Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.8% → 89.2%

Time: 22.6s

Alternatives: 19

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.8% 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: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_3 := x \cdot y + t_1\\ t_4 := \frac{t_3}{y + z \cdot \left(b - y\right)}\\ t_5 := \left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-173}:\\ \;\;\;\;\frac{t_3}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_1\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (- (/ (- a t) y) (/ x (+ z -1.0))))
        (t_3 (+ (* x y) t_1))
        (t_4 (/ t_3 (+ y (* z (- b y)))))
        (t_5
         (+
          (+ (/ x (/ (- b y) (/ y z))) (/ (- t a) (- b y)))
          (/ (* (/ y z) (- a t)) (pow (- b y) 2.0)))))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 -1e-173)
       (/ t_3 (+ y (- (* z b) (* y z))))
       (if (<= t_4 0.0)
         t_5
         (if (<= t_4 5e+276)
           (/ (fma x y t_1) (fma z (- b y) y))
           (if (<= t_4 INFINITY) t_2 t_5)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double t_3 = (x * y) + t_1;
	double t_4 = t_3 / (y + (z * (b - y)));
	double t_5 = ((x / ((b - y) / (y / z))) + ((t - a) / (b - y))) + (((y / z) * (a - t)) / pow((b - y), 2.0));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= -1e-173) {
		tmp = t_3 / (y + ((z * b) - (y * z)));
	} else if (t_4 <= 0.0) {
		tmp = t_5;
	} else if (t_4 <= 5e+276) {
		tmp = fma(x, y, t_1) / fma(z, (b - y), y);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_3 = Float64(Float64(x * y) + t_1)
	t_4 = Float64(t_3 / Float64(y + Float64(z * Float64(b - y))))
	t_5 = Float64(Float64(Float64(x / Float64(Float64(b - y) / Float64(y / z))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(Float64(y / z) * Float64(a - t)) / (Float64(b - y) ^ 2.0)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= -1e-173)
		tmp = Float64(t_3 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_4 <= 0.0)
		tmp = t_5;
	elseif (t_4 <= 5e+276)
		tmp = Float64(fma(x, y, t_1) / fma(z, Float64(b - y), y));
	elseif (t_4 <= Inf)
		tmp = t_2;
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, -1e-173], N[(t$95$3 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], t$95$5, If[LessEqual[t$95$4, 5e+276], N[(N[(x * y + t$95$1), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$2, 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)))) < -inf.0 or 5.00000000000000001e276 < (/.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 y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. associate-*r/ 64.5%

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

      4. neg-mul-1 64.5%

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

      5. sub-neg 64.5%

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

      6. metadata-eval 64.5%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 87.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e-173

   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
   3. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

   if -1e-173 < (/.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 14.4%

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

   3. Taylor expanded in z around inf 49.8%

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

      1. associate--r+ 49.8%

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

      2. +-commutative 49.8%

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

      3. associate--l+ 49.8%

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

      4. associate-/l* 51.8%

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

      5. *-commutative 51.8%

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

      6. associate-/l* 64.8%

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

      7. div-sub 64.8%

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

      8. times-frac 98.1%

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

      9. associate-*r/ 94.4%

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

   5. Simplified 94.4%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000001e276

   1. Initial program 99.6%

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

      1. fma-def 99.6%

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

      2. +-commutative 99.6%

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

      3. fma-def 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_4 := x \cdot y + t_2\\ t_5 := \frac{t_4}{t_1}\\ t_6 := \left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_5 \leq -1 \cdot 10^{-173}:\\ \;\;\;\;\frac{t_4}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (- (/ (- a t) y) (/ x (+ z -1.0))))
        (t_4 (+ (* x y) t_2))
        (t_5 (/ t_4 t_1))
        (t_6
         (+
          (+ (/ x (/ (- b y) (/ y z))) (/ (- t a) (- b y)))
          (/ (* (/ y z) (- a t)) (pow (- b y) 2.0)))))
   (if (<= t_5 (- INFINITY))
     t_3
     (if (<= t_5 -1e-173)
       (/ t_4 (+ y (- (* z b) (* y z))))
       (if (<= t_5 0.0)
         t_6
         (if (<= t_5 5e+276)
           (/ (fma x y t_2) t_1)
           (if (<= t_5 INFINITY) t_3 t_6)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((a - t) / y) - (x / (z + -1.0));
	double t_4 = (x * y) + t_2;
	double t_5 = t_4 / t_1;
	double t_6 = ((x / ((b - y) / (y / z))) + ((t - a) / (b - y))) + (((y / z) * (a - t)) / pow((b - y), 2.0));
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_5 <= -1e-173) {
		tmp = t_4 / (y + ((z * b) - (y * z)));
	} else if (t_5 <= 0.0) {
		tmp = t_6;
	} else if (t_5 <= 5e+276) {
		tmp = fma(x, y, t_2) / t_1;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_4 = Float64(Float64(x * y) + t_2)
	t_5 = Float64(t_4 / t_1)
	t_6 = Float64(Float64(Float64(x / Float64(Float64(b - y) / Float64(y / z))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(Float64(y / z) * Float64(a - t)) / (Float64(b - y) ^ 2.0)))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_5 <= -1e-173)
		tmp = Float64(t_4 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_5 <= 0.0)
		tmp = t_6;
	elseif (t_5 <= 5e+276)
		tmp = Float64(fma(x, y, t_2) / t_1);
	elseif (t_5 <= Inf)
		tmp = t_3;
	else
		tmp = t_6;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] * N[(a - t), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$3, If[LessEqual[t$95$5, -1e-173], N[(t$95$4 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 0.0], t$95$6, If[LessEqual[t$95$5, 5e+276], N[(N[(x * y + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$5, Infinity], t$95$3, t$95$6]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5.00000000000000001e276 < (/.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 y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. associate-*r/ 64.5%

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

      4. neg-mul-1 64.5%

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

      5. sub-neg 64.5%

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

      6. metadata-eval 64.5%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 87.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1e-173

   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
   3. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.7%

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

   4. Applied egg-rr 99.7%

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

   if -1e-173 < (/.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 14.4%

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

   3. Taylor expanded in z around inf 49.8%

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

      1. associate--r+ 49.8%

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

      2. +-commutative 49.8%

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

      3. associate--l+ 49.8%

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

      4. associate-/l* 51.8%

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

      5. *-commutative 51.8%

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

      6. associate-/l* 64.8%

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

      7. div-sub 64.8%

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

      8. times-frac 98.1%

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

      9. associate-*r/ 94.4%

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

   5. Simplified 94.4%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000001e276

   1. Initial program 99.6%

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

      1. fma-def 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{\frac{y}{z} \cdot \left(a - t\right)}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_4 := x \cdot y + t_2\\ t_5 := \frac{t_4}{t_1}\\ t_6 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_5 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\frac{t_4}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_1}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (- (/ (- a t) y) (/ x (+ z -1.0))))
        (t_4 (+ (* x y) t_2))
        (t_5 (/ t_4 t_1))
        (t_6 (/ (- t a) (- b y))))
   (if (<= t_5 (- INFINITY))
     t_3
     (if (<= t_5 -2e-293)
       (/ t_4 (+ y (- (* z b) (* y z))))
       (if (<= t_5 0.0)
         t_6
         (if (<= t_5 5e+276)
           (/ (fma x y t_2) t_1)
           (if (<= t_5 INFINITY) t_3 t_6)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = ((a - t) / y) - (x / (z + -1.0));
	double t_4 = (x * y) + t_2;
	double t_5 = t_4 / t_1;
	double t_6 = (t - a) / (b - y);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_5 <= -2e-293) {
		tmp = t_4 / (y + ((z * b) - (y * z)));
	} else if (t_5 <= 0.0) {
		tmp = t_6;
	} else if (t_5 <= 5e+276) {
		tmp = fma(x, y, t_2) / t_1;
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_6;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_4 = Float64(Float64(x * y) + t_2)
	t_5 = Float64(t_4 / t_1)
	t_6 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_5 <= -2e-293)
		tmp = Float64(t_4 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_5 <= 0.0)
		tmp = t_6;
	elseif (t_5 <= 5e+276)
		tmp = Float64(fma(x, y, t_2) / t_1);
	elseif (t_5 <= Inf)
		tmp = t_3;
	else
		tmp = t_6;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$3, If[LessEqual[t$95$5, -2e-293], N[(t$95$4 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 0.0], t$95$6, If[LessEqual[t$95$5, 5e+276], N[(N[(x * y + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$5, Infinity], t$95$3, t$95$6]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5.00000000000000001e276 < (/.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 y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. associate-*r/ 64.5%

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

      4. neg-mul-1 64.5%

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

      5. sub-neg 64.5%

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

      6. metadata-eval 64.5%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 87.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-293

   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
   3. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -2.0000000000000001e-293 < (/.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 5.7%

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

   3. Taylor expanded in z around inf 75.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000001e276

   1. Initial program 99.6%

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

      1. fma-def 99.6%

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

   3. Simplified 99.6%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+276}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_3 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e-293)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 5e+276) t_2 (if (<= t_2 INFINITY) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e-293) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+276) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -2e-293) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+276) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_3 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -2e-293:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 5e+276:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e-293)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+276)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_3 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -2e-293)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+276)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(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$3 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e-293], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 5e+276], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, t$95$1]]]]]]]]

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 5.00000000000000001e276 < (/.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 y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. associate-*r/ 64.5%

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

      4. neg-mul-1 64.5%

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

      5. sub-neg 64.5%

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

      6. metadata-eval 64.5%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 87.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-293 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000001e276

   1. Initial program 99.6%

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

   if -2.0000000000000001e-293 < (/.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 5.7%

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

   3. Taylor expanded in z around inf 75.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_2 := x \cdot y + z \cdot \left(t - a\right)\\ t_3 := \frac{t_2}{y + z \cdot \left(b - y\right)}\\ t_4 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\frac{t_2}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+276}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) y) (/ x (+ z -1.0))))
        (t_2 (+ (* x y) (* z (- t a))))
        (t_3 (/ t_2 (+ y (* z (- b y)))))
        (t_4 (/ (- t a) (- b y))))
   (if (<= t_3 (- INFINITY))
     t_1
     (if (<= t_3 -2e-293)
       (/ t_2 (+ y (- (* z b) (* y z))))
       (if (<= t_3 0.0)
         t_4
         (if (<= t_3 5e+276) t_3 (if (<= t_3 INFINITY) t_1 t_4)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = t_2 / (y + (z * (b - y)));
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_3 <= -2e-293) {
		tmp = t_2 / (y + ((z * b) - (y * z)));
	} else if (t_3 <= 0.0) {
		tmp = t_4;
	} else if (t_3 <= 5e+276) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double t_2 = (x * y) + (z * (t - a));
	double t_3 = t_2 / (y + (z * (b - y)));
	double t_4 = (t - a) / (b - y);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_3 <= -2e-293) {
		tmp = t_2 / (y + ((z * b) - (y * z)));
	} else if (t_3 <= 0.0) {
		tmp = t_4;
	} else if (t_3 <= 5e+276) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / y) - (x / (z + -1.0))
	t_2 = (x * y) + (z * (t - a))
	t_3 = t_2 / (y + (z * (b - y)))
	t_4 = (t - a) / (b - y)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_1
	elif t_3 <= -2e-293:
		tmp = t_2 / (y + ((z * b) - (y * z)))
	elif t_3 <= 0.0:
		tmp = t_4
	elif t_3 <= 5e+276:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_2 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_3 = Float64(t_2 / Float64(y + Float64(z * Float64(b - y))))
	t_4 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_3 <= -2e-293)
		tmp = Float64(t_2 / Float64(y + Float64(Float64(z * b) - Float64(y * z))));
	elseif (t_3 <= 0.0)
		tmp = t_4;
	elseif (t_3 <= 5e+276)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / y) - (x / (z + -1.0));
	t_2 = (x * y) + (z * (t - a));
	t_3 = t_2 / (y + (z * (b - y)));
	t_4 = (t - a) / (b - y);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_1;
	elseif (t_3 <= -2e-293)
		tmp = t_2 / (y + ((z * b) - (y * z)));
	elseif (t_3 <= 0.0)
		tmp = t_4;
	elseif (t_3 <= 5e+276)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$1, If[LessEqual[t$95$3, -2e-293], N[(t$95$2 / N[(y + N[(N[(z * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], t$95$4, If[LessEqual[t$95$3, 5e+276], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$1, t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5.00000000000000001e276 < (/.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 y around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

      3. associate-*r/ 64.5%

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

      4. neg-mul-1 64.5%

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

      5. sub-neg 64.5%

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

      6. metadata-eval 64.5%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in z around inf 87.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-293

   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
   3. Step-by-step derivation

      1. sub-neg 99.6%

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

      2. distribute-lft-in 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -2.0000000000000001e-293 < (/.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 5.7%

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

   3. Taylor expanded in z around inf 75.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000001e276

   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
3. Recombined 4 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-293}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + \left(z \cdot b - y \cdot z\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-119}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-86} \lor \neg \left(y \leq 0.0095\right) \land y \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.8e+46)
     t_1
     (if (<= y -3.4e-6)
       (/ t (- b y))
       (if (<= y -2.15e-119)
         (/ (- a) (- b y))
         (if (or (<= y 5.7e-86) (and (not (<= y 0.0095)) (<= y 7.5e+56)))
           (/ (- t 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 <= -7.8e+46) {
		tmp = t_1;
	} else if (y <= -3.4e-6) {
		tmp = t / (b - y);
	} else if (y <= -2.15e-119) {
		tmp = -a / (b - y);
	} else if ((y <= 5.7e-86) || (!(y <= 0.0095) && (y <= 7.5e+56))) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-7.8d+46)) then
        tmp = t_1
    else if (y <= (-3.4d-6)) then
        tmp = t / (b - y)
    else if (y <= (-2.15d-119)) then
        tmp = -a / (b - y)
    else if ((y <= 5.7d-86) .or. (.not. (y <= 0.0095d0)) .and. (y <= 7.5d+56)) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.8e+46) {
		tmp = t_1;
	} else if (y <= -3.4e-6) {
		tmp = t / (b - y);
	} else if (y <= -2.15e-119) {
		tmp = -a / (b - y);
	} else if ((y <= 5.7e-86) || (!(y <= 0.0095) && (y <= 7.5e+56))) {
		tmp = (t - 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 <= -7.8e+46:
		tmp = t_1
	elif y <= -3.4e-6:
		tmp = t / (b - y)
	elif y <= -2.15e-119:
		tmp = -a / (b - y)
	elif (y <= 5.7e-86) or (not (y <= 0.0095) and (y <= 7.5e+56)):
		tmp = (t - 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 <= -7.8e+46)
		tmp = t_1;
	elseif (y <= -3.4e-6)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -2.15e-119)
		tmp = Float64(Float64(-a) / Float64(b - y));
	elseif ((y <= 5.7e-86) || (!(y <= 0.0095) && (y <= 7.5e+56)))
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -7.8e+46)
		tmp = t_1;
	elseif (y <= -3.4e-6)
		tmp = t / (b - y);
	elseif (y <= -2.15e-119)
		tmp = -a / (b - y);
	elseif ((y <= 5.7e-86) || (~((y <= 0.0095)) && (y <= 7.5e+56)))
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e+46], t$95$1, If[LessEqual[y, -3.4e-6], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-119], N[((-a) / N[(b - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.7e-86], And[N[Not[LessEqual[y, 0.0095]], $MachinePrecision], LessEqual[y, 7.5e+56]]], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.7999999999999999e46 or 5.7000000000000004e-86 < y < 0.00949999999999999976 or 7.4999999999999999e56 < y

   1. Initial program 47.8%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. unsub-neg 58.5%

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

   5. Simplified 58.5%

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

   if -7.7999999999999999e46 < y < -3.40000000000000006e-6

   1. Initial program 57.7%

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

   3. Taylor expanded in t around inf 36.2%

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

      1. *-commutative 36.2%

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

   5. Simplified 36.2%

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

   6. Taylor expanded in z around inf 57.2%

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

   if -3.40000000000000006e-6 < y < -2.15e-119

   1. Initial program 80.0%

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

   3. Taylor expanded in a around inf 36.6%

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

      1. mul-1-neg 36.6%

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

      2. distribute-lft-neg-out 36.6%

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

      3. *-commutative 36.6%

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

   5. Simplified 36.6%

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

   6. Taylor expanded in z around inf 39.8%

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

      1. mul-1-neg 39.8%

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

      2. distribute-neg-frac 39.8%

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

   8. Simplified 39.8%

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

   if -2.15e-119 < y < 5.7000000000000004e-86 or 0.00949999999999999976 < y < 7.4999999999999999e56

   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 y around 0 58.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-119}:\\ \;\;\;\;\frac{-a}{b - y}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-86} \lor \neg \left(y \leq 0.0095\right) \land y \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z}{\frac{y}{x \cdot b + \left(a - t\right)}}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (/ z (/ y (+ (* x b) (- a t)))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -8.5e-7)
     t_2
     (if (<= z -2.55e-241)
       t_1
       (if (<= z 1.55e-142)
         (/ (+ (* x y) (* z (- t a))) y)
         (if (<= z 1.15e-28) 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 / ((x * b) + (a - t))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -8.5e-7) {
		tmp = t_2;
	} else if (z <= -2.55e-241) {
		tmp = t_1;
	} else if (z <= 1.55e-142) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1.15e-28) {
		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 / ((x * b) + (a - t))))
    t_2 = (t - a) / (b - y)
    if (z <= (-8.5d-7)) then
        tmp = t_2
    else if (z <= (-2.55d-241)) then
        tmp = t_1
    else if (z <= 1.55d-142) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if (z <= 1.15d-28) 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 / ((x * b) + (a - t))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -8.5e-7) {
		tmp = t_2;
	} else if (z <= -2.55e-241) {
		tmp = t_1;
	} else if (z <= 1.55e-142) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1.15e-28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (z / (y / ((x * b) + (a - t))))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -8.5e-7:
		tmp = t_2
	elif z <= -2.55e-241:
		tmp = t_1
	elif z <= 1.55e-142:
		tmp = ((x * y) + (z * (t - a))) / y
	elif z <= 1.15e-28:
		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(Float64(x * b) + Float64(a - t)))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -8.5e-7)
		tmp = t_2;
	elseif (z <= -2.55e-241)
		tmp = t_1;
	elseif (z <= 1.55e-142)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 1.15e-28)
		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 / ((x * b) + (a - t))));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -8.5e-7)
		tmp = t_2;
	elseif (z <= -2.55e-241)
		tmp = t_1;
	elseif (z <= 1.55e-142)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif (z <= 1.15e-28)
		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[(N[(x * b), $MachinePrecision] + N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-7], t$95$2, If[LessEqual[z, -2.55e-241], t$95$1, If[LessEqual[z, 1.55e-142], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.15e-28], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000014e-7 or 1.14999999999999993e-28 < z

   1. Initial program 44.4%

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

   3. Taylor expanded in z around inf 78.6%

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

   if -8.50000000000000014e-7 < z < -2.5499999999999999e-241 or 1.55e-142 < z < 1.14999999999999993e-28

   1. Initial program 77.7%

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

   3. Taylor expanded in b around inf 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in y around -inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. unsub-neg 77.9%

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

      3. sub-neg 77.9%

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

      4. *-commutative 77.9%

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

      5. associate-*r* 77.9%

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

      6. mul-1-neg 77.9%

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

      7. remove-double-neg 77.9%

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

      8. associate-*r* 71.3%

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

      9. distribute-rgt-in 71.3%

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

      10. associate-/l* 69.8%

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

      11. +-commutative 69.8%

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

      12. mul-1-neg 69.8%

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

      13. unsub-neg 69.8%

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

   8. Simplified 69.8%

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

   if -2.5499999999999999e-241 < z < 1.55e-142

   1. Initial program 83.3%

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

   3. Taylor expanded in b around inf 83.3%

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

      1. *-commutative 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in y around inf 70.1%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-241}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x \cdot b + \left(a - t\right)}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x \cdot b + \left(a - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -300000000000 \lor \neg \left(y \leq 2.06 \cdot 10^{-81} \lor \neg \left(y \leq 0.0095\right) \land y \leq 2.3 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -300000000000.0)
         (not (or (<= y 2.06e-81) (and (not (<= y 0.0095)) (<= y 2.3e+56)))))
   (/ 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 <= -300000000000.0) || !((y <= 2.06e-81) || (!(y <= 0.0095) && (y <= 2.3e+56)))) {
		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 <= (-300000000000.0d0)) .or. (.not. (y <= 2.06d-81) .or. (.not. (y <= 0.0095d0)) .and. (y <= 2.3d+56))) 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 <= -300000000000.0) || !((y <= 2.06e-81) || (!(y <= 0.0095) && (y <= 2.3e+56)))) {
		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 <= -300000000000.0) or not ((y <= 2.06e-81) or (not (y <= 0.0095) and (y <= 2.3e+56))):
		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 <= -300000000000.0) || !((y <= 2.06e-81) || (!(y <= 0.0095) && (y <= 2.3e+56))))
		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 <= -300000000000.0) || ~(((y <= 2.06e-81) || (~((y <= 0.0095)) && (y <= 2.3e+56)))))
		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, -300000000000.0], N[Not[Or[LessEqual[y, 2.06e-81], And[N[Not[LessEqual[y, 0.0095]], $MachinePrecision], LessEqual[y, 2.3e+56]]]], $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 < -3e11 or 2.0600000000000001e-81 < y < 0.00949999999999999976 or 2.30000000000000015e56 < y

   1. Initial program 48.7%

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

   3. Taylor expanded in y around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. unsub-neg 56.9%

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

   5. Simplified 56.9%

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

   if -3e11 < y < 2.0600000000000001e-81 or 0.00949999999999999976 < y < 2.30000000000000015e56

   1. Initial program 80.0%

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

   3. Taylor expanded in y around 0 52.1%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -300000000000 \lor \neg \left(y \leq 2.06 \cdot 10^{-81} \lor \neg \left(y \leq 0.0095\right) \land y \leq 2.3 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+54} \lor \neg \left(z \leq 550000000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e+54) (not (<= z 550000000000.0)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e+54) || !(z <= 550000000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.9d+54)) .or. (.not. (z <= 550000000000.0d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e+54) || !(z <= 550000000000.0)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e+54) or not (z <= 550000000000.0):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e+54) || !(z <= 550000000000.0))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.9e+54) || ~((z <= 550000000000.0)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e+54], N[Not[LessEqual[z, 550000000000.0]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000001e54 or 5.5e11 < z

   1. Initial program 39.1%

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

   3. Taylor expanded in z around inf 81.2%

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

   if -1.9000000000000001e54 < z < 5.5e11

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 79.1%

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

      1. *-commutative 79.1%

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

   5. Simplified 79.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+54} \lor \neg \left(z \leq 550000000000\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7} \lor \neg \left(z \leq 7.8 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + z \cdot \left(-1 + \frac{b}{y}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e-7) (not (<= z 7.8e-26)))
   (/ (- t a) (- b y))
   (/ x (+ 1.0 (* z (+ -1.0 (/ b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e-7) || !(z <= 7.8e-26)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 + (z * (-1.0 + (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 <= (-2.3d-7)) .or. (.not. (z <= 7.8d-26))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 + (z * ((-1.0d0) + (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 <= -2.3e-7) || !(z <= 7.8e-26)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 + (z * (-1.0 + (b / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e-7) or not (z <= 7.8e-26):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 + (z * (-1.0 + (b / y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e-7) || !(z <= 7.8e-26))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 + Float64(z * Float64(-1.0 + Float64(b / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e-7) || ~((z <= 7.8e-26)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 + (z * (-1.0 + (b / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e-7], N[Not[LessEqual[z, 7.8e-26]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(z * N[(-1.0 + N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999995e-7 or 7.79999999999999973e-26 < z

   1. Initial program 43.9%

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

   3. Taylor expanded in z around inf 79.3%

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

   if -2.29999999999999995e-7 < z < 7.79999999999999973e-26

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 37.2%

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

      1. associate-/l* 56.4%

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

      2. +-commutative 56.4%

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

      3. fma-def 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around 0 55.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-7} \lor \neg \left(z \leq 7.8 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + z \cdot \left(-1 + \frac{b}{y}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-6} \lor \neg \left(z \leq 7.4 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \frac{z \cdot \left(b - y\right)}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.4e-6) (not (<= z 7.4e-21)))
   (/ (- t a) (- b y))
   (/ x (+ 1.0 (/ (* z (- b y)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.4e-6) || !(z <= 7.4e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 + ((z * (b - y)) / 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 <= (-7.4d-6)) .or. (.not. (z <= 7.4d-21))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x / (1.0d0 + ((z * (b - y)) / 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 <= -7.4e-6) || !(z <= 7.4e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 + ((z * (b - y)) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.4e-6) or not (z <= 7.4e-21):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 + ((z * (b - y)) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.4e-6) || !(z <= 7.4e-21))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x / Float64(1.0 + Float64(Float64(z * Float64(b - y)) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.4e-6) || ~((z <= 7.4e-21)))
		tmp = (t - a) / (b - y);
	else
		tmp = x / (1.0 + ((z * (b - y)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.4e-6], N[Not[LessEqual[z, 7.4e-21]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4000000000000003e-6 or 7.40000000000000041e-21 < z

   1. Initial program 43.9%

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

   3. Taylor expanded in z around inf 79.3%

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

   if -7.4000000000000003e-6 < z < 7.40000000000000041e-21

   1. Initial program 79.9%

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

   3. Taylor expanded in x around inf 37.2%

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

      1. associate-/l* 56.4%

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

      2. +-commutative 56.4%

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

      3. fma-def 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in z around inf 56.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-6} \lor \neg \left(z \leq 7.4 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \frac{z \cdot \left(b - y\right)}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-7} \lor \neg \left(z \leq 1.45 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.1e-7) (not (<= z 1.45e-20)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e-7) || !(z <= 1.45e-20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / 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 <= (-1.1d-7)) .or. (.not. (z <= 1.45d-20))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / 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 <= -1.1e-7) || !(z <= 1.45e-20)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.1e-7) or not (z <= 1.45e-20):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.1e-7) || !(z <= 1.45e-20))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.1e-7) || ~((z <= 1.45e-20)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.1e-7], N[Not[LessEqual[z, 1.45e-20]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001e-7 or 1.45e-20 < z

   1. Initial program 43.9%

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

   3. Taylor expanded in z around inf 79.3%

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

   if -1.1000000000000001e-7 < z < 1.45e-20

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 79.6%

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

      1. *-commutative 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in y around inf 61.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-7} \lor \neg \left(z \leq 1.45 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-7} \lor \neg \left(z \leq 1.05 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.7e-7) (not (<= z 1.05e-18)))
   (/ (- t a) (- 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 <= -3.7e-7) || !(z <= 1.05e-18)) {
		tmp = (t - a) / (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 <= (-3.7d-7)) .or. (.not. (z <= 1.05d-18))) then
        tmp = (t - a) / (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 <= -3.7e-7) || !(z <= 1.05e-18)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.7e-7) or not (z <= 1.05e-18):
		tmp = (t - a) / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.7e-7) || !(z <= 1.05e-18))
		tmp = Float64(Float64(t - a) / 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 <= -3.7e-7) || ~((z <= 1.05e-18)))
		tmp = (t - a) / (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, -3.7e-7], N[Not[LessEqual[z, 1.05e-18]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000004e-7 or 1.05e-18 < z

   1. Initial program 43.9%

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

   3. Taylor expanded in z around inf 79.3%

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

   if -3.70000000000000004e-7 < z < 1.05e-18

   1. Initial program 79.9%

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

   3. Taylor expanded in y around inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

   5. Simplified 50.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-7} \lor \neg \left(z \leq 1.05 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15500 \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -15500.0) (not (<= z 0.065))) (/ 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 <= -15500.0) || !(z <= 0.065)) {
		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 <= (-15500.0d0)) .or. (.not. (z <= 0.065d0))) 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 <= -15500.0) || !(z <= 0.065)) {
		tmp = t / (b - y);
	} else {
		tmp = x + (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -15500.0) or not (z <= 0.065):
		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 <= -15500.0) || !(z <= 0.065))
		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 <= -15500.0) || ~((z <= 0.065)))
		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, -15500.0], N[Not[LessEqual[z, 0.065]], $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 < -15500 or 0.065000000000000002 < z

   1. Initial program 42.7%

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

   3. Taylor expanded in t around inf 21.6%

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

      1. *-commutative 21.6%

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

   5. Simplified 21.6%

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

   6. Taylor expanded in z around inf 45.7%

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

   if -15500 < z < 0.065000000000000002

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. unsub-neg 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in z around 0 49.1%

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

      1. *-commutative 49.1%

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

   8. Simplified 49.1%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15500 \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1120000000 \lor \neg \left(z \leq 0.072\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1120000000.0) (not (<= z 0.072)))
   (/ 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 <= -1120000000.0) || !(z <= 0.072)) {
		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 <= (-1120000000.0d0)) .or. (.not. (z <= 0.072d0))) 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 <= -1120000000.0) || !(z <= 0.072)) {
		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 <= -1120000000.0) or not (z <= 0.072):
		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 <= -1120000000.0) || !(z <= 0.072))
		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 <= -1120000000.0) || ~((z <= 0.072)))
		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, -1120000000.0], N[Not[LessEqual[z, 0.072]], $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 < -1.12e9 or 0.0719999999999999946 < z

   1. Initial program 42.7%

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

   3. Taylor expanded in t around inf 21.6%

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

      1. *-commutative 21.6%

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

   5. Simplified 21.6%

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

   6. Taylor expanded in z around inf 45.7%

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

   if -1.12e9 < z < 0.0719999999999999946

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. unsub-neg 50.1%

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

   5. Simplified 50.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1120000000 \lor \neg \left(z \leq 0.072\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.75) (/ (- x) z) (if (<= z 0.065) (+ x (* x z)) (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 0.065) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.75d0)) then
        tmp = -x / z
    else if (z <= 0.065d0) then
        tmp = x + (x * z)
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.75) {
		tmp = -x / z;
	} else if (z <= 0.065) {
		tmp = x + (x * z);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.75:
		tmp = -x / z
	elif z <= 0.065:
		tmp = x + (x * z)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.75)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 0.065)
		tmp = Float64(x + Float64(x * z));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.75)
		tmp = -x / z;
	elseif (z <= 0.065)
		tmp = x + (x * z);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.75], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 0.065], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.75

   1. Initial program 37.0%

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

   3. Taylor expanded in y around inf 23.2%

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

      1. mul-1-neg 23.2%

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

      2. unsub-neg 23.2%

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

   5. Simplified 23.2%

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

   6. Taylor expanded in z around inf 23.2%

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

      1. associate-*r/ 23.2%

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

      2. mul-1-neg 23.2%

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

   8. Simplified 23.2%

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

   if -0.75 < z < 0.065000000000000002

   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 y around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unsub-neg 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in z around 0 49.4%

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

      1. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   if 0.065000000000000002 < z

   1. Initial program 47.4%

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

   3. Taylor expanded in t around inf 19.2%

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

      1. *-commutative 19.2%

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

   5. Simplified 19.2%

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

   6. Taylor expanded in y around 0 28.2%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -35000 \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -35000.0) (not (<= z 0.065))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -35000.0) || !(z <= 0.065)) {
		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 <= (-35000.0d0)) .or. (.not. (z <= 0.065d0))) 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 <= -35000.0) || !(z <= 0.065)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -35000.0) or not (z <= 0.065):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -35000.0) || !(z <= 0.065))
		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 <= -35000.0) || ~((z <= 0.065)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -35000.0], N[Not[LessEqual[z, 0.065]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -35000 or 0.065000000000000002 < z

   1. Initial program 42.7%

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

   3. Taylor expanded in t around inf 21.6%

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

      1. *-commutative 21.6%

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

   5. Simplified 21.6%

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

   6. Taylor expanded in y around 0 25.4%

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

   if -35000 < z < 0.065000000000000002

   1. Initial program 79.4%

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

   3. Taylor expanded in z around 0 48.5%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -35000 \lor \neg \left(z \leq 0.065\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.56e+16) (/ (- x) z) (if (<= z 0.065) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.56e+16) {
		tmp = -x / z;
	} else if (z <= 0.065) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.56d+16)) then
        tmp = -x / z
    else if (z <= 0.065d0) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.56e+16) {
		tmp = -x / z;
	} else if (z <= 0.065) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.56e+16:
		tmp = -x / z
	elif z <= 0.065:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.56e+16)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 0.065)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.56e+16)
		tmp = -x / z;
	elseif (z <= 0.065)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.56e+16], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 0.065], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.56e16

   1. Initial program 32.5%

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

   3. Taylor expanded in y around inf 24.6%

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

      1. mul-1-neg 24.6%

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

      2. unsub-neg 24.6%

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

   5. Simplified 24.6%

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

   6. Taylor expanded in z around inf 24.6%

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

      1. associate-*r/ 24.6%

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

      2. mul-1-neg 24.6%

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

   8. Simplified 24.6%

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

   if -1.56e16 < z < 0.065000000000000002

   1. Initial program 79.7%

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

   3. Taylor expanded in z around 0 47.9%

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

   if 0.065000000000000002 < z

   1. Initial program 47.4%

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

   3. Taylor expanded in t around inf 19.2%

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

      1. *-commutative 19.2%

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

   5. Simplified 19.2%

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

   6. Taylor expanded in y around 0 28.2%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 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 63.8%

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

3. Taylor expanded in z around 0 29.4%

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

4. Final simplification 29.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 72.7% 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 2024020 
(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)))))