. Initial program 99.6%

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

   if -1.99999999999999988e-278 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 1e308 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 11.4%

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

   3. Taylor expanded in z around inf 67.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)} + 1\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-278} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+308}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{z \cdot \left(t - a\right)}{x \cdot t\_2}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(t\_3 + \frac{\frac{y}{z}}{b - y}\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15} \lor \neg \left(z \leq 4 \cdot 10^{+47}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_2} + t\_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (* z (- t a)) (* x t_2))))
   (if (<= z -9e+98)
     t_1
     (if (<= z -4.4e+61)
       (* x (+ t_3 (/ (/ y z) (- b y))))
       (if (or (<= z -1.6e+15) (not (<= z 4e+47)))
         t_1
         (* x (+ (/ y t_2) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double t_3 = (z * (t - a)) / (x * t_2);
	double tmp;
	if (z <= -9e+98) {
		tmp = t_1;
	} else if (z <= -4.4e+61) {
		tmp = x * (t_3 + ((y / z) / (b - y)));
	} else if ((z <= -1.6e+15) || !(z <= 4e+47)) {
		tmp = t_1;
	} else {
		tmp = x * ((y / t_2) + 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 = (t - a) / (b - y)
    t_2 = y + (z * (b - y))
    t_3 = (z * (t - a)) / (x * t_2)
    if (z <= (-9d+98)) then
        tmp = t_1
    else if (z <= (-4.4d+61)) then
        tmp = x * (t_3 + ((y / z) / (b - y)))
    else if ((z <= (-1.6d+15)) .or. (.not. (z <= 4d+47))) then
        tmp = t_1
    else
        tmp = x * ((y / t_2) + 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 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double t_3 = (z * (t - a)) / (x * t_2);
	double tmp;
	if (z <= -9e+98) {
		tmp = t_1;
	} else if (z <= -4.4e+61) {
		tmp = x * (t_3 + ((y / z) / (b - y)));
	} else if ((z <= -1.6e+15) || !(z <= 4e+47)) {
		tmp = t_1;
	} else {
		tmp = x * ((y / t_2) + t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = y + (z * (b - y))
	t_3 = (z * (t - a)) / (x * t_2)
	tmp = 0
	if z <= -9e+98:
		tmp = t_1
	elif z <= -4.4e+61:
		tmp = x * (t_3 + ((y / z) / (b - y)))
	elif (z <= -1.6e+15) or not (z <= 4e+47):
		tmp = t_1
	else:
		tmp = x * ((y / t_2) + t_3)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(z * Float64(t - a)) / Float64(x * t_2))
	tmp = 0.0
	if (z <= -9e+98)
		tmp = t_1;
	elseif (z <= -4.4e+61)
		tmp = Float64(x * Float64(t_3 + Float64(Float64(y / z) / Float64(b - y))));
	elseif ((z <= -1.6e+15) || !(z <= 4e+47))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y / t_2) + t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = y + (z * (b - y));
	t_3 = (z * (t - a)) / (x * t_2);
	tmp = 0.0;
	if (z <= -9e+98)
		tmp = t_1;
	elseif (z <= -4.4e+61)
		tmp = x * (t_3 + ((y / z) / (b - y)));
	elseif ((z <= -1.6e+15) || ~((z <= 4e+47)))
		tmp = t_1;
	else
		tmp = x * ((y / t_2) + t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+98], t$95$1, If[LessEqual[z, -4.4e+61], N[(x * N[(t$95$3 + N[(N[(y / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.6e+15], N[Not[LessEqual[z, 4e+47]], $MachinePrecision]], t$95$1, N[(x * N[(N[(y / t$95$2), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.0000000000000004e98 or -4.4000000000000001e61 < z < -1.6e15 or 4.0000000000000002e47 < z

   1. Initial program 38.1%

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

   3. Taylor expanded in z around inf 86.5%

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

   if -9.0000000000000004e98 < z < -4.4000000000000001e61

   1. Initial program 42.7%

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

   3. Taylor expanded in x around inf 43.6%

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

   4. Taylor expanded in z around inf 43.6%

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

      1. associate-/r* 83.5%

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

   6. Simplified 83.5%

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

   if -1.6e15 < z < 4.0000000000000002e47

   1. Initial program 83.6%

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

   3. Taylor expanded in x around inf 87.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+98}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(\frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)} + \frac{\frac{y}{z}}{b - y}\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+15} \lor \neg \left(z \leq 4 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := y + z \cdot b\\ t_3 := \frac{t\_1}{t\_2}\\ t_4 := \frac{t - a}{b - y}\\ t_5 := \frac{x \cdot y - z \cdot a}{t\_2}\\ \mathbf{if}\;z \leq -0.47:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-188}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-82}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-5}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{t\_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t)))
        (t_2 (+ y (* z b)))
        (t_3 (/ t_1 t_2))
        (t_4 (/ (- t a) (- b y)))
        (t_5 (/ (- (* x y) (* z a)) t_2)))
   (if (<= z -0.47)
     t_4
     (if (<= z -2.2e-188)
       t_3
       (if (<= z 1.3e-306)
         t_5
         (if (<= z 2e-82)
           t_3
           (if (<= z 1.52e-5)
             t_5
             (if (<= z 2.9e+44) (/ t_1 (+ y (* z (- b y)))) t_4))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = y + (z * b);
	double t_3 = t_1 / t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = ((x * y) - (z * a)) / t_2;
	double tmp;
	if (z <= -0.47) {
		tmp = t_4;
	} else if (z <= -2.2e-188) {
		tmp = t_3;
	} else if (z <= 1.3e-306) {
		tmp = t_5;
	} else if (z <= 2e-82) {
		tmp = t_3;
	} else if (z <= 1.52e-5) {
		tmp = t_5;
	} else if (z <= 2.9e+44) {
		tmp = t_1 / (y + (z * (b - y)));
	} 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) :: t_5
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = y + (z * b)
    t_3 = t_1 / t_2
    t_4 = (t - a) / (b - y)
    t_5 = ((x * y) - (z * a)) / t_2
    if (z <= (-0.47d0)) then
        tmp = t_4
    else if (z <= (-2.2d-188)) then
        tmp = t_3
    else if (z <= 1.3d-306) then
        tmp = t_5
    else if (z <= 2d-82) then
        tmp = t_3
    else if (z <= 1.52d-5) then
        tmp = t_5
    else if (z <= 2.9d+44) then
        tmp = t_1 / (y + (z * (b - y)))
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * t);
	double t_2 = y + (z * b);
	double t_3 = t_1 / t_2;
	double t_4 = (t - a) / (b - y);
	double t_5 = ((x * y) - (z * a)) / t_2;
	double tmp;
	if (z <= -0.47) {
		tmp = t_4;
	} else if (z <= -2.2e-188) {
		tmp = t_3;
	} else if (z <= 1.3e-306) {
		tmp = t_5;
	} else if (z <= 2e-82) {
		tmp = t_3;
	} else if (z <= 1.52e-5) {
		tmp = t_5;
	} else if (z <= 2.9e+44) {
		tmp = t_1 / (y + (z * (b - y)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * t)
	t_2 = y + (z * b)
	t_3 = t_1 / t_2
	t_4 = (t - a) / (b - y)
	t_5 = ((x * y) - (z * a)) / t_2
	tmp = 0
	if z <= -0.47:
		tmp = t_4
	elif z <= -2.2e-188:
		tmp = t_3
	elif z <= 1.3e-306:
		tmp = t_5
	elif z <= 2e-82:
		tmp = t_3
	elif z <= 1.52e-5:
		tmp = t_5
	elif z <= 2.9e+44:
		tmp = t_1 / (y + (z * (b - y)))
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(y + Float64(z * b))
	t_3 = Float64(t_1 / t_2)
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	t_5 = Float64(Float64(Float64(x * y) - Float64(z * a)) / t_2)
	tmp = 0.0
	if (z <= -0.47)
		tmp = t_4;
	elseif (z <= -2.2e-188)
		tmp = t_3;
	elseif (z <= 1.3e-306)
		tmp = t_5;
	elseif (z <= 2e-82)
		tmp = t_3;
	elseif (z <= 1.52e-5)
		tmp = t_5;
	elseif (z <= 2.9e+44)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * t);
	t_2 = y + (z * b);
	t_3 = t_1 / t_2;
	t_4 = (t - a) / (b - y);
	t_5 = ((x * y) - (z * a)) / t_2;
	tmp = 0.0;
	if (z <= -0.47)
		tmp = t_4;
	elseif (z <= -2.2e-188)
		tmp = t_3;
	elseif (z <= 1.3e-306)
		tmp = t_5;
	elseif (z <= 2e-82)
		tmp = t_3;
	elseif (z <= 1.52e-5)
		tmp = t_5;
	elseif (z <= 2.9e+44)
		tmp = t_1 / (y + (z * (b - y)));
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[z, -0.47], t$95$4, If[LessEqual[z, -2.2e-188], t$95$3, If[LessEqual[z, 1.3e-306], t$95$5, If[LessEqual[z, 2e-82], t$95$3, If[LessEqual[z, 1.52e-5], t$95$5, If[LessEqual[z, 2.9e+44], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.46999999999999997 or 2.9000000000000002e44 < z

   1. Initial program 40.1%

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

   3. Taylor expanded in z around inf 81.7%

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

   if -0.46999999999999997 < z < -2.2e-188 or 1.3e-306 < z < 2e-82

   1. Initial program 84.3%

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

   3. Taylor expanded in a around 0 70.4%

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

   4. Taylor expanded in b around inf 70.4%

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

      1. *-commutative 83.9%

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

   6. Simplified 70.4%

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

   if -2.2e-188 < z < 1.3e-306 or 2e-82 < z < 1.52e-5

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 74.4%

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

      1. *-commutative 74.4%

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

   5. Simplified 74.4%

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

   6. Taylor expanded in t around 0 67.5%

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

      1. +-commutative 67.5%

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

      2. mul-1-neg 67.5%

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

      3. unsub-neg 67.5%

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

      4. *-commutative 67.5%

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

      5. *-commutative 67.5%

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

   8. Simplified 67.5%

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

   if 1.52e-5 < z < 2.9000000000000002e44

   1. Initial program 99.6%

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

   3. Taylor expanded in a around 0 90.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.47:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-5}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.8:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 41000:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z t)) (+ y (* z b)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.8)
     t_2
     (if (<= z -3.8e-195)
       t_1
       (if (<= z 1.7e-306)
         (/ (+ (* x y) (* z (- t a))) y)
         (if (<= z 3.8e-63)
           t_1
           (if (<= z 3.3e-18)
             x
             (if (<= z 41000.0) (/ (* z a) (- (* z (- y b)) y)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * t)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.8) {
		tmp = t_2;
	} else if (z <= -3.8e-195) {
		tmp = t_1;
	} else if (z <= 1.7e-306) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 3.8e-63) {
		tmp = t_1;
	} else if (z <= 3.3e-18) {
		tmp = x;
	} else if (z <= 41000.0) {
		tmp = (z * a) / ((z * (y - b)) - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) / (y + (z * b))
    t_2 = (t - a) / (b - y)
    if (z <= (-1.8d0)) then
        tmp = t_2
    else if (z <= (-3.8d-195)) then
        tmp = t_1
    else if (z <= 1.7d-306) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if (z <= 3.8d-63) then
        tmp = t_1
    else if (z <= 3.3d-18) then
        tmp = x
    else if (z <= 41000.0d0) then
        tmp = (z * a) / ((z * (y - b)) - y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * t)) / (y + (z * b));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.8) {
		tmp = t_2;
	} else if (z <= -3.8e-195) {
		tmp = t_1;
	} else if (z <= 1.7e-306) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 3.8e-63) {
		tmp = t_1;
	} else if (z <= 3.3e-18) {
		tmp = x;
	} else if (z <= 41000.0) {
		tmp = (z * a) / ((z * (y - b)) - y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * t)) / (y + (z * b))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.8:
		tmp = t_2
	elif z <= -3.8e-195:
		tmp = t_1
	elif z <= 1.7e-306:
		tmp = ((x * y) + (z * (t - a))) / y
	elif z <= 3.8e-63:
		tmp = t_1
	elif z <= 3.3e-18:
		tmp = x
	elif z <= 41000.0:
		tmp = (z * a) / ((z * (y - b)) - y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) / Float64(y + Float64(z * b)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.8)
		tmp = t_2;
	elseif (z <= -3.8e-195)
		tmp = t_1;
	elseif (z <= 1.7e-306)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 3.8e-63)
		tmp = t_1;
	elseif (z <= 3.3e-18)
		tmp = x;
	elseif (z <= 41000.0)
		tmp = Float64(Float64(z * a) / Float64(Float64(z * Float64(y - b)) - y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * t)) / (y + (z * b));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.8)
		tmp = t_2;
	elseif (z <= -3.8e-195)
		tmp = t_1;
	elseif (z <= 1.7e-306)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif (z <= 3.8e-63)
		tmp = t_1;
	elseif (z <= 3.3e-18)
		tmp = x;
	elseif (z <= 41000.0)
		tmp = (z * a) / ((z * (y - b)) - y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8], t$95$2, If[LessEqual[z, -3.8e-195], t$95$1, If[LessEqual[z, 1.7e-306], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.8e-63], t$95$1, If[LessEqual[z, 3.3e-18], x, If[LessEqual[z, 41000.0], N[(N[(z * a), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.80000000000000004 or 41000 < z

   1. Initial program 43.8%

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

   3. Taylor expanded in z around inf 80.2%

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

   if -1.80000000000000004 < z < -3.80000000000000013e-195 or 1.6999999999999999e-306 < z < 3.80000000000000017e-63

   1. Initial program 84.0%

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

   3. Taylor expanded in a around 0 68.5%

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

   4. Taylor expanded in b around inf 68.5%

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

      1. *-commutative 83.6%

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

   6. Simplified 68.5%

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

   if -3.80000000000000013e-195 < z < 1.6999999999999999e-306

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in b around 0 83.2%

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

   if 3.80000000000000017e-63 < z < 3.3000000000000002e-18

   1. Initial program 49.0%

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

   3. Taylor expanded in z around 0 56.9%

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

   if 3.3000000000000002e-18 < z < 41000

   1. Initial program 99.7%

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

   3. Taylor expanded in a around inf 43.3%

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

      1. mul-1-neg 43.3%

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

      2. distribute-lft-neg-out 43.3%

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

      3. *-commutative 43.3%

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

   5. Simplified 43.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 41000:\\ \;\;\;\;\frac{z \cdot a}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot b\\ t_2 := \frac{x \cdot y + z \cdot t}{t\_1}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{x \cdot y - z \cdot a}{t\_1}\\ \mathbf{if}\;z \leq -0.7:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-306}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 64000:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z b)))
        (t_2 (/ (+ (* x y) (* z t)) t_1))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (/ (- (* x y) (* z a)) t_1)))
   (if (<= z -0.7)
     t_3
     (if (<= z -1.35e-189)
       t_2
       (if (<= z 1.25e-306)
         t_4
         (if (<= z 1.4e-72) t_2 (if (<= z 64000.0) t_4 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * b);
	double t_2 = ((x * y) + (z * t)) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = ((x * y) - (z * a)) / t_1;
	double tmp;
	if (z <= -0.7) {
		tmp = t_3;
	} else if (z <= -1.35e-189) {
		tmp = t_2;
	} else if (z <= 1.25e-306) {
		tmp = t_4;
	} else if (z <= 1.4e-72) {
		tmp = t_2;
	} else if (z <= 64000.0) {
		tmp = t_4;
	} 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)
    t_2 = ((x * y) + (z * t)) / t_1
    t_3 = (t - a) / (b - y)
    t_4 = ((x * y) - (z * a)) / t_1
    if (z <= (-0.7d0)) then
        tmp = t_3
    else if (z <= (-1.35d-189)) then
        tmp = t_2
    else if (z <= 1.25d-306) then
        tmp = t_4
    else if (z <= 1.4d-72) then
        tmp = t_2
    else if (z <= 64000.0d0) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * b);
	double t_2 = ((x * y) + (z * t)) / t_1;
	double t_3 = (t - a) / (b - y);
	double t_4 = ((x * y) - (z * a)) / t_1;
	double tmp;
	if (z <= -0.7) {
		tmp = t_3;
	} else if (z <= -1.35e-189) {
		tmp = t_2;
	} else if (z <= 1.25e-306) {
		tmp = t_4;
	} else if (z <= 1.4e-72) {
		tmp = t_2;
	} else if (z <= 64000.0) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * b)
	t_2 = ((x * y) + (z * t)) / t_1
	t_3 = (t - a) / (b - y)
	t_4 = ((x * y) - (z * a)) / t_1
	tmp = 0
	if z <= -0.7:
		tmp = t_3
	elif z <= -1.35e-189:
		tmp = t_2
	elif z <= 1.25e-306:
		tmp = t_4
	elif z <= 1.4e-72:
		tmp = t_2
	elif z <= 64000.0:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * b))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * t)) / t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(Float64(Float64(x * y) - Float64(z * a)) / t_1)
	tmp = 0.0
	if (z <= -0.7)
		tmp = t_3;
	elseif (z <= -1.35e-189)
		tmp = t_2;
	elseif (z <= 1.25e-306)
		tmp = t_4;
	elseif (z <= 1.4e-72)
		tmp = t_2;
	elseif (z <= 64000.0)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * b);
	t_2 = ((x * y) + (z * t)) / t_1;
	t_3 = (t - a) / (b - y);
	t_4 = ((x * y) - (z * a)) / t_1;
	tmp = 0.0;
	if (z <= -0.7)
		tmp = t_3;
	elseif (z <= -1.35e-189)
		tmp = t_2;
	elseif (z <= 1.25e-306)
		tmp = t_4;
	elseif (z <= 1.4e-72)
		tmp = t_2;
	elseif (z <= 64000.0)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[z, -0.7], t$95$3, If[LessEqual[z, -1.35e-189], t$95$2, If[LessEqual[z, 1.25e-306], t$95$4, If[LessEqual[z, 1.4e-72], t$95$2, If[LessEqual[z, 64000.0], t$95$4, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.69999999999999996 or 64000 < z

   1. Initial program 43.8%

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

   3. Taylor expanded in z around inf 80.2%

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

   if -0.69999999999999996 < z < -1.35e-189 or 1.25e-306 < z < 1.3999999999999999e-72

   1. Initial program 84.3%

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

   3. Taylor expanded in a around 0 70.4%

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

   4. Taylor expanded in b around inf 70.4%

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

      1. *-commutative 83.9%

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

   6. Simplified 70.4%

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

   if -1.35e-189 < z < 1.25e-306 or 1.3999999999999999e-72 < z < 64000

   1. Initial program 78.1%

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

   3. Taylor expanded in b around inf 72.5%

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

      1. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in t around 0 65.2%

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

      1. +-commutative 65.2%

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

      2. mul-1-neg 65.2%

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

      3. unsub-neg 65.2%

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

      4. *-commutative 65.2%

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

      5. *-commutative 65.2%

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

   8. Simplified 65.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.7:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-189}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 64000:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+15} \lor \neg \left(z \leq 5.1 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+15) (not (<= z 5.1e+45)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* 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 <= -1.4e+15) || !(z <= 5.1e+45)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (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 <= (-1.4d+15)) .or. (.not. (z <= 5.1d+45))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (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 <= -1.4e+15) || !(z <= 5.1e+45)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+15) or not (z <= 5.1e+45):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+15) || !(z <= 5.1e+45))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + 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 <= -1.4e+15) || ~((z <= 5.1e+45)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+15], N[Not[LessEqual[z, 5.1e+45]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e15 or 5.0999999999999997e45 < z

   1. Initial program 38.6%

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

   3. Taylor expanded in z around inf 82.0%

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

   if -1.4e15 < z < 5.0999999999999997e45

   1. Initial program 83.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+15} \lor \neg \left(z \leq 5.1 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 6.2 \cdot 10^{-5}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -4.6e+92)
     t_1
     (if (<= z -1.75e+61)
       (/ x (- z))
       (if (or (<= z -9.5e-153) (not (<= z 6.2e-5))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -4.6e+92) {
		tmp = t_1;
	} else if (z <= -1.75e+61) {
		tmp = x / -z;
	} else if ((z <= -9.5e-153) || !(z <= 6.2e-5)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (b - y)
    if (z <= (-4.6d+92)) then
        tmp = t_1
    else if (z <= (-1.75d+61)) then
        tmp = x / -z
    else if ((z <= (-9.5d-153)) .or. (.not. (z <= 6.2d-5))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -4.6e+92) {
		tmp = t_1;
	} else if (z <= -1.75e+61) {
		tmp = x / -z;
	} else if ((z <= -9.5e-153) || !(z <= 6.2e-5)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -4.6e+92:
		tmp = t_1
	elif z <= -1.75e+61:
		tmp = x / -z
	elif (z <= -9.5e-153) or not (z <= 6.2e-5):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -4.6e+92)
		tmp = t_1;
	elseif (z <= -1.75e+61)
		tmp = Float64(x / Float64(-z));
	elseif ((z <= -9.5e-153) || !(z <= 6.2e-5))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -4.6e+92)
		tmp = t_1;
	elseif (z <= -1.75e+61)
		tmp = x / -z;
	elseif ((z <= -9.5e-153) || ~((z <= 6.2e-5)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+92], t$95$1, If[LessEqual[z, -1.75e+61], N[(x / (-z)), $MachinePrecision], If[Or[LessEqual[z, -9.5e-153], N[Not[LessEqual[z, 6.2e-5]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999997e92 or -1.75000000000000009e61 < z < -9.50000000000000031e-153 or 6.20000000000000027e-5 < z

   1. Initial program 53.7%

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

   3. Taylor expanded in a around 0 38.8%

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

   4. Taylor expanded in z around inf 44.5%

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

   if -4.59999999999999997e92 < z < -1.75000000000000009e61

   1. Initial program 37.7%

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

   3. Taylor expanded in x around inf 11.8%

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

      1. *-commutative 11.8%

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

   5. Simplified 11.8%

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

   6. Taylor expanded in z around inf 11.8%

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

   7. Taylor expanded in y around inf 65.2%

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

      1. associate-*r/ 65.2%

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

      2. mul-1-neg 65.2%

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

   9. Simplified 65.2%

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

   if -9.50000000000000031e-153 < z < 6.20000000000000027e-5

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 56.8%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+92}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+61}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 6.2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-245}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -7.4e+56)
     t_2
     (if (<= y -4e-245)
       t_1
       (if (<= y -1.5e-277) (/ a (- b)) (if (<= y 4.4e-10) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -7.4e+56) {
		tmp = t_2;
	} else if (y <= -4e-245) {
		tmp = t_1;
	} else if (y <= -1.5e-277) {
		tmp = a / -b;
	} else if (y <= 4.4e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-7.4d+56)) then
        tmp = t_2
    else if (y <= (-4d-245)) then
        tmp = t_1
    else if (y <= (-1.5d-277)) then
        tmp = a / -b
    else if (y <= 4.4d-10) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -7.4e+56) {
		tmp = t_2;
	} else if (y <= -4e-245) {
		tmp = t_1;
	} else if (y <= -1.5e-277) {
		tmp = a / -b;
	} else if (y <= 4.4e-10) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -7.4e+56:
		tmp = t_2
	elif y <= -4e-245:
		tmp = t_1
	elif y <= -1.5e-277:
		tmp = a / -b
	elif y <= 4.4e-10:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7.4e+56)
		tmp = t_2;
	elseif (y <= -4e-245)
		tmp = t_1;
	elseif (y <= -1.5e-277)
		tmp = Float64(a / Float64(-b));
	elseif (y <= 4.4e-10)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -7.4e+56)
		tmp = t_2;
	elseif (y <= -4e-245)
		tmp = t_1;
	elseif (y <= -1.5e-277)
		tmp = a / -b;
	elseif (y <= 4.4e-10)
		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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e+56], t$95$2, If[LessEqual[y, -4e-245], t$95$1, If[LessEqual[y, -1.5e-277], N[(a / (-b)), $MachinePrecision], If[LessEqual[y, 4.4e-10], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999994e56 or 4.3999999999999998e-10 < y

   1. Initial program 49.9%

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

   3. Taylor expanded in y around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. unsub-neg 56.3%

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

   5. Simplified 56.3%

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

   if -7.39999999999999994e56 < y < -3.9999999999999997e-245 or -1.49999999999999989e-277 < y < 4.3999999999999998e-10

   1. Initial program 74.4%

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

   3. Taylor expanded in a around 0 53.2%

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

   4. Taylor expanded in z around inf 45.8%

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

   if -3.9999999999999997e-245 < y < -1.49999999999999989e-277

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 99.2%

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

   4. Taylor expanded in b around inf 83.1%

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

   5. Taylor expanded in a around inf 83.4%

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

      1. neg-mul-1 83.4%

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

   7. Simplified 83.4%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-245}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-277}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -185 \lor \neg \left(z \leq 41000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -185.0) (not (<= z 41000.0)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -185.0) || !(z <= 41000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-185.0d0)) .or. (.not. (z <= 41000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -185.0) || !(z <= 41000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -185.0) or not (z <= 41000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -185.0) || !(z <= 41000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -185.0) || ~((z <= 41000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -185.0], N[Not[LessEqual[z, 41000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -185 or 41000 < z

   1. Initial program 43.4%

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

   3. Taylor expanded in z around inf 80.0%

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

   if -185 < z < 41000

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 80.2%

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

      1. *-commutative 80.2%

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

   5. Simplified 80.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -185 \lor \neg \left(z \leq 41000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 7 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.4e+110)
   (/ t b)
   (if (<= z -1.65e+62)
     (/ x (- z))
     (if (or (<= z -9.5e-153) (not (<= z 7e-11))) (/ t b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.4e+110) {
		tmp = t / b;
	} else if (z <= -1.65e+62) {
		tmp = x / -z;
	} else if ((z <= -9.5e-153) || !(z <= 7e-11)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.4d+110)) then
        tmp = t / b
    else if (z <= (-1.65d+62)) then
        tmp = x / -z
    else if ((z <= (-9.5d-153)) .or. (.not. (z <= 7d-11))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.4e+110) {
		tmp = t / b;
	} else if (z <= -1.65e+62) {
		tmp = x / -z;
	} else if ((z <= -9.5e-153) || !(z <= 7e-11)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.4e+110:
		tmp = t / b
	elif z <= -1.65e+62:
		tmp = x / -z
	elif (z <= -9.5e-153) or not (z <= 7e-11):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.4e+110)
		tmp = Float64(t / b);
	elseif (z <= -1.65e+62)
		tmp = Float64(x / Float64(-z));
	elseif ((z <= -9.5e-153) || !(z <= 7e-11))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.4e+110)
		tmp = t / b;
	elseif (z <= -1.65e+62)
		tmp = x / -z;
	elseif ((z <= -9.5e-153) || ~((z <= 7e-11)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.4e+110], N[(t / b), $MachinePrecision], If[LessEqual[z, -1.65e+62], N[(x / (-z)), $MachinePrecision], If[Or[LessEqual[z, -9.5e-153], N[Not[LessEqual[z, 7e-11]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000012e110 or -1.65e62 < z < -9.50000000000000031e-153 or 7.00000000000000038e-11 < z

   1. Initial program 53.8%

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

   3. Taylor expanded in a around 0 38.9%

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

   4. Taylor expanded in y around 0 34.9%

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

   if -2.40000000000000012e110 < z < -1.65e62

   1. Initial program 48.5%

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

   3. Taylor expanded in x around inf 8.7%

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

      1. *-commutative 8.7%

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

   5. Simplified 8.7%

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

   6. Taylor expanded in z around inf 8.7%

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

   7. Taylor expanded in y around inf 43.3%

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

      1. associate-*r/ 43.3%

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

      2. mul-1-neg 43.3%

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

   9. Simplified 43.3%

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

   if -9.50000000000000031e-153 < z < 7.00000000000000038e-11

   1. Initial program 81.1%

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

   3. Taylor expanded in z around 0 58.0%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+110}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 7 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-160} \lor \neg \left(z \leq 0.0038\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-160) (not (<= z 0.0038)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-160) || !(z <= 0.0038)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.05d-160)) .or. (.not. (z <= 0.0038d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-160) || !(z <= 0.0038)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-160) or not (z <= 0.0038):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-160) || !(z <= 0.0038))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-160) || ~((z <= 0.0038)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-160], N[Not[LessEqual[z, 0.0038]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-160 or 0.00379999999999999999 < z

   1. Initial program 52.4%

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

   3. Taylor expanded in z around inf 71.7%

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

   if -1.05e-160 < z < 0.00379999999999999999

   1. Initial program 82.3%

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

   3. Taylor expanded in b around inf 80.8%

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

      1. *-commutative 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in b around 0 67.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-160} \lor \neg \left(z \leq 0.0038\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 44000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e-153) (not (<= z 44000.0)))
   (/ (- t a) (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 44000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.5d-153)) .or. (.not. (z <= 44000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 44000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e-153) or not (z <= 44000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e-153) || !(z <= 44000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e-153) || ~((z <= 44000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e-153], N[Not[LessEqual[z, 44000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000031e-153 or 44000 < z

   1. Initial program 52.1%

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

   3. Taylor expanded in z around inf 72.9%

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

   if -9.50000000000000031e-153 < z < 44000

   1. Initial program 81.9%

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

   3. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   5. Simplified 56.8%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 44000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+56} \lor \neg \left(y \leq 6.5 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -6.3e+56) (not (<= y 6.5e+63))) (/ 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 <= -6.3e+56) || !(y <= 6.5e+63)) {
		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 <= (-6.3d+56)) .or. (.not. (y <= 6.5d+63))) 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 <= -6.3e+56) || !(y <= 6.5e+63)) {
		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 <= -6.3e+56) or not (y <= 6.5e+63):
		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 <= -6.3e+56) || !(y <= 6.5e+63))
		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 <= -6.3e+56) || ~((y <= 6.5e+63)))
		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, -6.3e+56], N[Not[LessEqual[y, 6.5e+63]], $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 < -6.3000000000000001e56 or 6.49999999999999992e63 < y

   1. Initial program 48.8%

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

   3. Taylor expanded in y around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. unsub-neg 59.4%

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

   5. Simplified 59.4%

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

   if -6.3000000000000001e56 < y < 6.49999999999999992e63

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 56.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+56} \lor \neg \left(y \leq 6.5 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 1.2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e-153) (not (<= z 1.2e-7))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 1.2e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.5d-153)) .or. (.not. (z <= 1.2d-7))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-153) || !(z <= 1.2e-7)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e-153) or not (z <= 1.2e-7):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e-153) || !(z <= 1.2e-7))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e-153) || ~((z <= 1.2e-7)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e-153], N[Not[LessEqual[z, 1.2e-7]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000031e-153 or 1.19999999999999989e-7 < z

   1. Initial program 53.2%

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

   3. Taylor expanded in a around 0 37.7%

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

   4. Taylor expanded in y around 0 32.2%

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

   if -9.50000000000000031e-153 < z < 1.19999999999999989e-7

   1. Initial program 81.1%

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

   3. Taylor expanded in z around 0 58.0%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-153} \lor \neg \left(z \leq 1.2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.3% 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 63.0%

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

3. Taylor expanded in z around 0 25.1%

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

4. Final simplification 25.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.6% 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 2024053 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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