Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.4% → 86.6%

Time: 8.9s

Alternatives: 12

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+194} \lor \neg \left(t \leq 9.6 \cdot 10^{+23}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.25e+194) (not (<= t 9.6e+23)))
   (+ (- x (* a (/ y t))) (/ (* y z) t))
   (fma (- z t) (/ y (- t a)) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.25e+194) || !(t <= 9.6e+23)) {
		tmp = (x - (a * (y / t))) + ((y * z) / t);
	} else {
		tmp = fma((z - t), (y / (t - a)), (y + x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.25e+194) || !(t <= 9.6e+23))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(Float64(y * z) / t));
	else
		tmp = fma(Float64(z - t), Float64(y / Float64(t - a)), Float64(y + x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.25e+194], N[Not[LessEqual[t, 9.6e+23]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.24999999999999997e194 or 9.6e23 < t

   1. Initial program 61.3%

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

   3. Taylor expanded in t around inf 87.1%

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

      1. +-commutative 87.1%

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

      2. mul-1-neg 87.1%

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

      3. associate-/l* 92.2%

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

      4. associate-*r/ 92.2%

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

      5. associate-*r* 92.2%

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

      6. neg-mul-1 92.2%

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

   5. Simplified 92.2%

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

   if -1.24999999999999997e194 < t < 9.6e23

   1. Initial program 84.2%

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

      1. sub-neg 84.2%

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

      2. +-commutative 84.2%

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

      3. distribute-frac-neg 84.2%

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

      4. distribute-rgt-neg-out 84.2%

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

      5. associate-/l* 91.5%

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

      6. fma-define 91.6%

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

      7. distribute-frac-neg 91.6%

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

      8. distribute-neg-frac2 91.6%

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

      9. sub-neg 91.6%

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

      10. distribute-neg-in 91.6%

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

      11. remove-double-neg 91.6%

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

      12. +-commutative 91.6%

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

      13. sub-neg 91.6%

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

   3. Simplified 91.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+194} \lor \neg \left(t \leq 9.6 \cdot 10^{+23}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-157} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-117}\right):\\ \;\;\;\;\left(y + x\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ y x) (/ (* y (- t z)) (- a t)))))
   (if (or (<= t_1 -1e-157) (not (<= t_1 5e-117)))
     (+ (+ y x) (* (- z t) (/ y (- t a))))
     (+ x (/ (* y (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-157) || !(t_1 <= 5e-117)) {
		tmp = (y + x) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (y + x) + ((y * (t - z)) / (a - t))
    if ((t_1 <= (-1d-157)) .or. (.not. (t_1 <= 5d-117))) then
        tmp = (y + x) + ((z - t) * (y / (t - a)))
    else
        tmp = x + ((y * (z - a)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -1e-157) || !(t_1 <= 5e-117)) {
		tmp = (y + x) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) + ((y * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -1e-157) or not (t_1 <= 5e-117):
		tmp = (y + x) + ((z - t) * (y / (t - a)))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -1e-157) || !(t_1 <= 5e-117))
		tmp = Float64(Float64(y + x) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -1e-157) || ~((t_1 <= 5e-117)))
		tmp = (y + x) + ((z - t) * (y / (t - a)));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-157], N[Not[LessEqual[t$95$1, 5e-117]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.99999999999999943e-158 or 5e-117 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 83.0%

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

   3. Taylor expanded in y around 0 83.0%

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

      1. associate-*l/ 91.1%

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

   5. Simplified 91.1%

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

   if -9.99999999999999943e-158 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 5e-117

   1. Initial program 18.9%

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

   3. Taylor expanded in t around inf 94.5%

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

      1. associate--l+ 94.5%

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

      2. distribute-lft-out-- 94.5%

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

      3. div-sub 94.4%

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

      4. mul-1-neg 94.4%

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

      5. unsub-neg 94.4%

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

      6. *-commutative 94.4%

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

      7. distribute-lft-out-- 94.5%

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

   5. Simplified 94.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-157} \lor \neg \left(\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 5 \cdot 10^{-117}\right):\\ \;\;\;\;\left(y + x\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-97} \lor \neg \left(a \leq 9.2 \cdot 10^{-66}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a \cdot y}{t}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e-97) (not (<= a 9.2e-66)))
   (- (+ y x) (* y (/ z a)))
   (+ (- x (/ (* a y) t)) (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-97) || !(a <= 9.2e-66)) {
		tmp = (y + x) - (y * (z / a));
	} else {
		tmp = (x - ((a * y) / t)) + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((a <= (-1.6d-97)) .or. (.not. (a <= 9.2d-66))) then
        tmp = (y + x) - (y * (z / a))
    else
        tmp = (x - ((a * y) / t)) + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-97) || !(a <= 9.2e-66)) {
		tmp = (y + x) - (y * (z / a));
	} else {
		tmp = (x - ((a * y) / t)) + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e-97) or not (a <= 9.2e-66):
		tmp = (y + x) - (y * (z / a))
	else:
		tmp = (x - ((a * y) / t)) + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e-97) || !(a <= 9.2e-66))
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(Float64(x - Float64(Float64(a * y) / t)) + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.6e-97) || ~((a <= 9.2e-66)))
		tmp = (y + x) - (y * (z / a));
	else
		tmp = (x - ((a * y) / t)) + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e-97], N[Not[LessEqual[a, 9.2e-66]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5999999999999999e-97 or 9.19999999999999967e-66 < a

   1. Initial program 77.1%

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

   3. Taylor expanded in t around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 84.8%

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

   5. Simplified 84.8%

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

   if -1.5999999999999999e-97 < a < 9.19999999999999967e-66

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. mul-1-neg 90.6%

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

      3. associate-/l* 82.3%

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

      4. associate-*r/ 82.3%

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

      5. associate-*r* 82.3%

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

      6. neg-mul-1 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in a around 0 90.6%

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

      1. sub-neg 90.6%

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

      2. mul-1-neg 90.6%

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

      3. sub-neg 90.6%

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

      4. *-commutative 90.6%

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

      5. mul-1-neg 90.6%

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

      6. associate-*r/ 92.6%

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

      7. remove-double-neg 92.6%

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

      8. associate-*r/ 90.6%

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

      9. associate-*l/ 90.5%

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

      10. associate-/r/ 93.5%

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

   8. Simplified 93.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-97} \lor \neg \left(a \leq 9.2 \cdot 10^{-66}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{a \cdot y}{t}\right) + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+194} \lor \neg \left(t \leq 10^{+24}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.45e+194) (not (<= t 1e+24)))
   (+ (- x (* a (/ y t))) (/ (* y z) t))
   (+ (+ y x) (* (- z t) (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+194) || !(t <= 1e+24)) {
		tmp = (x - (a * (y / t))) + ((y * z) / t);
	} else {
		tmp = (y + x) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((t <= (-2.45d+194)) .or. (.not. (t <= 1d+24))) then
        tmp = (x - (a * (y / t))) + ((y * z) / t)
    else
        tmp = (y + x) + ((z - t) * (y / (t - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.45e+194) || !(t <= 1e+24)) {
		tmp = (x - (a * (y / t))) + ((y * z) / t);
	} else {
		tmp = (y + x) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.45e+194) or not (t <= 1e+24):
		tmp = (x - (a * (y / t))) + ((y * z) / t)
	else:
		tmp = (y + x) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.45e+194) || !(t <= 1e+24))
		tmp = Float64(Float64(x - Float64(a * Float64(y / t))) + Float64(Float64(y * z) / t));
	else
		tmp = Float64(Float64(y + x) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.45e+194) || ~((t <= 1e+24)))
		tmp = (x - (a * (y / t))) + ((y * z) / t);
	else
		tmp = (y + x) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.45e+194], N[Not[LessEqual[t, 1e+24]], $MachinePrecision]], N[(N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.45000000000000013e194 or 9.9999999999999998e23 < t

   1. Initial program 61.3%

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

   3. Taylor expanded in t around inf 87.1%

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

      1. +-commutative 87.1%

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

      2. mul-1-neg 87.1%

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

      3. associate-/l* 92.2%

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

      4. associate-*r/ 92.2%

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

      5. associate-*r* 92.2%

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

      6. neg-mul-1 92.2%

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

   5. Simplified 92.2%

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

   if -2.45000000000000013e194 < t < 9.9999999999999998e23

   1. Initial program 84.2%

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

   3. Taylor expanded in y around 0 84.2%

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

      1. associate-*l/ 91.5%

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

   5. Simplified 91.5%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+194} \lor \neg \left(t \leq 10^{+24}\right):\\ \;\;\;\;\left(x - a \cdot \frac{y}{t}\right) + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-98} \lor \neg \left(a \leq 3.3 \cdot 10^{-65}\right):\\ \;\;\;\;\left(y + x\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.6e-98) (not (<= a 3.3e-65)))
   (- (+ y x) (/ (* y z) a))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e-98) || !(a <= 3.3e-65)) {
		tmp = (y + x) - ((y * z) / a);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((a <= (-5.6d-98)) .or. (.not. (a <= 3.3d-65))) then
        tmp = (y + x) - ((y * z) / a)
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e-98) || !(a <= 3.3e-65)) {
		tmp = (y + x) - ((y * z) / a);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.6e-98) or not (a <= 3.3e-65):
		tmp = (y + x) - ((y * z) / a)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.6e-98) || !(a <= 3.3e-65))
		tmp = Float64(Float64(y + x) - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.6e-98) || ~((a <= 3.3e-65)))
		tmp = (y + x) - ((y * z) / a);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.6e-98], N[Not[LessEqual[a, 3.3e-65]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5999999999999998e-98 or 3.3000000000000001e-65 < a

   1. Initial program 77.1%

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

   3. Taylor expanded in t around 0 80.0%

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

   if -5.5999999999999998e-98 < a < 3.3000000000000001e-65

   1. Initial program 78.2%

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

   3. Taylor expanded in t around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. mul-1-neg 90.6%

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

      3. associate-/l* 82.3%

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

      4. associate-*r/ 82.3%

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

      5. associate-*r* 82.3%

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

      6. neg-mul-1 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in a around 0 89.4%

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

      1. sub-neg 89.4%

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

      2. mul-1-neg 89.4%

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

      3. associate-*r/ 91.3%

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

      4. remove-double-neg 91.3%

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

      5. associate-*r/ 89.4%

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

      6. associate-*l/ 89.7%

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

      7. associate-/r/ 92.2%

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

   8. Simplified 92.2%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-98} \lor \neg \left(a \leq 3.3 \cdot 10^{-65}\right):\\ \;\;\;\;\left(y + x\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-65} \lor \neg \left(a \leq 5 \cdot 10^{-73}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.4e-65) (not (<= a 5e-73)))
   (- (+ y x) (* y (/ z a)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.4e-65) || !(a <= 5e-73)) {
		tmp = (y + x) - (y * (z / a));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((a <= (-6.4d-65)) .or. (.not. (a <= 5d-73))) then
        tmp = (y + x) - (y * (z / a))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.4e-65) || !(a <= 5e-73)) {
		tmp = (y + x) - (y * (z / a));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.4e-65) or not (a <= 5e-73):
		tmp = (y + x) - (y * (z / a))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.4e-65) || !(a <= 5e-73))
		tmp = Float64(Float64(y + x) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.4e-65) || ~((a <= 5e-73)))
		tmp = (y + x) - (y * (z / a));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.4e-65], N[Not[LessEqual[a, 5e-73]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.3999999999999998e-65 or 4.9999999999999998e-73 < a

   1. Initial program 77.1%

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

   3. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

   if -6.3999999999999998e-65 < a < 4.9999999999999998e-73

   1. Initial program 78.1%

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

   3. Taylor expanded in t around inf 87.7%

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

      1. +-commutative 87.7%

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

      2. mul-1-neg 87.7%

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

      3. associate-/l* 80.0%

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

      4. associate-*r/ 80.0%

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

      5. associate-*r* 80.0%

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

      6. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in a around 0 87.5%

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

      1. sub-neg 87.5%

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

      2. mul-1-neg 87.5%

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

      3. associate-*r/ 89.2%

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

      4. remove-double-neg 89.2%

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

      5. associate-*r/ 87.5%

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

      6. associate-*l/ 87.8%

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

      7. associate-/r/ 90.1%

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

   8. Simplified 90.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-65} \lor \neg \left(a \leq 5 \cdot 10^{-73}\right):\\ \;\;\;\;\left(y + x\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-102} \lor \neg \left(x \leq 1.06 \cdot 10^{-108}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.45e-102) (not (<= x 1.06e-108)))
   (+ y x)
   (* y (/ z (- t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e-102) || !(x <= 1.06e-108)) {
		tmp = y + x;
	} else {
		tmp = y * (z / (t - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x <= (-1.45d-102)) .or. (.not. (x <= 1.06d-108))) then
        tmp = y + x
    else
        tmp = y * (z / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.45e-102) || !(x <= 1.06e-108)) {
		tmp = y + x;
	} else {
		tmp = y * (z / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.45e-102) or not (x <= 1.06e-108):
		tmp = y + x
	else:
		tmp = y * (z / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.45e-102) || !(x <= 1.06e-108))
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(z / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.45e-102) || ~((x <= 1.06e-108)))
		tmp = y + x;
	else
		tmp = y * (z / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.45e-102], N[Not[LessEqual[x, 1.06e-108]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999993e-102 or 1.06e-108 < x

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf 71.7%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 71.7%

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

   5. Simplified 71.7%

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

   if -1.44999999999999993e-102 < x < 1.06e-108

   1. Initial program 60.4%

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

      1. sub-neg 60.4%

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

      2. +-commutative 60.4%

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

      3. distribute-frac-neg 60.4%

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

      4. distribute-rgt-neg-out 60.4%

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

      5. associate-/l* 61.3%

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

      6. fma-define 61.9%

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

      7. distribute-frac-neg 61.9%

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

      8. distribute-neg-frac2 61.9%

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

      9. sub-neg 61.9%

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

      10. distribute-neg-in 61.9%

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

      11. remove-double-neg 61.9%

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

      12. +-commutative 61.9%

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

      13. sub-neg 61.9%

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

   3. Simplified 61.9%

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

   5. Taylor expanded in z around inf 55.9%

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

      1. associate-/l* 60.9%

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

   7. Simplified 60.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-102} \lor \neg \left(x \leq 1.06 \cdot 10^{-108}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -800 \lor \neg \left(a \leq 4.7 \cdot 10^{+55}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -800.0) (not (<= a 4.7e+55))) (+ y x) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -800.0) || !(a <= 4.7e+55)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((a <= (-800.0d0)) .or. (.not. (a <= 4.7d+55))) then
        tmp = y + x
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -800.0) || !(a <= 4.7e+55)) {
		tmp = y + x;
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -800.0) or not (a <= 4.7e+55):
		tmp = y + x
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -800.0) || !(a <= 4.7e+55))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -800.0) || ~((a <= 4.7e+55)))
		tmp = y + x;
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -800.0], N[Not[LessEqual[a, 4.7e+55]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -800 or 4.7000000000000001e55 < a

   1. Initial program 78.8%

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

   3. Taylor expanded in a around inf 78.8%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 78.8%

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

   5. Simplified 78.8%

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

   if -800 < a < 4.7000000000000001e55

   1. Initial program 76.5%

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

   3. Taylor expanded in t around inf 78.1%

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

      1. +-commutative 78.1%

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

      2. mul-1-neg 78.1%

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

      3. associate-/l* 72.5%

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

      4. associate-*r/ 72.5%

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

      5. associate-*r* 72.5%

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

      6. neg-mul-1 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in a around 0 78.1%

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

      1. sub-neg 78.1%

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

      2. mul-1-neg 78.1%

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

      3. associate-*r/ 80.0%

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

      4. remove-double-neg 80.0%

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

      5. associate-*r/ 78.1%

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

      6. associate-*l/ 78.3%

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

      7. associate-/r/ 80.6%

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

   8. Simplified 80.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -800 \lor \neg \left(a \leq 4.7 \cdot 10^{+55}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-104} \lor \neg \left(x \leq 3.9 \cdot 10^{-175}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5e-104) (not (<= x 3.9e-175))) (+ y x) (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5e-104) || !(x <= 3.9e-175)) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x <= (-5d-104)) .or. (.not. (x <= 3.9d-175))) then
        tmp = y + x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5e-104) || !(x <= 3.9e-175)) {
		tmp = y + x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5e-104) or not (x <= 3.9e-175):
		tmp = y + x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -5e-104) || !(x <= 3.9e-175))
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -5e-104) || ~((x <= 3.9e-175)))
		tmp = y + x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -5e-104], N[Not[LessEqual[x, 3.9e-175]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999979e-104 or 3.89999999999999998e-175 < x

   1. Initial program 83.9%

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

   3. Taylor expanded in a around inf 70.3%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 70.3%

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

   5. Simplified 70.3%

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

   if -4.99999999999999979e-104 < x < 3.89999999999999998e-175

   1. Initial program 58.0%

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

      1. sub-neg 58.0%

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

      2. +-commutative 58.0%

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

      3. distribute-frac-neg 58.0%

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

      4. distribute-rgt-neg-out 58.0%

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

      5. associate-/l* 56.1%

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

      6. fma-define 56.8%

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

      7. distribute-frac-neg 56.8%

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

      8. distribute-neg-frac2 56.8%

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

      9. sub-neg 56.8%

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

      10. distribute-neg-in 56.8%

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

      11. remove-double-neg 56.8%

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

      12. +-commutative 56.8%

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

      13. sub-neg 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in z around inf 58.8%

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

   6. Taylor expanded in t around inf 47.9%

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

      1. associate-/l* 49.4%

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

   8. Simplified 49.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-104} \lor \neg \left(x \leq 3.9 \cdot 10^{-175}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-104} \lor \neg \left(x \leq 2.35 \cdot 10^{-174}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7e-104) (not (<= x 2.35e-174))) (+ y x) (/ y (/ t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7e-104) || !(x <= 2.35e-174)) {
		tmp = y + x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x <= (-7d-104)) .or. (.not. (x <= 2.35d-174))) then
        tmp = y + x
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7e-104) || !(x <= 2.35e-174)) {
		tmp = y + x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7e-104) or not (x <= 2.35e-174):
		tmp = y + x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7e-104) || !(x <= 2.35e-174))
		tmp = Float64(y + x);
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7e-104) || ~((x <= 2.35e-174)))
		tmp = y + x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7e-104], N[Not[LessEqual[x, 2.35e-174]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.00000000000000057e-104 or 2.34999999999999993e-174 < x

   1. Initial program 83.9%

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

   3. Taylor expanded in a around inf 70.3%

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative 70.3%

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

   5. Simplified 70.3%

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

   if -7.00000000000000057e-104 < x < 2.34999999999999993e-174

   1. Initial program 58.0%

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

      1. sub-neg 58.0%

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

      2. +-commutative 58.0%

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

      3. distribute-frac-neg 58.0%

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

      4. distribute-rgt-neg-out 58.0%

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

      5. associate-/l* 56.1%

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

      6. fma-define 56.8%

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

      7. distribute-frac-neg 56.8%

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

      8. distribute-neg-frac2 56.8%

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

      9. sub-neg 56.8%

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

      10. distribute-neg-in 56.8%

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

      11. remove-double-neg 56.8%

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

      12. +-commutative 56.8%

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

      13. sub-neg 56.8%

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

   3. Simplified 56.8%

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

   5. Taylor expanded in z around inf 58.8%

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

   6. Taylor expanded in t around inf 47.9%

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

      1. associate-/l* 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in y around 0 47.9%

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

       1. associate-*l/ 44.8%

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

       2. associate-/r/ 49.4%

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

   11. Simplified 49.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-104} \lor \neg \left(x \leq 2.35 \cdot 10^{-174}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = y + x
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return Float64(y + x)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 77.5%

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

3. Taylor expanded in a around inf 59.0%

   \[\leadsto \color{blue}{x + y} \]
4. Step-by-step derivation

   1. +-commutative 59.0%

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

5. Simplified 59.0%

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

6. Final simplification 59.0%

   \[\leadsto y + x \]
7. Add Preprocessing

Alternative 12: 51.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.5%

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

3. Taylor expanded in x around inf 47.2%

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

4. Final simplification 47.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024115 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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