Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.1% → 97.8%

Time: 18.1s

Alternatives: 15

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: 65.1% 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: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := \frac{x}{1 - z} + t\_2\\ t_4 := \frac{t\_1}{y + z \cdot \left(b - y\right)}\\ t_5 := t\_2 + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{if}\;t\_4 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq -5 \cdot 10^{-282}:\\ \;\;\;\;\frac{t\_1}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (+ (/ x (- 1.0 z)) t_2))
        (t_4 (/ t_1 (+ y (* z (- b y)))))
        (t_5 (+ t_2 (* (/ x z) (/ y (- b y))))))
   (if (<= t_4 -5e+267)
     t_3
     (if (<= t_4 -5e-282)
       (/ t_1 (- (* z b) (* y (+ z -1.0))))
       (if (<= t_4 0.0)
         t_5
         (if (<= t_4 2e+290) t_4 (if (<= t_4 INFINITY) t_3 t_5)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x / (1.0 - z)) + t_2;
	double t_4 = t_1 / (y + (z * (b - y)));
	double t_5 = t_2 + ((x / z) * (y / (b - y)));
	double tmp;
	if (t_4 <= -5e+267) {
		tmp = t_3;
	} else if (t_4 <= -5e-282) {
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	} else if (t_4 <= 0.0) {
		tmp = t_5;
	} else if (t_4 <= 2e+290) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} 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 = (x * y) + (z * (t - a));
	double t_2 = (t - a) / (b - y);
	double t_3 = (x / (1.0 - z)) + t_2;
	double t_4 = t_1 / (y + (z * (b - y)));
	double t_5 = t_2 + ((x / z) * (y / (b - y)));
	double tmp;
	if (t_4 <= -5e+267) {
		tmp = t_3;
	} else if (t_4 <= -5e-282) {
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	} else if (t_4 <= 0.0) {
		tmp = t_5;
	} else if (t_4 <= 2e+290) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = (t - a) / (b - y)
	t_3 = (x / (1.0 - z)) + t_2
	t_4 = t_1 / (y + (z * (b - y)))
	t_5 = t_2 + ((x / z) * (y / (b - y)))
	tmp = 0
	if t_4 <= -5e+267:
		tmp = t_3
	elif t_4 <= -5e-282:
		tmp = t_1 / ((z * b) - (y * (z + -1.0)))
	elif t_4 <= 0.0:
		tmp = t_5
	elif t_4 <= 2e+290:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	t_4 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_5 = Float64(t_2 + Float64(Float64(x / z) * Float64(y / Float64(b - y))))
	tmp = 0.0
	if (t_4 <= -5e+267)
		tmp = t_3;
	elseif (t_4 <= -5e-282)
		tmp = Float64(t_1 / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	elseif (t_4 <= 0.0)
		tmp = t_5;
	elseif (t_4 <= 2e+290)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = (t - a) / (b - y);
	t_3 = (x / (1.0 - z)) + t_2;
	t_4 = t_1 / (y + (z * (b - y)));
	t_5 = t_2 + ((x / z) * (y / (b - y)));
	tmp = 0.0;
	if (t_4 <= -5e+267)
		tmp = t_3;
	elseif (t_4 <= -5e-282)
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	elseif (t_4 <= 0.0)
		tmp = t_5;
	elseif (t_4 <= 2e+290)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -5e+267], t$95$3, If[LessEqual[t$95$4, -5e-282], N[(t$95$1 / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], t$95$5, If[LessEqual[t$95$4, 2e+290], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$3, t$95$5]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.9999999999999999e267 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 27.0%

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

   3. Taylor expanded in x around 0 27.0%

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

   4. Taylor expanded in z around inf 59.9%

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

   5. Taylor expanded in y around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

   7. Simplified 98.5%

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

   if -4.9999999999999999e267 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000001e-282

   1. Initial program 99.5%

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

   3. Taylor expanded in y around -inf 99.5%

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

      1. +-commutative 99.5%

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

      2. mul-1-neg 99.5%

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

      3. unsub-neg 99.5%

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

      4. *-commutative 99.5%

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

      5. sub-neg 99.5%

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

      6. metadata-eval 99.5%

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

   5. Simplified 99.5%

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

   if -5.0000000000000001e-282 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.4%

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

   3. Taylor expanded in x around 0 12.4%

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

   4. Taylor expanded in z around inf 67.7%

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

   5. Taylor expanded in z around inf 67.7%

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

      1. times-frac 100.0%

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

   7. Simplified 100.0%

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

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

   1. Initial program 99.7%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+267}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ t_3 := t\_2 + \frac{x}{z} \cdot \frac{y}{b - y}\\ t_4 := \frac{x}{1 - z} + t\_2\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (+ t_2 (* (/ x z) (/ y (- b y)))))
        (t_4 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_1 -5e+267)
     t_4
     (if (<= t_1 -5e-282)
       t_1
       (if (<= t_1 0.0)
         t_3
         (if (<= t_1 2e+290) t_1 (if (<= t_1 INFINITY) t_4 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double t_3 = t_2 + ((x / z) * (y / (b - y)));
	double t_4 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_1 <= -5e+267) {
		tmp = t_4;
	} else if (t_1 <= -5e-282) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_3;
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double t_3 = t_2 + ((x / z) * (y / (b - y)));
	double t_4 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_1 <= -5e+267) {
		tmp = t_4;
	} else if (t_1 <= -5e-282) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t_3;
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	t_3 = t_2 + ((x / z) * (y / (b - y)))
	t_4 = (x / (1.0 - z)) + t_2
	tmp = 0
	if t_1 <= -5e+267:
		tmp = t_4
	elif t_1 <= -5e-282:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t_3
	elif t_1 <= 2e+290:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(t_2 + Float64(Float64(x / z) * Float64(y / Float64(b - y))))
	t_4 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_1 <= -5e+267)
		tmp = t_4;
	elseif (t_1 <= -5e-282)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_3;
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	t_3 = t_2 + ((x / z) * (y / (b - y)));
	t_4 = (x / (1.0 - z)) + t_2;
	tmp = 0.0;
	if (t_1 <= -5e+267)
		tmp = t_4;
	elseif (t_1 <= -5e-282)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t_3;
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+267], t$95$4, If[LessEqual[t$95$1, -5e-282], t$95$1, If[LessEqual[t$95$1, 0.0], t$95$3, If[LessEqual[t$95$1, 2e+290], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$4, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.9999999999999999e267 or 2.00000000000000012e290 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 27.0%

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

   3. Taylor expanded in x around 0 27.0%

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

   4. Taylor expanded in z around inf 59.9%

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

   5. Taylor expanded in y around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

   7. Simplified 98.5%

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

   if -4.9999999999999999e267 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -5.0000000000000001e-282 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.00000000000000012e290

   1. Initial program 99.6%

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

   if -5.0000000000000001e-282 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 12.4%

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

   3. Taylor expanded in x around 0 12.4%

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

   4. Taylor expanded in z around inf 67.7%

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

   5. Taylor expanded in z around inf 67.7%

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

      1. times-frac 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{+267}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-282}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{y}{t - \left(a + x \cdot b\right)}}\\ t_2 := \frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{if}\;z \leq -0.000122:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-146}:\\ \;\;\;\;\left(\frac{t}{b} + \frac{x \cdot y}{z \cdot b}\right) - \frac{a}{b}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-273}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ y (- t (+ a (* x b)))))))
        (t_2 (+ (/ (- t a) (- b y)) (* (/ x z) (/ y (- b y))))))
   (if (<= z -0.000122)
     t_2
     (if (<= z -2.9e-100)
       t_1
       (if (<= z -9.5e-146)
         (- (+ (/ t b) (/ (* x y) (* z b))) (/ a b))
         (if (<= z 1.2e-273)
           (- x (/ (* z a) y))
           (if (<= z 3.2e-48) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z / (y / (t - (a + (x * b)))));
	double t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)));
	double tmp;
	if (z <= -0.000122) {
		tmp = t_2;
	} else if (z <= -2.9e-100) {
		tmp = t_1;
	} else if (z <= -9.5e-146) {
		tmp = ((t / b) + ((x * y) / (z * b))) - (a / b);
	} else if (z <= 1.2e-273) {
		tmp = x - ((z * a) / y);
	} else if (z <= 3.2e-48) {
		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 = x + (z / (y / (t - (a + (x * b)))))
    t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)))
    if (z <= (-0.000122d0)) then
        tmp = t_2
    else if (z <= (-2.9d-100)) then
        tmp = t_1
    else if (z <= (-9.5d-146)) then
        tmp = ((t / b) + ((x * y) / (z * b))) - (a / b)
    else if (z <= 1.2d-273) then
        tmp = x - ((z * a) / y)
    else if (z <= 3.2d-48) 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 = x + (z / (y / (t - (a + (x * b)))));
	double t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)));
	double tmp;
	if (z <= -0.000122) {
		tmp = t_2;
	} else if (z <= -2.9e-100) {
		tmp = t_1;
	} else if (z <= -9.5e-146) {
		tmp = ((t / b) + ((x * y) / (z * b))) - (a / b);
	} else if (z <= 1.2e-273) {
		tmp = x - ((z * a) / y);
	} else if (z <= 3.2e-48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z / (y / (t - (a + (x * b)))))
	t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)))
	tmp = 0
	if z <= -0.000122:
		tmp = t_2
	elif z <= -2.9e-100:
		tmp = t_1
	elif z <= -9.5e-146:
		tmp = ((t / b) + ((x * y) / (z * b))) - (a / b)
	elif z <= 1.2e-273:
		tmp = x - ((z * a) / y)
	elif z <= 3.2e-48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z / Float64(y / Float64(t - Float64(a + Float64(x * b))))))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / Float64(b - y))))
	tmp = 0.0
	if (z <= -0.000122)
		tmp = t_2;
	elseif (z <= -2.9e-100)
		tmp = t_1;
	elseif (z <= -9.5e-146)
		tmp = Float64(Float64(Float64(t / b) + Float64(Float64(x * y) / Float64(z * b))) - Float64(a / b));
	elseif (z <= 1.2e-273)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 3.2e-48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z / (y / (t - (a + (x * b)))));
	t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)));
	tmp = 0.0;
	if (z <= -0.000122)
		tmp = t_2;
	elseif (z <= -2.9e-100)
		tmp = t_1;
	elseif (z <= -9.5e-146)
		tmp = ((t / b) + ((x * y) / (z * b))) - (a / b);
	elseif (z <= 1.2e-273)
		tmp = x - ((z * a) / y);
	elseif (z <= 3.2e-48)
		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[(x + N[(z / N[(y / N[(t - N[(a + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.000122], t$95$2, If[LessEqual[z, -2.9e-100], t$95$1, If[LessEqual[z, -9.5e-146], N[(N[(N[(t / b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-273], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-48], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.21999999999999997e-4 or 3.1999999999999998e-48 < z

   1. Initial program 51.7%

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

   3. Taylor expanded in x around 0 51.7%

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

   4. Taylor expanded in z around inf 83.9%

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

   5. Taylor expanded in z around inf 83.0%

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

      1. times-frac 95.8%

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

   7. Simplified 95.8%

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

   if -1.21999999999999997e-4 < z < -2.89999999999999975e-100 or 1.19999999999999991e-273 < z < 3.1999999999999998e-48

   1. Initial program 84.1%

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

   3. Taylor expanded in z around 0 57.6%

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

   4. Taylor expanded in y around 0 76.8%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -2.89999999999999975e-100 < z < -9.5000000000000005e-146

   1. Initial program 77.1%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in x around 0 75.0%

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

   if -9.5000000000000005e-146 < z < 1.19999999999999991e-273

   1. Initial program 79.2%

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

   3. Taylor expanded in z around 0 49.7%

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

   4. Taylor expanded in a around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. *-commutative 76.9%

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

   6. Simplified 76.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000122:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - \left(a + x \cdot b\right)}}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-146}:\\ \;\;\;\;\left(\frac{t}{b} + \frac{x \cdot y}{z \cdot b}\right) - \frac{a}{b}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-273}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - \left(a + x \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{\frac{y}{t - \left(a + x \cdot b\right)}}\\ t_2 := \frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{if}\;z \leq -0.000122:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-272}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-48}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ z (/ y (- t (+ a (* x b)))))))
        (t_2 (+ (/ (- t a) (- b y)) (* (/ x z) (/ y (- b y))))))
   (if (<= z -0.000122)
     t_2
     (if (<= z -4.7e-101)
       t_1
       (if (<= z -9.5e-146)
         (+ (/ (* x y) (+ y (* z (- b y)))) (/ (- t a) b))
         (if (<= z 2.1e-272)
           (- x (/ (* z a) y))
           (if (<= z 2.7e-48) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z / (y / (t - (a + (x * b)))));
	double t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)));
	double tmp;
	if (z <= -0.000122) {
		tmp = t_2;
	} else if (z <= -4.7e-101) {
		tmp = t_1;
	} else if (z <= -9.5e-146) {
		tmp = ((x * y) / (y + (z * (b - y)))) + ((t - a) / b);
	} else if (z <= 2.1e-272) {
		tmp = x - ((z * a) / y);
	} else if (z <= 2.7e-48) {
		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 = x + (z / (y / (t - (a + (x * b)))))
    t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)))
    if (z <= (-0.000122d0)) then
        tmp = t_2
    else if (z <= (-4.7d-101)) then
        tmp = t_1
    else if (z <= (-9.5d-146)) then
        tmp = ((x * y) / (y + (z * (b - y)))) + ((t - a) / b)
    else if (z <= 2.1d-272) then
        tmp = x - ((z * a) / y)
    else if (z <= 2.7d-48) 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 = x + (z / (y / (t - (a + (x * b)))));
	double t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)));
	double tmp;
	if (z <= -0.000122) {
		tmp = t_2;
	} else if (z <= -4.7e-101) {
		tmp = t_1;
	} else if (z <= -9.5e-146) {
		tmp = ((x * y) / (y + (z * (b - y)))) + ((t - a) / b);
	} else if (z <= 2.1e-272) {
		tmp = x - ((z * a) / y);
	} else if (z <= 2.7e-48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z / (y / (t - (a + (x * b)))))
	t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)))
	tmp = 0
	if z <= -0.000122:
		tmp = t_2
	elif z <= -4.7e-101:
		tmp = t_1
	elif z <= -9.5e-146:
		tmp = ((x * y) / (y + (z * (b - y)))) + ((t - a) / b)
	elif z <= 2.1e-272:
		tmp = x - ((z * a) / y)
	elif z <= 2.7e-48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z / Float64(y / Float64(t - Float64(a + Float64(x * b))))))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(x / z) * Float64(y / Float64(b - y))))
	tmp = 0.0
	if (z <= -0.000122)
		tmp = t_2;
	elseif (z <= -4.7e-101)
		tmp = t_1;
	elseif (z <= -9.5e-146)
		tmp = Float64(Float64(Float64(x * y) / Float64(y + Float64(z * Float64(b - y)))) + Float64(Float64(t - a) / b));
	elseif (z <= 2.1e-272)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 2.7e-48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z / (y / (t - (a + (x * b)))));
	t_2 = ((t - a) / (b - y)) + ((x / z) * (y / (b - y)));
	tmp = 0.0;
	if (z <= -0.000122)
		tmp = t_2;
	elseif (z <= -4.7e-101)
		tmp = t_1;
	elseif (z <= -9.5e-146)
		tmp = ((x * y) / (y + (z * (b - y)))) + ((t - a) / b);
	elseif (z <= 2.1e-272)
		tmp = x - ((z * a) / y);
	elseif (z <= 2.7e-48)
		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[(x + N[(z / N[(y / N[(t - N[(a + N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.000122], t$95$2, If[LessEqual[z, -4.7e-101], t$95$1, If[LessEqual[z, -9.5e-146], N[(N[(N[(x * y), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-272], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-48], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.21999999999999997e-4 or 2.70000000000000011e-48 < z

   1. Initial program 51.7%

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

   3. Taylor expanded in x around 0 51.7%

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

   4. Taylor expanded in z around inf 83.9%

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

   5. Taylor expanded in z around inf 83.0%

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

      1. times-frac 95.8%

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

   7. Simplified 95.8%

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

   if -1.21999999999999997e-4 < z < -4.6999999999999999e-101 or 2.09999999999999987e-272 < z < 2.70000000000000011e-48

   1. Initial program 84.1%

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

   3. Taylor expanded in z around 0 57.6%

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

   4. Taylor expanded in y around 0 76.8%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -4.6999999999999999e-101 < z < -9.5000000000000005e-146

   1. Initial program 77.1%

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

   3. Taylor expanded in x around 0 77.1%

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

   4. Taylor expanded in y around 0 76.1%

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

   if -9.5000000000000005e-146 < z < 2.09999999999999987e-272

   1. Initial program 79.2%

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

   3. Taylor expanded in z around 0 49.7%

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

   4. Taylor expanded in a around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. *-commutative 76.9%

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

   6. Simplified 76.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000122:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - \left(a + x \cdot b\right)}}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-146}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{t - a}{b}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-272}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-48}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t - \left(a + x \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x}{z} \cdot \frac{y}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+80} \lor \neg \left(y \leq 2.7 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e+80) (not (<= y 2.7e+87)))
   (+ (/ x (- 1.0 z)) (/ (- t a) (- b y)))
   (/ (- t a) (- (+ b (/ y z)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e+80) || !(y <= 2.7e+87)) {
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	} 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 ((y <= (-1.75d+80)) .or. (.not. (y <= 2.7d+87))) then
        tmp = (x / (1.0d0 - z)) + ((t - a) / (b - y))
    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 ((y <= -1.75e+80) || !(y <= 2.7e+87)) {
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	} else {
		tmp = (t - a) / ((b + (y / z)) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e+80) or not (y <= 2.7e+87):
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y))
	else:
		tmp = (t - a) / ((b + (y / z)) - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e+80) || !(y <= 2.7e+87))
		tmp = Float64(Float64(x / Float64(1.0 - z)) + Float64(Float64(t - a) / Float64(b - y)));
	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 ((y <= -1.75e+80) || ~((y <= 2.7e+87)))
		tmp = (x / (1.0 - z)) + ((t - a) / (b - y));
	else
		tmp = (t - a) / ((b + (y / z)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.75e+80], N[Not[LessEqual[y, 2.7e+87]], $MachinePrecision]], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.74999999999999997e80 or 2.70000000000000007e87 < y

   1. Initial program 47.6%

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

   3. Taylor expanded in x around 0 47.6%

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

   4. Taylor expanded in z around inf 47.0%

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

   5. Taylor expanded in y around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. unsub-neg 79.1%

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

   7. Simplified 79.1%

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

   if -1.74999999999999997e80 < y < 2.70000000000000007e87

   1. Initial program 78.1%

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

   3. Taylor expanded in x around 0 60.1%

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

      1. *-commutative 60.1%

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

      2. +-commutative 60.1%

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

      3. fma-udef 60.1%

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

      4. associate-/l* 70.6%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in z around 0 81.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+80} \lor \neg \left(y \leq 2.7 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.000122:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-305}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -0.000122)
     t_1
     (if (<= z -1.08e-305)
       (- x (/ (* z a) y))
       (if (<= z 2.5e-77) (+ x (/ z (/ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.000122) {
		tmp = t_1;
	} else if (z <= -1.08e-305) {
		tmp = x - ((z * a) / y);
	} else if (z <= 2.5e-77) {
		tmp = x + (z / (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-0.000122d0)) then
        tmp = t_1
    else if (z <= (-1.08d-305)) then
        tmp = x - ((z * a) / y)
    else if (z <= 2.5d-77) then
        tmp = x + (z / (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.000122) {
		tmp = t_1;
	} else if (z <= -1.08e-305) {
		tmp = x - ((z * a) / y);
	} else if (z <= 2.5e-77) {
		tmp = x + (z / (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -0.000122:
		tmp = t_1
	elif z <= -1.08e-305:
		tmp = x - ((z * a) / y)
	elif z <= 2.5e-77:
		tmp = x + (z / (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -0.000122)
		tmp = t_1;
	elseif (z <= -1.08e-305)
		tmp = Float64(x - Float64(Float64(z * a) / y));
	elseif (z <= 2.5e-77)
		tmp = Float64(x + Float64(z / Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.000122)
		tmp = t_1;
	elseif (z <= -1.08e-305)
		tmp = x - ((z * a) / y);
	elseif (z <= 2.5e-77)
		tmp = x + (z / (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.000122], t$95$1, If[LessEqual[z, -1.08e-305], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-77], N[(x + N[(z / N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999997e-4 or 2.49999999999999982e-77 < z

   1. Initial program 52.8%

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

   3. Taylor expanded in z around inf 80.1%

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

   if -1.21999999999999997e-4 < z < -1.08000000000000004e-305

   1. Initial program 81.2%

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

   3. Taylor expanded in z around 0 46.9%

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

   4. Taylor expanded in a around inf 66.2%

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

      1. mul-1-neg 66.2%

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

      2. *-commutative 66.2%

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

   6. Simplified 66.2%

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

   if -1.08000000000000004e-305 < z < 2.49999999999999982e-77

   1. Initial program 82.2%

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

   3. Taylor expanded in z around 0 60.1%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in t around inf 75.6%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.000122:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-305}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-77}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.86 \cdot 10^{+80} \lor \neg \left(y \leq 2.55 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.86e+80) (not (<= y 2.55e+81)))
   (/ x (- 1.0 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 ((y <= -1.86e+80) || !(y <= 2.55e+81)) {
		tmp = x / (1.0 - 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 ((y <= (-1.86d+80)) .or. (.not. (y <= 2.55d+81))) then
        tmp = x / (1.0d0 - 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 ((y <= -1.86e+80) || !(y <= 2.55e+81)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / ((b + (y / z)) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.86e+80) or not (y <= 2.55e+81):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / ((b + (y / z)) - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.86e+80) || !(y <= 2.55e+81))
		tmp = Float64(x / Float64(1.0 - 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 ((y <= -1.86e+80) || ~((y <= 2.55e+81)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / ((b + (y / z)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.86e+80], N[Not[LessEqual[y, 2.55e+81]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8599999999999999e80 or 2.5500000000000001e81 < y

   1. Initial program 48.6%

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

   3. Taylor expanded in y around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

   5. Simplified 66.6%

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

   if -1.8599999999999999e80 < y < 2.5500000000000001e81

   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 x around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. +-commutative 60.8%

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

      3. fma-udef 60.8%

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

      4. associate-/l* 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in z around 0 82.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.86 \cdot 10^{+80} \lor \neg \left(y \leq 2.55 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-27} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.22e-27) (not (<= z 5e-77)))
   (/ (- t a) (- b y))
   (+ x (/ z (/ y t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.22e-27) || !(z <= 5e-77)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z / (y / t));
	}
	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 <= (-1.22d-27)) .or. (.not. (z <= 5d-77))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z / (y / t))
    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 <= -1.22e-27) || !(z <= 5e-77)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z / (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.22e-27) or not (z <= 5e-77):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z / (y / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.22e-27) || !(z <= 5e-77))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z / Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.22e-27) || ~((z <= 5e-77)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z / (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.22e-27], N[Not[LessEqual[z, 5e-77]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e-27 or 4.99999999999999963e-77 < z

   1. Initial program 54.9%

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

   3. Taylor expanded in z around inf 76.6%

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

   if -1.22e-27 < z < 4.99999999999999963e-77

   1. Initial program 81.5%

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

   3. Taylor expanded in z around 0 54.4%

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

   4. Taylor expanded in y around 0 73.7%

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

      1. associate-/l* 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in t around inf 68.3%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-27} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-9} \lor \neg \left(z \leq 1.15 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e-9) (not (<= z 1.15e-79))) (/ (- a) b) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-9) || !(z <= 1.15e-79)) {
		tmp = -a / b;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9.5d-9)) .or. (.not. (z <= 1.15d-79))) then
        tmp = -a / b
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.5e-9) || !(z <= 1.15e-79)) {
		tmp = -a / b;
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.5e-9) or not (z <= 1.15e-79):
		tmp = -a / b
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.5e-9) || !(z <= 1.15e-79))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.5e-9) || ~((z <= 1.15e-79)))
		tmp = -a / b;
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e-9], N[Not[LessEqual[z, 1.15e-79]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000007e-9 or 1.15000000000000006e-79 < z

   1. Initial program 53.4%

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

   3. Taylor expanded in y around 0 46.2%

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

   4. Taylor expanded in t around 0 30.1%

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

      1. neg-mul-1 30.1%

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

      2. distribute-neg-frac 30.1%

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

   6. Simplified 30.1%

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

   if -9.5000000000000007e-9 < z < 1.15000000000000006e-79

   1. Initial program 81.2%

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

   3. Taylor expanded in z around 0 52.2%

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

   4. Taylor expanded in y around inf 56.2%

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

      1. *-commutative 56.2%

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

   6. Simplified 56.2%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-9} \lor \neg \left(z \leq 1.15 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-8} \lor \neg \left(z \leq 2.5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.1e-8) (not (<= z 2.5e-77))) (/ t (- b y)) (+ x (* x z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.1e-8) || !(z <= 2.5e-77)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.1d-8)) .or. (.not. (z <= 2.5d-77))) then
        tmp = t / (b - y)
    else
        tmp = x + (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.1e-8) || !(z <= 2.5e-77)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.1e-8) or not (z <= 2.5e-77):
		tmp = t / (b - y)
	else:
		tmp = x + (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.1e-8) || !(z <= 2.5e-77))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x + Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.1e-8) || ~((z <= 2.5e-77)))
		tmp = t / (b - y);
	else
		tmp = x + (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.1e-8], N[Not[LessEqual[z, 2.5e-77]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000032e-8 or 2.49999999999999982e-77 < z

   1. Initial program 53.4%

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

   3. Taylor expanded in t around inf 25.8%

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

      1. *-commutative 25.8%

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

   5. Simplified 25.8%

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

   6. Taylor expanded in z around inf 39.2%

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

   if -4.10000000000000032e-8 < z < 2.49999999999999982e-77

   1. Initial program 81.2%

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

   3. Taylor expanded in z around 0 52.2%

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

   4. Taylor expanded in y around inf 56.2%

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

      1. *-commutative 56.2%

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

   6. Simplified 56.2%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-8} \lor \neg \left(z \leq 2.5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+55} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.56e+55) (not (<= z 5e-77))) (/ t (- b y)) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.56e+55) || !(z <= 5e-77)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.56d+55)) .or. (.not. (z <= 5d-77))) then
        tmp = t / (b - y)
    else
        tmp = x / (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.56e+55) || !(z <= 5e-77)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.56e+55) or not (z <= 5e-77):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.56e+55) || !(z <= 5e-77))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.56e+55) || ~((z <= 5e-77)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.56e+55], N[Not[LessEqual[z, 5e-77]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5600000000000001e55 or 4.99999999999999963e-77 < z

   1. Initial program 47.7%

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

   3. Taylor expanded in t around inf 26.2%

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

      1. *-commutative 26.2%

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

   5. Simplified 26.2%

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

   6. Taylor expanded in z around inf 42.5%

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

   if -1.5600000000000001e55 < z < 4.99999999999999963e-77

   1. Initial program 82.5%

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

   3. Taylor expanded in y around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. unsub-neg 52.3%

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

   5. Simplified 52.3%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+55} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+74} \lor \neg \left(y \leq 2.6 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.6e+74) (not (<= y 2.6e+45))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+74) || !(y <= 2.6e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.6d+74)) .or. (.not. (y <= 2.6d+45))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+74) || !(y <= 2.6e+45)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.6e+74) or not (y <= 2.6e+45):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.6e+74) || !(y <= 2.6e+45))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.6e+74) || ~((y <= 2.6e+45)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.6e+74], N[Not[LessEqual[y, 2.6e+45]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.60000000000000003e74 or 2.60000000000000007e45 < y

   1. Initial program 50.5%

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

   3. Taylor expanded in y around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. unsub-neg 62.0%

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

   5. Simplified 62.0%

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

   if -5.60000000000000003e74 < y < 2.60000000000000007e45

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 52.7%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+74} \lor \neg \left(y \leq 2.6 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-8} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.2e-8) (not (<= z 5e-77))) (/ (- a) b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e-8) || !(z <= 5e-77)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.2d-8)) .or. (.not. (z <= 5d-77))) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.2e-8) || !(z <= 5e-77)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.2e-8) or not (z <= 5e-77):
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.2e-8) || !(z <= 5e-77))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.2e-8) || ~((z <= 5e-77)))
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.2e-8], N[Not[LessEqual[z, 5e-77]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002e-8 or 4.99999999999999963e-77 < z

   1. Initial program 53.4%

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

   3. Taylor expanded in y around 0 46.2%

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

   4. Taylor expanded in t around 0 30.1%

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

      1. neg-mul-1 30.1%

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

      2. distribute-neg-frac 30.1%

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

   6. Simplified 30.1%

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

   if -3.2000000000000002e-8 < z < 4.99999999999999963e-77

   1. Initial program 81.2%

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

   3. Taylor expanded in z around 0 55.6%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-8} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-9} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e-9) (not (<= z 5e-77))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-9) || !(z <= 5e-77)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.5d-9)) .or. (.not. (z <= 5d-77))) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-9) || !(z <= 5e-77)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.5e-9) or not (z <= 5e-77):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e-9) || !(z <= 5e-77))
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.5e-9) || ~((z <= 5e-77)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e-9], N[Not[LessEqual[z, 5e-77]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999976e-9 or 4.99999999999999963e-77 < z

   1. Initial program 53.4%

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

   3. Taylor expanded in t around inf 25.8%

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

      1. *-commutative 25.8%

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

   5. Simplified 25.8%

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

   6. Taylor expanded in y around 0 22.5%

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

   if -4.49999999999999976e-9 < z < 4.99999999999999963e-77

   1. Initial program 81.2%

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

   3. Taylor expanded in z around 0 55.6%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-9} \lor \neg \left(z \leq 5 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 25.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.0%

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

3. Taylor expanded in z around 0 27.1%

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

4. Final simplification 27.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 72.8% 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 2024031 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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