Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.5% → 96.5%

Time: 17.8s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.5% 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: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := b + \left(\frac{y}{z} - y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{y \cdot x + t\_3}{t\_1}\\ t_5 := \frac{t}{t\_2} + \left(x \cdot \frac{\frac{1}{z}}{\frac{1}{z} + -1} - \frac{a}{t\_2}\right)\\ t_6 := \frac{y \cdot x}{t\_1} + \frac{t\_3}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -5 \cdot 10^{-297}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;x \cdot \left(\frac{\frac{y}{z}}{t\_2} + \frac{\frac{t - a}{t\_2}}{x}\right)\\ \mathbf{elif}\;t\_4 \leq 10^{+287}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ b (- (/ y z) y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* y x) t_3) t_1))
        (t_5
         (+ (/ t t_2) (- (* x (/ (/ 1.0 z) (+ (/ 1.0 z) -1.0))) (/ a t_2))))
        (t_6 (+ (/ (* y x) t_1) (/ t_3 t_1))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -5e-297)
       t_6
       (if (<= t_4 0.0)
         (* x (+ (/ (/ y z) t_2) (/ (/ (- t a) t_2) x)))
         (if (<= t_4 1e+287) t_6 t_5))))))

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 = b + ((y / z) - y);
	double t_3 = z * (t - a);
	double t_4 = ((y * x) + t_3) / t_1;
	double t_5 = (t / t_2) + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_2));
	double t_6 = ((y * x) / t_1) + (t_3 / t_1);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -5e-297) {
		tmp = t_6;
	} else if (t_4 <= 0.0) {
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x));
	} else if (t_4 <= 1e+287) {
		tmp = t_6;
	} else {
		tmp = t_5;
	}
	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 = b + ((y / z) - y);
	double t_3 = z * (t - a);
	double t_4 = ((y * x) + t_3) / t_1;
	double t_5 = (t / t_2) + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_2));
	double t_6 = ((y * x) / t_1) + (t_3 / t_1);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -5e-297) {
		tmp = t_6;
	} else if (t_4 <= 0.0) {
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x));
	} else if (t_4 <= 1e+287) {
		tmp = t_6;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = b + ((y / z) - y)
	t_3 = z * (t - a)
	t_4 = ((y * x) + t_3) / t_1
	t_5 = (t / t_2) + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_2))
	t_6 = ((y * x) / t_1) + (t_3 / t_1)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -5e-297:
		tmp = t_6
	elif t_4 <= 0.0:
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x))
	elif t_4 <= 1e+287:
		tmp = t_6
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(b + Float64(Float64(y / z) - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(y * x) + t_3) / t_1)
	t_5 = Float64(Float64(t / t_2) + Float64(Float64(x * Float64(Float64(1.0 / z) / Float64(Float64(1.0 / z) + -1.0))) - Float64(a / t_2)))
	t_6 = Float64(Float64(Float64(y * x) / t_1) + Float64(t_3 / t_1))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -5e-297)
		tmp = t_6;
	elseif (t_4 <= 0.0)
		tmp = Float64(x * Float64(Float64(Float64(y / z) / t_2) + Float64(Float64(Float64(t - a) / t_2) / x)));
	elseif (t_4 <= 1e+287)
		tmp = t_6;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = b + ((y / z) - y);
	t_3 = z * (t - a);
	t_4 = ((y * x) + t_3) / t_1;
	t_5 = (t / t_2) + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_2));
	t_6 = ((y * x) / t_1) + (t_3 / t_1);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -5e-297)
		tmp = t_6;
	elseif (t_4 <= 0.0)
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x));
	elseif (t_4 <= 1e+287)
		tmp = t_6;
	else
		tmp = t_5;
	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[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(y * x), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t / t$95$2), $MachinePrecision] + N[(N[(x * N[(N[(1.0 / z), $MachinePrecision] / N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -5e-297], t$95$6, If[LessEqual[t$95$4, 0.0], N[(x * N[(N[(N[(y / z), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+287], t$95$6, t$95$5]]]]]]]]]]

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 1.0000000000000001e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 20.7%

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

   3. Taylor expanded in z around inf 19.9%

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

   4. Taylor expanded in x around 0 66.4%

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

      1. associate--l+ 66.4%

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

      2. associate-+r- 66.4%

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

      3. associate-/l* 79.1%

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

      4. associate-/r* 88.0%

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

      5. associate-+r- 88.0%

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

      6. associate-+r- 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in y around inf 93.5%

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

      1. associate-/r* 93.5%

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

      2. sub-neg 93.5%

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

      3. metadata-eval 93.5%

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

   9. Simplified 93.5%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5e-297 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e287

   1. Initial program 99.5%

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

      1. fma-define 99.5%

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

      2. +-commutative 99.5%

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

      3. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. 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 -5e-297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 25.0%

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

   3. Taylor expanded in z around inf 25.0%

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

   4. Taylor expanded in x around -inf 84.4%

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

      1. associate-*r* 84.4%

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

      2. mul-1-neg 84.4%

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

      3. mul-1-neg 84.4%

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

      4. unsub-neg 84.4%

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

      5. mul-1-neg 84.4%

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

      6. associate-/r* 99.8%

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

      7. associate-+r- 99.8%

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

   6. Simplified 99.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t}{b + \left(\frac{y}{z} - y\right)} + \left(x \cdot \frac{\frac{1}{z}}{\frac{1}{z} + -1} - \frac{a}{b + \left(\frac{y}{z} - y\right)}\right)\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-297}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;x \cdot \left(\frac{\frac{y}{z}}{b + \left(\frac{y}{z} - y\right)} + \frac{\frac{t - a}{b + \left(\frac{y}{z} - y\right)}}{x}\right)\\ \mathbf{elif}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+287}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b + \left(\frac{y}{z} - y\right)} + \left(x \cdot \frac{\frac{1}{z}}{\frac{1}{z} + -1} - \frac{a}{b + \left(\frac{y}{z} - y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := b + \left(\frac{y}{z} - y\right)\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{y \cdot x + t\_3}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty \lor \neg \left(t\_4 \leq -5 \cdot 10^{-297} \lor \neg \left(t\_4 \leq 0\right) \land t\_4 \leq 10^{+287}\right):\\ \;\;\;\;x \cdot \left(\frac{\frac{y}{z}}{t\_2} + \frac{\frac{t - a}{t\_2}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t\_1} + \frac{t\_3}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ b (- (/ y z) y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* y x) t_3) t_1)))
   (if (or (<= t_4 (- INFINITY))
           (not
            (or (<= t_4 -5e-297) (and (not (<= t_4 0.0)) (<= t_4 1e+287)))))
     (* x (+ (/ (/ y z) t_2) (/ (/ (- t a) t_2) x)))
     (+ (/ (* y x) t_1) (/ t_3 t_1)))))

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 = b + ((y / z) - y);
	double t_3 = z * (t - a);
	double t_4 = ((y * x) + t_3) / t_1;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !((t_4 <= -5e-297) || (!(t_4 <= 0.0) && (t_4 <= 1e+287)))) {
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x));
	} else {
		tmp = ((y * x) / t_1) + (t_3 / t_1);
	}
	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 = b + ((y / z) - y);
	double t_3 = z * (t - a);
	double t_4 = ((y * x) + t_3) / t_1;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !((t_4 <= -5e-297) || (!(t_4 <= 0.0) && (t_4 <= 1e+287)))) {
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x));
	} else {
		tmp = ((y * x) / t_1) + (t_3 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = b + ((y / z) - y)
	t_3 = z * (t - a)
	t_4 = ((y * x) + t_3) / t_1
	tmp = 0
	if (t_4 <= -math.inf) or not ((t_4 <= -5e-297) or (not (t_4 <= 0.0) and (t_4 <= 1e+287))):
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x))
	else:
		tmp = ((y * x) / t_1) + (t_3 / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(b + Float64(Float64(y / z) - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(y * x) + t_3) / t_1)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !((t_4 <= -5e-297) || (!(t_4 <= 0.0) && (t_4 <= 1e+287))))
		tmp = Float64(x * Float64(Float64(Float64(y / z) / t_2) + Float64(Float64(Float64(t - a) / t_2) / x)));
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) + Float64(t_3 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = b + ((y / z) - y);
	t_3 = z * (t - a);
	t_4 = ((y * x) + t_3) / t_1;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~(((t_4 <= -5e-297) || (~((t_4 <= 0.0)) && (t_4 <= 1e+287)))))
		tmp = x * (((y / z) / t_2) + (((t - a) / t_2) / x));
	else
		tmp = ((y * x) / t_1) + (t_3 / t_1);
	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[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(y * x), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[Or[LessEqual[t$95$4, -5e-297], And[N[Not[LessEqual[t$95$4, 0.0]], $MachinePrecision], LessEqual[t$95$4, 1e+287]]]], $MachinePrecision]], N[(x * N[(N[(N[(y / z), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / t$95$2), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or -5e-297 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or 1.0000000000000001e287 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 21.4%

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

   3. Taylor expanded in z around inf 20.8%

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

   4. Taylor expanded in x around -inf 72.8%

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

      1. associate-*r* 72.8%

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

      2. mul-1-neg 72.8%

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

      3. mul-1-neg 72.8%

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

      4. unsub-neg 72.8%

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

      5. mul-1-neg 72.8%

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

      6. associate-/r* 82.7%

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

      7. associate-+r- 82.7%

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

   6. Simplified 82.8%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5e-297 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.0000000000000001e287

   1. Initial program 99.5%

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

      1. fma-define 99.5%

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

      2. +-commutative 99.5%

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

      3. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty \lor \neg \left(\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-297} \lor \neg \left(\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 10^{+287}\right):\\ \;\;\;\;x \cdot \left(\frac{\frac{y}{z}}{b + \left(\frac{y}{z} - y\right)} + \frac{\frac{t - a}{b + \left(\frac{y}{z} - y\right)}}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b + \left(\frac{y}{z} - y\right)\\ t_2 := \frac{t}{t\_1}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+123} \lor \neg \left(y \leq 29000000\right):\\ \;\;\;\;t\_2 + \left(x \cdot \frac{\frac{1}{z}}{\frac{1}{z} + -1} - \frac{a}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \left(x \cdot \frac{\frac{y}{z}}{t\_1} + \frac{a}{\left(y - \frac{y}{z}\right) - b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ b (- (/ y z) y))) (t_2 (/ t t_1)))
   (if (or (<= y -1.5e+123) (not (<= y 29000000.0)))
     (+ t_2 (- (* x (/ (/ 1.0 z) (+ (/ 1.0 z) -1.0))) (/ a t_1)))
     (+ t_2 (+ (* x (/ (/ y z) t_1)) (/ a (- (- y (/ y z)) b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b + ((y / z) - y);
	double t_2 = t / t_1;
	double tmp;
	if ((y <= -1.5e+123) || !(y <= 29000000.0)) {
		tmp = t_2 + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_1));
	} else {
		tmp = t_2 + ((x * ((y / z) / t_1)) + (a / ((y - (y / z)) - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b + ((y / z) - y)
    t_2 = t / t_1
    if ((y <= (-1.5d+123)) .or. (.not. (y <= 29000000.0d0))) then
        tmp = t_2 + ((x * ((1.0d0 / z) / ((1.0d0 / z) + (-1.0d0)))) - (a / t_1))
    else
        tmp = t_2 + ((x * ((y / z) / t_1)) + (a / ((y - (y / z)) - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b + ((y / z) - y);
	double t_2 = t / t_1;
	double tmp;
	if ((y <= -1.5e+123) || !(y <= 29000000.0)) {
		tmp = t_2 + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_1));
	} else {
		tmp = t_2 + ((x * ((y / z) / t_1)) + (a / ((y - (y / z)) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b + ((y / z) - y)
	t_2 = t / t_1
	tmp = 0
	if (y <= -1.5e+123) or not (y <= 29000000.0):
		tmp = t_2 + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_1))
	else:
		tmp = t_2 + ((x * ((y / z) / t_1)) + (a / ((y - (y / z)) - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b + Float64(Float64(y / z) - y))
	t_2 = Float64(t / t_1)
	tmp = 0.0
	if ((y <= -1.5e+123) || !(y <= 29000000.0))
		tmp = Float64(t_2 + Float64(Float64(x * Float64(Float64(1.0 / z) / Float64(Float64(1.0 / z) + -1.0))) - Float64(a / t_1)));
	else
		tmp = Float64(t_2 + Float64(Float64(x * Float64(Float64(y / z) / t_1)) + Float64(a / Float64(Float64(y - Float64(y / z)) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b + ((y / z) - y);
	t_2 = t / t_1;
	tmp = 0.0;
	if ((y <= -1.5e+123) || ~((y <= 29000000.0)))
		tmp = t_2 + ((x * ((1.0 / z) / ((1.0 / z) + -1.0))) - (a / t_1));
	else
		tmp = t_2 + ((x * ((y / z) / t_1)) + (a / ((y - (y / z)) - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b + N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, If[Or[LessEqual[y, -1.5e+123], N[Not[LessEqual[y, 29000000.0]], $MachinePrecision]], N[(t$95$2 + N[(N[(x * N[(N[(1.0 / z), $MachinePrecision] / N[(N[(1.0 / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(x * N[(N[(y / z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(a / N[(N[(y - N[(y / z), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000004e123 or 2.9e7 < y

   1. Initial program 60.8%

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

   3. Taylor expanded in z around inf 39.6%

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

   4. Taylor expanded in x around 0 51.9%

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

      1. associate--l+ 51.9%

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

      2. associate-+r- 51.9%

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

      3. associate-/l* 60.1%

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

      4. associate-/r* 68.5%

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

      5. associate-+r- 68.5%

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

      6. associate-+r- 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in y around inf 91.4%

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

      1. associate-/r* 91.5%

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

      2. sub-neg 91.5%

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

      3. metadata-eval 91.5%

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

   9. Simplified 91.5%

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

   if -1.50000000000000004e123 < y < 2.9e7

   1. Initial program 77.8%

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

   3. Taylor expanded in z around inf 77.2%

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

   4. Taylor expanded in x around 0 98.0%

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

      1. associate--l+ 98.0%

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

      2. associate-+r- 98.0%

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

      3. associate-/l* 98.6%

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

      4. associate-/r* 98.6%

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

      5. associate-+r- 98.6%

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

      6. associate-+r- 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+123} \lor \neg \left(y \leq 29000000\right):\\ \;\;\;\;\frac{t}{b + \left(\frac{y}{z} - y\right)} + \left(x \cdot \frac{\frac{1}{z}}{\frac{1}{z} + -1} - \frac{a}{b + \left(\frac{y}{z} - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b + \left(\frac{y}{z} - y\right)} + \left(x \cdot \frac{\frac{y}{z}}{b + \left(\frac{y}{z} - y\right)} + \frac{a}{\left(y - \frac{y}{z}\right) - b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+65} \lor \neg \left(z \leq 5.8 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{t\_1} + \frac{z \cdot \left(t - a\right)}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -6.2e+65) (not (<= z 5.8e+45)))
     (/ (- t a) (- b y))
     (+ (/ (* y x) t_1) (/ (* z (- t a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -6.2e+65) || !(z <= 5.8e+45)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-6.2d+65)) .or. (.not. (z <= 5.8d+45))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) / t_1) + ((z * (t - a)) / 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 = y + (z * (b - y));
	double tmp;
	if ((z <= -6.2e+65) || !(z <= 5.8e+45)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -6.2e+65) or not (z <= 5.8e+45):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -6.2e+65) || !(z <= 5.8e+45))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) / t_1) + Float64(Float64(z * Float64(t - a)) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -6.2e+65) || ~((z <= 5.8e+45)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) / t_1) + ((z * (t - a)) / t_1);
	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]}, If[Or[LessEqual[z, -6.2e+65], N[Not[LessEqual[z, 5.8e+45]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999981e65 or 5.7999999999999994e45 < z

   1. Initial program 45.2%

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

      1. fma-define 45.2%

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

      2. +-commutative 45.2%

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

      3. fma-define 45.2%

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

   3. Simplified 45.2%

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

   5. Taylor expanded in z around inf 84.3%

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

   if -6.19999999999999981e65 < z < 5.7999999999999994e45

   1. Initial program 87.7%

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

      1. fma-define 87.7%

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

      2. +-commutative 87.7%

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

      3. fma-define 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 87.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+65} \lor \neg \left(z \leq 5.8 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.9 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+20}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.9e+121)
     t_1
     (if (<= y 8e+20)
       (/ (- t a) (- (+ b (/ y z)) y))
       (if (<= y 9.5e+106)
         (/ (- (* z (- a t)) (* y x)) (* y (+ z -1.0)))
         t_1)))))

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 <= -7.9e+121) {
		tmp = t_1;
	} else if (y <= 8e+20) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else if (y <= 9.5e+106) {
		tmp = ((z * (a - t)) - (y * x)) / (y * (z + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-7.9d+121)) then
        tmp = t_1
    else if (y <= 8d+20) then
        tmp = (t - a) / ((b + (y / z)) - y)
    else if (y <= 9.5d+106) then
        tmp = ((z * (a - t)) - (y * x)) / (y * (z + (-1.0d0)))
    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 = x / (1.0 - z);
	double tmp;
	if (y <= -7.9e+121) {
		tmp = t_1;
	} else if (y <= 8e+20) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else if (y <= 9.5e+106) {
		tmp = ((z * (a - t)) - (y * x)) / (y * (z + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -7.9e+121:
		tmp = t_1
	elif y <= 8e+20:
		tmp = (t - a) / ((b + (y / z)) - y)
	elif y <= 9.5e+106:
		tmp = ((z * (a - t)) - (y * x)) / (y * (z + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7.9e+121)
		tmp = t_1;
	elseif (y <= 8e+20)
		tmp = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y));
	elseif (y <= 9.5e+106)
		tmp = Float64(Float64(Float64(z * Float64(a - t)) - Float64(y * x)) / Float64(y * Float64(z + -1.0)));
	else
		tmp = t_1;
	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 <= -7.9e+121)
		tmp = t_1;
	elseif (y <= 8e+20)
		tmp = (t - a) / ((b + (y / z)) - y);
	elseif (y <= 9.5e+106)
		tmp = ((z * (a - t)) - (y * x)) / (y * (z + -1.0));
	else
		tmp = t_1;
	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, -7.9e+121], t$95$1, If[LessEqual[y, 8e+20], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+106], N[(N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] - N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9e121 or 9.4999999999999995e106 < y

   1. Initial program 51.0%

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

      1. fma-define 51.0%

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

      2. +-commutative 51.0%

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

      3. fma-define 51.1%

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

   3. Simplified 51.1%

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

   5. Taylor expanded in y around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   7. Simplified 67.4%

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

   if -7.9e121 < y < 8e20

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 77.3%

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

   4. Taylor expanded in x around 0 79.4%

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

   if 8e20 < y < 9.4999999999999995e106

   1. Initial program 85.4%

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

   3. Taylor expanded in y around inf 85.3%

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

      1. mul-1-neg 85.3%

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

      2. unsub-neg 85.3%

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

   5. Simplified 85.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.9 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+20}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{z \cdot \left(a - t\right) - y \cdot x}{y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+86}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+155}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.8e+121)
     t_1
     (if (<= y -8e+86)
       (/ a (- y b))
       (if (<= y 2.5e-94)
         (/ (- t a) b)
         (if (<= y 7e+155) (+ x (/ (* t z) y)) t_1))))))

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 <= -1.8e+121) {
		tmp = t_1;
	} else if (y <= -8e+86) {
		tmp = a / (y - b);
	} else if (y <= 2.5e-94) {
		tmp = (t - a) / b;
	} else if (y <= 7e+155) {
		tmp = x + ((t * z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.8d+121)) then
        tmp = t_1
    else if (y <= (-8d+86)) then
        tmp = a / (y - b)
    else if (y <= 2.5d-94) then
        tmp = (t - a) / b
    else if (y <= 7d+155) then
        tmp = x + ((t * z) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.8e+121) {
		tmp = t_1;
	} else if (y <= -8e+86) {
		tmp = a / (y - b);
	} else if (y <= 2.5e-94) {
		tmp = (t - a) / b;
	} else if (y <= 7e+155) {
		tmp = x + ((t * z) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.8e+121:
		tmp = t_1
	elif y <= -8e+86:
		tmp = a / (y - b)
	elif y <= 2.5e-94:
		tmp = (t - a) / b
	elif y <= 7e+155:
		tmp = x + ((t * z) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.8e+121)
		tmp = t_1;
	elseif (y <= -8e+86)
		tmp = Float64(a / Float64(y - b));
	elseif (y <= 2.5e-94)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 7e+155)
		tmp = Float64(x + Float64(Float64(t * z) / y));
	else
		tmp = t_1;
	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 <= -1.8e+121)
		tmp = t_1;
	elseif (y <= -8e+86)
		tmp = a / (y - b);
	elseif (y <= 2.5e-94)
		tmp = (t - a) / b;
	elseif (y <= 7e+155)
		tmp = x + ((t * z) / y);
	else
		tmp = t_1;
	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, -1.8e+121], t$95$1, If[LessEqual[y, -8e+86], N[(a / N[(y - b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-94], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 7e+155], N[(x + N[(N[(t * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.79999999999999991e121 or 6.99999999999999969e155 < y

   1. Initial program 49.2%

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

      1. fma-define 49.2%

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

      2. +-commutative 49.2%

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

      3. fma-define 49.3%

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

   3. Simplified 49.3%

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

   5. Taylor expanded in y around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   7. Simplified 70.0%

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

   if -1.79999999999999991e121 < y < -8.0000000000000001e86

   1. Initial program 46.5%

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

   3. Taylor expanded in z around inf 46.5%

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

   4. Taylor expanded in x around 0 88.6%

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

   5. Taylor expanded in t around 0 77.7%

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

      1. neg-mul-1 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in z around inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. neg-mul-1 67.3%

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

   10. Simplified 67.3%

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

   if -8.0000000000000001e86 < y < 2.4999999999999998e-94

   1. Initial program 79.7%

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

      1. fma-define 79.7%

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

      2. +-commutative 79.7%

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

      3. fma-define 79.7%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in y around 0 57.5%

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

   if 2.4999999999999998e-94 < y < 6.99999999999999969e155

   1. Initial program 79.3%

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

   3. Taylor expanded in z around 0 44.3%

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

   4. Taylor expanded in x around 0 51.0%

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

   5. Taylor expanded in t around inf 48.2%

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

      1. *-commutative 48.2%

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

   7. Simplified 48.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+86}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+155}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+66} \lor \neg \left(z \leq 1.9 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+66) (not (<= z 1.9e+46)))
   (/ (- t a) (- b y))
   (/ (+ (* y x) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+66) || !(z <= 1.9e+46)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.15d+66)) .or. (.not. (z <= 1.9d+46))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+66) || !(z <= 1.9e+46)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.15e+66) or not (z <= 1.9e+46):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+66) || !(z <= 1.9e+46))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.15e+66) || ~((z <= 1.9e+46)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((y * x) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+66], N[Not[LessEqual[z, 1.9e+46]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e66 or 1.9e46 < z

   1. Initial program 45.2%

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

      1. fma-define 45.2%

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

      2. +-commutative 45.2%

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

      3. fma-define 45.2%

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

   3. Simplified 45.2%

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

   5. Taylor expanded in z around inf 84.3%

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

   if -1.15e66 < z < 1.9e46

   1. Initial program 87.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+66} \lor \neg \left(z \leq 1.9 \cdot 10^{+46}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{y - b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{-30}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (- y b))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.95e+121)
     t_2
     (if (<= y -2.85e+81)
       t_1
       (if (<= y 1e-30) (/ (- t a) b) (if (<= y 5e+21) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (y - b);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.95e+121) {
		tmp = t_2;
	} else if (y <= -2.85e+81) {
		tmp = t_1;
	} else if (y <= 1e-30) {
		tmp = (t - a) / b;
	} else if (y <= 5e+21) {
		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 / (y - b)
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.95d+121)) then
        tmp = t_2
    else if (y <= (-2.85d+81)) then
        tmp = t_1
    else if (y <= 1d-30) then
        tmp = (t - a) / b
    else if (y <= 5d+21) 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 / (y - b);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.95e+121) {
		tmp = t_2;
	} else if (y <= -2.85e+81) {
		tmp = t_1;
	} else if (y <= 1e-30) {
		tmp = (t - a) / b;
	} else if (y <= 5e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (y - b)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.95e+121:
		tmp = t_2
	elif y <= -2.85e+81:
		tmp = t_1
	elif y <= 1e-30:
		tmp = (t - a) / b
	elif y <= 5e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(y - b))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.95e+121)
		tmp = t_2;
	elseif (y <= -2.85e+81)
		tmp = t_1;
	elseif (y <= 1e-30)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 5e+21)
		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 / (y - b);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.95e+121)
		tmp = t_2;
	elseif (y <= -2.85e+81)
		tmp = t_1;
	elseif (y <= 1e-30)
		tmp = (t - a) / b;
	elseif (y <= 5e+21)
		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 / N[(y - b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.95e+121], t$95$2, If[LessEqual[y, -2.85e+81], t$95$1, If[LessEqual[y, 1e-30], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 5e+21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.95000000000000007e121 or 5e21 < y

   1. Initial program 60.3%

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

      1. fma-define 60.3%

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

      2. +-commutative 60.3%

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

      3. fma-define 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in y around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

   7. Simplified 60.2%

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

   if -2.95000000000000007e121 < y < -2.85000000000000017e81 or 1e-30 < y < 5e21

   1. Initial program 63.5%

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

   3. Taylor expanded in z around inf 63.5%

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

   4. Taylor expanded in x around 0 90.4%

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

   5. Taylor expanded in t around 0 81.4%

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

      1. neg-mul-1 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in z around inf 67.1%

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

      1. associate-*r/ 67.1%

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

      2. neg-mul-1 67.1%

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

   10. Simplified 67.1%

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

   if -2.85000000000000017e81 < y < 1e-30

   1. Initial program 80.2%

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

      1. fma-define 80.2%

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

      2. +-commutative 80.2%

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

      3. fma-define 80.2%

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

   3. Simplified 80.2%

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

   5. Taylor expanded in y around 0 55.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+81}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{elif}\;y \leq 10^{-30}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+21}:\\ \;\;\;\;\frac{a}{y - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + b \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e+19)
   (/ (- t a) (- b y))
   (if (<= z 6.8e-19)
     (/ (+ (* y x) (* z (- t a))) (+ y (* b z)))
     (/ (- t a) (- (+ b (/ y z)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e+19) {
		tmp = (t - a) / (b - y);
	} else if (z <= 6.8e-19) {
		tmp = ((y * x) + (z * (t - a))) / (y + (b * z));
	} else {
		tmp = (t - a) / ((b + (y / z)) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.3d+19)) then
        tmp = (t - a) / (b - y)
    else if (z <= 6.8d-19) then
        tmp = ((y * x) + (z * (t - a))) / (y + (b * z))
    else
        tmp = (t - a) / ((b + (y / z)) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e+19) {
		tmp = (t - a) / (b - y);
	} else if (z <= 6.8e-19) {
		tmp = ((y * x) + (z * (t - a))) / (y + (b * z));
	} else {
		tmp = (t - a) / ((b + (y / z)) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3e+19:
		tmp = (t - a) / (b - y)
	elif z <= 6.8e-19:
		tmp = ((y * x) + (z * (t - a))) / (y + (b * z))
	else:
		tmp = (t - a) / ((b + (y / z)) - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e+19)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (z <= 6.8e-19)
		tmp = Float64(Float64(Float64(y * x) + Float64(z * Float64(t - a))) / Float64(y + Float64(b * z)));
	else
		tmp = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.3e+19)
		tmp = (t - a) / (b - y);
	elseif (z <= 6.8e-19)
		tmp = ((y * x) + (z * (t - a))) / (y + (b * z));
	else
		tmp = (t - a) / ((b + (y / z)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e+19], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-19], N[(N[(N[(y * x), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(b * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e19

   1. Initial program 52.2%

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

      1. fma-define 52.2%

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

      2. +-commutative 52.2%

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

      3. fma-define 52.2%

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

   3. Simplified 52.2%

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

   5. Taylor expanded in z around inf 84.6%

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

   if -2.3e19 < z < 6.8000000000000004e-19

   1. Initial program 87.7%

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

   3. Taylor expanded in b around inf 85.7%

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

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   if 6.8000000000000004e-19 < z

   1. Initial program 54.6%

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

   3. Taylor expanded in z around inf 54.7%

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

   4. Taylor expanded in x around 0 81.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{y \cdot x + z \cdot \left(t - a\right)}{y + b \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-18} \lor \neg \left(z \leq 2.8 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.5e-18) (not (<= z 2.8e-40)))
   (/ (- t a) (- (+ b (/ y z)) y))
   (- x (/ (* z (- a t)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.5e-18) || !(z <= 2.8e-40)) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else {
		tmp = x - ((z * (a - 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) :: tmp
    if ((z <= (-7.5d-18)) .or. (.not. (z <= 2.8d-40))) then
        tmp = (t - a) / ((b + (y / z)) - y)
    else
        tmp = x - ((z * (a - 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 tmp;
	if ((z <= -7.5e-18) || !(z <= 2.8e-40)) {
		tmp = (t - a) / ((b + (y / z)) - y);
	} else {
		tmp = x - ((z * (a - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.5e-18) or not (z <= 2.8e-40):
		tmp = (t - a) / ((b + (y / z)) - y)
	else:
		tmp = x - ((z * (a - t)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.5e-18) || !(z <= 2.8e-40))
		tmp = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.5e-18) || ~((z <= 2.8e-40)))
		tmp = (t - a) / ((b + (y / z)) - y);
	else
		tmp = x - ((z * (a - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.5e-18], N[Not[LessEqual[z, 2.8e-40]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000015e-18 or 2.8e-40 < z

   1. Initial program 57.0%

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

   3. Taylor expanded in z around inf 57.0%

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

   4. Taylor expanded in x around 0 80.6%

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

   if -7.50000000000000015e-18 < z < 2.8e-40

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 58.0%

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

   4. Taylor expanded in x around 0 68.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-18} \lor \neg \left(z \leq 2.8 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-239}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7e+96)
     t_1
     (if (<= y -1.05e-239) (/ t b) (if (<= y 1.45e-51) (/ a (- b)) t_1)))))

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 <= -7e+96) {
		tmp = t_1;
	} else if (y <= -1.05e-239) {
		tmp = t / b;
	} else if (y <= 1.45e-51) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-7d+96)) then
        tmp = t_1
    else if (y <= (-1.05d-239)) then
        tmp = t / b
    else if (y <= 1.45d-51) then
        tmp = a / -b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7e+96) {
		tmp = t_1;
	} else if (y <= -1.05e-239) {
		tmp = t / b;
	} else if (y <= 1.45e-51) {
		tmp = a / -b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -7e+96:
		tmp = t_1
	elif y <= -1.05e-239:
		tmp = t / b
	elif y <= 1.45e-51:
		tmp = a / -b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7e+96)
		tmp = t_1;
	elseif (y <= -1.05e-239)
		tmp = Float64(t / b);
	elseif (y <= 1.45e-51)
		tmp = Float64(a / Float64(-b));
	else
		tmp = t_1;
	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 <= -7e+96)
		tmp = t_1;
	elseif (y <= -1.05e-239)
		tmp = t / b;
	elseif (y <= 1.45e-51)
		tmp = a / -b;
	else
		tmp = t_1;
	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, -7e+96], t$95$1, If[LessEqual[y, -1.05e-239], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.45e-51], N[(a / (-b)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999998e96 or 1.44999999999999986e-51 < y

   1. Initial program 62.2%

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

      1. fma-define 62.2%

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

      2. +-commutative 62.2%

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

      3. fma-define 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in y around inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. unsub-neg 52.1%

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

   7. Simplified 52.1%

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

   if -6.9999999999999998e96 < y < -1.0500000000000001e-239

   1. Initial program 71.1%

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

      1. fma-define 71.1%

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

      2. +-commutative 71.1%

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

      3. fma-define 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. associate-/l* 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in b around inf 62.4%

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

   9. Taylor expanded in t around inf 37.5%

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

   if -1.0500000000000001e-239 < y < 1.44999999999999986e-51

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf 87.1%

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

   4. Taylor expanded in x around 0 79.7%

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

   5. Taylor expanded in t around 0 38.4%

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

      1. neg-mul-1 38.4%

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

   7. Simplified 38.4%

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

   8. Taylor expanded in b around inf 35.5%

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

      1. associate-*r/ 35.5%

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

      2. neg-mul-1 35.5%

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

   10. Simplified 35.5%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-239}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-51}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \lor \neg \left(z \leq 1.65 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.0) (not (<= z 1.65e-20)))
   (/ (- t a) (- b y))
   (- x (/ (* z (- a t)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.0) || !(z <= 1.65e-20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - 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) :: tmp
    if ((z <= (-5.0d0)) .or. (.not. (z <= 1.65d-20))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * (a - 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 tmp;
	if ((z <= -5.0) || !(z <= 1.65e-20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * (a - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.0) or not (z <= 1.65e-20):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * (a - t)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.0) || !(z <= 1.65e-20))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * Float64(a - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.0) || ~((z <= 1.65e-20)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * (a - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.0], N[Not[LessEqual[z, 1.65e-20]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * N[(a - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5 or 1.65e-20 < z

   1. Initial program 55.0%

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

      1. fma-define 55.0%

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

      2. +-commutative 55.0%

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

      3. fma-define 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around inf 78.5%

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

   if -5 < z < 1.65e-20

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 58.9%

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

   4. Taylor expanded in x around 0 68.6%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \lor \neg \left(z \leq 1.65 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot \left(a - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 33.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+17}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.5e+81)
   x
   (if (<= y -1.5e-239) (/ t b) (if (<= y 7e+17) (/ a (- b)) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.5e+81) {
		tmp = x;
	} else if (y <= -1.5e-239) {
		tmp = t / b;
	} else if (y <= 7e+17) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.5d+81)) then
        tmp = x
    else if (y <= (-1.5d-239)) then
        tmp = t / b
    else if (y <= 7d+17) then
        tmp = a / -b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.5e+81) {
		tmp = x;
	} else if (y <= -1.5e-239) {
		tmp = t / b;
	} else if (y <= 7e+17) {
		tmp = a / -b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.5e+81:
		tmp = x
	elif y <= -1.5e-239:
		tmp = t / b
	elif y <= 7e+17:
		tmp = a / -b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.5e+81)
		tmp = x;
	elseif (y <= -1.5e-239)
		tmp = Float64(t / b);
	elseif (y <= 7e+17)
		tmp = Float64(a / Float64(-b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.5e+81)
		tmp = x;
	elseif (y <= -1.5e-239)
		tmp = t / b;
	elseif (y <= 7e+17)
		tmp = a / -b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.5e+81], x, If[LessEqual[y, -1.5e-239], N[(t / b), $MachinePrecision], If[LessEqual[y, 7e+17], N[(a / (-b)), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e81 or 7e17 < y

   1. Initial program 59.5%

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

      1. fma-define 59.5%

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

      2. +-commutative 59.5%

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

      3. fma-define 59.5%

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

   3. Simplified 59.5%

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

   5. Taylor expanded in z around 0 38.8%

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

   if -2.4999999999999999e81 < y < -1.4999999999999999e-239

   1. Initial program 72.9%

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

      1. fma-define 72.9%

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

      2. +-commutative 72.9%

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

      3. fma-define 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around inf 68.9%

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

      1. associate--l+ 68.9%

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

      2. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in b around inf 64.1%

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

   9. Taylor expanded in t around inf 38.4%

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

   if -1.4999999999999999e-239 < y < 7e17

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf 85.5%

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

   4. Taylor expanded in x around 0 80.3%

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

   5. Taylor expanded in t around 0 43.9%

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

      1. neg-mul-1 43.9%

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

   7. Simplified 43.9%

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

   8. Taylor expanded in b around inf 33.1%

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

      1. associate-*r/ 33.1%

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

      2. neg-mul-1 33.1%

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

   10. Simplified 33.1%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+17}:\\ \;\;\;\;\frac{a}{-b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \lor \neg \left(z \leq 9.5 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.0) (not (<= z 9.5e-20)))
   (/ (- t a) (- b y))
   (+ x (/ (* t z) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.0) || !(z <= 9.5e-20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t * z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.0d0)) .or. (.not. (z <= 9.5d-20))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((t * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.0) || !(z <= 9.5e-20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((t * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.0) or not (z <= 9.5e-20):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((t * z) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.0) || !(z <= 9.5e-20))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(t * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.0) || ~((z <= 9.5e-20)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((t * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.0], N[Not[LessEqual[z, 9.5e-20]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5 or 9.5e-20 < z

   1. Initial program 55.0%

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

      1. fma-define 55.0%

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

      2. +-commutative 55.0%

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

      3. fma-define 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in z around inf 78.5%

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

   if -5 < z < 9.5e-20

   1. Initial program 87.9%

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

   3. Taylor expanded in z around 0 58.9%

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

   4. Taylor expanded in x around 0 68.6%

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

   5. Taylor expanded in t around inf 58.1%

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

      1. *-commutative 58.1%

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

   7. Simplified 58.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \lor \neg \left(z \leq 9.5 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 53.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+103} \lor \neg \left(y \leq 1.8 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.15e+103) (not (<= y 1.8e-40)))
   (/ 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 <= -2.15e+103) || !(y <= 1.8e-40)) {
		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 <= (-2.15d+103)) .or. (.not. (y <= 1.8d-40))) 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 <= -2.15e+103) || !(y <= 1.8e-40)) {
		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 <= -2.15e+103) or not (y <= 1.8e-40):
		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 <= -2.15e+103) || !(y <= 1.8e-40))
		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 <= -2.15e+103) || ~((y <= 1.8e-40)))
		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, -2.15e+103], N[Not[LessEqual[y, 1.8e-40]], $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 < -2.14999999999999984e103 or 1.8e-40 < y

   1. Initial program 62.4%

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

      1. fma-define 62.4%

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

      2. +-commutative 62.4%

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

      3. fma-define 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. unsub-neg 52.9%

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

   7. Simplified 52.9%

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

   if -2.14999999999999984e103 < y < 1.8e-40

   1. Initial program 78.6%

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

      1. fma-define 78.6%

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

      2. +-commutative 78.6%

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

      3. fma-define 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in y around 0 54.9%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+103} \lor \neg \left(y \leq 1.8 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 33.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-52}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.5e+81) x (if (<= y 3.05e-52) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.5e+81) {
		tmp = x;
	} else if (y <= 3.05e-52) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.5d+81)) then
        tmp = x
    else if (y <= 3.05d-52) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.5e+81) {
		tmp = x;
	} else if (y <= 3.05e-52) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.5e+81:
		tmp = x
	elif y <= 3.05e-52:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.5e+81)
		tmp = x;
	elseif (y <= 3.05e-52)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.5e+81)
		tmp = x;
	elseif (y <= 3.05e-52)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.5e+81], x, If[LessEqual[y, 3.05e-52], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4999999999999999e81 or 3.04999999999999995e-52 < y

   1. Initial program 61.2%

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

      1. fma-define 61.2%

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

      2. +-commutative 61.2%

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

      3. fma-define 61.2%

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

   3. Simplified 61.2%

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

   5. Taylor expanded in z around 0 36.8%

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

   if -2.4999999999999999e81 < y < 3.04999999999999995e-52

   1. Initial program 80.1%

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

      1. fma-define 80.1%

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

      2. +-commutative 80.1%

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

      3. fma-define 80.1%

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

   3. Simplified 80.1%

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

   5. Taylor expanded in z around inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in b around inf 67.8%

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

   9. Taylor expanded in t around inf 32.6%

      \[\leadsto \color{blue}{\frac{t}{b}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 24.6% 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 71.4%

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

   1. fma-define 71.4%

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

   2. +-commutative 71.4%

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

   3. fma-define 71.5%

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

3. Simplified 71.5%

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

5. Taylor expanded in z around 0 22.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 73.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024165 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

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