Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 93.0%

Time: 20.7s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{1}{\frac{\left(1 - z\right) \cdot \frac{y}{z}}{t - a}} + t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3 + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (+ (/ t (- b y)) (* (/ x z) (/ y (- b y))))
          (- (* (/ y z) (/ (- a t) (pow (- b y) 2.0))) (/ a (- b y)))))
        (t_2 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y)))))
        (t_3 (/ x (- 1.0 z))))
   (if (<= t_2 -5e+249)
     (+ (/ 1.0 (/ (* (- 1.0 z) (/ y z)) (- t a))) t_3)
     (if (<= t_2 -2e-255)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY) (+ t_3 (/ (- a t) y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / pow((b - y), 2.0))) - (a / (b - y)));
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_2 <= -5e+249) {
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / Math.pow((b - y), 2.0))) - (a / (b - y)));
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_2 <= -5e+249) {
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / math.pow((b - y), 2.0))) - (a / (b - y)))
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	t_3 = x / (1.0 - z)
	tmp = 0
	if t_2 <= -5e+249:
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3
	elif t_2 <= -2e-255:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3 + ((a - t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / Float64(b - y)))) + Float64(Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))) - Float64(a / Float64(b - y))))
	t_2 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (t_2 <= -5e+249)
		tmp = Float64(Float64(1.0 / Float64(Float64(Float64(1.0 - z) * Float64(y / z)) / Float64(t - a))) + t_3);
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(t_3 + Float64(Float64(a - t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t / (b - y)) + ((x / z) * (y / (b - y)))) + (((y / z) * ((a - t) / ((b - y) ^ 2.0))) - (a / (b - y)));
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (t_2 <= -5e+249)
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3 + ((a - t) / 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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+249], N[(N[(1.0 / N[(N[(N[(1.0 - z), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t$95$2, -2e-255], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], N[(t$95$3 + N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

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)))) < -4.9999999999999996e249

   1. Initial program 54.8%

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

   2. Taylor expanded in y around inf 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in x around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. times-frac 77.7%

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

   7. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. clear-num 77.7%

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

      3. frac-times 77.7%

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

      4. metadata-eval 77.7%

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

   9. Applied egg-rr 77.7%

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

       1. *-commutative 77.7%

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

       2. associate-*l/ 77.7%

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

   11. Simplified 77.7%

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

   if -4.9999999999999996e249 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-255 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -2e-255 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.5%

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

   2. Taylor expanded in z around inf 57.9%

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

      1. times-frac 77.5%

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

      2. times-frac 96.5%

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

   4. Simplified 96.5%

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

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

   1. Initial program 28.3%

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

   2. Taylor expanded in y around inf 20.1%

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

      1. mul-1-neg 20.1%

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

      2. unsub-neg 20.1%

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

   4. Simplified 20.1%

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

   5. Taylor expanded in x around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. times-frac 76.7%

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

   7. Simplified 76.7%

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

      1. clear-num 76.6%

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

      2. clear-num 76.6%

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

      3. frac-times 76.6%

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

      4. metadata-eval 76.6%

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

   9. Applied egg-rr 76.6%

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

       1. *-commutative 76.6%

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

       2. associate-*l/ 76.6%

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

   11. Simplified 76.6%

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

   12. Taylor expanded in z around inf 76.7%

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

       1. div-sub 76.7%

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

       2. distribute-lft-out-- 76.7%

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

       3. sub-neg 76.7%

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

       4. mul-1-neg 76.7%

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

       5. remove-double-neg 76.7%

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

       6. +-commutative 76.7%

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

       7. mul-1-neg 76.7%

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

       8. sub-neg 76.7%

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

       9. div-sub 76.7%

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

   14. Simplified 76.7%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{1}{\frac{\left(1 - z\right) \cdot \frac{y}{z}}{t - a}} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-255}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\right) + \left(\frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}} - \frac{a}{b - y}\right)\\ \end{array} \]

Alternative 2: 89.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{1}{\frac{\left(1 - z\right) \cdot \frac{y}{z}}{t - a}} + t_3\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(\frac{\frac{x \cdot y}{z}}{b - y} + t_2\right) - \frac{\frac{y}{\frac{z}{t - a}}}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_3 + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (/ x (- 1.0 z))))
   (if (<= t_1 -5e+249)
     (+ (/ 1.0 (/ (* (- 1.0 z) (/ y z)) (- t a))) t_3)
     (if (<= t_1 -2e-255)
       t_1
       (if (<= t_1 0.0)
         (-
          (+ (/ (/ (* x y) z) (- b y)) t_2)
          (/ (/ y (/ z (- t a))) (pow (- b y) 2.0)))
         (if (<= t_1 2e+306)
           t_1
           (if (<= t_1 INFINITY) (+ t_3 (/ (- a t) y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_1 <= -5e+249) {
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	} else if (t_1 <= -2e-255) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((((x * y) / z) / (b - y)) + t_2) - ((y / (z / (t - a))) / pow((b - y), 2.0));
	} else if (t_1 <= 2e+306) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_1 <= -5e+249) {
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	} else if (t_1 <= -2e-255) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((((x * y) / z) / (b - y)) + t_2) - ((y / (z / (t - a))) / Math.pow((b - y), 2.0));
	} else if (t_1 <= 2e+306) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	t_3 = x / (1.0 - z)
	tmp = 0
	if t_1 <= -5e+249:
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3
	elif t_1 <= -2e-255:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((((x * y) / z) / (b - y)) + t_2) - ((y / (z / (t - a))) / math.pow((b - y), 2.0))
	elif t_1 <= 2e+306:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_3 + ((a - t) / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (t_1 <= -5e+249)
		tmp = Float64(Float64(1.0 / Float64(Float64(Float64(1.0 - z) * Float64(y / z)) / Float64(t - a))) + t_3);
	elseif (t_1 <= -2e-255)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(Float64(x * y) / z) / Float64(b - y)) + t_2) - Float64(Float64(y / Float64(z / Float64(t - a))) / (Float64(b - y) ^ 2.0)));
	elseif (t_1 <= 2e+306)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(t_3 + Float64(Float64(a - t) / y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (t_1 <= -5e+249)
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	elseif (t_1 <= -2e-255)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((((x * y) / z) / (b - y)) + t_2) - ((y / (z / (t - a))) / ((b - y) ^ 2.0));
	elseif (t_1 <= 2e+306)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3 + ((a - t) / y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+249], N[(N[(1.0 / N[(N[(N[(1.0 - z), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t$95$1, -2e-255], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(N[(y / N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+306], t$95$1, If[LessEqual[t$95$1, Infinity], N[(t$95$3 + N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.9999999999999996e249

   1. Initial program 54.8%

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

   2. Taylor expanded in y around inf 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in x around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. times-frac 77.7%

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

   7. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. clear-num 77.7%

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

      3. frac-times 77.7%

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

      4. metadata-eval 77.7%

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

   9. Applied egg-rr 77.7%

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

       1. *-commutative 77.7%

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

       2. associate-*l/ 77.7%

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

   11. Simplified 77.7%

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

   if -4.9999999999999996e249 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-255 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -2e-255 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 34.5%

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

   2. Taylor expanded in z around inf 75.3%

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

      1. associate--r+ 75.3%

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

      2. +-commutative 75.3%

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

      3. associate--l+ 75.3%

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

      4. associate-/r* 86.3%

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

      5. *-commutative 86.3%

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

      6. div-sub 86.3%

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

      7. associate-/r* 86.4%

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

      8. associate-/l* 90.2%

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

   4. Simplified 90.2%

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

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

   1. Initial program 28.3%

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

   2. Taylor expanded in y around inf 20.1%

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

      1. mul-1-neg 20.1%

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

      2. unsub-neg 20.1%

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

   4. Simplified 20.1%

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

   5. Taylor expanded in x around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. times-frac 76.7%

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

   7. Simplified 76.7%

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

      1. clear-num 76.6%

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

      2. clear-num 76.6%

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

      3. frac-times 76.6%

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

      4. metadata-eval 76.6%

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

   9. Applied egg-rr 76.6%

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

       1. *-commutative 76.6%

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

       2. associate-*l/ 76.6%

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

   11. Simplified 76.6%

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

   12. Taylor expanded in z around inf 76.7%

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

       1. div-sub 76.7%

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

       2. distribute-lft-out-- 76.7%

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

       3. sub-neg 76.7%

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

       4. mul-1-neg 76.7%

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

       5. remove-double-neg 76.7%

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

       6. +-commutative 76.7%

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

       7. mul-1-neg 76.7%

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

       8. sub-neg 76.7%

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

       9. div-sub 76.7%

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

   14. Simplified 76.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf 69.2%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{1}{\frac{\left(1 - z\right) \cdot \frac{y}{z}}{t - a}} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-255}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{\frac{x \cdot y}{z}}{b - y} + \frac{t - a}{b - y}\right) - \frac{\frac{y}{\frac{z}{t - a}}}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 88.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+249}:\\ \;\;\;\;t_3 + \frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3 + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y)))))
        (t_3 (/ x (- 1.0 z))))
   (if (<= t_2 -5e+249)
     (+ t_3 (* (/ z y) (/ (- t a) (- 1.0 z))))
     (if (<= t_2 -2e-255)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY) (+ t_3 (/ (- a t) y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_2 <= -5e+249) {
		tmp = t_3 + ((z / y) * ((t - a) / (1.0 - z)));
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_2 <= -5e+249) {
		tmp = t_3 + ((z / y) * ((t - a) / (1.0 - z)));
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	t_3 = x / (1.0 - z)
	tmp = 0
	if t_2 <= -5e+249:
		tmp = t_3 + ((z / y) * ((t - a) / (1.0 - z)))
	elif t_2 <= -2e-255:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3 + ((a - t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (t_2 <= -5e+249)
		tmp = Float64(t_3 + Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z))));
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(t_3 + Float64(Float64(a - t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (t_2 <= -5e+249)
		tmp = t_3 + ((z / y) * ((t - a) / (1.0 - z)));
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3 + ((a - t) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+249], N[(t$95$3 + N[(N[(z / y), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-255], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], N[(t$95$3 + N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

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)))) < -4.9999999999999996e249

   1. Initial program 54.8%

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

   2. Taylor expanded in y around inf 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in x around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. times-frac 77.7%

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

   7. Simplified 77.7%

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

   if -4.9999999999999996e249 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-255 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -2e-255 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.5%

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

   2. Taylor expanded in z around inf 73.7%

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

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

   1. Initial program 28.3%

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

   2. Taylor expanded in y around inf 20.1%

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

      1. mul-1-neg 20.1%

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

      2. unsub-neg 20.1%

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

   4. Simplified 20.1%

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

   5. Taylor expanded in x around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. times-frac 76.7%

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

   7. Simplified 76.7%

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

      1. clear-num 76.6%

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

      2. clear-num 76.6%

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

      3. frac-times 76.6%

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

      4. metadata-eval 76.6%

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

   9. Applied egg-rr 76.6%

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

       1. *-commutative 76.6%

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

       2. associate-*l/ 76.6%

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

   11. Simplified 76.6%

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

   12. Taylor expanded in z around inf 76.7%

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

       1. div-sub 76.7%

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

       2. distribute-lft-out-- 76.7%

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

       3. sub-neg 76.7%

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

       4. mul-1-neg 76.7%

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

       5. remove-double-neg 76.7%

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

       6. +-commutative 76.7%

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

       7. mul-1-neg 76.7%

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

       8. sub-neg 76.7%

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

       9. div-sub 76.7%

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

   14. Simplified 76.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-255}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 88.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{1}{\frac{\left(1 - z\right) \cdot \frac{y}{z}}{t - a}} + t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3 + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y)))))
        (t_3 (/ x (- 1.0 z))))
   (if (<= t_2 -5e+249)
     (+ (/ 1.0 (/ (* (- 1.0 z) (/ y z)) (- t a))) t_3)
     (if (<= t_2 -2e-255)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 2e+306)
           t_2
           (if (<= t_2 INFINITY) (+ t_3 (/ (- a t) y)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_2 <= -5e+249) {
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	double t_3 = x / (1.0 - z);
	double tmp;
	if (t_2 <= -5e+249) {
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	} else if (t_2 <= -2e-255) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+306) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3 + ((a - t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	t_3 = x / (1.0 - z)
	tmp = 0
	if t_2 <= -5e+249:
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3
	elif t_2 <= -2e-255:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 2e+306:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3 + ((a - t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (t_2 <= -5e+249)
		tmp = Float64(Float64(1.0 / Float64(Float64(Float64(1.0 - z) * Float64(y / z)) / Float64(t - a))) + t_3);
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(t_3 + Float64(Float64(a - t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (t_2 <= -5e+249)
		tmp = (1.0 / (((1.0 - z) * (y / z)) / (t - a))) + t_3;
	elseif (t_2 <= -2e-255)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+306)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3 + ((a - t) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+249], N[(N[(1.0 / N[(N[(N[(1.0 - z), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[t$95$2, -2e-255], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+306], t$95$2, If[LessEqual[t$95$2, Infinity], N[(t$95$3 + N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

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)))) < -4.9999999999999996e249

   1. Initial program 54.8%

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

   2. Taylor expanded in y around inf 46.3%

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

      1. mul-1-neg 46.3%

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

      2. unsub-neg 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in x around 0 70.2%

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

      1. +-commutative 70.2%

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

      2. times-frac 77.7%

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

   7. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. clear-num 77.7%

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

      3. frac-times 77.7%

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

      4. metadata-eval 77.7%

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

   9. Applied egg-rr 77.7%

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

       1. *-commutative 77.7%

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

       2. associate-*l/ 77.7%

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

   11. Simplified 77.7%

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

   if -4.9999999999999996e249 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e-255 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000003e306

   1. Initial program 99.6%

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

   if -2e-255 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.5%

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

   2. Taylor expanded in z around inf 73.7%

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

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

   1. Initial program 28.3%

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

   2. Taylor expanded in y around inf 20.1%

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

      1. mul-1-neg 20.1%

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

      2. unsub-neg 20.1%

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

   4. Simplified 20.1%

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

   5. Taylor expanded in x around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. times-frac 76.7%

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

   7. Simplified 76.7%

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

      1. clear-num 76.6%

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

      2. clear-num 76.6%

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

      3. frac-times 76.6%

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

      4. metadata-eval 76.6%

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

   9. Applied egg-rr 76.6%

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

       1. *-commutative 76.6%

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

       2. associate-*l/ 76.6%

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

   11. Simplified 76.6%

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

   12. Taylor expanded in z around inf 76.7%

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

       1. div-sub 76.7%

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

       2. distribute-lft-out-- 76.7%

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

       3. sub-neg 76.7%

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

       4. mul-1-neg 76.7%

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

       5. remove-double-neg 76.7%

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

       6. +-commutative 76.7%

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

       7. mul-1-neg 76.7%

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

       8. sub-neg 76.7%

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

       9. div-sub 76.7%

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

   14. Simplified 76.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+249}:\\ \;\;\;\;\frac{1}{\frac{\left(1 - z\right) \cdot \frac{y}{z}}{t - a}} + \frac{x}{1 - z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-255}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z} + \frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot \frac{x}{b}}{z} + \frac{t - a}{b}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-187} \lor \neg \left(y \leq 1.02 \cdot 10^{-53}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + \frac{x}{\frac{z}{y}}\right) - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ x (- 1.0 z)) (* (/ z y) (/ (- t a) (- 1.0 z))))))
   (if (<= y -8.8e-63)
     t_1
     (if (<= y -2e-150)
       (+ (/ (* y (/ x b)) z) (/ (- t a) b))
       (if (or (<= y -1.65e-187) (not (<= y 1.02e-53)))
         t_1
         (/ (- (+ t (/ x (/ z y))) a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((z / y) * ((t - a) / (1.0 - z)));
	double tmp;
	if (y <= -8.8e-63) {
		tmp = t_1;
	} else if (y <= -2e-150) {
		tmp = ((y * (x / b)) / z) + ((t - a) / b);
	} else if ((y <= -1.65e-187) || !(y <= 1.02e-53)) {
		tmp = t_1;
	} else {
		tmp = ((t + (x / (z / y))) - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (1.0d0 - z)) + ((z / y) * ((t - a) / (1.0d0 - z)))
    if (y <= (-8.8d-63)) then
        tmp = t_1
    else if (y <= (-2d-150)) then
        tmp = ((y * (x / b)) / z) + ((t - a) / b)
    else if ((y <= (-1.65d-187)) .or. (.not. (y <= 1.02d-53))) then
        tmp = t_1
    else
        tmp = ((t + (x / (z / y))) - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (1.0 - z)) + ((z / y) * ((t - a) / (1.0 - z)));
	double tmp;
	if (y <= -8.8e-63) {
		tmp = t_1;
	} else if (y <= -2e-150) {
		tmp = ((y * (x / b)) / z) + ((t - a) / b);
	} else if ((y <= -1.65e-187) || !(y <= 1.02e-53)) {
		tmp = t_1;
	} else {
		tmp = ((t + (x / (z / y))) - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (1.0 - z)) + ((z / y) * ((t - a) / (1.0 - z)))
	tmp = 0
	if y <= -8.8e-63:
		tmp = t_1
	elif y <= -2e-150:
		tmp = ((y * (x / b)) / z) + ((t - a) / b)
	elif (y <= -1.65e-187) or not (y <= 1.02e-53):
		tmp = t_1
	else:
		tmp = ((t + (x / (z / y))) - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(z / y) * Float64(Float64(t - a) / Float64(1.0 - z))))
	tmp = 0.0
	if (y <= -8.8e-63)
		tmp = t_1;
	elseif (y <= -2e-150)
		tmp = Float64(Float64(Float64(y * Float64(x / b)) / z) + Float64(Float64(t - a) / b));
	elseif ((y <= -1.65e-187) || !(y <= 1.02e-53))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(t + Float64(x / Float64(z / y))) - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (1.0 - z)) + ((z / y) * ((t - a) / (1.0 - z)));
	tmp = 0.0;
	if (y <= -8.8e-63)
		tmp = t_1;
	elseif (y <= -2e-150)
		tmp = ((y * (x / b)) / z) + ((t - a) / b);
	elseif ((y <= -1.65e-187) || ~((y <= 1.02e-53)))
		tmp = t_1;
	else
		tmp = ((t + (x / (z / y))) - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(z / y), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.8e-63], t$95$1, If[LessEqual[y, -2e-150], N[(N[(N[(y * N[(x / b), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.65e-187], N[Not[LessEqual[y, 1.02e-53]], $MachinePrecision]], t$95$1, N[(N[(N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.7999999999999998e-63 or -2.00000000000000001e-150 < y < -1.65e-187 or 1.02000000000000002e-53 < y

   1. Initial program 61.7%

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

   2. Taylor expanded in y around inf 55.3%

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

      1. mul-1-neg 55.3%

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

      2. unsub-neg 55.3%

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

   4. Simplified 55.3%

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

   5. Taylor expanded in x around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. times-frac 81.7%

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

   7. Simplified 81.7%

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

   if -8.7999999999999998e-63 < y < -2.00000000000000001e-150

   1. Initial program 77.8%

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

      1. div-inv 77.5%

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

      2. fma-def 77.5%

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

      3. +-commutative 77.5%

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

      4. fma-udef 77.5%

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

   3. Applied egg-rr 77.5%

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

   4. Taylor expanded in b around inf 66.8%

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

      1. associate-/r* 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in x around 0 78.8%

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

      1. +-commutative 78.8%

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

      2. associate--l+ 78.8%

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

      3. times-frac 78.8%

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

      4. div-sub 78.8%

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

   9. Simplified 78.8%

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

       1. associate-*r/ 89.0%

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

   11. Applied egg-rr 89.0%

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

   if -1.65e-187 < y < 1.02000000000000002e-53

   1. Initial program 80.4%

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

      1. div-inv 80.3%

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

      2. fma-def 80.3%

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

      3. +-commutative 80.3%

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

      4. fma-udef 80.3%

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

   3. Applied egg-rr 80.3%

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

   4. Taylor expanded in b around inf 59.8%

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

      1. associate-/r* 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in x around 0 75.7%

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

      1. +-commutative 75.7%

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

      2. associate--l+ 75.7%

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

      3. times-frac 72.0%

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

      4. div-sub 72.0%

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

   9. Simplified 72.0%

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

   10. Taylor expanded in b around 0 76.7%

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

       1. associate-/l* 77.3%

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

   12. Simplified 77.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot \frac{x}{b}}{z} + \frac{t - a}{b}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-187} \lor \neg \left(y \leq 1.02 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{z}{y} \cdot \frac{t - a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + \frac{x}{\frac{z}{y}}\right) - a}{b}\\ \end{array} \]

Alternative 6: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-119}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) y)) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.9e-19)
     t_2
     (if (<= z -4.5e-93)
       t_1
       (if (<= z -1.55e-119) (/ (- t a) b) (if (<= z 2.2e-71) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.9e-19) {
		tmp = t_2;
	} else if (z <= -4.5e-93) {
		tmp = t_1;
	} else if (z <= -1.55e-119) {
		tmp = (t - a) / b;
	} else if (z <= 2.2e-71) {
		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 = ((z * (t - a)) + (x * y)) / y
    t_2 = (t - a) / (b - y)
    if (z <= (-1.9d-19)) then
        tmp = t_2
    else if (z <= (-4.5d-93)) then
        tmp = t_1
    else if (z <= (-1.55d-119)) then
        tmp = (t - a) / b
    else if (z <= 2.2d-71) 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 = ((z * (t - a)) + (x * y)) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.9e-19) {
		tmp = t_2;
	} else if (z <= -4.5e-93) {
		tmp = t_1;
	} else if (z <= -1.55e-119) {
		tmp = (t - a) / b;
	} else if (z <= 2.2e-71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / y
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.9e-19:
		tmp = t_2
	elif z <= -4.5e-93:
		tmp = t_1
	elif z <= -1.55e-119:
		tmp = (t - a) / b
	elif z <= 2.2e-71:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.9e-19)
		tmp = t_2;
	elseif (z <= -4.5e-93)
		tmp = t_1;
	elseif (z <= -1.55e-119)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 2.2e-71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (t - a)) + (x * y)) / y;
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.9e-19)
		tmp = t_2;
	elseif (z <= -4.5e-93)
		tmp = t_1;
	elseif (z <= -1.55e-119)
		tmp = (t - a) / b;
	elseif (z <= 2.2e-71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e-19], t$95$2, If[LessEqual[z, -4.5e-93], t$95$1, If[LessEqual[z, -1.55e-119], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.2e-71], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e-19 or 2.19999999999999997e-71 < z

   1. Initial program 55.4%

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

   2. Taylor expanded in z around inf 76.0%

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

   if -1.9e-19 < z < -4.5000000000000002e-93 or -1.54999999999999989e-119 < z < 2.19999999999999997e-71

   1. Initial program 86.7%

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

   2. Taylor expanded in z around 0 70.6%

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

   if -4.5000000000000002e-93 < z < -1.54999999999999989e-119

   1. Initial program 71.3%

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

   2. Taylor expanded in y around 0 62.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-119}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{\left(t + \frac{x}{\frac{z}{y}}\right) - a}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* z (- t a)) (* x y)) y)) (t_2 (/ (- t a) (- b y))))
   (if (<= z -1.15e-21)
     t_2
     (if (<= z -2.55e-73)
       t_1
       (if (<= z -5.6e-119)
         (/ (- (+ t (/ x (/ z y))) a) b)
         (if (<= z 2.2e-71) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((z * (t - a)) + (x * y)) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.15e-21) {
		tmp = t_2;
	} else if (z <= -2.55e-73) {
		tmp = t_1;
	} else if (z <= -5.6e-119) {
		tmp = ((t + (x / (z / y))) - a) / b;
	} else if (z <= 2.2e-71) {
		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 = ((z * (t - a)) + (x * y)) / y
    t_2 = (t - a) / (b - y)
    if (z <= (-1.15d-21)) then
        tmp = t_2
    else if (z <= (-2.55d-73)) then
        tmp = t_1
    else if (z <= (-5.6d-119)) then
        tmp = ((t + (x / (z / y))) - a) / b
    else if (z <= 2.2d-71) 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 = ((z * (t - a)) + (x * y)) / y;
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.15e-21) {
		tmp = t_2;
	} else if (z <= -2.55e-73) {
		tmp = t_1;
	} else if (z <= -5.6e-119) {
		tmp = ((t + (x / (z / y))) - a) / b;
	} else if (z <= 2.2e-71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((z * (t - a)) + (x * y)) / y
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.15e-21:
		tmp = t_2
	elif z <= -2.55e-73:
		tmp = t_1
	elif z <= -5.6e-119:
		tmp = ((t + (x / (z / y))) - a) / b
	elif z <= 2.2e-71:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / y)
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.15e-21)
		tmp = t_2;
	elseif (z <= -2.55e-73)
		tmp = t_1;
	elseif (z <= -5.6e-119)
		tmp = Float64(Float64(Float64(t + Float64(x / Float64(z / y))) - a) / b);
	elseif (z <= 2.2e-71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z * (t - a)) + (x * y)) / y;
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.15e-21)
		tmp = t_2;
	elseif (z <= -2.55e-73)
		tmp = t_1;
	elseif (z <= -5.6e-119)
		tmp = ((t + (x / (z / y))) - a) / b;
	elseif (z <= 2.2e-71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-21], t$95$2, If[LessEqual[z, -2.55e-73], t$95$1, If[LessEqual[z, -5.6e-119], N[(N[(N[(t + N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 2.2e-71], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e-21 or 2.19999999999999997e-71 < z

   1. Initial program 55.4%

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

   2. Taylor expanded in z around inf 76.0%

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

   if -1.15e-21 < z < -2.55e-73 or -5.6e-119 < z < 2.19999999999999997e-71

   1. Initial program 86.1%

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

   2. Taylor expanded in z around 0 72.1%

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

   if -2.55e-73 < z < -5.6e-119

   1. Initial program 80.6%

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

      1. div-inv 80.7%

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

      2. fma-def 80.7%

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

      3. +-commutative 80.7%

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

      4. fma-udef 80.7%

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

   3. Applied egg-rr 80.7%

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

   4. Taylor expanded in b around inf 60.3%

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

      1. associate-/r* 60.7%

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

   6. Simplified 60.7%

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

   7. Taylor expanded in x around 0 60.7%

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

      1. +-commutative 60.7%

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

      2. associate--l+ 60.7%

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

      3. times-frac 60.7%

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

      4. div-sub 60.7%

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

   9. Simplified 60.7%

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

   10. Taylor expanded in b around 0 60.8%

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

       1. associate-/l* 60.8%

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

   12. Simplified 60.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-21}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-73}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{\left(t + \frac{x}{\frac{z}{y}}\right) - a}{b}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-22} \lor \neg \left(z \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{1}{\frac{\frac{y}{z}}{t - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e-22) (not (<= z 2.2e-71)))
   (/ (- t a) (- b y))
   (+ (/ x (- 1.0 z)) (/ 1.0 (/ (/ y z) (- t a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e-22) || !(z <= 2.2e-71)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + (1.0 / ((y / z) / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.4d-22)) .or. (.not. (z <= 2.2d-71))) then
        tmp = (t - a) / (b - y)
    else
        tmp = (x / (1.0d0 - z)) + (1.0d0 / ((y / z) / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e-22) || !(z <= 2.2e-71)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + (1.0 / ((y / z) / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.4e-22) or not (z <= 2.2e-71):
		tmp = (t - a) / (b - y)
	else:
		tmp = (x / (1.0 - z)) + (1.0 / ((y / z) / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.4e-22) || !(z <= 2.2e-71))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(1.0 / Float64(Float64(y / z) / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.4e-22) || ~((z <= 2.2e-71)))
		tmp = (t - a) / (b - y);
	else
		tmp = (x / (1.0 - z)) + (1.0 / ((y / z) / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.4e-22], N[Not[LessEqual[z, 2.2e-71]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(y / z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000004e-22 or 2.19999999999999997e-71 < z

   1. Initial program 55.4%

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

   2. Taylor expanded in z around inf 76.0%

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

   if -5.4000000000000004e-22 < z < 2.19999999999999997e-71

   1. Initial program 85.4%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in x around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. times-frac 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 77.0%

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

      2. clear-num 77.0%

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

      3. frac-times 77.0%

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

      4. metadata-eval 77.0%

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

   9. Applied egg-rr 77.0%

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

       1. *-commutative 77.0%

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

       2. associate-*l/ 77.1%

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

   11. Simplified 77.1%

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

   12. Taylor expanded in z around 0 77.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-22} \lor \neg \left(z \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{1}{\frac{\frac{y}{z}}{t - a}}\\ \end{array} \]

Alternative 9: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \left(t - a\right) \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e-19) (not (<= z 2.2e-71)))
   (/ (- t a) (- b y))
   (+ (/ x (- 1.0 z)) (* (- t a) (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e-19) || !(z <= 2.2e-71)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + ((t - a) * (z / 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 <= (-2.3d-19)) .or. (.not. (z <= 2.2d-71))) then
        tmp = (t - a) / (b - y)
    else
        tmp = (x / (1.0d0 - z)) + ((t - a) * (z / 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 <= -2.3e-19) || !(z <= 2.2e-71)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + ((t - a) * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e-19) or not (z <= 2.2e-71):
		tmp = (t - a) / (b - y)
	else:
		tmp = (x / (1.0 - z)) + ((t - a) * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e-19) || !(z <= 2.2e-71))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e-19) || ~((z <= 2.2e-71)))
		tmp = (t - a) / (b - y);
	else
		tmp = (x / (1.0 - z)) + ((t - a) * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e-19], N[Not[LessEqual[z, 2.2e-71]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e-19 or 2.19999999999999997e-71 < z

   1. Initial program 55.4%

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

   2. Taylor expanded in z around inf 76.0%

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

   if -2.2999999999999998e-19 < z < 2.19999999999999997e-71

   1. Initial program 85.4%

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

   2. Taylor expanded in y around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. unsub-neg 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in x around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. times-frac 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in z around 0 77.0%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-19} \lor \neg \left(z \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \left(t - a\right) \cdot \frac{z}{y}\\ \end{array} \]

Alternative 10: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-58} \lor \neg \left(y \leq 2.05 \cdot 10^{-16}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.8e+175)
     t_1
     (if (<= y -4e+123)
       (/ t (- b y))
       (if (or (<= y -2.05e-58) (not (<= y 2.05e-16)))
         t_1
         (- (/ t b) (/ a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.8e+175) {
		tmp = t_1;
	} else if (y <= -4e+123) {
		tmp = t / (b - y);
	} else if ((y <= -2.05e-58) || !(y <= 2.05e-16)) {
		tmp = t_1;
	} else {
		tmp = (t / b) - (a / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.8d+175)) then
        tmp = t_1
    else if (y <= (-4d+123)) then
        tmp = t / (b - y)
    else if ((y <= (-2.05d-58)) .or. (.not. (y <= 2.05d-16))) then
        tmp = t_1
    else
        tmp = (t / b) - (a / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.8e+175) {
		tmp = t_1;
	} else if (y <= -4e+123) {
		tmp = t / (b - y);
	} else if ((y <= -2.05e-58) || !(y <= 2.05e-16)) {
		tmp = t_1;
	} else {
		tmp = (t / b) - (a / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.8e+175:
		tmp = t_1
	elif y <= -4e+123:
		tmp = t / (b - y)
	elif (y <= -2.05e-58) or not (y <= 2.05e-16):
		tmp = t_1
	else:
		tmp = (t / b) - (a / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.8e+175)
		tmp = t_1;
	elseif (y <= -4e+123)
		tmp = Float64(t / Float64(b - y));
	elseif ((y <= -2.05e-58) || !(y <= 2.05e-16))
		tmp = t_1;
	else
		tmp = Float64(Float64(t / b) - Float64(a / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.8e+175)
		tmp = t_1;
	elseif (y <= -4e+123)
		tmp = t / (b - y);
	elseif ((y <= -2.05e-58) || ~((y <= 2.05e-16)))
		tmp = t_1;
	else
		tmp = (t / b) - (a / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+175], t$95$1, If[LessEqual[y, -4e+123], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.05e-58], N[Not[LessEqual[y, 2.05e-16]], $MachinePrecision]], t$95$1, N[(N[(t / b), $MachinePrecision] - N[(a / b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999997e175 or -3.99999999999999991e123 < y < -2.05000000000000014e-58 or 2.05000000000000003e-16 < y

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

   4. Simplified 59.0%

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

   if -3.7999999999999997e175 < y < -3.99999999999999991e123

   1. Initial program 51.6%

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

   2. Taylor expanded in t around inf 22.1%

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

      1. *-commutative 22.1%

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

   4. Simplified 22.1%

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

   5. Taylor expanded in z around inf 50.2%

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

   if -2.05000000000000014e-58 < y < 2.05000000000000003e-16

   1. Initial program 81.8%

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

      1. div-inv 81.7%

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

      2. fma-def 81.7%

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

      3. +-commutative 81.7%

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

      4. fma-udef 81.7%

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

   3. Applied egg-rr 81.7%

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

   4. Taylor expanded in b around inf 55.6%

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

      1. associate-/r* 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in x around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. associate--l+ 70.1%

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

      3. times-frac 67.2%

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

      4. div-sub 67.2%

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

   9. Simplified 67.2%

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

   10. Taylor expanded in x around 0 60.4%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-58} \lor \neg \left(y \leq 2.05 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \end{array} \]

Alternative 11: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-71}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.65e-56)
     t_1
     (if (<= z -6.5e-93)
       (/ (* x y) (+ y (* z (- b y))))
       (if (<= z -5.6e-119)
         (/ (- t a) b)
         (if (<= z 1.5e-71) (+ x (* x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.65e-56) {
		tmp = t_1;
	} else if (z <= -6.5e-93) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -5.6e-119) {
		tmp = (t - a) / b;
	} else if (z <= 1.5e-71) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.65d-56)) then
        tmp = t_1
    else if (z <= (-6.5d-93)) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (z <= (-5.6d-119)) then
        tmp = (t - a) / b
    else if (z <= 1.5d-71) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.65e-56) {
		tmp = t_1;
	} else if (z <= -6.5e-93) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (z <= -5.6e-119) {
		tmp = (t - a) / b;
	} else if (z <= 1.5e-71) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.65e-56:
		tmp = t_1
	elif z <= -6.5e-93:
		tmp = (x * y) / (y + (z * (b - y)))
	elif z <= -5.6e-119:
		tmp = (t - a) / b
	elif z <= 1.5e-71:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.65e-56)
		tmp = t_1;
	elseif (z <= -6.5e-93)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= -5.6e-119)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 1.5e-71)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.65e-56)
		tmp = t_1;
	elseif (z <= -6.5e-93)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (z <= -5.6e-119)
		tmp = (t - a) / b;
	elseif (z <= 1.5e-71)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-56], t$95$1, If[LessEqual[z, -6.5e-93], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.6e-119], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.5e-71], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.64999999999999992e-56 or 1.5000000000000001e-71 < z

   1. Initial program 57.5%

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

   2. Taylor expanded in z around inf 74.0%

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

   if -1.64999999999999992e-56 < z < -6.5e-93

   1. Initial program 92.2%

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

   2. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

   4. Simplified 60.1%

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

   if -6.5e-93 < z < -5.6e-119

   1. Initial program 71.3%

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

   2. Taylor expanded in y around 0 62.2%

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

   if -5.6e-119 < z < 1.5000000000000001e-71

   1. Initial program 84.9%

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

   2. Taylor expanded in y around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in z around 0 62.2%

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

      1. *-commutative 62.2%

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

   7. Simplified 62.2%

      \[\leadsto \color{blue}{x + z \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-56}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-71}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 51.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-57} \lor \neg \left(y \leq 2.5 \cdot 10^{-14}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.5e+175)
     t_1
     (if (<= y -4e+123)
       (/ t (- b y))
       (if (or (<= y -3.8e-57) (not (<= y 2.5e-14))) t_1 (/ (- t a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e+175) {
		tmp = t_1;
	} else if (y <= -4e+123) {
		tmp = t / (b - y);
	} else if ((y <= -3.8e-57) || !(y <= 2.5e-14)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-3.5d+175)) then
        tmp = t_1
    else if (y <= (-4d+123)) then
        tmp = t / (b - y)
    else if ((y <= (-3.8d-57)) .or. (.not. (y <= 2.5d-14))) then
        tmp = t_1
    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 t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -3.5e+175) {
		tmp = t_1;
	} else if (y <= -4e+123) {
		tmp = t / (b - y);
	} else if ((y <= -3.8e-57) || !(y <= 2.5e-14)) {
		tmp = t_1;
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -3.5e+175:
		tmp = t_1
	elif y <= -4e+123:
		tmp = t / (b - y)
	elif (y <= -3.8e-57) or not (y <= 2.5e-14):
		tmp = t_1
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -3.5e+175)
		tmp = t_1;
	elseif (y <= -4e+123)
		tmp = Float64(t / Float64(b - y));
	elseif ((y <= -3.8e-57) || !(y <= 2.5e-14))
		tmp = t_1;
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -3.5e+175)
		tmp = t_1;
	elseif (y <= -4e+123)
		tmp = t / (b - y);
	elseif ((y <= -3.8e-57) || ~((y <= 2.5e-14)))
		tmp = t_1;
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+175], t$95$1, If[LessEqual[y, -4e+123], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.8e-57], N[Not[LessEqual[y, 2.5e-14]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000003e175 or -3.99999999999999991e123 < y < -3.7999999999999997e-57 or 2.5000000000000001e-14 < y

   1. Initial program 59.1%

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

   2. Taylor expanded in y around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. unsub-neg 59.0%

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

   4. Simplified 59.0%

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

   if -3.5000000000000003e175 < y < -3.99999999999999991e123

   1. Initial program 51.6%

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

   2. Taylor expanded in t around inf 22.1%

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

      1. *-commutative 22.1%

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

   4. Simplified 22.1%

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

   5. Taylor expanded in z around inf 50.2%

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

   if -3.7999999999999997e-57 < y < 2.5000000000000001e-14

   1. Initial program 81.8%

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

   2. Taylor expanded in y around 0 60.4%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+123}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-57} \lor \neg \left(y \leq 2.5 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 13: 35.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-71}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -1.9e+156)
     t_1
     (if (<= z -9.5e+55)
       (/ a y)
       (if (<= z -5.8e-6) (/ t b) (if (<= z 1.35e-71) (+ x (* x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -1.9e+156) {
		tmp = t_1;
	} else if (z <= -9.5e+55) {
		tmp = a / y;
	} else if (z <= -5.8e-6) {
		tmp = t / b;
	} else if (z <= 1.35e-71) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-1.9d+156)) then
        tmp = t_1
    else if (z <= (-9.5d+55)) then
        tmp = a / y
    else if (z <= (-5.8d-6)) then
        tmp = t / b
    else if (z <= 1.35d-71) then
        tmp = x + (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -1.9e+156) {
		tmp = t_1;
	} else if (z <= -9.5e+55) {
		tmp = a / y;
	} else if (z <= -5.8e-6) {
		tmp = t / b;
	} else if (z <= 1.35e-71) {
		tmp = x + (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -1.9e+156:
		tmp = t_1
	elif z <= -9.5e+55:
		tmp = a / y
	elif z <= -5.8e-6:
		tmp = t / b
	elif z <= 1.35e-71:
		tmp = x + (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -1.9e+156)
		tmp = t_1;
	elseif (z <= -9.5e+55)
		tmp = Float64(a / y);
	elseif (z <= -5.8e-6)
		tmp = Float64(t / b);
	elseif (z <= 1.35e-71)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -1.9e+156)
		tmp = t_1;
	elseif (z <= -9.5e+55)
		tmp = a / y;
	elseif (z <= -5.8e-6)
		tmp = t / b;
	elseif (z <= 1.35e-71)
		tmp = x + (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -1.9e+156], t$95$1, If[LessEqual[z, -9.5e+55], N[(a / y), $MachinePrecision], If[LessEqual[z, -5.8e-6], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.35e-71], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.90000000000000012e156 or 1.3500000000000001e-71 < z

   1. Initial program 46.9%

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

      1. div-inv 46.8%

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

      2. fma-def 46.8%

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

      3. +-commutative 46.8%

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

      4. fma-udef 46.8%

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

   3. Applied egg-rr 46.8%

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

   4. Taylor expanded in b around inf 30.0%

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

      1. associate-/r* 31.6%

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

   6. Simplified 31.6%

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

   7. Taylor expanded in a around inf 31.9%

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

      1. mul-1-neg 31.9%

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

      2. distribute-neg-frac 31.9%

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

   9. Simplified 31.9%

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

   if -1.90000000000000012e156 < z < -9.49999999999999989e55

   1. Initial program 74.0%

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

   2. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. unsub-neg 47.6%

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

   4. Simplified 47.6%

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

   5. Taylor expanded in z around inf 60.7%

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

      1. associate-*r/ 60.7%

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

      2. mul-1-neg 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 47.6%

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

   if -9.49999999999999989e55 < z < -5.8000000000000004e-6

   1. Initial program 80.2%

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

   2. Taylor expanded in t around inf 54.7%

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

      1. *-commutative 54.7%

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

   4. Simplified 54.7%

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

   5. Taylor expanded in y around 0 42.2%

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

   if -5.8000000000000004e-6 < z < 1.3500000000000001e-71

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. unsub-neg 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in z around 0 54.3%

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

      1. *-commutative 54.3%

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

   7. Simplified 54.3%

      \[\leadsto \color{blue}{x + z \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+156}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-71}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 14: 35.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= z -3.1e+156)
     t_1
     (if (<= z -9.2e+55)
       (/ a y)
       (if (<= z -1.05e-84) (/ t b) (if (<= z 1.9e-71) x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -3.1e+156) {
		tmp = t_1;
	} else if (z <= -9.2e+55) {
		tmp = a / y;
	} else if (z <= -1.05e-84) {
		tmp = t / b;
	} else if (z <= 1.9e-71) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (z <= (-3.1d+156)) then
        tmp = t_1
    else if (z <= (-9.2d+55)) then
        tmp = a / y
    else if (z <= (-1.05d-84)) then
        tmp = t / b
    else if (z <= 1.9d-71) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (z <= -3.1e+156) {
		tmp = t_1;
	} else if (z <= -9.2e+55) {
		tmp = a / y;
	} else if (z <= -1.05e-84) {
		tmp = t / b;
	} else if (z <= 1.9e-71) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if z <= -3.1e+156:
		tmp = t_1
	elif z <= -9.2e+55:
		tmp = a / y
	elif z <= -1.05e-84:
		tmp = t / b
	elif z <= 1.9e-71:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (z <= -3.1e+156)
		tmp = t_1;
	elseif (z <= -9.2e+55)
		tmp = Float64(a / y);
	elseif (z <= -1.05e-84)
		tmp = Float64(t / b);
	elseif (z <= 1.9e-71)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (z <= -3.1e+156)
		tmp = t_1;
	elseif (z <= -9.2e+55)
		tmp = a / y;
	elseif (z <= -1.05e-84)
		tmp = t / b;
	elseif (z <= 1.9e-71)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[z, -3.1e+156], t$95$1, If[LessEqual[z, -9.2e+55], N[(a / y), $MachinePrecision], If[LessEqual[z, -1.05e-84], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.9e-71], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1000000000000002e156 or 1.89999999999999996e-71 < z

   1. Initial program 46.9%

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

      1. div-inv 46.8%

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

      2. fma-def 46.8%

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

      3. +-commutative 46.8%

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

      4. fma-udef 46.8%

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

   3. Applied egg-rr 46.8%

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

   4. Taylor expanded in b around inf 30.0%

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

      1. associate-/r* 31.6%

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

   6. Simplified 31.6%

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

   7. Taylor expanded in a around inf 31.9%

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

      1. mul-1-neg 31.9%

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

      2. distribute-neg-frac 31.9%

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

   9. Simplified 31.9%

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

   if -3.1000000000000002e156 < z < -9.1999999999999995e55

   1. Initial program 74.0%

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

   2. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. unsub-neg 47.6%

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

   4. Simplified 47.6%

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

   5. Taylor expanded in z around inf 60.7%

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

      1. associate-*r/ 60.7%

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

      2. mul-1-neg 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in t around 0 47.6%

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

   if -9.1999999999999995e55 < z < -1.04999999999999999e-84

   1. Initial program 89.4%

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

   2. Taylor expanded in t around inf 47.1%

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

      1. *-commutative 47.1%

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

   4. Simplified 47.1%

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

   5. Taylor expanded in y around 0 30.8%

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

   if -1.04999999999999999e-84 < z < 1.89999999999999996e-71

   1. Initial program 83.8%

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

   2. Taylor expanded in z around 0 60.9%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+156}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 15: 64.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-119} \lor \neg \left(z \leq 1.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e-119) (not (<= z 1.2e-71)))
   (/ (- t a) (- b y))
   (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e-119) || !(z <= 1.2e-71)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.8d-119)) .or. (.not. (z <= 1.2d-71))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e-119) || !(z <= 1.2e-71)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.8e-119) or not (z <= 1.2e-71):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e-119) || !(z <= 1.2e-71))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.8e-119) || ~((z <= 1.2e-71)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e-119], N[Not[LessEqual[z, 1.2e-71]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999975e-119 or 1.2e-71 < z

   1. Initial program 60.8%

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

   2. Taylor expanded in z around inf 69.6%

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

   if -3.79999999999999975e-119 < z < 1.2e-71

   1. Initial program 84.9%

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

   2. Taylor expanded in y around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. unsub-neg 62.2%

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

   4. Simplified 62.2%

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

   5. Taylor expanded in z around 0 62.2%

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

      1. *-commutative 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-119} \lor \neg \left(z \leq 1.2 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 16: 45.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-6} \lor \neg \left(z \leq 5.1 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.7e-6) (not (<= z 5.1e-55))) (/ t (- b y)) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.7e-6) || !(z <= 5.1e-55)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.7d-6)) .or. (.not. (z <= 5.1d-55))) then
        tmp = t / (b - y)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.7e-6) || !(z <= 5.1e-55)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.7e-6) or not (z <= 5.1e-55):
		tmp = t / (b - y)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.7e-6) || !(z <= 5.1e-55))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.7e-6) || ~((z <= 5.1e-55)))
		tmp = t / (b - y);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.7e-6], N[Not[LessEqual[z, 5.1e-55]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000002e-6 or 5.09999999999999995e-55 < z

   1. Initial program 52.6%

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

   2. Taylor expanded in t around inf 28.7%

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

      1. *-commutative 28.7%

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

   4. Simplified 28.7%

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

   5. Taylor expanded in z around inf 42.3%

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

   if -3.7000000000000002e-6 < z < 5.09999999999999995e-55

   1. Initial program 86.3%

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

   2. Taylor expanded in y around inf 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

   4. Simplified 54.0%

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

   5. Taylor expanded in z around 0 53.8%

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

      1. *-commutative 53.8%

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

   7. Simplified 53.8%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-6} \lor \neg \left(z \leq 5.1 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 17: 45.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-6} \lor \neg \left(z \leq 5.4 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e-6) (not (<= z 5.4e-55))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e-6) || !(z <= 5.4e-55)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.2d-6)) .or. (.not. (z <= 5.4d-55))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e-6) || !(z <= 5.4e-55)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.2e-6) or not (z <= 5.4e-55):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e-6) || !(z <= 5.4e-55))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e-6) || ~((z <= 5.4e-55)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e-6], N[Not[LessEqual[z, 5.4e-55]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999996e-6 or 5.40000000000000008e-55 < z

   1. Initial program 52.6%

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

   2. Taylor expanded in t around inf 28.7%

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

      1. *-commutative 28.7%

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

   4. Simplified 28.7%

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

   5. Taylor expanded in z around inf 42.3%

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

   if -4.1999999999999996e-6 < z < 5.40000000000000008e-55

   1. Initial program 86.3%

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

   2. Taylor expanded in y around inf 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

   4. Simplified 54.0%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-6} \lor \neg \left(z \leq 5.4 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 18: 33.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -650 \lor \neg \left(z \leq 1.2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -650.0) (not (<= z 1.2e-32))) (/ a y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -650.0) || !(z <= 1.2e-32)) {
		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 <= (-650.0d0)) .or. (.not. (z <= 1.2d-32))) 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 <= -650.0) || !(z <= 1.2e-32)) {
		tmp = a / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -650.0) or not (z <= 1.2e-32):
		tmp = a / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -650.0) || !(z <= 1.2e-32))
		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 <= -650.0) || ~((z <= 1.2e-32)))
		tmp = a / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -650.0], N[Not[LessEqual[z, 1.2e-32]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -650 or 1.2000000000000001e-32 < z

   1. Initial program 49.9%

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

   2. Taylor expanded in y around inf 25.7%

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

      1. mul-1-neg 25.7%

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

      2. unsub-neg 25.7%

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

   4. Simplified 25.7%

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

   5. Taylor expanded in z around inf 34.5%

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

      1. associate-*r/ 34.5%

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

      2. mul-1-neg 34.5%

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

   7. Simplified 34.5%

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

   8. Taylor expanded in t around 0 17.0%

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

   if -650 < z < 1.2000000000000001e-32

   1. Initial program 86.5%

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

   2. Taylor expanded in z around 0 50.7%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -650 \lor \neg \left(z \leq 1.2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 36.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-84} \lor \neg \left(z \leq 1.85 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-84) (not (<= z 1.85e-36))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-84) || !(z <= 1.85e-36)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.05d-84)) .or. (.not. (z <= 1.85d-36))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-84) || !(z <= 1.85e-36)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-84) or not (z <= 1.85e-36):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-84) || !(z <= 1.85e-36))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-84) || ~((z <= 1.85e-36)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-84], N[Not[LessEqual[z, 1.85e-36]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999999e-84 or 1.85000000000000001e-36 < z

   1. Initial program 58.4%

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

   2. Taylor expanded in t around inf 30.7%

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

      1. *-commutative 30.7%

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

   4. Simplified 30.7%

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

   5. Taylor expanded in y around 0 27.5%

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

   if -1.04999999999999999e-84 < z < 1.85000000000000001e-36

   1. Initial program 84.0%

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

   2. Taylor expanded in z around 0 58.9%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-84} \lor \neg \left(z \leq 1.85 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 24.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.2%

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

2. Taylor expanded in z around 0 28.4%

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

3. Final simplification 28.4%

   \[\leadsto x \]

Developer target: 73.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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