Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.7% → 93.0%

Time: 18.9s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, b - y, y\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+70} \lor \neg \left(z \leq 3.55 \cdot 10^{+56}\right):\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{a}{\left(b + \frac{y}{z}\right) - y}, \frac{x}{\frac{t_1}{y}} + \frac{z \cdot t}{t_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma z (- b y) y)))
   (if (or (<= z -1.3e+70) (not (<= z 3.55e+56)))
     (+
      (+ (/ x (/ (- b y) (/ y z))) (/ (- t a) (- b y)))
      (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))
     (fma
      -1.0
      (/ a (- (+ b (/ y z)) y))
      (+ (/ x (/ t_1 y)) (/ (* z t) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, (b - y), y);
	double tmp;
	if ((z <= -1.3e+70) || !(z <= 3.55e+56)) {
		tmp = ((x / ((b - y) / (y / z))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	} else {
		tmp = fma(-1.0, (a / ((b + (y / z)) - y)), ((x / (t_1 / y)) + ((z * t) / t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(z, Float64(b - y), y)
	tmp = 0.0
	if ((z <= -1.3e+70) || !(z <= 3.55e+56))
		tmp = Float64(Float64(Float64(x / Float64(Float64(b - y) / Float64(y / z))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	else
		tmp = fma(-1.0, Float64(a / Float64(Float64(b + Float64(y / z)) - y)), Float64(Float64(x / Float64(t_1 / y)) + Float64(Float64(z * t) / t_1)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, If[Or[LessEqual[z, -1.3e+70], N[Not[LessEqual[z, 3.55e+56]], $MachinePrecision]], 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[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(a / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(N[(x / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e70 or 3.55e56 < z

   1. Initial program 25.0%

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

   3. Taylor expanded in z around inf 56.7%

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

      1. associate--r+ 56.7%

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

      2. +-commutative 56.7%

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

      3. associate--l+ 56.7%

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

      4. associate-/l* 58.7%

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

      5. *-commutative 58.7%

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

      6. associate-/l* 65.1%

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

      7. div-sub 65.1%

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

      8. times-frac 87.6%

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

   5. Simplified 87.6%

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

   if -1.3e70 < z < 3.55e56

   1. Initial program 87.4%

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

   3. Taylor expanded in t around 0 87.4%

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

      1. fma-def 87.4%

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

      2. associate-/l* 87.5%

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

      3. +-commutative 87.5%

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

      4. fma-def 87.5%

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

      5. +-commutative 87.5%

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

      6. associate-/l* 97.3%

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

      7. +-commutative 97.3%

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

      8. fma-def 97.3%

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

      9. *-commutative 97.3%

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

      10. +-commutative 97.3%

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

      11. fma-def 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in z around 0 97.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+70} \lor \neg \left(z \leq 3.55 \cdot 10^{+56}\right):\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{a}{\left(b + \frac{y}{z}\right) - y}, \frac{x}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{y}} + \frac{z \cdot t}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{a}{\left(b + \frac{y}{z}\right) - y}, x + \frac{z \cdot t}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-270} \lor \neg \left(t_2 \leq 0\right) \land t_2 \leq 4 \cdot 10^{+293}:\\ \;\;\;\;\frac{t_1}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a)))) (t_2 (/ t_1 (+ y (* z (- b y))))))
   (if (<= t_2 (- INFINITY))
     (fma -1.0 (/ a (- (+ b (/ y z)) y)) (+ x (/ (* z t) (fma z (- b y) y))))
     (if (or (<= t_2 -2e-270) (and (not (<= t_2 0.0)) (<= t_2 4e+293)))
       (/ t_1 (- (* z b) (* y (+ z -1.0))))
       (+
        (+ (/ x (/ (- b y) (/ y z))) (/ (- t a) (- b y)))
        (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(-1.0, (a / ((b + (y / z)) - y)), (x + ((z * t) / fma(z, (b - y), y))));
	} else if ((t_2 <= -2e-270) || (!(t_2 <= 0.0) && (t_2 <= 4e+293))) {
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = ((x / ((b - y) / (y / z))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(-1.0, Float64(a / Float64(Float64(b + Float64(y / z)) - y)), Float64(x + Float64(Float64(z * t) / fma(z, Float64(b - y), y))));
	elseif ((t_2 <= -2e-270) || (!(t_2 <= 0.0) && (t_2 <= 4e+293)))
		tmp = Float64(t_1 / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	else
		tmp = Float64(Float64(Float64(x / Float64(Float64(b - y) / Float64(y / z))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(-1.0 * N[(a / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(N[(z * t), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -2e-270], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 4e+293]]], N[(t$95$1 / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

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

   1. Initial program 37.5%

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

   3. Taylor expanded in t around 0 33.4%

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

      1. fma-def 33.4%

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

      2. associate-/l* 44.2%

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

      3. +-commutative 44.2%

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

      4. fma-def 44.2%

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

      5. +-commutative 44.2%

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

      6. associate-/l* 82.4%

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

      7. +-commutative 82.4%

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

      8. fma-def 82.4%

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

      9. *-commutative 82.4%

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

      10. +-commutative 82.4%

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

      11. fma-def 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in z around 0 82.4%

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

   7. Taylor expanded in z around 0 68.3%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-270 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.9999999999999997e293

   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. Taylor expanded in y around -inf 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. unsub-neg 99.6%

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

      4. *-commutative 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

   if -2.0000000000000001e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 3.9999999999999997e293 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 11.3%

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

   3. Taylor expanded in z around inf 43.2%

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

      1. associate--r+ 43.2%

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

      2. +-commutative 43.2%

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

      3. associate--l+ 43.2%

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

      4. associate-/l* 44.5%

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

      5. *-commutative 44.5%

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

      6. associate-/l* 52.0%

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

      7. div-sub 52.0%

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

      8. times-frac 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{a}{\left(b + \frac{y}{z}\right) - y}, x + \frac{z \cdot t}{\mathsf{fma}\left(z, b - y, y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-270} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{+293}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-270} \lor \neg \left(t_2 \leq 0\right) \land t_2 \leq 4 \cdot 10^{+293}:\\ \;\;\;\;\frac{t_1}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + t_3\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (/ t_1 (+ y (* z (- b y)))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (or (<= t_2 -2e-270) (and (not (<= t_2 0.0)) (<= t_2 4e+293)))
       (/ t_1 (- (* z b) (* y (+ z -1.0))))
       (+
        (+ (/ x (/ (- b y) (/ y z))) t_3)
        (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if ((t_2 <= -2e-270) || (!(t_2 <= 0.0) && (t_2 <= 4e+293))) {
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = ((x / ((b - y) / (y / z))) + t_3) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = t_1 / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if ((t_2 <= -2e-270) || (!(t_2 <= 0.0) && (t_2 <= 4e+293))) {
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = ((x / ((b - y) / (y / z))) + t_3) + ((y / z) * ((a - t) / Math.pow((b - y), 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = t_1 / (y + (z * (b - y)))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif (t_2 <= -2e-270) or (not (t_2 <= 0.0) and (t_2 <= 4e+293)):
		tmp = t_1 / ((z * b) - (y * (z + -1.0)))
	else:
		tmp = ((x / ((b - y) / (y / z))) + t_3) + ((y / z) * ((a - t) / math.pow((b - y), 2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif ((t_2 <= -2e-270) || (!(t_2 <= 0.0) && (t_2 <= 4e+293)))
		tmp = Float64(t_1 / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	else
		tmp = Float64(Float64(Float64(x / Float64(Float64(b - y) / Float64(y / z))) + t_3) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = t_1 / (y + (z * (b - y)));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif ((t_2 <= -2e-270) || (~((t_2 <= 0.0)) && (t_2 <= 4e+293)))
		tmp = t_1 / ((z * b) - (y * (z + -1.0)));
	else
		tmp = ((x / ((b - y) / (y / z))) + t_3) + ((y / z) * ((a - t) / ((b - y) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[Or[LessEqual[t$95$2, -2e-270], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 4e+293]]], N[(t$95$1 / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

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

   1. Initial program 37.5%

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

   3. Taylor expanded in z around inf 60.0%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.0000000000000001e-270 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 3.9999999999999997e293

   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. Taylor expanded in y around -inf 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. unsub-neg 99.6%

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

      4. *-commutative 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

   if -2.0000000000000001e-270 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0 or 3.9999999999999997e293 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 11.3%

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

   3. Taylor expanded in z around inf 43.2%

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

      1. associate--r+ 43.2%

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

      2. +-commutative 43.2%

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

      3. associate--l+ 43.2%

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

      4. associate-/l* 44.5%

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

      5. *-commutative 44.5%

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

      6. associate-/l* 52.0%

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

      7. div-sub 52.0%

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

      8. times-frac 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-270} \lor \neg \left(\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0\right) \land \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 4 \cdot 10^{+293}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{\frac{b - y}{\frac{y}{z}}} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := x \cdot y + t_1\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{t_2}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-219}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+74}:\\ \;\;\;\;\frac{t_2}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (+ (* x y) t_1)) (t_3 (/ (- t a) (- b y))))
   (if (<= z -1.05e+20)
     t_3
     (if (<= z 1.4e-287)
       (/ t_2 (+ y (* z (- b y))))
       (if (<= z 3.1e-219)
         (+ x (/ t_1 y))
         (if (<= z 1.75e+74) (/ t_2 (- (* z b) (* y (+ z -1.0)))) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x * y) + t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.05e+20) {
		tmp = t_3;
	} else if (z <= 1.4e-287) {
		tmp = t_2 / (y + (z * (b - y)));
	} else if (z <= 3.1e-219) {
		tmp = x + (t_1 / y);
	} else if (z <= 1.75e+74) {
		tmp = t_2 / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (x * y) + t_1
    t_3 = (t - a) / (b - y)
    if (z <= (-1.05d+20)) then
        tmp = t_3
    else if (z <= 1.4d-287) then
        tmp = t_2 / (y + (z * (b - y)))
    else if (z <= 3.1d-219) then
        tmp = x + (t_1 / y)
    else if (z <= 1.75d+74) then
        tmp = t_2 / ((z * b) - (y * (z + (-1.0d0))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (x * y) + t_1;
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.05e+20) {
		tmp = t_3;
	} else if (z <= 1.4e-287) {
		tmp = t_2 / (y + (z * (b - y)));
	} else if (z <= 3.1e-219) {
		tmp = x + (t_1 / y);
	} else if (z <= 1.75e+74) {
		tmp = t_2 / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (x * y) + t_1
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.05e+20:
		tmp = t_3
	elif z <= 1.4e-287:
		tmp = t_2 / (y + (z * (b - y)))
	elif z <= 3.1e-219:
		tmp = x + (t_1 / y)
	elif z <= 1.75e+74:
		tmp = t_2 / ((z * b) - (y * (z + -1.0)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(x * y) + t_1)
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.05e+20)
		tmp = t_3;
	elseif (z <= 1.4e-287)
		tmp = Float64(t_2 / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 3.1e-219)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 1.75e+74)
		tmp = Float64(t_2 / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (x * y) + t_1;
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.05e+20)
		tmp = t_3;
	elseif (z <= 1.4e-287)
		tmp = t_2 / (y + (z * (b - y)));
	elseif (z <= 3.1e-219)
		tmp = x + (t_1 / y);
	elseif (z <= 1.75e+74)
		tmp = t_2 / ((z * b) - (y * (z + -1.0)));
	else
		tmp = t_3;
	end
	tmp_2 = 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[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+20], t$95$3, If[LessEqual[z, 1.4e-287], N[(t$95$2 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-219], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+74], N[(t$95$2 / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e20 or 1.75000000000000007e74 < z

   1. Initial program 29.2%

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

   3. Taylor expanded in z around inf 83.8%

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

   if -1.05e20 < z < 1.4000000000000001e-287

   1. Initial program 91.5%

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

   if 1.4000000000000001e-287 < z < 3.0999999999999997e-219

   1. Initial program 75.3%

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

   3. Taylor expanded in z around 0 75.3%

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

   4. Taylor expanded in x around 0 99.9%

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

   if 3.0999999999999997e-219 < z < 1.75000000000000007e74

   1. Initial program 85.3%

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

   3. Taylor expanded in y around -inf 85.4%

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

      1. +-commutative 85.4%

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

      2. mul-1-neg 85.4%

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

      3. unsub-neg 85.4%

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

      4. *-commutative 85.4%

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

      5. sub-neg 85.4%

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

      6. metadata-eval 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-219}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-286}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-219}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot y + t_1}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -9.5e+40)
     t_2
     (if (<= z 2.8e-286)
       (/ (+ (* x y) (- (* z t) (* z a))) (+ y (* z (- b y))))
       (if (<= z 1.6e-219)
         (+ x (/ t_1 y))
         (if (<= z 2.95e+74)
           (/ (+ (* x y) t_1) (- (* z b) (* y (+ z -1.0))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e+40) {
		tmp = t_2;
	} else if (z <= 2.8e-286) {
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	} else if (z <= 1.6e-219) {
		tmp = x + (t_1 / y);
	} else if (z <= 2.95e+74) {
		tmp = ((x * y) + t_1) / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = (t - a) / (b - y)
    if (z <= (-9.5d+40)) then
        tmp = t_2
    else if (z <= 2.8d-286) then
        tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
    else if (z <= 1.6d-219) then
        tmp = x + (t_1 / y)
    else if (z <= 2.95d+74) then
        tmp = ((x * y) + t_1) / ((z * b) - (y * (z + (-1.0d0))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -9.5e+40) {
		tmp = t_2;
	} else if (z <= 2.8e-286) {
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	} else if (z <= 1.6e-219) {
		tmp = x + (t_1 / y);
	} else if (z <= 2.95e+74) {
		tmp = ((x * y) + t_1) / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -9.5e+40:
		tmp = t_2
	elif z <= 2.8e-286:
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)))
	elif z <= 1.6e-219:
		tmp = x + (t_1 / y)
	elif z <= 2.95e+74:
		tmp = ((x * y) + t_1) / ((z * b) - (y * (z + -1.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -9.5e+40)
		tmp = t_2;
	elseif (z <= 2.8e-286)
		tmp = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(z * a))) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 1.6e-219)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 2.95e+74)
		tmp = Float64(Float64(Float64(x * y) + t_1) / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -9.5e+40)
		tmp = t_2;
	elseif (z <= 2.8e-286)
		tmp = ((x * y) + ((z * t) - (z * a))) / (y + (z * (b - y)));
	elseif (z <= 1.6e-219)
		tmp = x + (t_1 / y);
	elseif (z <= 2.95e+74)
		tmp = ((x * y) + t_1) / ((z * b) - (y * (z + -1.0)));
	else
		tmp = t_2;
	end
	tmp_2 = 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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+40], t$95$2, If[LessEqual[z, 2.8e-286], N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-219], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e+74], N[(N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5000000000000003e40 or 2.9500000000000001e74 < z

   1. Initial program 27.2%

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

   3. Taylor expanded in z around inf 83.3%

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

   if -9.5000000000000003e40 < z < 2.8e-286

   1. Initial program 91.8%

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

      1. sub-neg 91.8%

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

      2. distribute-lft-in 91.8%

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

   4. Applied egg-rr 91.8%

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

   if 2.8e-286 < z < 1.59999999999999999e-219

   1. Initial program 75.3%

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

   3. Taylor expanded in z around 0 75.3%

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

   4. Taylor expanded in x around 0 99.9%

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

   if 1.59999999999999999e-219 < z < 2.9500000000000001e74

   1. Initial program 85.3%

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

   3. Taylor expanded in y around -inf 85.4%

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

      1. +-commutative 85.4%

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

      2. mul-1-neg 85.4%

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

      3. unsub-neg 85.4%

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

      4. *-commutative 85.4%

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

      5. sub-neg 85.4%

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

      6. metadata-eval 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-286}:\\ \;\;\;\;\frac{x \cdot y + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-219}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y}{t_1} + \frac{t_3}{t_1}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{t_3}{y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot y + t_3}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a))))
   (if (<= z -5.6e+19)
     t_2
     (if (<= z 1.8e-288)
       (+ (/ (* x y) t_1) (/ t_3 t_1))
       (if (<= z 1.2e-220)
         (+ x (/ t_3 y))
         (if (<= z 9.5e+74)
           (/ (+ (* x y) t_3) (- (* z b) (* y (+ z -1.0))))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -5.6e+19) {
		tmp = t_2;
	} else if (z <= 1.8e-288) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else if (z <= 1.2e-220) {
		tmp = x + (t_3 / y);
	} else if (z <= 9.5e+74) {
		tmp = ((x * y) + t_3) / ((z * b) - (y * (z + -1.0)));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    t_2 = (t - a) / (b - y)
    t_3 = z * (t - a)
    if (z <= (-5.6d+19)) then
        tmp = t_2
    else if (z <= 1.8d-288) then
        tmp = ((x * y) / t_1) + (t_3 / t_1)
    else if (z <= 1.2d-220) then
        tmp = x + (t_3 / y)
    else if (z <= 9.5d+74) then
        tmp = ((x * y) + t_3) / ((z * b) - (y * (z + (-1.0d0))))
    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 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -5.6e+19) {
		tmp = t_2;
	} else if (z <= 1.8e-288) {
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	} else if (z <= 1.2e-220) {
		tmp = x + (t_3 / y);
	} else if (z <= 9.5e+74) {
		tmp = ((x * y) + t_3) / ((z * b) - (y * (z + -1.0)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	tmp = 0
	if z <= -5.6e+19:
		tmp = t_2
	elif z <= 1.8e-288:
		tmp = ((x * y) / t_1) + (t_3 / t_1)
	elif z <= 1.2e-220:
		tmp = x + (t_3 / y)
	elif z <= 9.5e+74:
		tmp = ((x * y) + t_3) / ((z * b) - (y * (z + -1.0)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -5.6e+19)
		tmp = t_2;
	elseif (z <= 1.8e-288)
		tmp = Float64(Float64(Float64(x * y) / t_1) + Float64(t_3 / t_1));
	elseif (z <= 1.2e-220)
		tmp = Float64(x + Float64(t_3 / y));
	elseif (z <= 9.5e+74)
		tmp = Float64(Float64(Float64(x * y) + t_3) / Float64(Float64(z * b) - Float64(y * Float64(z + -1.0))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	tmp = 0.0;
	if (z <= -5.6e+19)
		tmp = t_2;
	elseif (z <= 1.8e-288)
		tmp = ((x * y) / t_1) + (t_3 / t_1);
	elseif (z <= 1.2e-220)
		tmp = x + (t_3 / y);
	elseif (z <= 9.5e+74)
		tmp = ((x * y) + t_3) / ((z * b) - (y * (z + -1.0)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+19], t$95$2, If[LessEqual[z, 1.8e-288], N[(N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-220], N[(x + N[(t$95$3 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+74], N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / N[(N[(z * b), $MachinePrecision] - N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.6e19 or 9.5000000000000006e74 < z

   1. Initial program 29.2%

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

   3. Taylor expanded in z around inf 83.8%

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

   if -5.6e19 < z < 1.8000000000000001e-288

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 91.5%

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

   if 1.8000000000000001e-288 < z < 1.2000000000000001e-220

   1. Initial program 75.3%

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

   3. Taylor expanded in z around 0 75.3%

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

   4. Taylor expanded in x around 0 99.9%

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

   if 1.2000000000000001e-220 < z < 9.5000000000000006e74

   1. Initial program 85.3%

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

   3. Taylor expanded in y around -inf 85.4%

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

      1. +-commutative 85.4%

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

      2. mul-1-neg 85.4%

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

      3. unsub-neg 85.4%

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

      4. *-commutative 85.4%

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

      5. sub-neg 85.4%

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

      6. metadata-eval 85.4%

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

   5. Simplified 85.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b - y \cdot \left(z + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{x \cdot y + t_1}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{t_1}{y}\\ \mathbf{elif}\;z \leq 2.12 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (+ (* x y) t_1) (+ y (* z (- b y)))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -5.6e+19)
     t_3
     (if (<= z 6.2e-285)
       t_2
       (if (<= z 3.4e-220) (+ x (/ t_1 y)) (if (<= z 2.12e+74) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((x * y) + t_1) / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.6e+19) {
		tmp = t_3;
	} else if (z <= 6.2e-285) {
		tmp = t_2;
	} else if (z <= 3.4e-220) {
		tmp = x + (t_1 / y);
	} else if (z <= 2.12e+74) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = ((x * y) + t_1) / (y + (z * (b - y)))
    t_3 = (t - a) / (b - y)
    if (z <= (-5.6d+19)) then
        tmp = t_3
    else if (z <= 6.2d-285) then
        tmp = t_2
    else if (z <= 3.4d-220) then
        tmp = x + (t_1 / y)
    else if (z <= 2.12d+74) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = ((x * y) + t_1) / (y + (z * (b - y)));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.6e+19) {
		tmp = t_3;
	} else if (z <= 6.2e-285) {
		tmp = t_2;
	} else if (z <= 3.4e-220) {
		tmp = x + (t_1 / y);
	} else if (z <= 2.12e+74) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = ((x * y) + t_1) / (y + (z * (b - y)))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.6e+19:
		tmp = t_3
	elif z <= 6.2e-285:
		tmp = t_2
	elif z <= 3.4e-220:
		tmp = x + (t_1 / y)
	elif z <= 2.12e+74:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(Float64(x * y) + t_1) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.6e+19)
		tmp = t_3;
	elseif (z <= 6.2e-285)
		tmp = t_2;
	elseif (z <= 3.4e-220)
		tmp = Float64(x + Float64(t_1 / y));
	elseif (z <= 2.12e+74)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = ((x * y) + t_1) / (y + (z * (b - y)));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.6e+19)
		tmp = t_3;
	elseif (z <= 6.2e-285)
		tmp = t_2;
	elseif (z <= 3.4e-220)
		tmp = x + (t_1 / y);
	elseif (z <= 2.12e+74)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = 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[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+19], t$95$3, If[LessEqual[z, 6.2e-285], t$95$2, If[LessEqual[z, 3.4e-220], N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.12e+74], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6e19 or 2.11999999999999998e74 < z

   1. Initial program 29.2%

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

   3. Taylor expanded in z around inf 83.8%

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

   if -5.6e19 < z < 6.2000000000000002e-285 or 3.39999999999999993e-220 < z < 2.11999999999999998e74

   1. Initial program 88.6%

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

   if 6.2000000000000002e-285 < z < 3.39999999999999993e-220

   1. Initial program 75.3%

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

   3. Taylor expanded in z around 0 75.3%

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

   4. Taylor expanded in x around 0 99.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-285}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 2.12 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* z a)) (+ y (* z (- b y)))))
        (t_2 (/ (- t a) (- b y))))
   (if (<= z -2.7e+18)
     t_2
     (if (<= z -9e-145)
       t_1
       (if (<= z 8.5e-136)
         (+ x (/ (* z (- t a)) y))
         (if (<= z 1.1e+74) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) - (z * a)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.7e+18) {
		tmp = t_2;
	} else if (z <= -9e-145) {
		tmp = t_1;
	} else if (z <= 8.5e-136) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.1e+74) {
		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 * y) - (z * a)) / (y + (z * (b - y)))
    t_2 = (t - a) / (b - y)
    if (z <= (-2.7d+18)) then
        tmp = t_2
    else if (z <= (-9d-145)) then
        tmp = t_1
    else if (z <= 8.5d-136) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 1.1d+74) 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 * y) - (z * a)) / (y + (z * (b - y)));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.7e+18) {
		tmp = t_2;
	} else if (z <= -9e-145) {
		tmp = t_1;
	} else if (z <= 8.5e-136) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.1e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) - (z * a)) / (y + (z * (b - y)))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.7e+18:
		tmp = t_2
	elif z <= -9e-145:
		tmp = t_1
	elif z <= 8.5e-136:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 1.1e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * a)) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.7e+18)
		tmp = t_2;
	elseif (z <= -9e-145)
		tmp = t_1;
	elseif (z <= 8.5e-136)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 1.1e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) - (z * a)) / (y + (z * (b - y)));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.7e+18)
		tmp = t_2;
	elseif (z <= -9e-145)
		tmp = t_1;
	elseif (z <= 8.5e-136)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 1.1e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+18], t$95$2, If[LessEqual[z, -9e-145], t$95$1, If[LessEqual[z, 8.5e-136], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e18 or 1.1000000000000001e74 < z

   1. Initial program 29.2%

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

   3. Taylor expanded in z around inf 83.8%

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

   if -2.7e18 < z < -9.0000000000000001e-145 or 8.49999999999999973e-136 < z < 1.1000000000000001e74

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. *-commutative 72.6%

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

      5. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   if -9.0000000000000001e-145 < z < 8.49999999999999973e-136

   1. Initial program 85.3%

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

   3. Taylor expanded in z around 0 72.9%

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

   4. Taylor expanded in x around 0 87.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-145}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+74}:\\ \;\;\;\;\frac{x \cdot y - z \cdot a}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-81} \lor \neg \left(z \leq 1.48 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e-81) (not (<= z 1.48e-6)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-81) || !(z <= 1.48e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((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 <= (-4.5d-81)) .or. (.not. (z <= 1.48d-6))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((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 <= -4.5e-81) || !(z <= 1.48e-6)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.5e-81) or not (z <= 1.48e-6):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e-81) || !(z <= 1.48e-6))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(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 <= -4.5e-81) || ~((z <= 1.48e-6)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e-81], N[Not[LessEqual[z, 1.48e-6]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e-81 or 1.48000000000000002e-6 < z

   1. Initial program 46.5%

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

   3. Taylor expanded in z around inf 74.1%

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

   if -4.5e-81 < z < 1.48000000000000002e-6

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 64.1%

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

   4. Taylor expanded in x around 0 77.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-81} \lor \neg \left(z \leq 1.48 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-65} \lor \neg \left(z \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e-65) (not (<= z 4.4e-7)))
   (/ (- t a) (- b y))
   (+ x (* z (/ t y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-65) || !(z <= 4.4e-7)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.2d-65)) .or. (.not. (z <= 4.4d-7))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e-65) || !(z <= 4.4e-7)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.2e-65) or not (z <= 4.4e-7):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * (t / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.2e-65) || !(z <= 4.4e-7))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.2e-65) || ~((z <= 4.4e-7)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.2e-65], N[Not[LessEqual[z, 4.4e-7]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2000000000000001e-65 or 4.4000000000000002e-7 < z

   1. Initial program 45.0%

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

   3. Taylor expanded in z around inf 74.7%

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

   if -1.2000000000000001e-65 < z < 4.4000000000000002e-7

   1. Initial program 85.3%

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

   3. Taylor expanded in z around 0 53.0%

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

   4. Taylor expanded in t around inf 63.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-65} \lor \neg \left(z \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+52} \lor \neg \left(y \leq 3 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+52) (not (<= y 3e-13))) (/ x (- 1.0 z)) (/ (- a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+52) || !(y <= 3e-13)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = -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 <= (-1.05d+52)) .or. (.not. (y <= 3d-13))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = -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 <= -1.05e+52) || !(y <= 3e-13)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+52) or not (y <= 3e-13):
		tmp = x / (1.0 - z)
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+52) || !(y <= 3e-13))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e+52) || ~((y <= 3e-13)))
		tmp = x / (1.0 - z);
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+52], N[Not[LessEqual[y, 3e-13]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[((-a) / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e52 or 2.99999999999999984e-13 < y

   1. Initial program 46.0%

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

   3. Taylor expanded in y around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   5. Simplified 53.4%

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

   if -1.05e52 < y < 2.99999999999999984e-13

   1. Initial program 78.7%

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

   3. Taylor expanded in a around inf 37.2%

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

      1. mul-1-neg 37.2%

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

      2. distribute-lft-neg-out 37.2%

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

      3. *-commutative 37.2%

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

   5. Simplified 37.2%

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

   6. Taylor expanded in y around 0 31.1%

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

      1. associate-*r/ 31.1%

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

      2. neg-mul-1 31.1%

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

   8. Simplified 31.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+52} \lor \neg \left(y \leq 3 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+56} \lor \neg \left(y \leq 1.15 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.9e+56) (not (<= y 1.15e-12))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e+56) || !(y <= 1.15e-12)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.9d+56)) .or. (.not. (y <= 1.15d-12))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.9e+56) || !(y <= 1.15e-12)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.9e+56) or not (y <= 1.15e-12):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.9e+56) || !(y <= 1.15e-12))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.9e+56) || ~((y <= 1.15e-12)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.9e+56], N[Not[LessEqual[y, 1.15e-12]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.90000000000000007e56 or 1.14999999999999995e-12 < y

   1. Initial program 46.0%

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

   3. Taylor expanded in y around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   5. Simplified 53.4%

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

   if -2.90000000000000007e56 < y < 1.14999999999999995e-12

   1. Initial program 78.7%

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

   3. Taylor expanded in y around 0 50.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+56} \lor \neg \left(y \leq 1.15 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-81}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4e-81) (/ (- a) b) (if (<= z 1.0) (+ x (* z x)) (/ (- x) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4e-81) {
		tmp = -a / b;
	} else if (z <= 1.0) {
		tmp = x + (z * x);
	} else {
		tmp = -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 <= (-4d-81)) then
        tmp = -a / b
    else if (z <= 1.0d0) then
        tmp = x + (z * x)
    else
        tmp = -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 <= -4e-81) {
		tmp = -a / b;
	} else if (z <= 1.0) {
		tmp = x + (z * x);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4e-81:
		tmp = -a / b
	elif z <= 1.0:
		tmp = x + (z * x)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4e-81)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4e-81)
		tmp = -a / b;
	elseif (z <= 1.0)
		tmp = x + (z * x);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4e-81], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999998e-81

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf 26.5%

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

      1. mul-1-neg 26.5%

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

      2. distribute-lft-neg-out 26.5%

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

      3. *-commutative 26.5%

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

   5. Simplified 26.5%

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

   6. Taylor expanded in y around 0 26.0%

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

      1. associate-*r/ 26.0%

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

      2. neg-mul-1 26.0%

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

   8. Simplified 26.0%

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

   if -3.9999999999999998e-81 < z < 1

   1. Initial program 84.8%

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

   3. Taylor expanded in y around inf 52.6%

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

      1. mul-1-neg 52.6%

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

      2. unsub-neg 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in z around 0 52.6%

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

      1. *-commutative 52.6%

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

   8. Simplified 52.6%

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

   if 1 < z

   1. Initial program 39.2%

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

   3. Taylor expanded in y around inf 18.9%

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

      1. mul-1-neg 18.9%

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

      2. unsub-neg 18.9%

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

   5. Simplified 18.9%

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

   6. Taylor expanded in z around inf 18.0%

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

      1. associate-*r/ 18.0%

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

      2. mul-1-neg 18.0%

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

   8. Simplified 18.0%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-81}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-81} \lor \neg \left(z \leq 3.5 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e-81) (not (<= z 3.5e-10))) (/ (- a) b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-81) || !(z <= 3.5e-10)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.5d-81)) .or. (.not. (z <= 3.5d-10))) then
        tmp = -a / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-81) || !(z <= 3.5e-10)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.5e-81) or not (z <= 3.5e-10):
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e-81) || !(z <= 3.5e-10))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.5e-81) || ~((z <= 3.5e-10)))
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e-81], N[Not[LessEqual[z, 3.5e-10]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e-81 or 3.4999999999999998e-10 < z

   1. Initial program 46.5%

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

   3. Taylor expanded in a around inf 22.6%

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

      1. mul-1-neg 22.6%

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

      2. distribute-lft-neg-out 22.6%

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

      3. *-commutative 22.6%

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

   5. Simplified 22.6%

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

   6. Taylor expanded in y around 0 21.8%

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

      1. associate-*r/ 21.8%

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

      2. neg-mul-1 21.8%

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

   8. Simplified 21.8%

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

   if -4.5e-81 < z < 3.4999999999999998e-10

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 52.6%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-81} \lor \neg \left(z \leq 3.5 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-81}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e-81) (/ (- a) b) (if (<= z 1.0) x (/ (- x) z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e-81) {
		tmp = -a / b;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -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 <= (-2d-81)) then
        tmp = -a / b
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = -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 <= -2e-81) {
		tmp = -a / b;
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2e-81:
		tmp = -a / b
	elif z <= 1.0:
		tmp = x
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2e-81)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2e-81)
		tmp = -a / b;
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2e-81], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 1.0], x, N[((-x) / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e-81

   1. Initial program 52.2%

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

   3. Taylor expanded in a around inf 26.5%

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

      1. mul-1-neg 26.5%

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

      2. distribute-lft-neg-out 26.5%

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

      3. *-commutative 26.5%

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

   5. Simplified 26.5%

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

   6. Taylor expanded in y around 0 26.0%

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

      1. associate-*r/ 26.0%

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

      2. neg-mul-1 26.0%

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

   8. Simplified 26.0%

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

   if -1.9999999999999999e-81 < z < 1

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 52.6%

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

   if 1 < z

   1. Initial program 39.2%

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

   3. Taylor expanded in y around inf 18.9%

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

      1. mul-1-neg 18.9%

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

      2. unsub-neg 18.9%

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

   5. Simplified 18.9%

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

   6. Taylor expanded in z around inf 18.0%

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

      1. associate-*r/ 18.0%

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

      2. mul-1-neg 18.0%

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

   8. Simplified 18.0%

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

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-81}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.1% 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 62.3%

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

3. Taylor expanded in z around 0 25.0%

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

4. Final simplification 25.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 74.2% 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 2024018 
(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)))))