Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.0% → 94.3%

Time: 26.7s

Alternatives: 25

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: 66.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(y - b\right) - y\\ t_2 := z \cdot \left(a - t\right) - y \cdot x\\ t_3 := \frac{t\_2}{t\_1}\\ t_4 := \frac{a - t}{y - b}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;z \cdot \frac{a - t}{t\_1} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\frac{t\_2}{\left(z \cdot y - z \cdot b\right) - y}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_4 + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* z (- y b)) y))
        (t_2 (- (* z (- a t)) (* y x)))
        (t_3 (/ t_2 t_1))
        (t_4 (/ (- a t) (- y b))))
   (if (<= t_3 (- INFINITY))
     (+ (* z (/ (- a t) t_1)) (* x (/ y (+ y (* z (- b y))))))
     (if (<= t_3 -2e-294)
       (/ t_2 (- (- (* z y) (* z b)) y))
       (if (<= t_3 0.0)
         (+ t_4 (/ 1.0 (/ (- 1.0 z) x)))
         (if (<= t_3 2e+297) t_3 (+ t_4 (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y - b)) - y;
	double t_2 = (z * (a - t)) - (y * x);
	double t_3 = t_2 / t_1;
	double t_4 = (a - t) / (y - b);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (z * ((a - t) / t_1)) + (x * (y / (y + (z * (b - y)))));
	} else if (t_3 <= -2e-294) {
		tmp = t_2 / (((z * y) - (z * b)) - y);
	} else if (t_3 <= 0.0) {
		tmp = t_4 + (1.0 / ((1.0 - z) / x));
	} else if (t_3 <= 2e+297) {
		tmp = t_3;
	} else {
		tmp = t_4 + (x / (1.0 - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (y - b)) - y;
	double t_2 = (z * (a - t)) - (y * x);
	double t_3 = t_2 / t_1;
	double t_4 = (a - t) / (y - b);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (z * ((a - t) / t_1)) + (x * (y / (y + (z * (b - y)))));
	} else if (t_3 <= -2e-294) {
		tmp = t_2 / (((z * y) - (z * b)) - y);
	} else if (t_3 <= 0.0) {
		tmp = t_4 + (1.0 / ((1.0 - z) / x));
	} else if (t_3 <= 2e+297) {
		tmp = t_3;
	} else {
		tmp = t_4 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (y - b)) - y
	t_2 = (z * (a - t)) - (y * x)
	t_3 = t_2 / t_1
	t_4 = (a - t) / (y - b)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (z * ((a - t) / t_1)) + (x * (y / (y + (z * (b - y)))))
	elif t_3 <= -2e-294:
		tmp = t_2 / (((z * y) - (z * b)) - y)
	elif t_3 <= 0.0:
		tmp = t_4 + (1.0 / ((1.0 - z) / x))
	elif t_3 <= 2e+297:
		tmp = t_3
	else:
		tmp = t_4 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(y - b)) - y)
	t_2 = Float64(Float64(z * Float64(a - t)) - Float64(y * x))
	t_3 = Float64(t_2 / t_1)
	t_4 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(z * Float64(Float64(a - t) / t_1)) + Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y))))));
	elseif (t_3 <= -2e-294)
		tmp = Float64(t_2 / Float64(Float64(Float64(z * y) - Float64(z * b)) - y));
	elseif (t_3 <= 0.0)
		tmp = Float64(t_4 + Float64(1.0 / Float64(Float64(1.0 - z) / x)));
	elseif (t_3 <= 2e+297)
		tmp = t_3;
	else
		tmp = Float64(t_4 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (y - b)) - y;
	t_2 = (z * (a - t)) - (y * x);
	t_3 = t_2 / t_1;
	t_4 = (a - t) / (y - b);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (z * ((a - t) / t_1)) + (x * (y / (y + (z * (b - y)))));
	elseif (t_3 <= -2e-294)
		tmp = t_2 / (((z * y) - (z * b)) - y);
	elseif (t_3 <= 0.0)
		tmp = t_4 + (1.0 / ((1.0 - z) / x));
	elseif (t_3 <= 2e+297)
		tmp = t_3;
	else
		tmp = t_4 + (x / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(z * N[(N[(a - t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -2e-294], N[(t$95$2 / N[(N[(N[(z * y), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t$95$4 + N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+297], t$95$3, N[(t$95$4 + N[(x / N[(1.0 - z), $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

   1. Initial program 24.8%

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

   3. Simplified 24.8%

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

   5. Taylor expanded in a around 0 23.5%

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

      1. +-commutative 23.5%

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

      2. mul-1-neg 23.5%

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

      3. unsub-neg 23.5%

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

      4. div-sub 23.5%

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

      5. unsub-neg 23.5%

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

      6. distribute-lft-neg-out 23.5%

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

      7. distribute-rgt-out 24.8%

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

      8. sub-neg 24.8%

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

      9. associate-/l* 49.6%

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

      10. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000003e-294

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -2.00000000000000003e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in a around 0 24.7%

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

      1. +-commutative 24.7%

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

      2. mul-1-neg 24.7%

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

      3. unsub-neg 24.7%

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

      4. div-sub 24.7%

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

      5. unsub-neg 24.7%

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

      6. distribute-lft-neg-out 24.7%

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

      7. distribute-rgt-out 24.7%

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

      8. sub-neg 24.7%

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

      9. associate-/l* 31.4%

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

      10. associate-*r/ 32.5%

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

   7. Simplified 32.5%

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

   8. Taylor expanded in z around inf 57.5%

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

   9. Taylor expanded in y around inf 71.8%

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

       1. clear-num 72.3%

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

       2. inv-pow 72.3%

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

       3. sub-neg 72.3%

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

       4. metadata-eval 72.3%

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

   11. Applied egg-rr 72.3%

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

       1. unpow-1 72.3%

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

       2. +-commutative 72.3%

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

   13. Simplified 72.3%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e297

   1. Initial program 99.5%

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

   if 2e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.2%

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

   3. Simplified 16.2%

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

   5. Taylor expanded in a around 0 14.3%

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

      1. +-commutative 14.3%

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

      2. mul-1-neg 14.3%

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

      3. unsub-neg 14.3%

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

      4. div-sub 16.1%

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

      5. unsub-neg 16.1%

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

      6. distribute-lft-neg-out 16.1%

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

      7. distribute-rgt-out 16.2%

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

      8. sub-neg 16.2%

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

      9. associate-/l* 32.4%

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

      10. associate-*r/ 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in z around inf 86.1%

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

   9. Taylor expanded in y around inf 93.2%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -\infty:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{\left(z \cdot y - z \cdot b\right) - y}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 0:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+14} \lor \neg \left(z \leq 135000000000\right):\\ \;\;\;\;\frac{a - t}{y - b} + \frac{\left(a - t\right) \cdot \frac{y}{{\left(y - b\right)}^{2}} + x \cdot \frac{y}{b - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e+14) (not (<= z 135000000000.0)))
   (+
    (/ (- a t) (- y b))
    (/ (+ (* (- a t) (/ y (pow (- y b) 2.0))) (* x (/ y (- b y)))) z))
   (+ (/ (* z (- a t)) (- (* z (- y b)) y)) (* x (/ y (+ y (* z (- b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e+14) || !(z <= 135000000000.0)) {
		tmp = ((a - t) / (y - b)) + ((((a - t) * (y / pow((y - b), 2.0))) + (x * (y / (b - y)))) / z);
	} else {
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2d+14)) .or. (.not. (z <= 135000000000.0d0))) then
        tmp = ((a - t) / (y - b)) + ((((a - t) * (y / ((y - b) ** 2.0d0))) + (x * (y / (b - y)))) / z)
    else
        tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e+14) || !(z <= 135000000000.0)) {
		tmp = ((a - t) / (y - b)) + ((((a - t) * (y / Math.pow((y - b), 2.0))) + (x * (y / (b - y)))) / z);
	} else {
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e+14) or not (z <= 135000000000.0):
		tmp = ((a - t) / (y - b)) + ((((a - t) * (y / math.pow((y - b), 2.0))) + (x * (y / (b - y)))) / z)
	else:
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e+14) || !(z <= 135000000000.0))
		tmp = Float64(Float64(Float64(a - t) / Float64(y - b)) + Float64(Float64(Float64(Float64(a - t) * Float64(y / (Float64(y - b) ^ 2.0))) + Float64(x * Float64(y / Float64(b - y)))) / z));
	else
		tmp = Float64(Float64(Float64(z * Float64(a - t)) / Float64(Float64(z * Float64(y - b)) - y)) + Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e+14) || ~((z <= 135000000000.0)))
		tmp = ((a - t) / (y - b)) + ((((a - t) * (y / ((y - b) ^ 2.0))) + (x * (y / (b - y)))) / z);
	else
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e+14], N[Not[LessEqual[z, 135000000000.0]], $MachinePrecision]], N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(a - t), $MachinePrecision] * N[(y / N[Power[N[(y - b), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e14 or 1.35e11 < z

   1. Initial program 48.2%

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

   3. Simplified 48.2%

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

   5. Taylor expanded in z around inf 67.8%

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

   7. Simplified 93.4%

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

   if -2e14 < z < 1.35e11

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

      1. div-sub 83.7%

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

      2. associate-/l* 96.6%

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

   6. Applied egg-rr 96.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+14} \lor \neg \left(z \leq 135000000000\right):\\ \;\;\;\;\frac{a - t}{y - b} + \frac{\left(a - t\right) \cdot \frac{y}{{\left(y - b\right)}^{2}} + x \cdot \frac{y}{b - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ t_2 := \frac{a - t}{y - b}\\ t_3 := t\_2 + \frac{x}{1 - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+302}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t\_2 + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* z (- a t)) (* y x)) (- (* z (- y b)) y)))
        (t_2 (/ (- a t) (- y b)))
        (t_3 (+ t_2 (/ x (- 1.0 z)))))
   (if (<= t_1 -5e+302)
     t_3
     (if (<= t_1 -2e-294)
       t_1
       (if (<= t_1 0.0)
         (+ t_2 (/ 1.0 (/ (- 1.0 z) x)))
         (if (<= t_1 2e+297) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y);
	double t_2 = (a - t) / (y - b);
	double t_3 = t_2 + (x / (1.0 - z));
	double tmp;
	if (t_1 <= -5e+302) {
		tmp = t_3;
	} else if (t_1 <= -2e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2 + (1.0 / ((1.0 - z) / x));
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y)
    t_2 = (a - t) / (y - b)
    t_3 = t_2 + (x / (1.0d0 - z))
    if (t_1 <= (-5d+302)) then
        tmp = t_3
    else if (t_1 <= (-2d-294)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t_2 + (1.0d0 / ((1.0d0 - z) / x))
    else if (t_1 <= 2d+297) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y);
	double t_2 = (a - t) / (y - b);
	double t_3 = t_2 + (x / (1.0 - z));
	double tmp;
	if (t_1 <= -5e+302) {
		tmp = t_3;
	} else if (t_1 <= -2e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2 + (1.0 / ((1.0 - z) / x));
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y)
	t_2 = (a - t) / (y - b)
	t_3 = t_2 + (x / (1.0 - z))
	tmp = 0
	if t_1 <= -5e+302:
		tmp = t_3
	elif t_1 <= -2e-294:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t_2 + (1.0 / ((1.0 - z) / x))
	elif t_1 <= 2e+297:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(a - t)) - Float64(y * x)) / Float64(Float64(z * Float64(y - b)) - y))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	t_3 = Float64(t_2 + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= -5e+302)
		tmp = t_3;
	elseif (t_1 <= -2e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t_2 + Float64(1.0 / Float64(Float64(1.0 - z) / x)));
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y);
	t_2 = (a - t) / (y - b);
	t_3 = t_2 + (x / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= -5e+302)
		tmp = t_3;
	elseif (t_1 <= -2e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2 + (1.0 / ((1.0 - z) / x));
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+302], t$95$3, If[LessEqual[t$95$1, -2e-294], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t$95$2 + N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+297], t$95$1, t$95$3]]]]]]]

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)))) < -5e302 or 2e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.8%

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

   3. Simplified 19.8%

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

   5. Taylor expanded in a around 0 18.2%

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

      1. +-commutative 18.2%

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

      2. mul-1-neg 18.2%

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

      3. unsub-neg 18.2%

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

      4. div-sub 19.4%

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

      5. unsub-neg 19.4%

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

      6. distribute-lft-neg-out 19.4%

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

      7. distribute-rgt-out 19.8%

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

      8. sub-neg 19.8%

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

      9. associate-/l* 38.6%

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

      10. associate-*r/ 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in z around inf 89.4%

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

   9. Taylor expanded in y around inf 93.0%

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

   if -5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000003e-294 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e297

   1. Initial program 99.6%

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

   if -2.00000000000000003e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in a around 0 24.7%

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

      1. +-commutative 24.7%

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

      2. mul-1-neg 24.7%

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

      3. unsub-neg 24.7%

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

      4. div-sub 24.7%

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

      5. unsub-neg 24.7%

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

      6. distribute-lft-neg-out 24.7%

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

      7. distribute-rgt-out 24.7%

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

      8. sub-neg 24.7%

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

      9. associate-/l* 31.4%

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

      10. associate-*r/ 32.5%

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

   7. Simplified 32.5%

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

   8. Taylor expanded in z around inf 57.5%

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

   9. Taylor expanded in y around inf 71.8%

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

       1. clear-num 72.3%

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

       2. inv-pow 72.3%

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

       3. sub-neg 72.3%

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

       4. metadata-eval 72.3%

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

   11. Applied egg-rr 72.3%

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

       1. unpow-1 72.3%

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

       2. +-commutative 72.3%

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

   13. Simplified 72.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -5 \cdot 10^{+302}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 0:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ t_2 := \frac{a - t}{y - b}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+251}:\\ \;\;\;\;t\_2 + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t\_2 + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* z (- a t)) (* y x)) (- (* z (- y b)) y)))
        (t_2 (/ (- a t) (- y b))))
   (if (<= t_1 -1e+251)
     (+ t_2 (* x (/ y (+ y (* z (- b y))))))
     (if (<= t_1 -2e-294)
       t_1
       (if (<= t_1 0.0)
         (+ t_2 (/ 1.0 (/ (- 1.0 z) x)))
         (if (<= t_1 2e+297) t_1 (+ t_2 (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y);
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (t_1 <= -1e+251) {
		tmp = t_2 + (x * (y / (y + (z * (b - y)))));
	} else if (t_1 <= -2e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2 + (1.0 / ((1.0 - z) / x));
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = t_2 + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y)
    t_2 = (a - t) / (y - b)
    if (t_1 <= (-1d+251)) then
        tmp = t_2 + (x * (y / (y + (z * (b - y)))))
    else if (t_1 <= (-2d-294)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t_2 + (1.0d0 / ((1.0d0 - z) / x))
    else if (t_1 <= 2d+297) then
        tmp = t_1
    else
        tmp = t_2 + (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 t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y);
	double t_2 = (a - t) / (y - b);
	double tmp;
	if (t_1 <= -1e+251) {
		tmp = t_2 + (x * (y / (y + (z * (b - y)))));
	} else if (t_1 <= -2e-294) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_2 + (1.0 / ((1.0 - z) / x));
	} else if (t_1 <= 2e+297) {
		tmp = t_1;
	} else {
		tmp = t_2 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y)
	t_2 = (a - t) / (y - b)
	tmp = 0
	if t_1 <= -1e+251:
		tmp = t_2 + (x * (y / (y + (z * (b - y)))))
	elif t_1 <= -2e-294:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t_2 + (1.0 / ((1.0 - z) / x))
	elif t_1 <= 2e+297:
		tmp = t_1
	else:
		tmp = t_2 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(a - t)) - Float64(y * x)) / Float64(Float64(z * Float64(y - b)) - y))
	t_2 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (t_1 <= -1e+251)
		tmp = Float64(t_2 + Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y))))));
	elseif (t_1 <= -2e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t_2 + Float64(1.0 / Float64(Float64(1.0 - z) / x)));
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (a - t)) - (y * x)) / ((z * (y - b)) - y);
	t_2 = (a - t) / (y - b);
	tmp = 0.0;
	if (t_1 <= -1e+251)
		tmp = t_2 + (x * (y / (y + (z * (b - y)))));
	elseif (t_1 <= -2e-294)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_2 + (1.0 / ((1.0 - z) / x));
	elseif (t_1 <= 2e+297)
		tmp = t_1;
	else
		tmp = t_2 + (x / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+251], N[(t$95$2 + N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-294], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t$95$2 + N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+297], t$95$1, N[(t$95$2 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e251

   1. Initial program 38.7%

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

   3. Simplified 38.7%

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

   5. Taylor expanded in a around 0 37.7%

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

      1. +-commutative 37.7%

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

      2. mul-1-neg 37.7%

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

      3. unsub-neg 37.7%

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

      4. div-sub 37.7%

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

      5. unsub-neg 37.7%

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

      6. distribute-lft-neg-out 37.7%

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

      7. distribute-rgt-out 38.7%

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

      8. sub-neg 38.7%

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

      9. associate-/l* 58.9%

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

      10. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 96.8%

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

   if -1e251 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000003e-294 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e297

   1. Initial program 99.6%

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

   if -2.00000000000000003e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in a around 0 24.7%

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

      1. +-commutative 24.7%

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

      2. mul-1-neg 24.7%

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

      3. unsub-neg 24.7%

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

      4. div-sub 24.7%

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

      5. unsub-neg 24.7%

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

      6. distribute-lft-neg-out 24.7%

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

      7. distribute-rgt-out 24.7%

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

      8. sub-neg 24.7%

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

      9. associate-/l* 31.4%

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

      10. associate-*r/ 32.5%

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

   7. Simplified 32.5%

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

   8. Taylor expanded in z around inf 57.5%

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

   9. Taylor expanded in y around inf 71.8%

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

       1. clear-num 72.3%

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

       2. inv-pow 72.3%

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

       3. sub-neg 72.3%

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

       4. metadata-eval 72.3%

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

   11. Applied egg-rr 72.3%

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

       1. unpow-1 72.3%

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

       2. +-commutative 72.3%

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

   13. Simplified 72.3%

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

   if 2e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.2%

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

   3. Simplified 16.2%

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

   5. Taylor expanded in a around 0 14.3%

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

      1. +-commutative 14.3%

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

      2. mul-1-neg 14.3%

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

      3. unsub-neg 14.3%

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

      4. div-sub 16.1%

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

      5. unsub-neg 16.1%

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

      6. distribute-lft-neg-out 16.1%

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

      7. distribute-rgt-out 16.2%

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

      8. sub-neg 16.2%

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

      9. associate-/l* 32.4%

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

      10. associate-*r/ 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in z around inf 86.1%

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

   9. Taylor expanded in y around inf 93.2%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -1 \cdot 10^{+251}:\\ \;\;\;\;\frac{a - t}{y - b} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 0:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a - t\right) - y \cdot x\\ t_2 := \frac{t\_1}{z \cdot \left(y - b\right) - y}\\ t_3 := \frac{a - t}{y - b}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+302}:\\ \;\;\;\;t\_3 + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\frac{t\_1}{\left(z \cdot y - z \cdot b\right) - y}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_3 + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 + \frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (* z (- a t)) (* y x)))
        (t_2 (/ t_1 (- (* z (- y b)) y)))
        (t_3 (/ (- a t) (- y b))))
   (if (<= t_2 -5e+302)
     (+ t_3 (* x (/ y (+ y (* z (- b y))))))
     (if (<= t_2 -2e-294)
       (/ t_1 (- (- (* z y) (* z b)) y))
       (if (<= t_2 0.0)
         (+ t_3 (/ 1.0 (/ (- 1.0 z) x)))
         (if (<= t_2 2e+297) t_2 (+ t_3 (/ x (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * (a - t)) - (y * x);
	double t_2 = t_1 / ((z * (y - b)) - y);
	double t_3 = (a - t) / (y - b);
	double tmp;
	if (t_2 <= -5e+302) {
		tmp = t_3 + (x * (y / (y + (z * (b - y)))));
	} else if (t_2 <= -2e-294) {
		tmp = t_1 / (((z * y) - (z * b)) - y);
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (1.0 / ((1.0 - z) / x));
	} else if (t_2 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = t_3 + (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * (a - t)) - (y * x)
    t_2 = t_1 / ((z * (y - b)) - y)
    t_3 = (a - t) / (y - b)
    if (t_2 <= (-5d+302)) then
        tmp = t_3 + (x * (y / (y + (z * (b - y)))))
    else if (t_2 <= (-2d-294)) then
        tmp = t_1 / (((z * y) - (z * b)) - y)
    else if (t_2 <= 0.0d0) then
        tmp = t_3 + (1.0d0 / ((1.0d0 - z) / x))
    else if (t_2 <= 2d+297) then
        tmp = t_2
    else
        tmp = t_3 + (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 t_1 = (z * (a - t)) - (y * x);
	double t_2 = t_1 / ((z * (y - b)) - y);
	double t_3 = (a - t) / (y - b);
	double tmp;
	if (t_2 <= -5e+302) {
		tmp = t_3 + (x * (y / (y + (z * (b - y)))));
	} else if (t_2 <= -2e-294) {
		tmp = t_1 / (((z * y) - (z * b)) - y);
	} else if (t_2 <= 0.0) {
		tmp = t_3 + (1.0 / ((1.0 - z) / x));
	} else if (t_2 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = t_3 + (x / (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * (a - t)) - (y * x)
	t_2 = t_1 / ((z * (y - b)) - y)
	t_3 = (a - t) / (y - b)
	tmp = 0
	if t_2 <= -5e+302:
		tmp = t_3 + (x * (y / (y + (z * (b - y)))))
	elif t_2 <= -2e-294:
		tmp = t_1 / (((z * y) - (z * b)) - y)
	elif t_2 <= 0.0:
		tmp = t_3 + (1.0 / ((1.0 - z) / x))
	elif t_2 <= 2e+297:
		tmp = t_2
	else:
		tmp = t_3 + (x / (1.0 - z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(a - t)) - Float64(y * x))
	t_2 = Float64(t_1 / Float64(Float64(z * Float64(y - b)) - y))
	t_3 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (t_2 <= -5e+302)
		tmp = Float64(t_3 + Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y))))));
	elseif (t_2 <= -2e-294)
		tmp = Float64(t_1 / Float64(Float64(Float64(z * y) - Float64(z * b)) - y));
	elseif (t_2 <= 0.0)
		tmp = Float64(t_3 + Float64(1.0 / Float64(Float64(1.0 - z) / x)));
	elseif (t_2 <= 2e+297)
		tmp = t_2;
	else
		tmp = Float64(t_3 + Float64(x / Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * (a - t)) - (y * x);
	t_2 = t_1 / ((z * (y - b)) - y);
	t_3 = (a - t) / (y - b);
	tmp = 0.0;
	if (t_2 <= -5e+302)
		tmp = t_3 + (x * (y / (y + (z * (b - y)))));
	elseif (t_2 <= -2e-294)
		tmp = t_1 / (((z * y) - (z * b)) - y);
	elseif (t_2 <= 0.0)
		tmp = t_3 + (1.0 / ((1.0 - z) / x));
	elseif (t_2 <= 2e+297)
		tmp = t_2;
	else
		tmp = t_3 + (x / (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+302], N[(t$95$3 + N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-294], N[(t$95$1 / N[(N[(N[(z * y), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t$95$3 + N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+297], t$95$2, N[(t$95$3 + N[(x / N[(1.0 - z), $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)))) < -5e302

   1. Initial program 27.5%

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

   3. Simplified 27.5%

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

   5. Taylor expanded in a around 0 26.3%

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

      1. +-commutative 26.3%

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

      2. mul-1-neg 26.3%

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

      3. unsub-neg 26.3%

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

      4. div-sub 26.3%

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

      5. unsub-neg 26.3%

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

      6. distribute-lft-neg-out 26.3%

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

      7. distribute-rgt-out 27.5%

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

      8. sub-neg 27.5%

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

      9. associate-/l* 51.4%

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

      10. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 96.3%

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

   if -5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000003e-294

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-lft-in 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -2.00000000000000003e-294 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in a around 0 24.7%

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

      1. +-commutative 24.7%

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

      2. mul-1-neg 24.7%

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

      3. unsub-neg 24.7%

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

      4. div-sub 24.7%

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

      5. unsub-neg 24.7%

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

      6. distribute-lft-neg-out 24.7%

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

      7. distribute-rgt-out 24.7%

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

      8. sub-neg 24.7%

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

      9. associate-/l* 31.4%

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

      10. associate-*r/ 32.5%

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

   7. Simplified 32.5%

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

   8. Taylor expanded in z around inf 57.5%

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

   9. Taylor expanded in y around inf 71.8%

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

       1. clear-num 72.3%

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

       2. inv-pow 72.3%

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

       3. sub-neg 72.3%

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

       4. metadata-eval 72.3%

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

   11. Applied egg-rr 72.3%

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

       1. unpow-1 72.3%

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

       2. +-commutative 72.3%

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

   13. Simplified 72.3%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e297

   1. Initial program 99.5%

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

   if 2e297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 16.2%

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

   3. Simplified 16.2%

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

   5. Taylor expanded in a around 0 14.3%

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

      1. +-commutative 14.3%

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

      2. mul-1-neg 14.3%

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

      3. unsub-neg 14.3%

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

      4. div-sub 16.1%

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

      5. unsub-neg 16.1%

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

      6. distribute-lft-neg-out 16.1%

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

      7. distribute-rgt-out 16.2%

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

      8. sub-neg 16.2%

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

      9. associate-/l* 32.4%

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

      10. associate-*r/ 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in z around inf 86.1%

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

   9. Taylor expanded in y around inf 93.2%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -5 \cdot 10^{+302}:\\ \;\;\;\;\frac{a - t}{y - b} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq -2 \cdot 10^{-294}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{\left(z \cdot y - z \cdot b\right) - y}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 0:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{1}{\frac{1 - z}{x}}\\ \mathbf{elif}\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ t_2 := t\_1 + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{1}{\frac{1 - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))) (t_2 (+ t_1 (/ x (- 1.0 z)))))
   (if (<= z -1.5e-89)
     t_2
     (if (<= z -2.8e-150)
       (/ (+ (* y x) (* z (- t a))) (* z b))
       (if (<= z -5.2e-174)
         t_2
         (if (<= z 1.3e-82)
           (* x (/ y (+ y (* z b))))
           (if (<= z 1.36e+17)
             (* z (/ (- a t) (- (* z (- y b)) y)))
             (+ t_1 (/ 1.0 (/ (- 1.0 z) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = t_1 + (x / (1.0 - z));
	double tmp;
	if (z <= -1.5e-89) {
		tmp = t_2;
	} else if (z <= -2.8e-150) {
		tmp = ((y * x) + (z * (t - a))) / (z * b);
	} else if (z <= -5.2e-174) {
		tmp = t_2;
	} else if (z <= 1.3e-82) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 1.36e+17) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    t_2 = t_1 + (x / (1.0d0 - z))
    if (z <= (-1.5d-89)) then
        tmp = t_2
    else if (z <= (-2.8d-150)) then
        tmp = ((y * x) + (z * (t - a))) / (z * b)
    else if (z <= (-5.2d-174)) then
        tmp = t_2
    else if (z <= 1.3d-82) then
        tmp = x * (y / (y + (z * b)))
    else if (z <= 1.36d+17) then
        tmp = z * ((a - t) / ((z * (y - b)) - y))
    else
        tmp = t_1 + (1.0d0 / ((1.0d0 - z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = t_1 + (x / (1.0 - z));
	double tmp;
	if (z <= -1.5e-89) {
		tmp = t_2;
	} else if (z <= -2.8e-150) {
		tmp = ((y * x) + (z * (t - a))) / (z * b);
	} else if (z <= -5.2e-174) {
		tmp = t_2;
	} else if (z <= 1.3e-82) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 1.36e+17) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	t_2 = t_1 + (x / (1.0 - z))
	tmp = 0
	if z <= -1.5e-89:
		tmp = t_2
	elif z <= -2.8e-150:
		tmp = ((y * x) + (z * (t - a))) / (z * b)
	elif z <= -5.2e-174:
		tmp = t_2
	elif z <= 1.3e-82:
		tmp = x * (y / (y + (z * b)))
	elif z <= 1.36e+17:
		tmp = z * ((a - t) / ((z * (y - b)) - y))
	else:
		tmp = t_1 + (1.0 / ((1.0 - z) / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	t_2 = Float64(t_1 + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (z <= -1.5e-89)
		tmp = t_2;
	elseif (z <= -2.8e-150)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(z * b));
	elseif (z <= -5.2e-174)
		tmp = t_2;
	elseif (z <= 1.3e-82)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * b))));
	elseif (z <= 1.36e+17)
		tmp = Float64(z * Float64(Float64(a - t) / Float64(Float64(z * Float64(y - b)) - y)));
	else
		tmp = Float64(t_1 + Float64(1.0 / Float64(Float64(1.0 - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	t_2 = t_1 + (x / (1.0 - z));
	tmp = 0.0;
	if (z <= -1.5e-89)
		tmp = t_2;
	elseif (z <= -2.8e-150)
		tmp = ((y * x) + (z * (t - a))) / (z * b);
	elseif (z <= -5.2e-174)
		tmp = t_2;
	elseif (z <= 1.3e-82)
		tmp = x * (y / (y + (z * b)));
	elseif (z <= 1.36e+17)
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	else
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-89], t$95$2, If[LessEqual[z, -2.8e-150], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-174], t$95$2, If[LessEqual[z, 1.3e-82], N[(x * N[(y / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.36e+17], N[(z * N[(N[(a - t), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5e-89 or -2.79999999999999996e-150 < z < -5.2000000000000004e-174

   1. Initial program 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in a around 0 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. div-sub 61.2%

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

      5. unsub-neg 61.2%

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

      6. distribute-lft-neg-out 61.2%

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

      7. distribute-rgt-out 61.4%

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

      8. sub-neg 61.4%

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

      9. associate-/l* 63.0%

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

      10. associate-*r/ 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in z around inf 81.8%

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

   9. Taylor expanded in y around inf 78.2%

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

   if -1.5e-89 < z < -2.79999999999999996e-150

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in b around inf 75.9%

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

      1. associate-*r/ 75.9%

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

      2. *-commutative 75.9%

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

      3. cancel-sign-sub-inv 75.9%

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

      4. *-commutative 75.9%

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

      5. +-commutative 75.9%

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

      6. distribute-lft-in 75.9%

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

      7. neg-mul-1 75.9%

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

      8. distribute-rgt-neg-in 75.9%

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

      9. remove-double-neg 75.9%

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

      10. *-commutative 75.9%

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

      11. neg-mul-1 75.9%

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

      12. unsub-neg 75.9%

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

   7. Simplified 75.9%

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

   if -5.2000000000000004e-174 < z < 1.3e-82

   1. Initial program 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around inf 50.9%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. distribute-neg-frac 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-lft-neg-out 68.8%

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

      3. *-commutative 68.8%

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

   10. Simplified 68.8%

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

   if 1.3e-82 < z < 1.36e17

   1. Initial program 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around 0 81.4%

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

      1. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

   if 1.36e17 < z

   1. Initial program 43.6%

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

   3. Simplified 43.6%

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

   5. Taylor expanded in a around 0 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. div-sub 43.3%

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

      5. unsub-neg 43.3%

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

      6. distribute-lft-neg-out 43.3%

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

      7. distribute-rgt-out 43.6%

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

      8. sub-neg 43.6%

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

      9. associate-/l* 58.1%

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

      10. associate-*r/ 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in z around inf 86.0%

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

   9. Taylor expanded in y around inf 89.8%

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

       1. clear-num 90.0%

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

       2. inv-pow 90.0%

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

       3. sub-neg 90.0%

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

       4. metadata-eval 90.0%

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

   11. Applied egg-rr 90.0%

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

       1. unpow-1 90.0%

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

       2. +-commutative 90.0%

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

   13. Simplified 90.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{1}{\frac{1 - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (- a t) (- y b)) (/ x (- 1.0 z)))))
   (if (<= z -6.2e-93)
     t_1
     (if (<= z -2.8e-150)
       (/ (+ (* y x) (* z (- t a))) (* z b))
       (if (<= z -7.8e-174)
         t_1
         (if (<= z 2.1e-83)
           (* x (/ y (+ y (* z b))))
           (if (<= z 9.2e+17) (* z (/ (- a t) (- (* z (- y b)) y))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (z <= -6.2e-93) {
		tmp = t_1;
	} else if (z <= -2.8e-150) {
		tmp = ((y * x) + (z * (t - a))) / (z * b);
	} else if (z <= -7.8e-174) {
		tmp = t_1;
	} else if (z <= 2.1e-83) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 9.2e+17) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) + (x / (1.0d0 - z))
    if (z <= (-6.2d-93)) then
        tmp = t_1
    else if (z <= (-2.8d-150)) then
        tmp = ((y * x) + (z * (t - a))) / (z * b)
    else if (z <= (-7.8d-174)) then
        tmp = t_1
    else if (z <= 2.1d-83) then
        tmp = x * (y / (y + (z * b)))
    else if (z <= 9.2d+17) then
        tmp = z * ((a - t) / ((z * (y - b)) - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (z <= -6.2e-93) {
		tmp = t_1;
	} else if (z <= -2.8e-150) {
		tmp = ((y * x) + (z * (t - a))) / (z * b);
	} else if (z <= -7.8e-174) {
		tmp = t_1;
	} else if (z <= 2.1e-83) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 9.2e+17) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) + (x / (1.0 - z))
	tmp = 0
	if z <= -6.2e-93:
		tmp = t_1
	elif z <= -2.8e-150:
		tmp = ((y * x) + (z * (t - a))) / (z * b)
	elif z <= -7.8e-174:
		tmp = t_1
	elif z <= 2.1e-83:
		tmp = x * (y / (y + (z * b)))
	elif z <= 9.2e+17:
		tmp = z * ((a - t) / ((z * (y - b)) - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (z <= -6.2e-93)
		tmp = t_1;
	elseif (z <= -2.8e-150)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(z * b));
	elseif (z <= -7.8e-174)
		tmp = t_1;
	elseif (z <= 2.1e-83)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * b))));
	elseif (z <= 9.2e+17)
		tmp = Float64(z * Float64(Float64(a - t) / Float64(Float64(z * Float64(y - b)) - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	tmp = 0.0;
	if (z <= -6.2e-93)
		tmp = t_1;
	elseif (z <= -2.8e-150)
		tmp = ((y * x) + (z * (t - a))) / (z * b);
	elseif (z <= -7.8e-174)
		tmp = t_1;
	elseif (z <= 2.1e-83)
		tmp = x * (y / (y + (z * b)));
	elseif (z <= 9.2e+17)
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-93], t$95$1, If[LessEqual[z, -2.8e-150], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e-174], t$95$1, If[LessEqual[z, 2.1e-83], N[(x * N[(y / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+17], N[(z * N[(N[(a - t), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.19999999999999999e-93 or -2.79999999999999996e-150 < z < -7.7999999999999997e-174 or 9.2e17 < z

   1. Initial program 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in a around 0 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

      4. div-sub 52.6%

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

      5. unsub-neg 52.6%

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

      6. distribute-lft-neg-out 52.6%

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

      7. distribute-rgt-out 52.9%

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

      8. sub-neg 52.9%

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

      9. associate-/l* 60.6%

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

      10. associate-*r/ 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in z around inf 83.8%

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

   9. Taylor expanded in y around inf 83.7%

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

   if -6.19999999999999999e-93 < z < -2.79999999999999996e-150

   1. Initial program 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in b around inf 75.9%

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

      1. associate-*r/ 75.9%

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

      2. *-commutative 75.9%

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

      3. cancel-sign-sub-inv 75.9%

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

      4. *-commutative 75.9%

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

      5. +-commutative 75.9%

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

      6. distribute-lft-in 75.9%

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

      7. neg-mul-1 75.9%

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

      8. distribute-rgt-neg-in 75.9%

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

      9. remove-double-neg 75.9%

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

      10. *-commutative 75.9%

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

      11. neg-mul-1 75.9%

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

      12. unsub-neg 75.9%

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

   7. Simplified 75.9%

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

   if -7.7999999999999997e-174 < z < 2.0999999999999999e-83

   1. Initial program 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around inf 50.9%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. distribute-neg-frac 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-lft-neg-out 68.8%

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

      3. *-commutative 68.8%

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

   10. Simplified 68.8%

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

   if 2.0999999999999999e-83 < z < 9.2e17

   1. Initial program 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around 0 81.4%

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

      1. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+38}:\\ \;\;\;\;t\_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{1}{\frac{1 - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -1.65e+38)
     (- t_1 (/ x z))
     (if (<= z 1.4e+22)
       (+
        (/ (* z (- a t)) (- (* z (- y b)) y))
        (* x (/ y (+ y (* z (- b y))))))
       (+ t_1 (/ 1.0 (/ (- 1.0 z) x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.65e+38) {
		tmp = t_1 - (x / z);
	} else if (z <= 1.4e+22) {
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))));
	} else {
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-1.65d+38)) then
        tmp = t_1 - (x / z)
    else if (z <= 1.4d+22) then
        tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))))
    else
        tmp = t_1 + (1.0d0 / ((1.0d0 - z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -1.65e+38) {
		tmp = t_1 - (x / z);
	} else if (z <= 1.4e+22) {
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))));
	} else {
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -1.65e+38:
		tmp = t_1 - (x / z)
	elif z <= 1.4e+22:
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))))
	else:
		tmp = t_1 + (1.0 / ((1.0 - z) / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -1.65e+38)
		tmp = Float64(t_1 - Float64(x / z));
	elseif (z <= 1.4e+22)
		tmp = Float64(Float64(Float64(z * Float64(a - t)) / Float64(Float64(z * Float64(y - b)) - y)) + Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y))))));
	else
		tmp = Float64(t_1 + Float64(1.0 / Float64(Float64(1.0 - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -1.65e+38)
		tmp = t_1 - (x / z);
	elseif (z <= 1.4e+22)
		tmp = ((z * (a - t)) / ((z * (y - b)) - y)) + (x * (y / (y + (z * (b - y)))));
	else
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+38], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+22], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e38

   1. Initial program 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in a around 0 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

      4. div-sub 49.8%

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

      5. unsub-neg 49.8%

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

      6. distribute-lft-neg-out 49.8%

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

      7. distribute-rgt-out 50.1%

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

      8. sub-neg 50.1%

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

      9. associate-/l* 54.3%

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

      10. associate-*r/ 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in z around inf 84.3%

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

   9. Taylor expanded in y around inf 90.3%

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

   10. Taylor expanded in z around inf 90.3%

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

   if -1.65e38 < z < 1.4e22

   1. Initial program 83.6%

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

   3. Simplified 83.6%

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

      1. div-sub 83.7%

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

      2. associate-/l* 96.1%

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

   6. Applied egg-rr 96.1%

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

   if 1.4e22 < z

   1. Initial program 43.6%

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

   3. Simplified 43.6%

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

   5. Taylor expanded in a around 0 43.3%

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

      1. +-commutative 43.3%

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

      2. mul-1-neg 43.3%

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

      3. unsub-neg 43.3%

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

      4. div-sub 43.3%

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

      5. unsub-neg 43.3%

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

      6. distribute-lft-neg-out 43.3%

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

      7. distribute-rgt-out 43.6%

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

      8. sub-neg 43.6%

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

      9. associate-/l* 58.1%

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

      10. associate-*r/ 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in z around inf 86.0%

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

   9. Taylor expanded in y around inf 89.8%

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

       1. clear-num 90.0%

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

       2. inv-pow 90.0%

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

       3. sub-neg 90.0%

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

       4. metadata-eval 90.0%

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

   11. Applied egg-rr 90.0%

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

       1. unpow-1 90.0%

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

       2. +-commutative 90.0%

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

   13. Simplified 90.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+38}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right)}{z \cdot \left(y - b\right) - y} + x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{1}{\frac{1 - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{a}{y - b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+36}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-248}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 11.2:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ a (- y b))) (t_3 (/ x (- 1.0 z))))
   (if (<= y -2.35e+36)
     t_3
     (if (<= y -2.05e-172)
       t_1
       (if (<= y -1e-248)
         t_2
         (if (<= y 1.75e-268) t_1 (if (<= y 11.2) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = a / (y - b);
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -2.35e+36) {
		tmp = t_3;
	} else if (y <= -2.05e-172) {
		tmp = t_1;
	} else if (y <= -1e-248) {
		tmp = t_2;
	} else if (y <= 1.75e-268) {
		tmp = t_1;
	} else if (y <= 11.2) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = a / (y - b)
    t_3 = x / (1.0d0 - z)
    if (y <= (-2.35d+36)) then
        tmp = t_3
    else if (y <= (-2.05d-172)) then
        tmp = t_1
    else if (y <= (-1d-248)) then
        tmp = t_2
    else if (y <= 1.75d-268) then
        tmp = t_1
    else if (y <= 11.2d0) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = a / (y - b);
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -2.35e+36) {
		tmp = t_3;
	} else if (y <= -2.05e-172) {
		tmp = t_1;
	} else if (y <= -1e-248) {
		tmp = t_2;
	} else if (y <= 1.75e-268) {
		tmp = t_1;
	} else if (y <= 11.2) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = a / (y - b)
	t_3 = x / (1.0 - z)
	tmp = 0
	if y <= -2.35e+36:
		tmp = t_3
	elif y <= -2.05e-172:
		tmp = t_1
	elif y <= -1e-248:
		tmp = t_2
	elif y <= 1.75e-268:
		tmp = t_1
	elif y <= 11.2:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(a / Float64(y - b))
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.35e+36)
		tmp = t_3;
	elseif (y <= -2.05e-172)
		tmp = t_1;
	elseif (y <= -1e-248)
		tmp = t_2;
	elseif (y <= 1.75e-268)
		tmp = t_1;
	elseif (y <= 11.2)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = a / (y - b);
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.35e+36)
		tmp = t_3;
	elseif (y <= -2.05e-172)
		tmp = t_1;
	elseif (y <= -1e-248)
		tmp = t_2;
	elseif (y <= 1.75e-268)
		tmp = t_1;
	elseif (y <= 11.2)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.35e+36], t$95$3, If[LessEqual[y, -2.05e-172], t$95$1, If[LessEqual[y, -1e-248], t$95$2, If[LessEqual[y, 1.75e-268], t$95$1, If[LessEqual[y, 11.2], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.34999999999999994e36 or 11.199999999999999 < y

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   5. Taylor expanded in y around -inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

   7. Simplified 62.4%

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

   if -2.34999999999999994e36 < y < -2.05e-172 or -9.9999999999999998e-249 < y < 1.75000000000000003e-268

   1. Initial program 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in a around 0 79.2%

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

      1. +-commutative 79.2%

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

      2. mul-1-neg 79.2%

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

      3. unsub-neg 79.2%

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

      4. div-sub 80.6%

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

      5. unsub-neg 80.6%

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

      6. distribute-lft-neg-out 80.6%

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

      7. distribute-rgt-out 81.1%

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

      8. sub-neg 81.1%

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

      9. associate-/l* 85.0%

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

      10. associate-*r/ 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in z around inf 81.8%

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

   9. Taylor expanded in y around inf 57.8%

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

   10. Taylor expanded in t around inf 44.7%

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

       1. associate-*r/ 44.7%

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

       2. neg-mul-1 44.7%

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

   12. Simplified 44.7%

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

   if -2.05e-172 < y < -9.9999999999999998e-249 or 1.75000000000000003e-268 < y < 11.199999999999999

   1. Initial program 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in a around inf 41.9%

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

      1. *-commutative 41.9%

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

   7. Simplified 41.9%

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

   8. Taylor expanded in z around inf 46.6%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-172}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-248}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-268}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 11.2:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -1.75e+36)
     t_1
     (if (<= z 1.6e-81)
       (* x (/ y (+ y (* z (- b y)))))
       (if (<= z 2.1e+16) (* z (/ (- a t) (- (* z (- y b)) y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 1.6e-81) {
		tmp = x * (y / (y + (z * (b - y))));
	} else if (z <= 2.1e+16) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-1.75d+36)) then
        tmp = t_1
    else if (z <= 1.6d-81) then
        tmp = x * (y / (y + (z * (b - y))))
    else if (z <= 2.1d+16) then
        tmp = z * ((a - t) / ((z * (y - b)) - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 1.6e-81) {
		tmp = x * (y / (y + (z * (b - y))));
	} else if (z <= 2.1e+16) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -1.75e+36:
		tmp = t_1
	elif z <= 1.6e-81:
		tmp = x * (y / (y + (z * (b - y))))
	elif z <= 2.1e+16:
		tmp = z * ((a - t) / ((z * (y - b)) - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 1.6e-81)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 2.1e+16)
		tmp = Float64(z * Float64(Float64(a - t) / Float64(Float64(z * Float64(y - b)) - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 1.6e-81)
		tmp = x * (y / (y + (z * (b - y))));
	elseif (z <= 2.1e+16)
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+36], t$95$1, If[LessEqual[z, 1.6e-81], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+16], N[(z * N[(N[(a - t), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e36 or 2.1e16 < z

   1. Initial program 46.3%

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

   3. Simplified 46.3%

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

   5. Taylor expanded in a around 0 46.0%

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

      1. +-commutative 46.0%

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

      2. mul-1-neg 46.0%

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

      3. unsub-neg 46.0%

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

      4. div-sub 46.0%

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

      5. unsub-neg 46.0%

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

      6. distribute-lft-neg-out 46.0%

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

      7. distribute-rgt-out 46.3%

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

      8. sub-neg 46.3%

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

      9. associate-/l* 56.5%

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

      10. associate-*r/ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around inf 85.2%

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

   9. Taylor expanded in y around inf 90.0%

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

   10. Taylor expanded in z around inf 90.0%

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

   if -1.7499999999999999e36 < z < 1.6e-81

   1. Initial program 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around inf 48.1%

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

      1. associate-*r/ 62.5%

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

      2. neg-mul-1 62.5%

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

      3. distribute-rgt-neg-in 62.5%

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

      4. distribute-neg-frac 62.5%

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

   7. Simplified 62.5%

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

   if 1.6e-81 < z < 2.1e16

   1. Initial program 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around 0 81.4%

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

      1. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (- a t) (- y b)) (/ x (- 1.0 z)))))
   (if (<= z -7.8e-174)
     t_1
     (if (<= z 9e-85)
       (* x (/ y (+ y (* z b))))
       (if (<= z 2.1e+16) (* z (/ (- a t) (- (* z (- y b)) y))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (z <= -7.8e-174) {
		tmp = t_1;
	} else if (z <= 9e-85) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 2.1e+16) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) + (x / (1.0d0 - z))
    if (z <= (-7.8d-174)) then
        tmp = t_1
    else if (z <= 9d-85) then
        tmp = x * (y / (y + (z * b)))
    else if (z <= 2.1d+16) then
        tmp = z * ((a - t) / ((z * (y - b)) - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	double tmp;
	if (z <= -7.8e-174) {
		tmp = t_1;
	} else if (z <= 9e-85) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 2.1e+16) {
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) + (x / (1.0 - z))
	tmp = 0
	if z <= -7.8e-174:
		tmp = t_1
	elif z <= 9e-85:
		tmp = x * (y / (y + (z * b)))
	elif z <= 2.1e+16:
		tmp = z * ((a - t) / ((z * (y - b)) - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) + Float64(x / Float64(1.0 - z)))
	tmp = 0.0
	if (z <= -7.8e-174)
		tmp = t_1;
	elseif (z <= 9e-85)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * b))));
	elseif (z <= 2.1e+16)
		tmp = Float64(z * Float64(Float64(a - t) / Float64(Float64(z * Float64(y - b)) - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) + (x / (1.0 - z));
	tmp = 0.0;
	if (z <= -7.8e-174)
		tmp = t_1;
	elseif (z <= 9e-85)
		tmp = x * (y / (y + (z * b)));
	elseif (z <= 2.1e+16)
		tmp = z * ((a - t) / ((z * (y - b)) - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-174], t$95$1, If[LessEqual[z, 9e-85], N[(x * N[(y / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+16], N[(z * N[(N[(a - t), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.7999999999999997e-174 or 2.1e16 < z

   1. Initial program 55.8%

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

   3. Simplified 55.8%

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

   5. Taylor expanded in a around 0 55.0%

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

      1. +-commutative 55.0%

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

      2. mul-1-neg 55.0%

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

      3. unsub-neg 55.0%

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

      4. div-sub 55.6%

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

      5. unsub-neg 55.6%

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

      6. distribute-lft-neg-out 55.6%

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

      7. distribute-rgt-out 55.8%

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

      8. sub-neg 55.8%

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

      9. associate-/l* 62.2%

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

      10. associate-*r/ 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in z around inf 83.9%

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

   9. Taylor expanded in y around inf 80.2%

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

   if -7.7999999999999997e-174 < z < 9.00000000000000008e-85

   1. Initial program 79.4%

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

   3. Simplified 79.4%

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

   5. Taylor expanded in x around inf 50.9%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. distribute-neg-frac 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-lft-neg-out 68.8%

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

      3. *-commutative 68.8%

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

   10. Simplified 68.8%

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

   if 9.00000000000000008e-85 < z < 2.1e16

   1. Initial program 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in x around 0 81.4%

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

      1. associate-/l* 81.2%

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

   7. Simplified 81.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \frac{a - t}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+41} \lor \neg \left(y \leq 12\right) \land \left(y \leq 1.35 \cdot 10^{+101} \lor \neg \left(y \leq 6 \cdot 10^{+159}\right)\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.9e+41)
         (and (not (<= y 12.0)) (or (<= y 1.35e+101) (not (<= y 6e+159)))))
   (/ x (- 1.0 z))
   (/ (- a t) (- y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e+41) || (!(y <= 12.0) && ((y <= 1.35e+101) || !(y <= 6e+159)))) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (a - t) / (y - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.9d+41)) .or. (.not. (y <= 12.0d0)) .and. (y <= 1.35d+101) .or. (.not. (y <= 6d+159))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (a - t) / (y - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e+41) || (!(y <= 12.0) && ((y <= 1.35e+101) || !(y <= 6e+159)))) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (a - t) / (y - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.9e+41) or (not (y <= 12.0) and ((y <= 1.35e+101) or not (y <= 6e+159))):
		tmp = x / (1.0 - z)
	else:
		tmp = (a - t) / (y - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.9e+41) || (!(y <= 12.0) && ((y <= 1.35e+101) || !(y <= 6e+159))))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(a - t) / Float64(y - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.9e+41) || (~((y <= 12.0)) && ((y <= 1.35e+101) || ~((y <= 6e+159)))))
		tmp = x / (1.0 - z);
	else
		tmp = (a - t) / (y - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.9e+41], And[N[Not[LessEqual[y, 12.0]], $MachinePrecision], Or[LessEqual[y, 1.35e+101], N[Not[LessEqual[y, 6e+159]], $MachinePrecision]]]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999988e41 or 12 < y < 1.35000000000000003e101 or 6.0000000000000004e159 < y

   1. Initial program 50.1%

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

   3. Simplified 50.1%

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

   5. Taylor expanded in y around -inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   7. Simplified 66.7%

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

   if -2.89999999999999988e41 < y < 12 or 1.35000000000000003e101 < y < 6.0000000000000004e159

   1. Initial program 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in z around inf 66.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+41} \lor \neg \left(y \leq 12\right) \land \left(y \leq 1.35 \cdot 10^{+101} \lor \neg \left(y \leq 6 \cdot 10^{+159}\right)\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 11.2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \frac{y}{y - z \cdot y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -1.4e+45)
     t_2
     (if (<= y 11.2)
       t_1
       (if (<= y 1.85e+101)
         (* x (/ y (- y (* z y))))
         (if (<= y 6e+159) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.4e+45) {
		tmp = t_2;
	} else if (y <= 11.2) {
		tmp = t_1;
	} else if (y <= 1.85e+101) {
		tmp = x * (y / (y - (z * y)));
	} else if (y <= 6e+159) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    t_2 = x / (1.0d0 - z)
    if (y <= (-1.4d+45)) then
        tmp = t_2
    else if (y <= 11.2d0) then
        tmp = t_1
    else if (y <= 1.85d+101) then
        tmp = x * (y / (y - (z * y)))
    else if (y <= 6d+159) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.4e+45) {
		tmp = t_2;
	} else if (y <= 11.2) {
		tmp = t_1;
	} else if (y <= 1.85e+101) {
		tmp = x * (y / (y - (z * y)));
	} else if (y <= 6e+159) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -1.4e+45:
		tmp = t_2
	elif y <= 11.2:
		tmp = t_1
	elif y <= 1.85e+101:
		tmp = x * (y / (y - (z * y)))
	elif y <= 6e+159:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.4e+45)
		tmp = t_2;
	elseif (y <= 11.2)
		tmp = t_1;
	elseif (y <= 1.85e+101)
		tmp = Float64(x * Float64(y / Float64(y - Float64(z * y))));
	elseif (y <= 6e+159)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.4e+45)
		tmp = t_2;
	elseif (y <= 11.2)
		tmp = t_1;
	elseif (y <= 1.85e+101)
		tmp = x * (y / (y - (z * y)));
	elseif (y <= 6e+159)
		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[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+45], t$95$2, If[LessEqual[y, 11.2], t$95$1, If[LessEqual[y, 1.85e+101], N[(x * N[(y / N[(y - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+159], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e45 or 6.0000000000000004e159 < y

   1. Initial program 45.7%

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

   3. Simplified 45.7%

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

   5. Taylor expanded in y around -inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. unsub-neg 66.2%

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

   7. Simplified 66.2%

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

   if -1.4e45 < y < 11.199999999999999 or 1.8499999999999999e101 < y < 6.0000000000000004e159

   1. Initial program 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in z around inf 66.3%

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

   if 11.199999999999999 < y < 1.8499999999999999e101

   1. Initial program 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in x around inf 65.9%

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

      1. associate-*r/ 72.4%

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

      2. neg-mul-1 72.4%

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

      3. distribute-rgt-neg-in 72.4%

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

      4. distribute-neg-frac 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   10. Simplified 69.9%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 11.2:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \frac{y}{y - z \cdot y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+159}:\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 10:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -1.75e+36)
     t_1
     (if (<= z 1.15e-79)
       (* x (/ y (+ y (* z b))))
       (if (<= z 10.0) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 1.15e-79) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 10.0) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-1.75d+36)) then
        tmp = t_1
    else if (z <= 1.15d-79) then
        tmp = x * (y / (y + (z * b)))
    else if (z <= 10.0d0) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 1.15e-79) {
		tmp = x * (y / (y + (z * b)));
	} else if (z <= 10.0) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -1.75e+36:
		tmp = t_1
	elif z <= 1.15e-79:
		tmp = x * (y / (y + (z * b)))
	elif z <= 10.0:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 1.15e-79)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * b))));
	elseif (z <= 10.0)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 1.15e-79)
		tmp = x * (y / (y + (z * b)));
	elseif (z <= 10.0)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+36], t$95$1, If[LessEqual[z, 1.15e-79], N[(x * N[(y / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 10.0], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e36 or 10 < z

   1. Initial program 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in a around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. div-sub 48.2%

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

      5. unsub-neg 48.2%

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

      6. distribute-lft-neg-out 48.2%

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

      7. distribute-rgt-out 48.5%

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

      8. sub-neg 48.5%

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

      9. associate-/l* 58.3%

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

      10. associate-*r/ 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in z around inf 85.3%

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

   9. Taylor expanded in y around inf 89.0%

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

   10. Taylor expanded in z around inf 88.5%

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

   if -1.7499999999999999e36 < z < 1.15000000000000006e-79

   1. Initial program 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around inf 47.7%

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

      1. associate-*r/ 62.0%

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

      2. neg-mul-1 62.0%

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

      3. distribute-rgt-neg-in 62.0%

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

      4. distribute-neg-frac 62.0%

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

   7. Simplified 62.0%

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

   8. Taylor expanded in y around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. distribute-lft-neg-out 60.8%

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

      3. *-commutative 60.8%

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

   10. Simplified 60.8%

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

   if 1.15000000000000006e-79 < z < 10

   1. Initial program 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-neg-frac2 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 10:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 36:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -1.75e+36)
     t_1
     (if (<= z 3.5e-76)
       (* x (/ y (+ y (* z (- b y)))))
       (if (<= z 36.0) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 3.5e-76) {
		tmp = x * (y / (y + (z * (b - y))));
	} else if (z <= 36.0) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-1.75d+36)) then
        tmp = t_1
    else if (z <= 3.5d-76) then
        tmp = x * (y / (y + (z * (b - y))))
    else if (z <= 36.0d0) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 3.5e-76) {
		tmp = x * (y / (y + (z * (b - y))));
	} else if (z <= 36.0) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -1.75e+36:
		tmp = t_1
	elif z <= 3.5e-76:
		tmp = x * (y / (y + (z * (b - y))))
	elif z <= 36.0:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 3.5e-76)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 36.0)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 3.5e-76)
		tmp = x * (y / (y + (z * (b - y))));
	elseif (z <= 36.0)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+36], t$95$1, If[LessEqual[z, 3.5e-76], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 36.0], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e36 or 36 < z

   1. Initial program 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in a around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. div-sub 48.2%

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

      5. unsub-neg 48.2%

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

      6. distribute-lft-neg-out 48.2%

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

      7. distribute-rgt-out 48.5%

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

      8. sub-neg 48.5%

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

      9. associate-/l* 58.3%

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

      10. associate-*r/ 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in z around inf 85.3%

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

   9. Taylor expanded in y around inf 89.0%

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

   10. Taylor expanded in z around inf 88.5%

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

   if -1.7499999999999999e36 < z < 3.49999999999999997e-76

   1. Initial program 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around inf 47.7%

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

      1. associate-*r/ 62.0%

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

      2. neg-mul-1 62.0%

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

      3. distribute-rgt-neg-in 62.0%

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

      4. distribute-neg-frac 62.0%

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

   7. Simplified 62.0%

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

   if 3.49999999999999997e-76 < z < 36

   1. Initial program 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0 58.1%

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

      1. mul-1-neg 58.1%

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

      2. distribute-neg-frac2 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 36:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) (- y b)) (/ x z))))
   (if (<= z -1.75e+36)
     t_1
     (if (<= z 4.4e-81)
       (* x (/ y (+ y (* z (- b y)))))
       (if (<= z 1.0) (* z (/ (- t a) (+ y (* z b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 4.4e-81) {
		tmp = x * (y / (y + (z * (b - y))));
	} else if (z <= 1.0) {
		tmp = z * ((t - a) / (y + (z * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - t) / (y - b)) - (x / z)
    if (z <= (-1.75d+36)) then
        tmp = t_1
    else if (z <= 4.4d-81) then
        tmp = x * (y / (y + (z * (b - y))))
    else if (z <= 1.0d0) then
        tmp = z * ((t - a) / (y + (z * b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / (y - b)) - (x / z);
	double tmp;
	if (z <= -1.75e+36) {
		tmp = t_1;
	} else if (z <= 4.4e-81) {
		tmp = x * (y / (y + (z * (b - y))));
	} else if (z <= 1.0) {
		tmp = z * ((t - a) / (y + (z * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / (y - b)) - (x / z)
	tmp = 0
	if z <= -1.75e+36:
		tmp = t_1
	elif z <= 4.4e-81:
		tmp = x * (y / (y + (z * (b - y))))
	elif z <= 1.0:
		tmp = z * ((t - a) / (y + (z * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / Float64(y - b)) - Float64(x / z))
	tmp = 0.0
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 4.4e-81)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 1.0)
		tmp = Float64(z * Float64(Float64(t - a) / Float64(y + Float64(z * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / (y - b)) - (x / z);
	tmp = 0.0;
	if (z <= -1.75e+36)
		tmp = t_1;
	elseif (z <= 4.4e-81)
		tmp = x * (y / (y + (z * (b - y))));
	elseif (z <= 1.0)
		tmp = z * ((t - a) / (y + (z * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+36], t$95$1, If[LessEqual[z, 4.4e-81], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(z * N[(N[(t - a), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e36 or 1 < z

   1. Initial program 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in a around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. mul-1-neg 48.2%

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

      3. unsub-neg 48.2%

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

      4. div-sub 48.2%

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

      5. unsub-neg 48.2%

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

      6. distribute-lft-neg-out 48.2%

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

      7. distribute-rgt-out 48.5%

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

      8. sub-neg 48.5%

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

      9. associate-/l* 58.3%

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

      10. associate-*r/ 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in z around inf 85.3%

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

   9. Taylor expanded in y around inf 89.0%

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

   10. Taylor expanded in z around inf 88.5%

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

   if -1.7499999999999999e36 < z < 4.3999999999999998e-81

   1. Initial program 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around inf 48.1%

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

      1. associate-*r/ 62.5%

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

      2. neg-mul-1 62.5%

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

      3. distribute-rgt-neg-in 62.5%

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

      4. distribute-neg-frac 62.5%

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

   7. Simplified 62.5%

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

   if 4.3999999999999998e-81 < z < 1

   1. Initial program 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around 0 81.7%

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

      1. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in y around 0 80.4%

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

      1. mul-1-neg 19.0%

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

      2. distribute-lft-neg-out 19.0%

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

      3. *-commutative 19.0%

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

   10. Simplified 80.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+36}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;z \cdot \frac{t - a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 83.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y - b}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-6}:\\ \;\;\;\;t\_1 + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.85:\\ \;\;\;\;x - \frac{z \cdot \left(t - a\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{1}{\frac{1 - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a t) (- y b))))
   (if (<= z -2.2e-6)
     (+ t_1 (/ x (- 1.0 z)))
     (if (<= z 1.85)
       (- x (/ (* z (- t a)) (- (* z (- y b)) y)))
       (+ t_1 (/ 1.0 (/ (- 1.0 z) x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.2e-6) {
		tmp = t_1 + (x / (1.0 - z));
	} else if (z <= 1.85) {
		tmp = x - ((z * (t - a)) / ((z * (y - b)) - y));
	} else {
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a - t) / (y - b)
    if (z <= (-2.2d-6)) then
        tmp = t_1 + (x / (1.0d0 - z))
    else if (z <= 1.85d0) then
        tmp = x - ((z * (t - a)) / ((z * (y - b)) - y))
    else
        tmp = t_1 + (1.0d0 / ((1.0d0 - z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a - t) / (y - b);
	double tmp;
	if (z <= -2.2e-6) {
		tmp = t_1 + (x / (1.0 - z));
	} else if (z <= 1.85) {
		tmp = x - ((z * (t - a)) / ((z * (y - b)) - y));
	} else {
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a - t) / (y - b)
	tmp = 0
	if z <= -2.2e-6:
		tmp = t_1 + (x / (1.0 - z))
	elif z <= 1.85:
		tmp = x - ((z * (t - a)) / ((z * (y - b)) - y))
	else:
		tmp = t_1 + (1.0 / ((1.0 - z) / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a - t) / Float64(y - b))
	tmp = 0.0
	if (z <= -2.2e-6)
		tmp = Float64(t_1 + Float64(x / Float64(1.0 - z)));
	elseif (z <= 1.85)
		tmp = Float64(x - Float64(Float64(z * Float64(t - a)) / Float64(Float64(z * Float64(y - b)) - y)));
	else
		tmp = Float64(t_1 + Float64(1.0 / Float64(Float64(1.0 - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a - t) / (y - b);
	tmp = 0.0;
	if (z <= -2.2e-6)
		tmp = t_1 + (x / (1.0 - z));
	elseif (z <= 1.85)
		tmp = x - ((z * (t - a)) / ((z * (y - b)) - y));
	else
		tmp = t_1 + (1.0 / ((1.0 - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-6], N[(t$95$1 + N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85], N[(x - N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(y - b), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(1.0 / N[(N[(1.0 - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e-6

   1. Initial program 51.1%

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

   3. Simplified 51.1%

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

   5. Taylor expanded in a around 0 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. div-sub 50.9%

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

      5. unsub-neg 50.9%

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

      6. distribute-lft-neg-out 50.9%

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

      7. distribute-rgt-out 51.2%

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

      8. sub-neg 51.2%

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

      9. associate-/l* 55.0%

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

      10. associate-*r/ 58.8%

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

   7. Simplified 58.8%

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

   8. Taylor expanded in z around inf 83.9%

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

   9. Taylor expanded in y around inf 85.9%

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

   if -2.2000000000000001e-6 < z < 1.8500000000000001

   1. Initial program 83.9%

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

   3. Simplified 83.9%

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

      1. div-sub 83.9%

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

      2. associate-/l* 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around 0 77.1%

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

      1. mul-1-neg 77.1%

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

   9. Simplified 77.1%

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

   if 1.8500000000000001 < z

   1. Initial program 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in a around 0 47.2%

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

      1. +-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

      4. div-sub 47.2%

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

      5. unsub-neg 47.2%

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

      6. distribute-lft-neg-out 47.2%

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

      7. distribute-rgt-out 47.5%

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

      8. sub-neg 47.5%

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

      9. associate-/l* 61.0%

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

      10. associate-*r/ 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in z around inf 86.0%

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

   9. Taylor expanded in y around inf 88.2%

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

       1. clear-num 88.4%

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

       2. inv-pow 88.4%

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

       3. sub-neg 88.4%

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

       4. metadata-eval 88.4%

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

   11. Applied egg-rr 88.4%

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

       1. unpow-1 88.4%

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

       2. +-commutative 88.4%

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

   13. Simplified 88.4%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{x}{1 - z}\\ \mathbf{elif}\;z \leq 1.85:\\ \;\;\;\;x - \frac{z \cdot \left(t - a\right)}{z \cdot \left(y - b\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y - b} + \frac{1}{\frac{1 - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 36.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\frac{a}{b}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -15.5 \lor \neg \left(z \leq 3.3 \cdot 10^{-70}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ a b))))
   (if (<= z -1.05e+221)
     t_1
     (if (<= z -1.36e+98)
       (/ x (- z))
       (if (or (<= z -15.5) (not (<= z 3.3e-70))) t_1 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(a / b);
	double tmp;
	if (z <= -1.05e+221) {
		tmp = t_1;
	} else if (z <= -1.36e+98) {
		tmp = x / -z;
	} else if ((z <= -15.5) || !(z <= 3.3e-70)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(a / b)
    if (z <= (-1.05d+221)) then
        tmp = t_1
    else if (z <= (-1.36d+98)) then
        tmp = x / -z
    else if ((z <= (-15.5d0)) .or. (.not. (z <= 3.3d-70))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -(a / b);
	double tmp;
	if (z <= -1.05e+221) {
		tmp = t_1;
	} else if (z <= -1.36e+98) {
		tmp = x / -z;
	} else if ((z <= -15.5) || !(z <= 3.3e-70)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -(a / b)
	tmp = 0
	if z <= -1.05e+221:
		tmp = t_1
	elif z <= -1.36e+98:
		tmp = x / -z
	elif (z <= -15.5) or not (z <= 3.3e-70):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-Float64(a / b))
	tmp = 0.0
	if (z <= -1.05e+221)
		tmp = t_1;
	elseif (z <= -1.36e+98)
		tmp = Float64(x / Float64(-z));
	elseif ((z <= -15.5) || !(z <= 3.3e-70))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -(a / b);
	tmp = 0.0;
	if (z <= -1.05e+221)
		tmp = t_1;
	elseif (z <= -1.36e+98)
		tmp = x / -z;
	elseif ((z <= -15.5) || ~((z <= 3.3e-70)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = (-N[(a / b), $MachinePrecision])}, If[LessEqual[z, -1.05e+221], t$95$1, If[LessEqual[z, -1.36e+98], N[(x / (-z)), $MachinePrecision], If[Or[LessEqual[z, -15.5], N[Not[LessEqual[z, 3.3e-70]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000001e221 or -1.36000000000000004e98 < z < -15.5 or 3.30000000000000016e-70 < z

   1. Initial program 54.0%

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

   3. Simplified 54.0%

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

   5. Taylor expanded in a around inf 28.1%

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

      1. *-commutative 28.1%

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

   7. Simplified 28.1%

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

   8. Taylor expanded in y around 0 30.4%

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

      1. associate-*r/ 30.4%

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

      2. mul-1-neg 30.4%

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

   10. Simplified 30.4%

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

   if -1.05000000000000001e221 < z < -1.36000000000000004e98

   1. Initial program 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in x around inf 17.6%

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

      1. associate-*r/ 21.6%

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

      2. neg-mul-1 21.6%

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

      3. distribute-rgt-neg-in 21.6%

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

      4. distribute-neg-frac 21.6%

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

   7. Simplified 21.6%

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

   8. Taylor expanded in z around inf 21.6%

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

      1. mul-1-neg 21.6%

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

      2. associate-/r* 43.8%

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

      3. sub-neg 43.8%

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

      4. mul-1-neg 43.8%

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

      5. distribute-neg-frac2 43.8%

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

      6. mul-1-neg 43.8%

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

      7. sub-neg 43.8%

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

   10. Simplified 43.8%

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

   11. Taylor expanded in y around inf 33.9%

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

       1. associate-*r/ 33.9%

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

       2. neg-mul-1 33.9%

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

   13. Simplified 33.9%

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

   if -15.5 < z < 3.30000000000000016e-70

   1. Initial program 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around 0 48.9%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+221}:\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -15.5 \lor \neg \left(z \leq 3.3 \cdot 10^{-70}\right):\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 67.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.43 \lor \neg \left(z \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.43) (not (<= z 2.05e-78)))
   (/ (- a t) (- y b))
   (* x (/ y (+ y (* z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.43) || !(z <= 2.05e-78)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * (y / (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 <= (-0.43d0)) .or. (.not. (z <= 2.05d-78))) then
        tmp = (a - t) / (y - b)
    else
        tmp = x * (y / (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 <= -0.43) || !(z <= 2.05e-78)) {
		tmp = (a - t) / (y - b);
	} else {
		tmp = x * (y / (y + (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.43) or not (z <= 2.05e-78):
		tmp = (a - t) / (y - b)
	else:
		tmp = x * (y / (y + (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.43) || !(z <= 2.05e-78))
		tmp = Float64(Float64(a - t) / Float64(y - b));
	else
		tmp = Float64(x * Float64(y / 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 <= -0.43) || ~((z <= 2.05e-78)))
		tmp = (a - t) / (y - b);
	else
		tmp = x * (y / (y + (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.43], N[Not[LessEqual[z, 2.05e-78]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / N[(y - b), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.429999999999999993 or 2.0499999999999999e-78 < z

   1. Initial program 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in z around inf 70.5%

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

   if -0.429999999999999993 < z < 2.0499999999999999e-78

   1. Initial program 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in x around inf 48.0%

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

      1. associate-*r/ 62.7%

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

      2. neg-mul-1 62.7%

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

      3. distribute-rgt-neg-in 62.7%

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

      4. distribute-neg-frac 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in y around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-lft-neg-out 61.4%

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

      3. *-commutative 61.4%

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

   10. Simplified 61.4%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.43 \lor \neg \left(z \leq 2.05 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{a - t}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 45.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.45 \lor \neg \left(z \leq 2.5 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.45) (not (<= z 2.5e-71))) (/ a (- y b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.45) || !(z <= 2.5e-71)) {
		tmp = a / (y - b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.45d0)) .or. (.not. (z <= 2.5d-71))) then
        tmp = a / (y - b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.45) || !(z <= 2.5e-71)) {
		tmp = a / (y - b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.45) or not (z <= 2.5e-71):
		tmp = a / (y - b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.45) || !(z <= 2.5e-71))
		tmp = Float64(a / Float64(y - b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.45) || ~((z <= 2.5e-71)))
		tmp = a / (y - b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.45], N[Not[LessEqual[z, 2.5e-71]], $MachinePrecision]], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.450000000000000011 or 2.49999999999999999e-71 < z

   1. Initial program 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in a around inf 26.5%

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

      1. *-commutative 26.5%

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

   7. Simplified 26.5%

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

   8. Taylor expanded in z around inf 42.2%

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

   if -0.450000000000000011 < z < 2.49999999999999999e-71

   1. Initial program 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around 0 48.9%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.45 \lor \neg \left(z \leq 2.5 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 44.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-91} \lor \neg \left(y \leq 9.2\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e-91) (not (<= y 9.2))) (/ x (- 1.0 z)) (/ a (- y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1e-91) || !(y <= 9.2)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = a / (y - 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 <= (-1d-91)) .or. (.not. (y <= 9.2d0))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = a / (y - 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 <= -1e-91) || !(y <= 9.2)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = a / (y - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1e-91) or not (y <= 9.2):
		tmp = x / (1.0 - z)
	else:
		tmp = a / (y - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1e-91) || !(y <= 9.2))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(a / Float64(y - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1e-91) || ~((y <= 9.2)))
		tmp = x / (1.0 - z);
	else
		tmp = a / (y - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1e-91], N[Not[LessEqual[y, 9.2]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000002e-91 or 9.1999999999999993 < y

   1. Initial program 56.1%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around -inf 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

   7. Simplified 53.8%

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

   if -1.00000000000000002e-91 < y < 9.1999999999999993

   1. Initial program 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in a around inf 36.3%

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

      1. *-commutative 36.3%

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

   7. Simplified 36.3%

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

   8. Taylor expanded in z around inf 40.0%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-91} \lor \neg \left(y \leq 9.2\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y - b}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 54.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+43} \lor \neg \left(y \leq 10\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.1e+43) (not (<= y 10.0))) (/ 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 <= -4.1e+43) || !(y <= 10.0)) {
		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 <= (-4.1d+43)) .or. (.not. (y <= 10.0d0))) 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 <= -4.1e+43) || !(y <= 10.0)) {
		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 <= -4.1e+43) or not (y <= 10.0):
		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 <= -4.1e+43) || !(y <= 10.0))
		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 <= -4.1e+43) || ~((y <= 10.0)))
		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, -4.1e+43], N[Not[LessEqual[y, 10.0]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e43 or 10 < y

   1. Initial program 49.7%

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

   3. Simplified 49.7%

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

   5. Taylor expanded in y around -inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

   7. Simplified 62.6%

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

   if -4.1e43 < y < 10

   1. Initial program 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. distribute-neg-frac2 54.6%

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

   7. Simplified 54.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+43} \lor \neg \left(y \leq 10\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.43 \lor \neg \left(z \leq 3.6 \cdot 10^{-70}\right):\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.43) (not (<= z 3.6e-70))) (- (/ a b)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.43) || !(z <= 3.6e-70)) {
		tmp = -(a / b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.43d0)) .or. (.not. (z <= 3.6d-70))) then
        tmp = -(a / b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.43) || !(z <= 3.6e-70)) {
		tmp = -(a / b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.43) or not (z <= 3.6e-70):
		tmp = -(a / b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.43) || !(z <= 3.6e-70))
		tmp = Float64(-Float64(a / b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.43) || ~((z <= 3.6e-70)))
		tmp = -(a / b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.43], N[Not[LessEqual[z, 3.6e-70]], $MachinePrecision]], (-N[(a / b), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if z < -0.429999999999999993 or 3.6000000000000002e-70 < z

   1. Initial program 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in a around inf 26.5%

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

      1. *-commutative 26.5%

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

   7. Simplified 26.5%

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

   8. Taylor expanded in y around 0 27.6%

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

      1. associate-*r/ 27.6%

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

      2. mul-1-neg 27.6%

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

   10. Simplified 27.6%

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

   if -0.429999999999999993 < z < 3.6000000000000002e-70

   1. Initial program 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in z around 0 48.9%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.43 \lor \neg \left(z \leq 3.6 \cdot 10^{-70}\right):\\ \;\;\;\;-\frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 34.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+38} \lor \neg \left(z \leq 0.19\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e+38) (not (<= z 0.19))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.9e+38) || !(z <= 0.19)) {
		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 <= (-2.9d+38)) .or. (.not. (z <= 0.19d0))) 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 <= -2.9e+38) || !(z <= 0.19)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.9e+38) or not (z <= 0.19):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.9e+38) || !(z <= 0.19))
		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 <= -2.9e+38) || ~((z <= 0.19)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e+38], N[Not[LessEqual[z, 0.19]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.90000000000000007e38 or 0.19 < z

   1. Initial program 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in a around inf 23.9%

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

      1. *-commutative 23.9%

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

   7. Simplified 23.9%

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

   8. Taylor expanded in z around inf 43.8%

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

   9. Taylor expanded in y around inf 21.4%

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

   if -2.90000000000000007e38 < z < 0.19

   1. Initial program 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in z around 0 43.3%

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

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+38} \lor \neg \left(z \leq 0.19\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 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 66.7%

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

3. Simplified 66.7%

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

5. Taylor expanded in z around 0 24.4%

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

6. Final simplification 24.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 73.1% 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 2024048 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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