Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 92.8%

Time: 20.9s

Alternatives: 22

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_3}{t_1}\\ \mathbf{elif}\;t_4 \leq 4 \cdot 10^{-303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+274}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (+
          (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
          (* (/ y z) (/ (- a t) (pow (- b y) 2.0)))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -5e-306)
       (+ (/ (* x y) t_1) (/ t_3 t_1))
       (if (<= t_4 4e-303)
         t_2
         (if (<= t_4 2e+274) t_4 (if (<= t_4 INFINITY) t_5 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -5e-306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else if (t_4 <= 4e-303) {
		tmp = t_2;
	} else if (t_4 <= 2e+274) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = y + (z * (b - y));
	double t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -5e-306) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else if (t_4 <= 4e-303) {
		tmp = t_2;
	} else if (t_4 <= 2e+274) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	t_5 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -5e-306:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	elif t_4 <= 4e-303:
		tmp = t_2
	elif t_4 <= 2e+274:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -5e-306)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	elseif (t_4 <= 4e-303)
		tmp = t_2;
	elseif (t_4 <= 2e+274)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	t_5 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -5e-306)
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	elseif (t_4 <= 4e-303)
		tmp = t_2;
	elseif (t_4 <= 2e+274)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -5e-306], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 4e-303], t$95$2, If[LessEqual[t$95$4, 2e+274], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.99999999999999984e274 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.8%

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

   2. Taylor expanded in y around -inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. unsub-neg 48.0%

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

      3. associate-*r/ 48.0%

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

      4. neg-mul-1 48.0%

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

      5. sub-neg 48.0%

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

      6. metadata-eval 48.0%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in z around inf 69.7%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999998e-306

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.5%

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

   if -4.99999999999999998e-306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.99999999999999972e-303 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 9.0%

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

   2. Taylor expanded in z around inf 48.6%

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

      1. associate--r+ 48.6%

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

      2. +-commutative 48.6%

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

      3. associate--l+ 48.6%

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

      4. *-commutative 48.6%

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

      5. times-frac 67.9%

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

      6. div-sub 67.9%

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

      7. times-frac 96.4%

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

   4. Simplified 96.4%

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

   if 3.99999999999999972e-303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999984e274

   1. Initial program 99.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{-303}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]

Alternative 2: 85.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{-303}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+274}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-306)
       t_1
       (if (<= t_1 4e-303)
         (/ (- t a) (- b y))
         (if (<= t_1 2e+274) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 4e-303) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 2e+274) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -5e-306) {
		tmp = t_1;
	} else if (t_1 <= 4e-303) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 2e+274) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -5e-306:
		tmp = t_1
	elif t_1 <= 4e-303:
		tmp = (t - a) / (b - y)
	elif t_1 <= 2e+274:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 4e-303)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_1 <= 2e+274)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -5e-306)
		tmp = t_1;
	elseif (t_1 <= 4e-303)
		tmp = (t - a) / (b - y);
	elseif (t_1 <= 2e+274)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-306], t$95$1, If[LessEqual[t$95$1, 4e-303], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+274], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.99999999999999984e274 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 18.2%

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

   2. Taylor expanded in y around -inf 30.7%

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

      1. mul-1-neg 30.7%

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

      2. unsub-neg 30.7%

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

      3. associate-*r/ 30.7%

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

      4. neg-mul-1 30.7%

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

      5. sub-neg 30.7%

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

      6. metadata-eval 30.7%

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

   4. Simplified 48.5%

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

   5. Taylor expanded in z around inf 68.2%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999998e-306 or 3.99999999999999972e-303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999984e274

   1. Initial program 99.6%

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

   if -4.99999999999999998e-306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.99999999999999972e-303

   1. Initial program 22.8%

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

   2. Taylor expanded in z around inf 78.2%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{-303}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]

Alternative 3: 85.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t_2}{t_1}\\ t_4 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_2}{t_1}\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{-303}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+274}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) t_1))
        (t_4 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -5e-306)
       (+ (/ (* x y) t_1) (/ t_2 t_1))
       (if (<= t_3 4e-303)
         (/ (- t a) (- b y))
         (if (<= t_3 2e+274) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double t_4 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -5e-306) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else if (t_3 <= 4e-303) {
		tmp = (t - a) / (b - y);
	} else if (t_3 <= 2e+274) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / t_1;
	double t_4 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_3 <= -5e-306) {
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	} else if (t_3 <= 4e-303) {
		tmp = (t - a) / (b - y);
	} else if (t_3 <= 2e+274) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = ((x * y) + t_2) / t_1
	t_4 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_4
	elif t_3 <= -5e-306:
		tmp = ((x * y) / t_1) + (t_2 / t_1)
	elif t_3 <= 4e-303:
		tmp = (t - a) / (b - y)
	elif t_3 <= 2e+274:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / t_1)
	t_4 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -5e-306)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_2 / t_1));
	elseif (t_3 <= 4e-303)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_3 <= 2e+274)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = ((x * y) + t_2) / t_1;
	t_4 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_4;
	elseif (t_3 <= -5e-306)
		tmp = ((x * y) / t_1) + (t_2 / t_1);
	elseif (t_3 <= 4e-303)
		tmp = (t - a) / (b - y);
	elseif (t_3 <= 2e+274)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -5e-306], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e-303], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+274], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.99999999999999984e274 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 18.2%

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

   2. Taylor expanded in y around -inf 30.7%

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

      1. mul-1-neg 30.7%

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

      2. unsub-neg 30.7%

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

      3. associate-*r/ 30.7%

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

      4. neg-mul-1 30.7%

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

      5. sub-neg 30.7%

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

      6. metadata-eval 30.7%

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

   4. Simplified 48.5%

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

   5. Taylor expanded in z around inf 68.2%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999998e-306

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.5%

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

   if -4.99999999999999998e-306 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.99999999999999972e-303

   1. Initial program 22.8%

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

   2. Taylor expanded in z around inf 78.2%

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

   if 3.99999999999999972e-303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999984e274

   1. Initial program 99.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{-303}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+274}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]

Alternative 4: 80.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.42:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+64} \lor \neg \left(z \leq 3.9 \cdot 10^{+80}\right) \land z \leq 3 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) y) (/ x (+ z -1.0)))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -5e+141)
     t_2
     (if (<= z -7.5e+19)
       t_1
       (if (<= z 1.42)
         (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))
         (if (or (<= z 2e+64) (and (not (<= z 3.9e+80)) (<= z 3e+101)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5e+141) {
		tmp = t_2;
	} else if (z <= -7.5e+19) {
		tmp = t_1;
	} else if (z <= 1.42) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	} else if ((z <= 2e+64) || (!(z <= 3.9e+80) && (z <= 3e+101))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a - t) / y) - (x / (z + (-1.0d0)))
    t_2 = (t - a) / (b - y)
    if (z <= (-5d+141)) then
        tmp = t_2
    else if (z <= (-7.5d+19)) then
        tmp = t_1
    else if (z <= 1.42d0) then
        tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
    else if ((z <= 2d+64) .or. (.not. (z <= 3.9d+80)) .and. (z <= 3d+101)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5e+141) {
		tmp = t_2;
	} else if (z <= -7.5e+19) {
		tmp = t_1;
	} else if (z <= 1.42) {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	} else if ((z <= 2e+64) || (!(z <= 3.9e+80) && (z <= 3e+101))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / y) - (x / (z + -1.0))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -5e+141:
		tmp = t_2
	elif z <= -7.5e+19:
		tmp = t_1
	elif z <= 1.42:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
	elif (z <= 2e+64) or (not (z <= 3.9e+80) and (z <= 3e+101)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5e+141)
		tmp = t_2;
	elseif (z <= -7.5e+19)
		tmp = t_1;
	elseif (z <= 1.42)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	elseif ((z <= 2e+64) || (!(z <= 3.9e+80) && (z <= 3e+101)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / y) - (x / (z + -1.0));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5e+141)
		tmp = t_2;
	elseif (z <= -7.5e+19)
		tmp = t_1;
	elseif (z <= 1.42)
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	elseif ((z <= 2e+64) || (~((z <= 3.9e+80)) && (z <= 3e+101)))
		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[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+141], t$95$2, If[LessEqual[z, -7.5e+19], t$95$1, If[LessEqual[z, 1.42], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2e+64], And[N[Not[LessEqual[z, 3.9e+80]], $MachinePrecision], LessEqual[z, 3e+101]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000025e141 or 2.00000000000000004e64 < z < 3.89999999999999999e80 or 2.99999999999999993e101 < z

   1. Initial program 36.9%

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

   2. Taylor expanded in z around inf 87.1%

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

   if -5.00000000000000025e141 < z < -7.5e19 or 1.4199999999999999 < z < 2.00000000000000004e64 or 3.89999999999999999e80 < z < 2.99999999999999993e101

   1. Initial program 50.5%

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

   2. Taylor expanded in y around -inf 52.0%

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

      1. mul-1-neg 52.0%

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

      2. unsub-neg 52.0%

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

      3. associate-*r/ 52.0%

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

      4. neg-mul-1 52.0%

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

      5. sub-neg 52.0%

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

      6. metadata-eval 52.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in z around inf 72.7%

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

   if -7.5e19 < z < 1.4199999999999999

   1. Initial program 87.0%

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

   2. Taylor expanded in b around inf 84.7%

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

      1. *-commutative 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+141}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq 1.42:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+64} \lor \neg \left(z \leq 3.9 \cdot 10^{+80}\right) \land z \leq 3 \cdot 10^{+101}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 62.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;y \leq -0.145:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= y -0.145)
     t_2
     (if (<= y 6.2e-88)
       t_1
       (if (<= y 5.1e+28)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= y 7.5e+102)
           t_1
           (if (<= y 1.9e+120)
             (/ x (- 1.0 z))
             (if (<= y 9.8e+148) t_1 t_2))))))))

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 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -0.145) {
		tmp = t_2;
	} else if (y <= 6.2e-88) {
		tmp = t_1;
	} else if (y <= 5.1e+28) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (y <= 7.5e+102) {
		tmp = t_1;
	} else if (y <= 1.9e+120) {
		tmp = x / (1.0 - z);
	} else if (y <= 9.8e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((a - t) / y) - (x / (z + (-1.0d0)))
    if (y <= (-0.145d0)) then
        tmp = t_2
    else if (y <= 6.2d-88) then
        tmp = t_1
    else if (y <= 5.1d+28) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (y <= 7.5d+102) then
        tmp = t_1
    else if (y <= 1.9d+120) then
        tmp = x / (1.0d0 - z)
    else if (y <= 9.8d+148) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -0.145) {
		tmp = t_2;
	} else if (y <= 6.2e-88) {
		tmp = t_1;
	} else if (y <= 5.1e+28) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (y <= 7.5e+102) {
		tmp = t_1;
	} else if (y <= 1.9e+120) {
		tmp = x / (1.0 - z);
	} else if (y <= 9.8e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if y <= -0.145:
		tmp = t_2
	elif y <= 6.2e-88:
		tmp = t_1
	elif y <= 5.1e+28:
		tmp = (x * y) / (y + (z * (b - y)))
	elif y <= 7.5e+102:
		tmp = t_1
	elif y <= 1.9e+120:
		tmp = x / (1.0 - z)
	elif y <= 9.8e+148:
		tmp = t_1
	else:
		tmp = t_2
	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(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (y <= -0.145)
		tmp = t_2;
	elseif (y <= 6.2e-88)
		tmp = t_1;
	elseif (y <= 5.1e+28)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (y <= 7.5e+102)
		tmp = t_1;
	elseif (y <= 1.9e+120)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (y <= 9.8e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (y <= -0.145)
		tmp = t_2;
	elseif (y <= 6.2e-88)
		tmp = t_1;
	elseif (y <= 5.1e+28)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (y <= 7.5e+102)
		tmp = t_1;
	elseif (y <= 1.9e+120)
		tmp = x / (1.0 - z);
	elseif (y <= 9.8e+148)
		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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.145], t$95$2, If[LessEqual[y, 6.2e-88], t$95$1, If[LessEqual[y, 5.1e+28], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+102], t$95$1, If[LessEqual[y, 1.9e+120], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+148], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.14499999999999999 or 9.8e148 < y

   1. Initial program 49.8%

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

   2. Taylor expanded in y around -inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

      3. associate-*r/ 66.1%

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

      4. neg-mul-1 66.1%

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

      5. sub-neg 66.1%

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

      6. metadata-eval 66.1%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in z around inf 70.6%

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

   if -0.14499999999999999 < y < 6.1999999999999995e-88 or 5.1000000000000004e28 < y < 7.5e102 or 1.8999999999999999e120 < y < 9.8e148

   1. Initial program 71.5%

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

   2. Taylor expanded in z around inf 67.6%

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

   if 6.1999999999999995e-88 < y < 5.1000000000000004e28

   1. Initial program 83.0%

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

   2. Taylor expanded in x around inf 55.3%

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

      1. *-commutative 55.3%

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

   4. Simplified 55.3%

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

   if 7.5e102 < y < 1.8999999999999999e120

   1. Initial program 83.3%

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

   2. Taylor expanded in y around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.145:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]

Alternative 6: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;y \leq -0.155:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= y -0.155)
     (- (/ a y) (/ x (+ z -1.0)))
     (if (<= y 8.4e-88)
       t_1
       (if (<= y 4.2e+28)
         (/ (* x y) (+ y (* z (- b y))))
         (if (<= y 1.7e+103)
           t_1
           (if (<= y 1.1e+120)
             (/ x (- 1.0 z))
             (if (<= y 4.6e+149) t_1 (- (/ (- x) (+ z -1.0)) (/ t y))))))))))

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 (y <= -0.155) {
		tmp = (a / y) - (x / (z + -1.0));
	} else if (y <= 8.4e-88) {
		tmp = t_1;
	} else if (y <= 4.2e+28) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (y <= 1.7e+103) {
		tmp = t_1;
	} else if (y <= 1.1e+120) {
		tmp = x / (1.0 - z);
	} else if (y <= 4.6e+149) {
		tmp = t_1;
	} else {
		tmp = (-x / (z + -1.0)) - (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (y <= (-0.155d0)) then
        tmp = (a / y) - (x / (z + (-1.0d0)))
    else if (y <= 8.4d-88) then
        tmp = t_1
    else if (y <= 4.2d+28) then
        tmp = (x * y) / (y + (z * (b - y)))
    else if (y <= 1.7d+103) then
        tmp = t_1
    else if (y <= 1.1d+120) then
        tmp = x / (1.0d0 - z)
    else if (y <= 4.6d+149) then
        tmp = t_1
    else
        tmp = (-x / (z + (-1.0d0))) - (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (y <= -0.155) {
		tmp = (a / y) - (x / (z + -1.0));
	} else if (y <= 8.4e-88) {
		tmp = t_1;
	} else if (y <= 4.2e+28) {
		tmp = (x * y) / (y + (z * (b - y)));
	} else if (y <= 1.7e+103) {
		tmp = t_1;
	} else if (y <= 1.1e+120) {
		tmp = x / (1.0 - z);
	} else if (y <= 4.6e+149) {
		tmp = t_1;
	} else {
		tmp = (-x / (z + -1.0)) - (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if y <= -0.155:
		tmp = (a / y) - (x / (z + -1.0))
	elif y <= 8.4e-88:
		tmp = t_1
	elif y <= 4.2e+28:
		tmp = (x * y) / (y + (z * (b - y)))
	elif y <= 1.7e+103:
		tmp = t_1
	elif y <= 1.1e+120:
		tmp = x / (1.0 - z)
	elif y <= 4.6e+149:
		tmp = t_1
	else:
		tmp = (-x / (z + -1.0)) - (t / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (y <= -0.155)
		tmp = Float64(Float64(a / y) - Float64(x / Float64(z + -1.0)));
	elseif (y <= 8.4e-88)
		tmp = t_1;
	elseif (y <= 4.2e+28)
		tmp = Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y))));
	elseif (y <= 1.7e+103)
		tmp = t_1;
	elseif (y <= 1.1e+120)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (y <= 4.6e+149)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-x) / Float64(z + -1.0)) - Float64(t / y));
	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 (y <= -0.155)
		tmp = (a / y) - (x / (z + -1.0));
	elseif (y <= 8.4e-88)
		tmp = t_1;
	elseif (y <= 4.2e+28)
		tmp = (x * y) / (y + (z * (b - y)));
	elseif (y <= 1.7e+103)
		tmp = t_1;
	elseif (y <= 1.1e+120)
		tmp = x / (1.0 - z);
	elseif (y <= 4.6e+149)
		tmp = t_1;
	else
		tmp = (-x / (z + -1.0)) - (t / y);
	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[y, -0.155], N[(N[(a / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e-88], t$95$1, If[LessEqual[y, 4.2e+28], N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+103], t$95$1, If[LessEqual[y, 1.1e+120], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+149], t$95$1, N[(N[((-x) / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.154999999999999999

   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 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

      3. associate-*r/ 63.3%

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

      4. neg-mul-1 63.3%

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

      5. sub-neg 63.3%

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

      6. metadata-eval 63.3%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in z around inf 65.4%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. sub-neg 58.6%

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

      3. metadata-eval 58.6%

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

      4. neg-mul-1 58.6%

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

      5. unsub-neg 58.6%

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

      6. +-commutative 58.6%

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

   8. Simplified 58.6%

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

   if -0.154999999999999999 < y < 8.3999999999999998e-88 or 4.19999999999999978e28 < y < 1.6999999999999999e103 or 1.1000000000000001e120 < y < 4.5999999999999997e149

   1. Initial program 71.5%

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

   2. Taylor expanded in z around inf 67.6%

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

   if 8.3999999999999998e-88 < y < 4.19999999999999978e28

   1. Initial program 83.0%

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

   2. Taylor expanded in x around inf 55.3%

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

      1. *-commutative 55.3%

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

   4. Simplified 55.3%

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

   if 1.6999999999999999e103 < y < 1.1000000000000001e120

   1. Initial program 83.3%

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

   2. Taylor expanded in y around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   4. Simplified 83.7%

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

   if 4.5999999999999997e149 < y

   1. Initial program 38.6%

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

   2. Taylor expanded in y around -inf 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. associate-*r/ 72.4%

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

      4. neg-mul-1 72.4%

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

      5. sub-neg 72.4%

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

      6. metadata-eval 72.4%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in z around inf 82.2%

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

   6. Taylor expanded in t around inf 81.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.155:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+103}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \end{array} \]

Alternative 7: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{y} - \frac{x}{z}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3300000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{\frac{y}{z} - y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+124} \lor \neg \left(y \leq 1.9 \cdot 10^{+141}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ a y) (/ x z))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -1.65e+42)
     t_2
     (if (<= y -3300000000.0)
       t_1
       (if (<= y -4.6e-49)
         t_2
         (if (<= y 3.4e+46)
           (/ (- t a) b)
           (if (<= y 6.8e+102)
             (/ t (- (/ y z) y))
             (if (or (<= y 3.9e+124) (not (<= y 1.9e+141))) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a / y) - (x / z);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.65e+42) {
		tmp = t_2;
	} else if (y <= -3300000000.0) {
		tmp = t_1;
	} else if (y <= -4.6e-49) {
		tmp = t_2;
	} else if (y <= 3.4e+46) {
		tmp = (t - a) / b;
	} else if (y <= 6.8e+102) {
		tmp = t / ((y / z) - y);
	} else if ((y <= 3.9e+124) || !(y <= 1.9e+141)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (a / y) - (x / z)
    t_2 = x / (1.0d0 - z)
    if (y <= (-1.65d+42)) then
        tmp = t_2
    else if (y <= (-3300000000.0d0)) then
        tmp = t_1
    else if (y <= (-4.6d-49)) then
        tmp = t_2
    else if (y <= 3.4d+46) then
        tmp = (t - a) / b
    else if (y <= 6.8d+102) then
        tmp = t / ((y / z) - y)
    else if ((y <= 3.9d+124) .or. (.not. (y <= 1.9d+141))) then
        tmp = t_2
    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 / y) - (x / z);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -1.65e+42) {
		tmp = t_2;
	} else if (y <= -3300000000.0) {
		tmp = t_1;
	} else if (y <= -4.6e-49) {
		tmp = t_2;
	} else if (y <= 3.4e+46) {
		tmp = (t - a) / b;
	} else if (y <= 6.8e+102) {
		tmp = t / ((y / z) - y);
	} else if ((y <= 3.9e+124) || !(y <= 1.9e+141)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a / y) - (x / z)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -1.65e+42:
		tmp = t_2
	elif y <= -3300000000.0:
		tmp = t_1
	elif y <= -4.6e-49:
		tmp = t_2
	elif y <= 3.4e+46:
		tmp = (t - a) / b
	elif y <= 6.8e+102:
		tmp = t / ((y / z) - y)
	elif (y <= 3.9e+124) or not (y <= 1.9e+141):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a / y) - Float64(x / z))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.65e+42)
		tmp = t_2;
	elseif (y <= -3300000000.0)
		tmp = t_1;
	elseif (y <= -4.6e-49)
		tmp = t_2;
	elseif (y <= 3.4e+46)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 6.8e+102)
		tmp = Float64(t / Float64(Float64(y / z) - y));
	elseif ((y <= 3.9e+124) || !(y <= 1.9e+141))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a / y) - (x / z);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.65e+42)
		tmp = t_2;
	elseif (y <= -3300000000.0)
		tmp = t_1;
	elseif (y <= -4.6e-49)
		tmp = t_2;
	elseif (y <= 3.4e+46)
		tmp = (t - a) / b;
	elseif (y <= 6.8e+102)
		tmp = t / ((y / z) - y);
	elseif ((y <= 3.9e+124) || ~((y <= 1.9e+141)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+42], t$95$2, If[LessEqual[y, -3300000000.0], t$95$1, If[LessEqual[y, -4.6e-49], t$95$2, If[LessEqual[y, 3.4e+46], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 6.8e+102], N[(t / N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.9e+124], N[Not[LessEqual[y, 1.9e+141]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6499999999999999e42 or -3.3e9 < y < -4.5999999999999998e-49 or 6.8000000000000001e102 < y < 3.9e124 or 1.89999999999999988e141 < y

   1. Initial program 51.7%

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

   2. Taylor expanded in y around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

   4. Simplified 62.4%

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

   if -1.6499999999999999e42 < y < -3.3e9 or 3.9e124 < y < 1.89999999999999988e141

   1. Initial program 56.0%

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

   2. Taylor expanded in y around -inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. unsub-neg 33.0%

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

      3. associate-*r/ 33.0%

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

      4. neg-mul-1 33.0%

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

      5. sub-neg 33.0%

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

      6. metadata-eval 33.0%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in z around inf 77.2%

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

   6. Taylor expanded in t around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. sub-neg 76.9%

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

      3. metadata-eval 76.9%

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

      4. neg-mul-1 76.9%

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

      5. unsub-neg 76.9%

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

      6. +-commutative 76.9%

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

   8. Simplified 76.9%

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

   9. Taylor expanded in z around inf 77.5%

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

   if -4.5999999999999998e-49 < y < 3.3999999999999998e46

   1. Initial program 76.7%

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

   2. Taylor expanded in y around 0 56.3%

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

   if 3.3999999999999998e46 < y < 6.8000000000000001e102

   1. Initial program 61.4%

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

   2. Taylor expanded in t around inf 36.4%

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

      1. associate-/l* 55.2%

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

      2. +-commutative 55.2%

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

      3. fma-def 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in z around 0 55.3%

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

   6. Taylor expanded in b around 0 46.6%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3300000000:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{t}{\frac{y}{z} - y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+124} \lor \neg \left(y \leq 1.9 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \end{array} \]

Alternative 8: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-9} \lor \neg \left(z \leq 230\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{z}{\frac{y}{t - a}}}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.7e+134)
     t_1
     (if (<= z -7.5e+77)
       (- (/ a y) (/ x z))
       (if (or (<= z -1.75e-9) (not (<= z 230.0)))
         t_1
         (- x (/ (/ z (/ y (- t a))) (+ z -1.0))))))))

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 <= -2.7e+134) {
		tmp = t_1;
	} else if (z <= -7.5e+77) {
		tmp = (a / y) - (x / z);
	} else if ((z <= -1.75e-9) || !(z <= 230.0)) {
		tmp = t_1;
	} else {
		tmp = x - ((z / (y / (t - a))) / (z + -1.0));
	}
	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 <= (-2.7d+134)) then
        tmp = t_1
    else if (z <= (-7.5d+77)) then
        tmp = (a / y) - (x / z)
    else if ((z <= (-1.75d-9)) .or. (.not. (z <= 230.0d0))) then
        tmp = t_1
    else
        tmp = x - ((z / (y / (t - a))) / (z + (-1.0d0)))
    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 <= -2.7e+134) {
		tmp = t_1;
	} else if (z <= -7.5e+77) {
		tmp = (a / y) - (x / z);
	} else if ((z <= -1.75e-9) || !(z <= 230.0)) {
		tmp = t_1;
	} else {
		tmp = x - ((z / (y / (t - a))) / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.7e+134:
		tmp = t_1
	elif z <= -7.5e+77:
		tmp = (a / y) - (x / z)
	elif (z <= -1.75e-9) or not (z <= 230.0):
		tmp = t_1
	else:
		tmp = x - ((z / (y / (t - a))) / (z + -1.0))
	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 <= -2.7e+134)
		tmp = t_1;
	elseif (z <= -7.5e+77)
		tmp = Float64(Float64(a / y) - Float64(x / z));
	elseif ((z <= -1.75e-9) || !(z <= 230.0))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z / Float64(y / Float64(t - a))) / Float64(z + -1.0)));
	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 <= -2.7e+134)
		tmp = t_1;
	elseif (z <= -7.5e+77)
		tmp = (a / y) - (x / z);
	elseif ((z <= -1.75e-9) || ~((z <= 230.0)))
		tmp = t_1;
	else
		tmp = x - ((z / (y / (t - a))) / (z + -1.0));
	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, -2.7e+134], t$95$1, If[LessEqual[z, -7.5e+77], N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.75e-9], N[Not[LessEqual[z, 230.0]], $MachinePrecision]], t$95$1, N[(x - N[(N[(z / N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e134 or -7.49999999999999955e77 < z < -1.75e-9 or 230 < z

   1. Initial program 42.9%

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

   2. Taylor expanded in z around inf 77.3%

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

   if -2.7e134 < z < -7.49999999999999955e77

   1. Initial program 44.1%

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

   2. Taylor expanded in y around -inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. associate-*r/ 53.7%

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

      4. neg-mul-1 53.7%

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

      5. sub-neg 53.7%

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

      6. metadata-eval 53.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in z around inf 80.1%

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

   6. Taylor expanded in t around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. sub-neg 80.4%

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

      3. metadata-eval 80.4%

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

      4. neg-mul-1 80.4%

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

      5. unsub-neg 80.4%

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

      6. +-commutative 80.4%

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

   8. Simplified 80.4%

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

   9. Taylor expanded in z around inf 80.4%

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

   if -1.75e-9 < z < 230

   1. Initial program 88.0%

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

   2. Taylor expanded in y around -inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. associate-*r/ 75.3%

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

      4. neg-mul-1 75.3%

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

      5. sub-neg 75.3%

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

      6. metadata-eval 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in x around 0 76.7%

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

      1. associate-/r* 76.7%

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

      2. associate-/l* 70.8%

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

      3. sub-neg 70.8%

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

      4. metadata-eval 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in z around 0 70.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+134}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-9} \lor \neg \left(z \leq 230\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{z}{\frac{y}{t - a}}}{z + -1}\\ \end{array} \]

Alternative 9: 58.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+49} \lor \neg \left(y \leq -4.2 \cdot 10^{+22} \lor \neg \left(y \leq -1.3 \cdot 10^{-49}\right) \land \left(y \leq 3 \cdot 10^{+103} \lor \neg \left(y \leq 3 \cdot 10^{+119}\right) \land y \leq 1.4 \cdot 10^{+149}\right)\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e+49)
         (not
          (or (<= y -4.2e+22)
              (and (not (<= y -1.3e-49))
                   (or (<= y 3e+103)
                       (and (not (<= y 3e+119)) (<= y 1.4e+149)))))))
   (/ x (- 1.0 z))
   (/ (- t a) (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5e+49) || !((y <= -4.2e+22) || (!(y <= -1.3e-49) && ((y <= 3e+103) || (!(y <= 3e+119) && (y <= 1.4e+149)))))) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5d+49)) .or. (.not. (y <= (-4.2d+22)) .or. (.not. (y <= (-1.3d-49))) .and. (y <= 3d+103) .or. (.not. (y <= 3d+119)) .and. (y <= 1.4d+149))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5e+49) || !((y <= -4.2e+22) || (!(y <= -1.3e-49) && ((y <= 3e+103) || (!(y <= 3e+119) && (y <= 1.4e+149)))))) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5e+49) or not ((y <= -4.2e+22) or (not (y <= -1.3e-49) and ((y <= 3e+103) or (not (y <= 3e+119) and (y <= 1.4e+149))))):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5e+49) || !((y <= -4.2e+22) || (!(y <= -1.3e-49) && ((y <= 3e+103) || (!(y <= 3e+119) && (y <= 1.4e+149))))))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5e+49) || ~(((y <= -4.2e+22) || (~((y <= -1.3e-49)) && ((y <= 3e+103) || (~((y <= 3e+119)) && (y <= 1.4e+149)))))))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5e+49], N[Not[Or[LessEqual[y, -4.2e+22], And[N[Not[LessEqual[y, -1.3e-49]], $MachinePrecision], Or[LessEqual[y, 3e+103], And[N[Not[LessEqual[y, 3e+119]], $MachinePrecision], LessEqual[y, 1.4e+149]]]]]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000004e49 or -4.1999999999999996e22 < y < -1.29999999999999997e-49 or 3e103 < y < 3.00000000000000001e119 or 1.4e149 < y

   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 y around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   4. Simplified 64.2%

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

   if -5.0000000000000004e49 < y < -4.1999999999999996e22 or -1.29999999999999997e-49 < y < 3e103 or 3.00000000000000001e119 < y < 1.4e149

   1. Initial program 73.2%

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

   2. Taylor expanded in z around inf 65.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+49} \lor \neg \left(y \leq -4.2 \cdot 10^{+22} \lor \neg \left(y \leq -1.3 \cdot 10^{-49}\right) \land \left(y \leq 3 \cdot 10^{+103} \lor \neg \left(y \leq 3 \cdot 10^{+119}\right) \land y \leq 1.4 \cdot 10^{+149}\right)\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 10: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;y \leq -0.082:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= y -0.082)
     (- (/ a y) (/ x (+ z -1.0)))
     (if (<= y 4e+103)
       t_1
       (if (<= y 1.06e+120)
         (/ x (- 1.0 z))
         (if (<= y 1.6e+150) t_1 (- (/ (- x) (+ z -1.0)) (/ t y))))))))

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 (y <= -0.082) {
		tmp = (a / y) - (x / (z + -1.0));
	} else if (y <= 4e+103) {
		tmp = t_1;
	} else if (y <= 1.06e+120) {
		tmp = x / (1.0 - z);
	} else if (y <= 1.6e+150) {
		tmp = t_1;
	} else {
		tmp = (-x / (z + -1.0)) - (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (y <= (-0.082d0)) then
        tmp = (a / y) - (x / (z + (-1.0d0)))
    else if (y <= 4d+103) then
        tmp = t_1
    else if (y <= 1.06d+120) then
        tmp = x / (1.0d0 - z)
    else if (y <= 1.6d+150) then
        tmp = t_1
    else
        tmp = (-x / (z + (-1.0d0))) - (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (y <= -0.082) {
		tmp = (a / y) - (x / (z + -1.0));
	} else if (y <= 4e+103) {
		tmp = t_1;
	} else if (y <= 1.06e+120) {
		tmp = x / (1.0 - z);
	} else if (y <= 1.6e+150) {
		tmp = t_1;
	} else {
		tmp = (-x / (z + -1.0)) - (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if y <= -0.082:
		tmp = (a / y) - (x / (z + -1.0))
	elif y <= 4e+103:
		tmp = t_1
	elif y <= 1.06e+120:
		tmp = x / (1.0 - z)
	elif y <= 1.6e+150:
		tmp = t_1
	else:
		tmp = (-x / (z + -1.0)) - (t / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (y <= -0.082)
		tmp = Float64(Float64(a / y) - Float64(x / Float64(z + -1.0)));
	elseif (y <= 4e+103)
		tmp = t_1;
	elseif (y <= 1.06e+120)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (y <= 1.6e+150)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-x) / Float64(z + -1.0)) - Float64(t / y));
	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 (y <= -0.082)
		tmp = (a / y) - (x / (z + -1.0));
	elseif (y <= 4e+103)
		tmp = t_1;
	elseif (y <= 1.06e+120)
		tmp = x / (1.0 - z);
	elseif (y <= 1.6e+150)
		tmp = t_1;
	else
		tmp = (-x / (z + -1.0)) - (t / y);
	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[y, -0.082], N[(N[(a / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+103], t$95$1, If[LessEqual[y, 1.06e+120], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+150], t$95$1, N[(N[((-x) / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.0820000000000000034

   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 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

      3. associate-*r/ 63.3%

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

      4. neg-mul-1 63.3%

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

      5. sub-neg 63.3%

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

      6. metadata-eval 63.3%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in z around inf 65.4%

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

   6. Taylor expanded in t around 0 58.6%

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

      1. +-commutative 58.6%

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

      2. sub-neg 58.6%

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

      3. metadata-eval 58.6%

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

      4. neg-mul-1 58.6%

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

      5. unsub-neg 58.6%

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

      6. +-commutative 58.6%

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

   8. Simplified 58.6%

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

   if -0.0820000000000000034 < y < 4e103 or 1.05999999999999994e120 < y < 1.60000000000000008e150

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 62.9%

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

   if 4e103 < y < 1.05999999999999994e120

   1. Initial program 83.3%

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

   2. Taylor expanded in y around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   4. Simplified 83.7%

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

   if 1.60000000000000008e150 < y

   1. Initial program 38.6%

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

   2. Taylor expanded in y around -inf 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. associate-*r/ 72.4%

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

      4. neg-mul-1 72.4%

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

      5. sub-neg 72.4%

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

      6. metadata-eval 72.4%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in z around inf 82.2%

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

   6. Taylor expanded in t around inf 81.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.082:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+103}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+150}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z + -1} - \frac{t}{y}\\ \end{array} \]

Alternative 11: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;y \leq -0.102:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (- (/ a y) (/ x (+ z -1.0)))))
   (if (<= y -0.102)
     t_2
     (if (<= y 8.8e+102)
       t_1
       (if (<= y 4.2e+119) (/ x (- 1.0 z)) (if (<= y 9.8e+148) t_1 t_2))))))

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 = (a / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -0.102) {
		tmp = t_2;
	} else if (y <= 8.8e+102) {
		tmp = t_1;
	} else if (y <= 4.2e+119) {
		tmp = x / (1.0 - z);
	} else if (y <= 9.8e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = (a / y) - (x / (z + (-1.0d0)))
    if (y <= (-0.102d0)) then
        tmp = t_2
    else if (y <= 8.8d+102) then
        tmp = t_1
    else if (y <= 4.2d+119) then
        tmp = x / (1.0d0 - z)
    else if (y <= 9.8d+148) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = (a / y) - (x / (z + -1.0));
	double tmp;
	if (y <= -0.102) {
		tmp = t_2;
	} else if (y <= 8.8e+102) {
		tmp = t_1;
	} else if (y <= 4.2e+119) {
		tmp = x / (1.0 - z);
	} else if (y <= 9.8e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = (a / y) - (x / (z + -1.0))
	tmp = 0
	if y <= -0.102:
		tmp = t_2
	elif y <= 8.8e+102:
		tmp = t_1
	elif y <= 4.2e+119:
		tmp = x / (1.0 - z)
	elif y <= 9.8e+148:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(a / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (y <= -0.102)
		tmp = t_2;
	elseif (y <= 8.8e+102)
		tmp = t_1;
	elseif (y <= 4.2e+119)
		tmp = Float64(x / Float64(1.0 - z));
	elseif (y <= 9.8e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = (a / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (y <= -0.102)
		tmp = t_2;
	elseif (y <= 8.8e+102)
		tmp = t_1;
	elseif (y <= 4.2e+119)
		tmp = x / (1.0 - z);
	elseif (y <= 9.8e+148)
		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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.102], t$95$2, If[LessEqual[y, 8.8e+102], t$95$1, If[LessEqual[y, 4.2e+119], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+148], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.101999999999999993 or 9.8e148 < y

   1. Initial program 49.8%

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

   2. Taylor expanded in y around -inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

      3. associate-*r/ 66.1%

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

      4. neg-mul-1 66.1%

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

      5. sub-neg 66.1%

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

      6. metadata-eval 66.1%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in z around inf 70.6%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. +-commutative 64.9%

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

      2. sub-neg 64.9%

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

      3. metadata-eval 64.9%

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

      4. neg-mul-1 64.9%

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

      5. unsub-neg 64.9%

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

      6. +-commutative 64.9%

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

   8. Simplified 64.9%

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

   if -0.101999999999999993 < y < 8.8000000000000003e102 or 4.19999999999999966e119 < y < 9.8e148

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 62.9%

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

   if 8.8000000000000003e102 < y < 4.19999999999999966e119

   1. Initial program 83.3%

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

   2. Taylor expanded in y around inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

   4. Simplified 83.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.102:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \end{array} \]

Alternative 12: 53.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1420000000000:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-49} \lor \neg \left(y \leq 1.12 \cdot 10^{+55}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -9.5e+40)
     t_1
     (if (<= y -1420000000000.0)
       (- (/ a y) (/ x z))
       (if (or (<= y -5e-49) (not (<= y 1.12e+55))) 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 <= -9.5e+40) {
		tmp = t_1;
	} else if (y <= -1420000000000.0) {
		tmp = (a / y) - (x / z);
	} else if ((y <= -5e-49) || !(y <= 1.12e+55)) {
		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 <= (-9.5d+40)) then
        tmp = t_1
    else if (y <= (-1420000000000.0d0)) then
        tmp = (a / y) - (x / z)
    else if ((y <= (-5d-49)) .or. (.not. (y <= 1.12d+55))) 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 <= -9.5e+40) {
		tmp = t_1;
	} else if (y <= -1420000000000.0) {
		tmp = (a / y) - (x / z);
	} else if ((y <= -5e-49) || !(y <= 1.12e+55)) {
		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 <= -9.5e+40:
		tmp = t_1
	elif y <= -1420000000000.0:
		tmp = (a / y) - (x / z)
	elif (y <= -5e-49) or not (y <= 1.12e+55):
		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 <= -9.5e+40)
		tmp = t_1;
	elseif (y <= -1420000000000.0)
		tmp = Float64(Float64(a / y) - Float64(x / z));
	elseif ((y <= -5e-49) || !(y <= 1.12e+55))
		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 <= -9.5e+40)
		tmp = t_1;
	elseif (y <= -1420000000000.0)
		tmp = (a / y) - (x / z);
	elseif ((y <= -5e-49) || ~((y <= 1.12e+55)))
		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, -9.5e+40], t$95$1, If[LessEqual[y, -1420000000000.0], N[(N[(a / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5e-49], N[Not[LessEqual[y, 1.12e+55]], $MachinePrecision]], t$95$1, N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000003e40 or -1.42e12 < y < -4.9999999999999999e-49 or 1.12000000000000006e55 < y

   1. Initial program 52.4%

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

   2. Taylor expanded in y around inf 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 -9.5000000000000003e40 < y < -1.42e12

   1. Initial program 63.6%

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

   2. Taylor expanded in y around -inf 40.1%

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

      1. mul-1-neg 40.1%

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

      2. unsub-neg 40.1%

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

      3. associate-*r/ 40.1%

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

      4. neg-mul-1 40.1%

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

      5. sub-neg 40.1%

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

      6. metadata-eval 40.1%

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

   4. Simplified 63.9%

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

   5. Taylor expanded in z around inf 76.3%

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

   6. Taylor expanded in t around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. sub-neg 75.8%

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

      3. metadata-eval 75.8%

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

      4. neg-mul-1 75.8%

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

      5. unsub-neg 75.8%

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

      6. +-commutative 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in z around inf 76.6%

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

   if -4.9999999999999999e-49 < y < 1.12000000000000006e55

   1. Initial program 75.5%

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

   2. Taylor expanded in y around 0 54.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1420000000000:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-49} \lor \neg \left(y \leq 1.12 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 13: 41.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-170}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 7.8:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.5e-51)
     t_2
     (if (<= y 2.5e-267)
       t_1
       (if (<= y 2e-170) (/ t (- b y)) (if (<= y 7.8) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.5e-51) {
		tmp = t_2;
	} else if (y <= 2.5e-267) {
		tmp = t_1;
	} else if (y <= 2e-170) {
		tmp = t / (b - y);
	} else if (y <= 7.8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -a / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.5d-51)) then
        tmp = t_2
    else if (y <= 2.5d-267) then
        tmp = t_1
    else if (y <= 2d-170) then
        tmp = t / (b - y)
    else if (y <= 7.8d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.5e-51) {
		tmp = t_2;
	} else if (y <= 2.5e-267) {
		tmp = t_1;
	} else if (y <= 2e-170) {
		tmp = t / (b - y);
	} else if (y <= 7.8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.5e-51:
		tmp = t_2
	elif y <= 2.5e-267:
		tmp = t_1
	elif y <= 2e-170:
		tmp = t / (b - y)
	elif y <= 7.8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.5e-51)
		tmp = t_2;
	elseif (y <= 2.5e-267)
		tmp = t_1;
	elseif (y <= 2e-170)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 7.8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.5e-51)
		tmp = t_2;
	elseif (y <= 2.5e-267)
		tmp = t_1;
	elseif (y <= 2e-170)
		tmp = t / (b - y);
	elseif (y <= 7.8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-51], t$95$2, If[LessEqual[y, 2.5e-267], t$95$1, If[LessEqual[y, 2e-170], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000002e-51 or 7.79999999999999982 < y

   1. Initial program 53.3%

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

   2. Taylor expanded in y around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. unsub-neg 54.3%

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

   4. Simplified 54.3%

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

   if -2.50000000000000002e-51 < y < 2.5e-267 or 1.99999999999999997e-170 < y < 7.79999999999999982

   1. Initial program 79.4%

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

   2. Taylor expanded in a around inf 36.3%

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

      1. mul-1-neg 36.3%

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

      2. distribute-lft-neg-out 36.3%

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

      3. *-commutative 36.3%

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

   4. Simplified 36.3%

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

   5. Taylor expanded in y around 0 37.4%

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

      1. associate-*r/ 37.4%

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

      2. neg-mul-1 37.4%

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

   7. Simplified 37.4%

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

   if 2.5e-267 < y < 1.99999999999999997e-170

   1. Initial program 74.2%

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

   2. Taylor expanded in t around inf 38.8%

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

      1. associate-/l* 55.8%

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

      2. +-commutative 55.8%

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

      3. fma-def 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in z around inf 51.6%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-267}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-170}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 7.8:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14: 53.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-49} \lor \neg \left(y \leq 9.6 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e-49) (not (<= y 9.6e+54))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e-49) || !(y <= 9.6e+54)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4d-49)) .or. (.not. (y <= 9.6d+54))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e-49) || !(y <= 9.6e+54)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e-49) or not (y <= 9.6e+54):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e-49) || !(y <= 9.6e+54))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4e-49) || ~((y <= 9.6e+54)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e-49], N[Not[LessEqual[y, 9.6e+54]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999975e-49 or 9.59999999999999993e54 < y

   1. Initial program 53.1%

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

   2. Taylor expanded in y around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   4. Simplified 57.1%

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

   if -3.99999999999999975e-49 < y < 9.59999999999999993e54

   1. Initial program 75.5%

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

   2. Taylor expanded in y around 0 54.7%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-49} \lor \neg \left(y \leq 9.6 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 15: 35.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.75) (/ (- x) z) (if (<= z 12.0) (+ x (* x z)) (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 12.0) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.75d0)) then
        tmp = -x / z
    else if (z <= 12.0d0) then
        tmp = x + (x * z)
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 12.0) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.75:
		tmp = -x / z
	elif z <= 12.0:
		tmp = x + (x * z)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.75)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 12.0)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.75)
		tmp = -x / z;
	elseif (z <= 12.0)
		tmp = x + (x * z);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.75], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 12.0], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.75

   1. Initial program 36.9%

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

   2. Taylor expanded in y around inf 34.5%

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

      1. mul-1-neg 34.5%

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

      2. unsub-neg 34.5%

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

   4. Simplified 34.5%

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

   5. Taylor expanded in z around inf 32.0%

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

      1. associate-*r/ 32.0%

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

      2. mul-1-neg 32.0%

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

   7. Simplified 32.0%

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

   if -0.75 < z < 12

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unsub-neg 44.9%

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

   4. Simplified 44.9%

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

   5. Taylor expanded in z around 0 44.9%

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

      1. *-commutative 44.9%

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

   7. Simplified 44.9%

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

   if 12 < z

   1. Initial program 47.4%

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

   2. Taylor expanded in t around inf 22.5%

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

      1. associate-/l* 30.5%

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

      2. +-commutative 30.5%

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

      3. fma-def 30.5%

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

   4. Simplified 30.5%

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

   5. Taylor expanded in b around inf 30.6%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16: 39.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.35:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.75) (/ (- x) z) (if (<= z 0.35) (+ x (* x z)) (/ t (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 0.35) {
		tmp = x + (x * z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.75d0)) then
        tmp = -x / z
    else if (z <= 0.35d0) then
        tmp = x + (x * z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 0.35) {
		tmp = x + (x * z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.75:
		tmp = -x / z
	elif z <= 0.35:
		tmp = x + (x * z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.75)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 0.35)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.75)
		tmp = -x / z;
	elseif (z <= 0.35)
		tmp = x + (x * z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.75], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 0.35], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.75

   1. Initial program 36.9%

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

   2. Taylor expanded in y around inf 34.5%

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

      1. mul-1-neg 34.5%

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

      2. unsub-neg 34.5%

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

   4. Simplified 34.5%

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

   5. Taylor expanded in z around inf 32.0%

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

      1. associate-*r/ 32.0%

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

      2. mul-1-neg 32.0%

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

   7. Simplified 32.0%

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

   if -0.75 < z < 0.34999999999999998

   1. Initial program 88.0%

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

   2. Taylor expanded in y around inf 45.2%

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

      1. mul-1-neg 45.2%

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

      2. unsub-neg 45.2%

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

   4. Simplified 45.2%

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

   5. Taylor expanded in z around 0 45.2%

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

      1. *-commutative 45.2%

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

   7. Simplified 45.2%

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

   if 0.34999999999999998 < z

   1. Initial program 48.1%

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

   2. Taylor expanded in t around inf 23.5%

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

      1. associate-/l* 31.4%

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

      2. +-commutative 31.4%

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

      3. fma-def 31.4%

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

   4. Simplified 31.4%

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

   5. Taylor expanded in z around inf 43.9%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.35:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 17: 42.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.5e+111)
   (/ (- a t) y)
   (if (<= z 4e+63) (/ x (- 1.0 z)) (/ t (- b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+111) {
		tmp = (a - t) / y;
	} else if (z <= 4e+63) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5.5d+111)) then
        tmp = (a - t) / y
    else if (z <= 4d+63) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+111) {
		tmp = (a - t) / y;
	} else if (z <= 4e+63) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.5e+111:
		tmp = (a - t) / y
	elif z <= 4e+63:
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.5e+111)
		tmp = Float64(Float64(a - t) / y);
	elseif (z <= 4e+63)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.5e+111)
		tmp = (a - t) / y;
	elseif (z <= 4e+63)
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.5e+111], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4e+63], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999998e111

   1. Initial program 31.6%

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

   2. Taylor expanded in y around -inf 18.2%

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

      1. mul-1-neg 18.2%

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

      2. unsub-neg 18.2%

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

      3. associate-*r/ 18.2%

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

      4. neg-mul-1 18.2%

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

      5. sub-neg 18.2%

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

      6. metadata-eval 18.2%

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

   4. Simplified 42.4%

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

   5. Taylor expanded in z around inf 59.4%

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

   6. Taylor expanded in x around 0 40.5%

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

      1. div-sub 40.6%

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

   8. Simplified 40.6%

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

   if -5.4999999999999998e111 < z < 4.00000000000000023e63

   1. Initial program 78.1%

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

   2. Taylor expanded in y around inf 45.8%

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

      1. mul-1-neg 45.8%

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

      2. unsub-neg 45.8%

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

   4. Simplified 45.8%

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

   if 4.00000000000000023e63 < z

   1. Initial program 44.8%

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

   2. Taylor expanded in t around inf 23.7%

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

      1. associate-/l* 32.1%

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

      2. +-commutative 32.1%

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

      3. fma-def 32.1%

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

   4. Simplified 32.1%

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

   5. Taylor expanded in z around inf 49.0%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 18: 34.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -650 \lor \neg \left(z \leq 12\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -650.0) (not (<= z 12.0))) (/ 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 <= 12.0)) {
		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 <= 12.0d0))) 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 <= 12.0)) {
		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 <= 12.0):
		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 <= 12.0))
		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 <= 12.0)))
		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, 12.0]], $MachinePrecision]], N[(a / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -650 or 12 < z

   1. Initial program 42.5%

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

   2. Taylor expanded in y around -inf 27.6%

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

      1. mul-1-neg 27.6%

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

      2. unsub-neg 27.6%

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

      3. associate-*r/ 27.6%

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

      4. neg-mul-1 27.6%

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

      5. sub-neg 27.6%

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

      6. metadata-eval 27.6%

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

   4. Simplified 39.8%

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

   5. Taylor expanded in z around inf 56.7%

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

   6. Taylor expanded in a around inf 21.9%

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

   if -650 < z < 12

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 44.4%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -650 \lor \neg \left(z \leq 12\right):\\ \;\;\;\;\frac{a}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 36.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -32:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -32.0) (/ a y) (if (<= z 12.0) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -32.0) {
		tmp = a / y;
	} else if (z <= 12.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-32.0d0)) then
        tmp = a / y
    else if (z <= 12.0d0) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -32.0) {
		tmp = a / y;
	} else if (z <= 12.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -32.0:
		tmp = a / y
	elif z <= 12.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -32.0)
		tmp = Float64(a / y);
	elseif (z <= 12.0)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -32.0)
		tmp = a / y;
	elseif (z <= 12.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -32.0], N[(a / y), $MachinePrecision], If[LessEqual[z, 12.0], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -32

   1. Initial program 36.4%

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

   2. Taylor expanded in y around -inf 24.9%

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

      1. mul-1-neg 24.9%

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

      2. unsub-neg 24.9%

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

      3. associate-*r/ 24.9%

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

      4. neg-mul-1 24.9%

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

      5. sub-neg 24.9%

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

      6. metadata-eval 24.9%

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

   4. Simplified 43.9%

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

   5. Taylor expanded in z around inf 60.5%

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

   6. Taylor expanded in a around inf 26.2%

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

   if -32 < z < 12

   1. Initial program 87.5%

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

   2. Taylor expanded in z around 0 44.4%

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

   if 12 < z

   1. Initial program 47.4%

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

   2. Taylor expanded in t around inf 22.5%

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

      1. associate-/l* 30.5%

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

      2. +-commutative 30.5%

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

      3. fma-def 30.5%

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

   4. Simplified 30.5%

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

   5. Taylor expanded in b around inf 30.6%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -32:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 20: 37.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-11}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6e-11) (/ (- a) b) (if (<= z 12.0) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e-11) {
		tmp = -a / b;
	} else if (z <= 12.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6d-11)) then
        tmp = -a / b
    else if (z <= 12.0d0) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e-11) {
		tmp = -a / b;
	} else if (z <= 12.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6e-11:
		tmp = -a / b
	elif z <= 12.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e-11)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 12.0)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6e-11)
		tmp = -a / b;
	elseif (z <= 12.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6e-11], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 12.0], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e-11

   1. Initial program 37.9%

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

   2. Taylor expanded in a around inf 27.6%

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

      1. mul-1-neg 27.6%

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

      2. distribute-lft-neg-out 27.6%

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

      3. *-commutative 27.6%

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

   4. Simplified 27.6%

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

   5. Taylor expanded in y around 0 26.5%

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

      1. associate-*r/ 26.5%

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

      2. neg-mul-1 26.5%

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

   7. Simplified 26.5%

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

   if -6e-11 < z < 12

   1. Initial program 88.0%

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

   2. Taylor expanded in z around 0 45.2%

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

   if 12 < z

   1. Initial program 47.4%

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

   2. Taylor expanded in t around inf 22.5%

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

      1. associate-/l* 30.5%

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

      2. +-commutative 30.5%

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

      3. fma-def 30.5%

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

   4. Simplified 30.5%

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

   5. Taylor expanded in b around inf 30.6%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-11}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 21: 35.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.0) (/ (- x) z) (if (<= z 12.0) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x / z;
	} else if (z <= 12.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = -x / z
    else if (z <= 12.0d0) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x / z;
	} else if (z <= 12.0) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.0:
		tmp = -x / z
	elif z <= 12.0:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 12.0)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x / z;
	elseif (z <= 12.0)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.0], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 12.0], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 36.9%

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

   2. Taylor expanded in y around inf 34.5%

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

      1. mul-1-neg 34.5%

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

      2. unsub-neg 34.5%

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

   4. Simplified 34.5%

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

   5. Taylor expanded in z around inf 32.0%

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

      1. associate-*r/ 32.0%

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

      2. mul-1-neg 32.0%

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

   7. Simplified 32.0%

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

   if -1 < z < 12

   1. Initial program 88.1%

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

   2. Taylor expanded in z around 0 44.9%

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

   if 12 < z

   1. Initial program 47.4%

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

   2. Taylor expanded in t around inf 22.5%

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

      1. associate-/l* 30.5%

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

      2. +-commutative 30.5%

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

      3. fma-def 30.5%

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

   4. Simplified 30.5%

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

   5. Taylor expanded in b around inf 30.6%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 22: 25.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.8%

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

2. Taylor expanded in z around 0 22.7%

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

3. Final simplification 22.7%

   \[\leadsto x \]

Developer target: 74.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023336 
(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)))))