Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.6% → 98.0%

Time: 20.1s

Alternatives: 19

Speedup: 0.9×

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: 66.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := {\left(b - y\right)}^{2}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{x \cdot y + t\_4}{t\_1}\\ t_6 := \frac{x}{1 - z} + t\_3\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_5 \leq 0:\\ \;\;\;\;t\_3 + \frac{\frac{x \cdot y}{b - y} - \frac{y}{\frac{t\_2}{t - a}}}{z}\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_4}{t\_1}\\ \mathbf{elif}\;t\_5 \leq \infty:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;\left(t\_3 + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (pow (- b y) 2.0))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (* z (- t a)))
        (t_5 (/ (+ (* x y) t_4) t_1))
        (t_6 (+ (/ x (- 1.0 z)) t_3)))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -5e-287)
       t_5
       (if (<= t_5 0.0)
         (+ t_3 (/ (- (/ (* x y) (- b y)) (/ y (/ t_2 (- t a)))) z))
         (if (<= t_5 2e+290)
           (+ (/ (* x y) t_1) (/ t_4 t_1))
           (if (<= t_5 INFINITY)
             t_6
             (+
              (+ t_3 (* (/ y z) (/ x (- b y))))
              (* (/ y z) (/ (- a t) 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 = pow((b - y), 2.0);
	double t_3 = (t - a) / (b - y);
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double t_6 = (x / (1.0 - z)) + t_3;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -5e-287) {
		tmp = t_5;
	} else if (t_5 <= 0.0) {
		tmp = t_3 + ((((x * y) / (b - y)) - (y / (t_2 / (t - a)))) / z);
	} else if (t_5 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_6;
	} else {
		tmp = (t_3 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / t_2));
	}
	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 = Math.pow((b - y), 2.0);
	double t_3 = (t - a) / (b - y);
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double t_6 = (x / (1.0 - z)) + t_3;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else if (t_5 <= -5e-287) {
		tmp = t_5;
	} else if (t_5 <= 0.0) {
		tmp = t_3 + ((((x * y) / (b - y)) - (y / (t_2 / (t - a)))) / z);
	} else if (t_5 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	} else if (t_5 <= Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else {
		tmp = (t_3 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / t_2));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = math.pow((b - y), 2.0)
	t_3 = (t - a) / (b - y)
	t_4 = z * (t - a)
	t_5 = ((x * y) + t_4) / t_1
	t_6 = (x / (1.0 - z)) + t_3
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_6
	elif t_5 <= -5e-287:
		tmp = t_5
	elif t_5 <= 0.0:
		tmp = t_3 + ((((x * y) / (b - y)) - (y / (t_2 / (t - a)))) / z)
	elif t_5 <= 2e+290:
		tmp = ((x * y) / t_1) + (t_4 / t_1)
	elif t_5 <= math.inf:
		tmp = t_6
	else:
		tmp = (t_3 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / 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(b - y) ^ 2.0
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(z * Float64(t - a))
	t_5 = Float64(Float64(Float64(x * y) + t_4) / t_1)
	t_6 = Float64(Float64(x / Float64(1.0 - z)) + t_3)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -5e-287)
		tmp = t_5;
	elseif (t_5 <= 0.0)
		tmp = Float64(t_3 + Float64(Float64(Float64(Float64(x * y) / Float64(b - y)) - Float64(y / Float64(t_2 / Float64(t - a)))) / z));
	elseif (t_5 <= 2e+290)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_4 / t_1));
	elseif (t_5 <= Inf)
		tmp = t_6;
	else
		tmp = Float64(Float64(t_3 + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) + Float64(Float64(y / z) * Float64(Float64(a - t) / t_2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (b - y) ^ 2.0;
	t_3 = (t - a) / (b - y);
	t_4 = z * (t - a);
	t_5 = ((x * y) + t_4) / t_1;
	t_6 = (x / (1.0 - z)) + t_3;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_6;
	elseif (t_5 <= -5e-287)
		tmp = t_5;
	elseif (t_5 <= 0.0)
		tmp = t_3 + ((((x * y) / (b - y)) - (y / (t_2 / (t - a)))) / z);
	elseif (t_5 <= 2e+290)
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	elseif (t_5 <= Inf)
		tmp = t_6;
	else
		tmp = (t_3 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / t_2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -5e-287], t$95$5, If[LessEqual[t$95$5, 0.0], N[(t$95$3 + N[(N[(N[(N[(x * y), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$2 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 2e+290], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, Infinity], t$95$6, N[(N[(t$95$3 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 27.7%

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

   3. Taylor expanded in x around 0 27.7%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. neg-mul-1 61.7%

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

      2. sub-neg 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in z around inf 96.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287

   1. Initial program 99.0%

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

   if -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 37.3%

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

   3. Taylor expanded in z around -inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-lft-out-- 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   5. Simplified 100.0%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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 x around 0 99.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 31.4%

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

      1. associate--r+ 31.4%

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

      2. +-commutative 31.4%

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

      3. associate--l+ 31.4%

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

      4. *-commutative 31.4%

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

      5. times-frac 45.6%

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

      6. div-sub 45.6%

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

      7. times-frac 99.7%

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

   5. Simplified 99.7%

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{x \cdot y}{b - y} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \left(t\_2 + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ t_4 := z \cdot \left(t - a\right)\\ t_5 := \frac{x \cdot y + t\_4}{t\_1}\\ t_6 := \frac{x}{1 - z} + t\_2\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_5 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_5 \leq 0:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_4}{t\_1}\\ \mathbf{elif}\;t\_5 \leq \infty:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3
         (+
          (+ t_2 (* (/ y z) (/ x (- b y))))
          (* (/ y z) (/ (- a t) (pow (- b y) 2.0)))))
        (t_4 (* z (- t a)))
        (t_5 (/ (+ (* x y) t_4) t_1))
        (t_6 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_5 (- INFINITY))
     t_6
     (if (<= t_5 -5e-287)
       t_5
       (if (<= t_5 0.0)
         t_3
         (if (<= t_5 2e+290)
           (+ (/ (* x y) t_1) (/ t_4 t_1))
           (if (<= t_5 INFINITY) t_6 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double t_6 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_6;
	} else if (t_5 <= -5e-287) {
		tmp = t_5;
	} else if (t_5 <= 0.0) {
		tmp = t_3;
	} else if (t_5 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_6;
	} else {
		tmp = t_3;
	}
	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 = (t - a) / (b - y);
	double t_3 = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	double t_4 = z * (t - a);
	double t_5 = ((x * y) + t_4) / t_1;
	double t_6 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else if (t_5 <= -5e-287) {
		tmp = t_5;
	} else if (t_5 <= 0.0) {
		tmp = t_3;
	} else if (t_5 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	} else if (t_5 <= Double.POSITIVE_INFINITY) {
		tmp = t_6;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	t_4 = z * (t - a)
	t_5 = ((x * y) + t_4) / t_1
	t_6 = (x / (1.0 - z)) + t_2
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_6
	elif t_5 <= -5e-287:
		tmp = t_5
	elif t_5 <= 0.0:
		tmp = t_3
	elif t_5 <= 2e+290:
		tmp = ((x * y) / t_1) + (t_4 / t_1)
	elif t_5 <= math.inf:
		tmp = t_6
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(t_2 + Float64(Float64(y / z) * Float64(x / Float64(b - y)))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))))
	t_4 = Float64(z * Float64(t - a))
	t_5 = Float64(Float64(Float64(x * y) + t_4) / t_1)
	t_6 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_6;
	elseif (t_5 <= -5e-287)
		tmp = t_5;
	elseif (t_5 <= 0.0)
		tmp = t_3;
	elseif (t_5 <= 2e+290)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_4 / t_1));
	elseif (t_5 <= Inf)
		tmp = t_6;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = (t_2 + ((y / z) * (x / (b - y)))) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	t_4 = z * (t - a);
	t_5 = ((x * y) + t_4) / t_1;
	t_6 = (x / (1.0 - z)) + t_2;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_6;
	elseif (t_5 <= -5e-287)
		tmp = t_5;
	elseif (t_5 <= 0.0)
		tmp = t_3;
	elseif (t_5 <= 2e+290)
		tmp = ((x * y) / t_1) + (t_4 / t_1);
	elseif (t_5 <= Inf)
		tmp = t_6;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x * y), $MachinePrecision] + t$95$4), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$6, If[LessEqual[t$95$5, -5e-287], t$95$5, If[LessEqual[t$95$5, 0.0], t$95$3, If[LessEqual[t$95$5, 2e+290], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, Infinity], t$95$6, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 27.7%

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

   3. Taylor expanded in x around 0 27.7%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. neg-mul-1 61.7%

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

      2. sub-neg 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in z around inf 96.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287

   1. Initial program 99.0%

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

   if -5.00000000000000025e-287 < (/.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 10.1%

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

   3. Taylor expanded in z around inf 41.0%

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

      1. associate--r+ 41.0%

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

      2. +-commutative 41.0%

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

      3. associate--l+ 41.0%

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

      4. *-commutative 41.0%

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

      5. times-frac 60.3%

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

      6. div-sub 60.3%

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

      7. times-frac 99.7%

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

   5. Simplified 99.7%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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 x around 0 99.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t - a}{b - y} + \frac{y}{z} \cdot \frac{x}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{t\_1}\\ t_4 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} + \frac{y \cdot a}{{\left(b - y\right)}^{2}}}{z} - \frac{a}{b - y}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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))
        (t_4 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -5e-287)
       t_3
       (if (<= t_3 0.0)
         (-
          (/ (+ (/ x (/ (- b y) y)) (/ (* y a) (pow (- b y) 2.0))) z)
          (/ a (- b y)))
         (if (<= t_3 2e+290) (+ (/ (* x y) t_1) (/ t_2 t_1)) t_4))))))

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 t_4 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -5e-287) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (((x / ((b - y) / y)) + ((y * a) / pow((b - y), 2.0))) / z) - (a / (b - y));
	} else if (t_3 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_4;
	}
	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 t_4 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -5e-287) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (((x / ((b - y) / y)) + ((y * a) / Math.pow((b - y), 2.0))) / z) - (a / (b - y));
	} else if (t_3 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_4;
	}
	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
	t_4 = (x / (1.0 - z)) + ((t - a) / (b - y))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -5e-287:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (((x / ((b - y) / y)) + ((y * a) / math.pow((b - y), 2.0))) / z) - (a / (b - y))
	elif t_3 <= 2e+290:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	else:
		tmp = t_4
	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)
	t_4 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -5e-287)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) + Float64(Float64(y * a) / (Float64(b - y) ^ 2.0))) / z) - Float64(a / Float64(b - y)));
	elseif (t_3 <= 2e+290)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	else
		tmp = t_4;
	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;
	t_4 = (x / (1.0 - z)) + ((t - a) / (b - y));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -5e-287)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (((x / ((b - y) / y)) + ((y * a) / ((b - y) ^ 2.0))) / z) - (a / (b - y));
	elseif (t_3 <= 2e+290)
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	else
		tmp = t_4;
	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]}, Block[{t$95$4 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -5e-287], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+290], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.9%

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

   3. Taylor expanded in x around 0 15.9%

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

   4. Taylor expanded in y around inf 42.3%

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

      1. neg-mul-1 42.3%

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

      2. sub-neg 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in z around inf 93.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287

   1. Initial program 99.0%

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

   if -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 37.3%

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

   3. Taylor expanded in t around 0 37.3%

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

      1. +-commutative 37.3%

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

      2. mul-1-neg 37.3%

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

      3. unsub-neg 37.3%

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

      4. *-commutative 37.3%

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

      5. *-commutative 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in z around -inf 85.1%

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

      1. distribute-lft-out 85.1%

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

      2. mul-1-neg 85.1%

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

      3. associate-/l* 85.1%

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

   8. Simplified 85.1%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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 x around 0 99.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} + \frac{y \cdot a}{{\left(b - y\right)}^{2}}}{z} - \frac{a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{t\_1}\\ t_4 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{t\_1} + \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

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))
        (t_4 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -5e-287)
       t_3
       (if (<= t_3 0.0)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= t_3 2e+290) (+ (/ (* x y) t_1) (/ t_2 t_1)) t_4))))))

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 t_4 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -5e-287) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_3 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_4;
	}
	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 t_4 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -5e-287) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_3 <= 2e+290) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else {
		tmp = t_4;
	}
	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
	t_4 = (x / (1.0 - z)) + ((t - a) / (b - y))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -5e-287:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif t_3 <= 2e+290:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	else:
		tmp = t_4
	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)
	t_4 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -5e-287)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (t_3 <= 2e+290)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	else
		tmp = t_4;
	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;
	t_4 = (x / (1.0 - z)) + ((t - a) / (b - y));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -5e-287)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (t_3 <= 2e+290)
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	else
		tmp = t_4;
	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]}, Block[{t$95$4 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -5e-287], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$3, 2e+290], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.9%

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

   3. Taylor expanded in x around 0 15.9%

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

   4. Taylor expanded in y around inf 42.3%

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

      1. neg-mul-1 42.3%

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

      2. sub-neg 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in z around inf 93.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287

   1. Initial program 99.0%

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

   if -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 37.3%

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

   3. Taylor expanded in x around 0 37.3%

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

   4. Taylor expanded in b around inf 77.8%

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

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   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 x around 0 99.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-287)
       t_1
       (if (<= t_1 0.0)
         (/ (- (+ t (/ (* x y) z)) a) b)
         (if (<= t_1 2e+290) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-287) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -5e-287) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((t + ((x * y) / z)) - a) / b;
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -5e-287:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((t + ((x * y) / z)) - a) / b
	elif t_1 <= 2e+290:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e-287)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(t + Float64(Float64(x * y) / z)) - a) / b);
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = (x / (1.0 - z)) + ((t - a) / (b - y));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -5e-287)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((t + ((x * y) / z)) - a) / b;
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-287], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], t$95$1, t$95$2]]]]]]

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 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.9%

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

   3. Taylor expanded in x around 0 15.9%

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

   4. Taylor expanded in y around inf 42.3%

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

      1. neg-mul-1 42.3%

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

      2. sub-neg 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in z around inf 93.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.00000000000000025e-287 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   1. Initial program 99.4%

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

   if -5.00000000000000025e-287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 37.3%

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

   3. Taylor expanded in x around 0 37.3%

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

   4. Taylor expanded in b around inf 77.8%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\left(t + \frac{x \cdot y}{z}\right) - a}{b}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x}{1 - z}\\ t_4 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;t\_3 + t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;t\_3 + \frac{t\_4}{y}\\ \mathbf{elif}\;z \leq 0.082:\\ \;\;\;\;\frac{t\_4}{t\_1}\\ \mathbf{elif}\;z \leq 750:\\ \;\;\;\;\frac{x \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ x (- 1.0 z)))
        (t_4 (* z (- t a))))
   (if (<= z -0.05)
     (+ t_3 t_2)
     (if (<= z 1.1e-73)
       (+ t_3 (/ t_4 y))
       (if (<= z 0.082) (/ t_4 t_1) (if (<= z 750.0) (/ (* x y) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = x / (1.0 - z);
	double t_4 = z * (t - a);
	double tmp;
	if (z <= -0.05) {
		tmp = t_3 + t_2;
	} else if (z <= 1.1e-73) {
		tmp = t_3 + (t_4 / y);
	} else if (z <= 0.082) {
		tmp = t_4 / t_1;
	} else if (z <= 750.0) {
		tmp = (x * y) / 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    t_3 = x / (1.0d0 - z)
    t_4 = z * (t - a)
    if (z <= (-0.05d0)) then
        tmp = t_3 + t_2
    else if (z <= 1.1d-73) then
        tmp = t_3 + (t_4 / y)
    else if (z <= 0.082d0) then
        tmp = t_4 / t_1
    else if (z <= 750.0d0) then
        tmp = (x * y) / t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = x / (1.0 - z);
	double t_4 = z * (t - a);
	double tmp;
	if (z <= -0.05) {
		tmp = t_3 + t_2;
	} else if (z <= 1.1e-73) {
		tmp = t_3 + (t_4 / y);
	} else if (z <= 0.082) {
		tmp = t_4 / t_1;
	} else if (z <= 750.0) {
		tmp = (x * y) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = x / (1.0 - z)
	t_4 = z * (t - a)
	tmp = 0
	if z <= -0.05:
		tmp = t_3 + t_2
	elif z <= 1.1e-73:
		tmp = t_3 + (t_4 / y)
	elif z <= 0.082:
		tmp = t_4 / t_1
	elif z <= 750.0:
		tmp = (x * y) / t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(x / Float64(1.0 - z))
	t_4 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -0.05)
		tmp = Float64(t_3 + t_2);
	elseif (z <= 1.1e-73)
		tmp = Float64(t_3 + Float64(t_4 / y));
	elseif (z <= 0.082)
		tmp = Float64(t_4 / t_1);
	elseif (z <= 750.0)
		tmp = Float64(Float64(x * y) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = x / (1.0 - z);
	t_4 = z * (t - a);
	tmp = 0.0;
	if (z <= -0.05)
		tmp = t_3 + t_2;
	elseif (z <= 1.1e-73)
		tmp = t_3 + (t_4 / y);
	elseif (z <= 0.082)
		tmp = t_4 / t_1;
	elseif (z <= 750.0)
		tmp = (x * y) / t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.05], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[z, 1.1e-73], N[(t$95$3 + N[(t$95$4 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.082], N[(t$95$4 / t$95$1), $MachinePrecision], If[LessEqual[z, 750.0], N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.050000000000000003

   1. Initial program 52.7%

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

   3. Taylor expanded in x around 0 52.7%

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

   4. Taylor expanded in y around inf 52.9%

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

      1. neg-mul-1 52.9%

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

      2. sub-neg 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in z around inf 85.9%

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

   if -0.050000000000000003 < z < 1.1e-73

   1. Initial program 86.4%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in y around inf 85.3%

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

      1. neg-mul-1 85.3%

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

      2. sub-neg 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in z around 0 77.3%

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

   if 1.1e-73 < z < 0.0820000000000000034

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 63.7%

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

   if 0.0820000000000000034 < z < 750

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   if 750 < z

   1. Initial program 44.9%

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

   3. Taylor expanded in z around inf 82.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 0.082:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 750:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x}{1 - z}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;t\_2 + t\_4\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-73}:\\ \;\;\;\;t\_2 + \frac{1}{\frac{y}{t\_3}}\\ \mathbf{elif}\;z \leq 0.045:\\ \;\;\;\;\frac{t\_3}{t\_1}\\ \mathbf{elif}\;z \leq 42000:\\ \;\;\;\;\frac{x \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ x (- 1.0 z)))
        (t_3 (* z (- t a)))
        (t_4 (/ (- t a) (- b y))))
   (if (<= z -0.05)
     (+ t_2 t_4)
     (if (<= z 1.55e-73)
       (+ t_2 (/ 1.0 (/ y t_3)))
       (if (<= z 0.045)
         (/ t_3 t_1)
         (if (<= z 42000.0) (/ (* x y) t_1) t_4))))))

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 / (1.0 - z);
	double t_3 = z * (t - a);
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.05) {
		tmp = t_2 + t_4;
	} else if (z <= 1.55e-73) {
		tmp = t_2 + (1.0 / (y / t_3));
	} else if (z <= 0.045) {
		tmp = t_3 / t_1;
	} else if (z <= 42000.0) {
		tmp = (x * y) / t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = x / (1.0d0 - z)
    t_3 = z * (t - a)
    t_4 = (t - a) / (b - y)
    if (z <= (-0.05d0)) then
        tmp = t_2 + t_4
    else if (z <= 1.55d-73) then
        tmp = t_2 + (1.0d0 / (y / t_3))
    else if (z <= 0.045d0) then
        tmp = t_3 / t_1
    else if (z <= 42000.0d0) then
        tmp = (x * y) / t_1
    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 = y + (z * (b - y));
	double t_2 = x / (1.0 - z);
	double t_3 = z * (t - a);
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.05) {
		tmp = t_2 + t_4;
	} else if (z <= 1.55e-73) {
		tmp = t_2 + (1.0 / (y / t_3));
	} else if (z <= 0.045) {
		tmp = t_3 / t_1;
	} else if (z <= 42000.0) {
		tmp = (x * y) / t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = x / (1.0 - z)
	t_3 = z * (t - a)
	t_4 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.05:
		tmp = t_2 + t_4
	elif z <= 1.55e-73:
		tmp = t_2 + (1.0 / (y / t_3))
	elif z <= 0.045:
		tmp = t_3 / t_1
	elif z <= 42000.0:
		tmp = (x * y) / t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(x / Float64(1.0 - z))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.05)
		tmp = Float64(t_2 + t_4);
	elseif (z <= 1.55e-73)
		tmp = Float64(t_2 + Float64(1.0 / Float64(y / t_3)));
	elseif (z <= 0.045)
		tmp = Float64(t_3 / t_1);
	elseif (z <= 42000.0)
		tmp = Float64(Float64(x * y) / t_1);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = x / (1.0 - z);
	t_3 = z * (t - a);
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.05)
		tmp = t_2 + t_4;
	elseif (z <= 1.55e-73)
		tmp = t_2 + (1.0 / (y / t_3));
	elseif (z <= 0.045)
		tmp = t_3 / t_1;
	elseif (z <= 42000.0)
		tmp = (x * y) / t_1;
	else
		tmp = t_4;
	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[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.05], N[(t$95$2 + t$95$4), $MachinePrecision], If[LessEqual[z, 1.55e-73], N[(t$95$2 + N[(1.0 / N[(y / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.045], N[(t$95$3 / t$95$1), $MachinePrecision], If[LessEqual[z, 42000.0], N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.050000000000000003

   1. Initial program 52.7%

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

   3. Taylor expanded in x around 0 52.7%

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

   4. Taylor expanded in y around inf 52.9%

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

      1. neg-mul-1 52.9%

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

      2. sub-neg 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in z around inf 85.9%

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

   if -0.050000000000000003 < z < 1.54999999999999985e-73

   1. Initial program 86.4%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in y around inf 85.3%

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

      1. neg-mul-1 85.3%

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

      2. sub-neg 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in z around 0 77.3%

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

      1. clear-num 77.3%

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

      2. inv-pow 77.3%

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

      3. *-commutative 77.3%

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

   9. Applied egg-rr 77.3%

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

       1. unpow-1 77.3%

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

   11. Simplified 77.3%

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

   if 1.54999999999999985e-73 < z < 0.044999999999999998

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 63.7%

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

   if 0.044999999999999998 < z < 42000

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   if 42000 < z

   1. Initial program 44.9%

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

   3. Taylor expanded in z around inf 82.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{1}{\frac{y}{z \cdot \left(t - a\right)}}\\ \mathbf{elif}\;z \leq 0.045:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 42000:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.3 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e-13) (not (<= z 1.3e+17)))
   (+ (/ x (- 1.0 z)) (/ (- 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 <= -2.4e-13) || !(z <= 1.3e+17)) {
		tmp = (x / (1.0 - z)) + ((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 <= (-2.4d-13)) .or. (.not. (z <= 1.3d+17))) then
        tmp = (x / (1.0d0 - z)) + ((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 <= -2.4e-13) || !(z <= 1.3e+17)) {
		tmp = (x / (1.0 - z)) + ((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 <= -2.4e-13) or not (z <= 1.3e+17):
		tmp = (x / (1.0 - z)) + ((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 <= -2.4e-13) || !(z <= 1.3e+17))
		tmp = Float64(Float64(x / Float64(1.0 - z)) + 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 <= -2.4e-13) || ~((z <= 1.3e+17)))
		tmp = (x / (1.0 - z)) + ((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, -2.4e-13], N[Not[LessEqual[z, 1.3e+17]], $MachinePrecision]], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $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 < -2.3999999999999999e-13 or 1.3e17 < z

   1. Initial program 46.0%

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

   3. Taylor expanded in x around 0 46.0%

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

   4. Taylor expanded in y around inf 46.3%

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

      1. neg-mul-1 46.3%

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

      2. sub-neg 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in z around inf 83.1%

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

   if -2.3999999999999999e-13 < z < 1.3e17

   1. Initial program 89.2%

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

   3. Taylor expanded in b around inf 87.4%

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

      1. *-commutative 87.4%

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

   5. Simplified 87.4%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-13} \lor \neg \left(z \leq 1.3 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+185} \lor \neg \left(z \leq 2.6 \cdot 10^{+272}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e+34)
   (/ a y)
   (if (<= z 2.5e-14)
     x
     (if (or (<= z 1.75e+185) (not (<= z 2.6e+272))) (/ t b) (/ a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+34) {
		tmp = a / y;
	} else if (z <= 2.5e-14) {
		tmp = x;
	} else if ((z <= 1.75e+185) || !(z <= 2.6e+272)) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8.5d+34)) then
        tmp = a / y
    else if (z <= 2.5d-14) then
        tmp = x
    else if ((z <= 1.75d+185) .or. (.not. (z <= 2.6d+272))) then
        tmp = t / b
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+34) {
		tmp = a / y;
	} else if (z <= 2.5e-14) {
		tmp = x;
	} else if ((z <= 1.75e+185) || !(z <= 2.6e+272)) {
		tmp = t / b;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.5e+34:
		tmp = a / y
	elif z <= 2.5e-14:
		tmp = x
	elif (z <= 1.75e+185) or not (z <= 2.6e+272):
		tmp = t / b
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e+34)
		tmp = Float64(a / y);
	elseif (z <= 2.5e-14)
		tmp = x;
	elseif ((z <= 1.75e+185) || !(z <= 2.6e+272))
		tmp = Float64(t / b);
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.5e+34)
		tmp = a / y;
	elseif (z <= 2.5e-14)
		tmp = x;
	elseif ((z <= 1.75e+185) || ~((z <= 2.6e+272)))
		tmp = t / b;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e+34], N[(a / y), $MachinePrecision], If[LessEqual[z, 2.5e-14], x, If[Or[LessEqual[z, 1.75e+185], N[Not[LessEqual[z, 2.6e+272]], $MachinePrecision]], N[(t / b), $MachinePrecision], N[(a / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000003e34 or 1.75000000000000012e185 < z < 2.59999999999999999e272

   1. Initial program 42.0%

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

   3. Taylor expanded in t around 0 27.3%

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

      1. +-commutative 27.3%

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

      2. mul-1-neg 27.3%

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

      3. unsub-neg 27.3%

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

      4. *-commutative 27.3%

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

      5. *-commutative 27.3%

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

   5. Simplified 27.3%

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

   6. Taylor expanded in z around inf 51.1%

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

      1. associate-*r/ 51.1%

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

      2. neg-mul-1 51.1%

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

   8. Simplified 51.1%

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

   9. Taylor expanded in b around 0 36.2%

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

   if -8.5000000000000003e34 < z < 2.5000000000000001e-14

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 47.3%

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

   if 2.5000000000000001e-14 < z < 1.75000000000000012e185 or 2.59999999999999999e272 < z

   1. Initial program 57.6%

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

   3. Taylor expanded in t around inf 25.9%

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

      1. *-commutative 25.9%

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

   5. Simplified 25.9%

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

   6. Taylor expanded in y around 0 30.8%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+185} \lor \neg \left(z \leq 2.6 \cdot 10^{+272}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+22} \lor \neg \left(z \leq 3.9 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4e+22) (not (<= z 3.9e-26)))
   (/ (- t a) (- b y))
   (+ (/ x (- 1.0 z)) (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e+22) || !(z <= 3.9e-26)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + ((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 <= (-4d+22)) .or. (.not. (z <= 3.9d-26))) then
        tmp = (t - a) / (b - y)
    else
        tmp = (x / (1.0d0 - z)) + ((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 <= -4e+22) || !(z <= 3.9e-26)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4e+22) or not (z <= 3.9e-26):
		tmp = (t - a) / (b - y)
	else:
		tmp = (x / (1.0 - z)) + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4e+22) || !(z <= 3.9e-26))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(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 <= -4e+22) || ~((z <= 3.9e-26)))
		tmp = (t - a) / (b - y);
	else
		tmp = (x / (1.0 - z)) + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4e+22], N[Not[LessEqual[z, 3.9e-26]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e22 or 3.89999999999999986e-26 < z

   1. Initial program 50.9%

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

   3. Taylor expanded in z around inf 81.2%

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

   if -4e22 < z < 3.89999999999999986e-26

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0 86.6%

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

   4. Taylor expanded in y around inf 82.3%

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

      1. neg-mul-1 82.3%

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

      2. sub-neg 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in z around 0 73.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+22} \lor \neg \left(z \leq 3.9 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -0.078 \lor \neg \left(z \leq 1.9 \cdot 10^{-26}\right):\\ \;\;\;\;t\_1 + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (or (<= z -0.078) (not (<= z 1.9e-26)))
     (+ t_1 (/ (- t a) (- b y)))
     (+ t_1 (/ (* z (- t a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if ((z <= -0.078) || !(z <= 1.9e-26)) {
		tmp = t_1 + ((t - a) / (b - y));
	} else {
		tmp = t_1 + ((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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if ((z <= (-0.078d0)) .or. (.not. (z <= 1.9d-26))) then
        tmp = t_1 + ((t - a) / (b - y))
    else
        tmp = t_1 + ((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 t_1 = x / (1.0 - z);
	double tmp;
	if ((z <= -0.078) || !(z <= 1.9e-26)) {
		tmp = t_1 + ((t - a) / (b - y));
	} else {
		tmp = t_1 + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if (z <= -0.078) or not (z <= 1.9e-26):
		tmp = t_1 + ((t - a) / (b - y))
	else:
		tmp = t_1 + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if ((z <= -0.078) || !(z <= 1.9e-26))
		tmp = Float64(t_1 + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(t_1 + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if ((z <= -0.078) || ~((z <= 1.9e-26)))
		tmp = t_1 + ((t - a) / (b - y));
	else
		tmp = t_1 + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -0.078], N[Not[LessEqual[z, 1.9e-26]], $MachinePrecision]], N[(t$95$1 + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0779999999999999999 or 1.90000000000000007e-26 < z

   1. Initial program 51.4%

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

   3. Taylor expanded in x around 0 51.4%

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

   4. Taylor expanded in y around inf 47.9%

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

      1. neg-mul-1 47.9%

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

      2. sub-neg 47.9%

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

   6. Simplified 47.9%

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

   7. Taylor expanded in z around inf 81.5%

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

   if -0.0779999999999999999 < z < 1.90000000000000007e-26

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 87.6%

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

   4. Taylor expanded in y around inf 82.3%

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

      1. neg-mul-1 82.3%

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

      2. sub-neg 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in z around 0 74.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.078 \lor \neg \left(z \leq 1.9 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+35}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+164}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.1e+35)
   (/ (- a) (- b y))
   (if (<= z 6.6e-80)
     (/ x (- 1.0 z))
     (if (<= z 1.25e+164) (/ (- t a) b) (/ t (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.1e+35) {
		tmp = -a / (b - y);
	} else if (z <= 6.6e-80) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.25e+164) {
		tmp = (t - a) / b;
	} else {
		tmp = t / (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 <= (-3.1d+35)) then
        tmp = -a / (b - y)
    else if (z <= 6.6d-80) then
        tmp = x / (1.0d0 - z)
    else if (z <= 1.25d+164) then
        tmp = (t - a) / b
    else
        tmp = t / (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 <= -3.1e+35) {
		tmp = -a / (b - y);
	} else if (z <= 6.6e-80) {
		tmp = x / (1.0 - z);
	} else if (z <= 1.25e+164) {
		tmp = (t - a) / b;
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.1e+35:
		tmp = -a / (b - y)
	elif z <= 6.6e-80:
		tmp = x / (1.0 - z)
	elif z <= 1.25e+164:
		tmp = (t - a) / b
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.1e+35)
		tmp = Float64(Float64(-a) / Float64(b - y));
	elseif (z <= 6.6e-80)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (z <= 1.25e+164)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.1e+35)
		tmp = -a / (b - y);
	elseif (z <= 6.6e-80)
		tmp = x / (1.0 - z);
	elseif (z <= 1.25e+164)
		tmp = (t - a) / b;
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.1e+35], N[((-a) / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-80], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+164], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.09999999999999987e35

   1. Initial program 50.4%

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

   3. Taylor expanded in t around 0 32.6%

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

      1. +-commutative 32.6%

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

      2. mul-1-neg 32.6%

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

      3. unsub-neg 32.6%

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

      4. *-commutative 32.6%

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

      5. *-commutative 32.6%

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

   5. Simplified 32.6%

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

   6. Taylor expanded in z around inf 51.9%

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

      1. associate-*r/ 51.9%

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

      2. neg-mul-1 51.9%

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

   8. Simplified 51.9%

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

   if -3.09999999999999987e35 < z < 6.5999999999999999e-80

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. unsub-neg 53.5%

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

   5. Simplified 53.5%

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

   if 6.5999999999999999e-80 < z < 1.24999999999999987e164

   1. Initial program 78.0%

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

   3. Taylor expanded in y around 0 47.5%

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

   if 1.24999999999999987e164 < z

   1. Initial program 25.2%

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

   3. Taylor expanded in t around inf 17.1%

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

      1. *-commutative 17.1%

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

   5. Simplified 17.1%

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

   6. Taylor expanded in z around inf 50.1%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+35}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+164}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.05 \lor \neg \left(z \leq 1.14 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.05) (not (<= z 1.14e-29)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.05) || !(z <= 1.14e-29)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.05d0)) .or. (.not. (z <= 1.14d-29))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.05) || !(z <= 1.14e-29)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.05) or not (z <= 1.14e-29):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.05) || !(z <= 1.14e-29))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(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 <= -0.05) || ~((z <= 1.14e-29)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.05], N[Not[LessEqual[z, 1.14e-29]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.050000000000000003 or 1.13999999999999995e-29 < z

   1. Initial program 51.4%

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

   3. Taylor expanded in z around inf 79.3%

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

   if -0.050000000000000003 < z < 1.13999999999999995e-29

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 87.6%

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

   4. Taylor expanded in y around inf 82.3%

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

      1. neg-mul-1 82.3%

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

      2. sub-neg 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in z around 0 74.2%

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

   8. Taylor expanded in z around 0 74.1%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05 \lor \neg \left(z \leq 1.14 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+23} \lor \neg \left(z \leq 1.6 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e+23) (not (<= z 1.6e-73)))
   (/ (- 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 <= -8e+23) || !(z <= 1.6e-73)) {
		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 <= (-8d+23)) .or. (.not. (z <= 1.6d-73))) 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 <= -8e+23) || !(z <= 1.6e-73)) {
		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 <= -8e+23) or not (z <= 1.6e-73):
		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 <= -8e+23) || !(z <= 1.6e-73))
		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 <= -8e+23) || ~((z <= 1.6e-73)))
		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, -8e+23], N[Not[LessEqual[z, 1.6e-73]], $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 < -7.9999999999999993e23 or 1.59999999999999993e-73 < z

   1. Initial program 55.0%

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

   3. Taylor expanded in z around inf 76.6%

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

   if -7.9999999999999993e23 < z < 1.59999999999999993e-73

   1. Initial program 84.9%

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

   3. Taylor expanded in y around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. unsub-neg 53.9%

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

   5. Simplified 53.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+23} \lor \neg \left(z \leq 1.6 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-19} \lor \neg \left(z \leq 1.4 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e-19) (not (<= z 1.4e-10))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e-19) || !(z <= 1.4e-10)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.7d-19)) .or. (.not. (z <= 1.4d-10))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e-19) || !(z <= 1.4e-10)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.7e-19) or not (z <= 1.4e-10):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.7e-19) || !(z <= 1.4e-10))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.7e-19) || ~((z <= 1.4e-10)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.7e-19], N[Not[LessEqual[z, 1.4e-10]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.7000000000000001e-19 or 1.40000000000000008e-10 < z

   1. Initial program 51.0%

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

   3. Taylor expanded in t around inf 23.4%

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

      1. *-commutative 23.4%

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

   5. Simplified 23.4%

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

   6. Taylor expanded in z around inf 42.0%

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

   if -1.7000000000000001e-19 < z < 1.40000000000000008e-10

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 50.8%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-19} \lor \neg \left(z \leq 1.4 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+29} \lor \neg \left(z \leq 1.7 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.2e+29) (not (<= z 1.7e-6))) (/ t (- 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 <= -5.2e+29) || !(z <= 1.7e-6)) {
		tmp = t / (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 <= (-5.2d+29)) .or. (.not. (z <= 1.7d-6))) then
        tmp = t / (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 <= -5.2e+29) || !(z <= 1.7e-6)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.2e+29) or not (z <= 1.7e-6):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.2e+29) || !(z <= 1.7e-6))
		tmp = Float64(t / 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 <= -5.2e+29) || ~((z <= 1.7e-6)))
		tmp = t / (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, -5.2e+29], N[Not[LessEqual[z, 1.7e-6]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e29 or 1.70000000000000003e-6 < z

   1. Initial program 49.6%

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

   3. Taylor expanded in t around inf 23.7%

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

      1. *-commutative 23.7%

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

   5. Simplified 23.7%

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

   6. Taylor expanded in z around inf 44.1%

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

   if -5.2e29 < z < 1.70000000000000003e-6

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf 49.7%

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

      1. mul-1-neg 49.7%

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

      2. unsub-neg 49.7%

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

   5. Simplified 49.7%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+29} \lor \neg \left(z \leq 1.7 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-34} \lor \neg \left(y \leq 1.9 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.6e-34) (not (<= y 1.9e-35))) (/ 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 <= -5.6e-34) || !(y <= 1.9e-35)) {
		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 <= (-5.6d-34)) .or. (.not. (y <= 1.9d-35))) 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 <= -5.6e-34) || !(y <= 1.9e-35)) {
		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 <= -5.6e-34) or not (y <= 1.9e-35):
		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 <= -5.6e-34) || !(y <= 1.9e-35))
		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 <= -5.6e-34) || ~((y <= 1.9e-35)))
		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, -5.6e-34], N[Not[LessEqual[y, 1.9e-35]], $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 < -5.59999999999999994e-34 or 1.9000000000000001e-35 < y

   1. Initial program 59.7%

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

   3. Taylor expanded in y around inf 45.9%

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

      1. mul-1-neg 45.9%

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

      2. unsub-neg 45.9%

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

   5. Simplified 45.9%

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

   if -5.59999999999999994e-34 < y < 1.9000000000000001e-35

   1. Initial program 84.5%

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

   3. Taylor expanded in y around 0 55.7%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-34} \lor \neg \left(y \leq 1.9 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34} \lor \neg \left(z \leq 0.082\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e+34) (not (<= z 0.082))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e+34) || !(z <= 0.082)) {
		tmp = a / y;
	} 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 <= (-8.5d+34)) .or. (.not. (z <= 0.082d0))) then
        tmp = a / y
    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 <= -8.5e+34) || !(z <= 0.082)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e+34) or not (z <= 0.082):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e+34) || !(z <= 0.082))
		tmp = Float64(a / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e+34) || ~((z <= 0.082)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e+34], N[Not[LessEqual[z, 0.082]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000003e34 or 0.0820000000000000034 < z

   1. Initial program 48.4%

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

   3. Taylor expanded in t around 0 31.3%

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

      1. +-commutative 31.3%

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

      2. mul-1-neg 31.3%

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

      3. unsub-neg 31.3%

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

      4. *-commutative 31.3%

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

      5. *-commutative 31.3%

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

   5. Simplified 31.3%

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

   6. Taylor expanded in z around inf 45.1%

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

      1. associate-*r/ 45.1%

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

      2. neg-mul-1 45.1%

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

   8. Simplified 45.1%

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

   9. Taylor expanded in b around 0 26.4%

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

   if -8.5000000000000003e34 < z < 0.0820000000000000034

   1. Initial program 86.7%

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

   3. Taylor expanded in z around 0 46.7%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+34} \lor \neg \left(z \leq 0.082\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.5%

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

3. Taylor expanded in z around 0 27.1%

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

4. Final simplification 27.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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