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

Percentage Accurate: 76.5% → 92.8%

Time: 10.2s

Alternatives: 13

Speedup: 1.0×

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: 76.5% 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: 92.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-271}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (<= t_1 -4e-271)
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (if (<= t_1 0.0)
       (+ x (* y (- (/ z t) (/ a t))))
       (+ x (fma (/ (- t z) (- a t)) y y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -4e-271) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else if (t_1 <= 0.0) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = x + fma(((t - z) / (a - t)), y, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -4e-271)
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = Float64(x + fma(Float64(Float64(t - z) / Float64(a - t)), y, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-271], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -3.99999999999999985e-271

   1. Initial program 84.5%

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

      1. associate--l+ 84.5%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   if -3.99999999999999985e-271 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate--l+ 37.2%

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

      2. associate-/l* 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. mul-1-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. associate-/l* 99.7%

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

      6. mul-1-neg 99.7%

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

      7. remove-double-neg 99.7%

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

      8. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.9%

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

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

   1. Initial program 83.7%

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

      1. associate--l+ 83.7%

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

      2. sub-neg 83.7%

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

      3. +-commutative 83.7%

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

      4. associate-/l* 95.1%

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

      5. distribute-neg-frac 95.1%

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

      6. associate-/r/ 95.5%

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

      7. fma-def 95.5%

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

      8. sub-neg 95.5%

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

      9. +-commutative 95.5%

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

      10. distribute-neg-in 95.5%

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

      11. unsub-neg 95.5%

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

      12. remove-double-neg 95.5%

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

   3. Simplified 95.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -4 \cdot 10^{-271}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{t - z}{a - t}, y, y\right)\\ \end{array} \]

Alternative 2: 92.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-271} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (or (<= t_1 -4e-271) (not (<= t_1 0.0)))
     (+ x (+ y (/ (- t z) (/ (- a t) y))))
     (+ x (* y (- (/ z t) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-271) || !(t_1 <= 0.0)) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + (y * ((z / t) - (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 = (x + y) + ((y * (t - z)) / (a - t))
    if ((t_1 <= (-4d-271)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + (y + ((t - z) / ((a - t) / y)))
    else
        tmp = x + (y * ((z / t) - (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 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -4e-271) || !(t_1 <= 0.0)) {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	} else {
		tmp = x + (y * ((z / t) - (a / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((y * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -4e-271) or not (t_1 <= 0.0):
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	else:
		tmp = x + (y * ((z / t) - (a / t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -4e-271) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -4e-271) || ~((t_1 <= 0.0)))
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	else
		tmp = x + (y * ((z / t) - (a / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-271], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -3.99999999999999985e-271 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 84.1%

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

      1. associate--l+ 84.1%

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

      2. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   if -3.99999999999999985e-271 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.5%

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

      1. associate--l+ 37.2%

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

      2. associate-/l* 28.1%

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

   3. Simplified 28.1%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. mul-1-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. associate-/l* 99.7%

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

      6. mul-1-neg 99.7%

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

      7. remove-double-neg 99.7%

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

      8. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.9%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -4 \cdot 10^{-271} \lor \neg \left(\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0\right):\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \end{array} \]

Alternative 3: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-56} \lor \neg \left(a \leq 8.6 \cdot 10^{-63}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e-56) (not (<= a 8.6e-63)))
   (+ x (- y (/ y (/ (- a t) z))))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e-56) || !(a <= 8.6e-63)) {
		tmp = x + (y - (y / ((a - t) / z)));
	} 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) :: tmp
    if ((a <= (-7d-56)) .or. (.not. (a <= 8.6d-63))) then
        tmp = x + (y - (y / ((a - t) / z)))
    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 tmp;
	if ((a <= -7e-56) || !(a <= 8.6e-63)) {
		tmp = x + (y - (y / ((a - t) / z)));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7e-56) or not (a <= 8.6e-63):
		tmp = x + (y - (y / ((a - t) / z)))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7e-56) || !(a <= 8.6e-63))
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	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)
	tmp = 0.0;
	if ((a <= -7e-56) || ~((a <= 8.6e-63)))
		tmp = x + (y - (y / ((a - t) / z)));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7e-56], N[Not[LessEqual[a, 8.6e-63]], $MachinePrecision]], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $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 a < -6.9999999999999996e-56 or 8.5999999999999997e-63 < a

   1. Initial program 78.9%

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

      1. associate--l+ 79.5%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around inf 81.7%

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

      1. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

   if -6.9999999999999996e-56 < a < 8.5999999999999997e-63

   1. Initial program 76.2%

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

      1. associate--l+ 81.8%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in t around -inf 87.8%

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

      1. +-commutative 87.8%

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

      2. sub-neg 87.8%

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

      3. mul-1-neg 87.8%

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

      4. mul-1-neg 87.8%

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

      5. unsub-neg 87.8%

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

      6. mul-1-neg 87.8%

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

      7. sub-neg 87.8%

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

      8. distribute-lft-out-- 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-56} \lor \neg \left(a \leq 8.6 \cdot 10^{-63}\right):\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 4: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+90} \lor \neg \left(t \leq 3.1 \cdot 10^{+106}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+90) (not (<= t 3.1e+106)))
   (+ x (* y (- (/ z t) (/ a t))))
   (+ x (- y (/ y (/ (- a t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+90) || !(t <= 3.1e+106)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = x + (y - (y / ((a - 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 ((t <= (-2.1d+90)) .or. (.not. (t <= 3.1d+106))) then
        tmp = x + (y * ((z / t) - (a / t)))
    else
        tmp = x + (y - (y / ((a - 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 ((t <= -2.1e+90) || !(t <= 3.1e+106)) {
		tmp = x + (y * ((z / t) - (a / t)));
	} else {
		tmp = x + (y - (y / ((a - t) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+90) or not (t <= 3.1e+106):
		tmp = x + (y * ((z / t) - (a / t)))
	else:
		tmp = x + (y - (y / ((a - t) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+90) || !(t <= 3.1e+106))
		tmp = Float64(x + Float64(y * Float64(Float64(z / t) - Float64(a / t))));
	else
		tmp = Float64(x + Float64(y - Float64(y / Float64(Float64(a - t) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+90) || ~((t <= 3.1e+106)))
		tmp = x + (y * ((z / t) - (a / t)));
	else
		tmp = x + (y - (y / ((a - t) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+90], N[Not[LessEqual[t, 3.1e+106]], $MachinePrecision]], N[(x + N[(y * N[(N[(z / t), $MachinePrecision] - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.09999999999999981e90 or 3.0999999999999999e106 < t

   1. Initial program 55.1%

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

      1. associate--l+ 61.1%

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

      2. associate-/l* 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in t around inf 76.0%

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

      1. sub-neg 76.0%

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

      2. +-commutative 76.0%

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

      3. mul-1-neg 76.0%

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

      4. unsub-neg 76.0%

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

      5. associate-/l* 83.5%

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

      6. mul-1-neg 83.5%

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

      7. remove-double-neg 83.5%

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

      8. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in y around 0 90.9%

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

   if -2.09999999999999981e90 < t < 3.0999999999999999e106

   1. Initial program 87.8%

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

      1. associate--l+ 88.9%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 87.8%

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

      1. associate-/l* 91.3%

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

   6. Simplified 91.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+90} \lor \neg \left(t \leq 3.1 \cdot 10^{+106}\right):\\ \;\;\;\;x + y \cdot \left(\frac{z}{t} - \frac{a}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{y}{\frac{a - t}{z}}\right)\\ \end{array} \]

Alternative 5: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 52:\\ \;\;\;\;y - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+57)
   (+ x y)
   (if (<= a 1.48e-37)
     (+ x (/ y (/ t z)))
     (if (<= a 52.0) (- y (/ z (/ a y))) (if (<= a 9e+107) x (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+57) {
		tmp = x + y;
	} else if (a <= 1.48e-37) {
		tmp = x + (y / (t / z));
	} else if (a <= 52.0) {
		tmp = y - (z / (a / y));
	} else if (a <= 9e+107) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	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 <= (-1.35d+57)) then
        tmp = x + y
    else if (a <= 1.48d-37) then
        tmp = x + (y / (t / z))
    else if (a <= 52.0d0) then
        tmp = y - (z / (a / y))
    else if (a <= 9d+107) then
        tmp = x
    else
        tmp = x + y
    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 <= -1.35e+57) {
		tmp = x + y;
	} else if (a <= 1.48e-37) {
		tmp = x + (y / (t / z));
	} else if (a <= 52.0) {
		tmp = y - (z / (a / y));
	} else if (a <= 9e+107) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+57:
		tmp = x + y
	elif a <= 1.48e-37:
		tmp = x + (y / (t / z))
	elif a <= 52.0:
		tmp = y - (z / (a / y))
	elif a <= 9e+107:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+57)
		tmp = Float64(x + y);
	elseif (a <= 1.48e-37)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (a <= 52.0)
		tmp = Float64(y - Float64(z / Float64(a / y)));
	elseif (a <= 9e+107)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e+57)
		tmp = x + y;
	elseif (a <= 1.48e-37)
		tmp = x + (y / (t / z));
	elseif (a <= 52.0)
		tmp = y - (z / (a / y));
	elseif (a <= 9e+107)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+57], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.48e-37], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 52.0], N[(y - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+107], x, N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3499999999999999e57 or 9e107 < a

   1. Initial program 75.3%

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

      1. associate--l+ 75.2%

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

      2. sub-neg 75.2%

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

      3. +-commutative 75.2%

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

      4. associate-/l* 94.0%

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

      5. distribute-neg-frac 94.0%

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

      6. associate-/r/ 93.8%

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

      7. fma-def 93.8%

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

      8. sub-neg 93.8%

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

      9. +-commutative 93.8%

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

      10. distribute-neg-in 93.8%

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

      11. unsub-neg 93.8%

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

      12. remove-double-neg 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in a around inf 85.5%

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

   if -1.3499999999999999e57 < a < 1.48e-37

   1. Initial program 78.0%

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

      1. associate--l+ 82.3%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 80.1%

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

      1. sub-neg 80.1%

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

      2. +-commutative 80.1%

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

      3. mul-1-neg 80.1%

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

      4. unsub-neg 80.1%

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

      5. associate-/l* 79.4%

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

      6. mul-1-neg 79.4%

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

      7. remove-double-neg 79.4%

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

      8. associate-/l* 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in y around 0 82.4%

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

   8. Taylor expanded in z around inf 79.0%

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

      1. associate-/l* 79.0%

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

   10. Simplified 79.0%

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

   if 1.48e-37 < a < 52

   1. Initial program 99.6%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 99.6%

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

   5. Taylor expanded in x around 0 78.4%

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

      1. associate-*r/ 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-/r/ 78.6%

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

   7. Simplified 78.6%

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

   if 52 < a < 9e107

   1. Initial program 80.2%

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

      1. associate--l+ 84.7%

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

      2. sub-neg 84.7%

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

      3. +-commutative 84.7%

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

      4. associate-/l* 93.3%

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

      5. distribute-neg-frac 93.3%

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

      6. associate-/r/ 97.8%

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

      7. fma-def 97.9%

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

      8. sub-neg 97.9%

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

      9. +-commutative 97.9%

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

      10. distribute-neg-in 97.9%

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

      11. unsub-neg 97.9%

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

      12. remove-double-neg 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 72.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 52:\\ \;\;\;\;y - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 52:\\ \;\;\;\;y - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e+57)
   (+ x y)
   (if (<= a 1.48e-37)
     (+ x (/ (* y (- z a)) t))
     (if (<= a 52.0) (- y (/ z (/ a y))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e+57) {
		tmp = x + y;
	} else if (a <= 1.48e-37) {
		tmp = x + ((y * (z - a)) / t);
	} else if (a <= 52.0) {
		tmp = y - (z / (a / y));
	} else {
		tmp = x + y;
	}
	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 <= (-1.35d+57)) then
        tmp = x + y
    else if (a <= 1.48d-37) then
        tmp = x + ((y * (z - a)) / t)
    else if (a <= 52.0d0) then
        tmp = y - (z / (a / y))
    else
        tmp = x + y
    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 <= -1.35e+57) {
		tmp = x + y;
	} else if (a <= 1.48e-37) {
		tmp = x + ((y * (z - a)) / t);
	} else if (a <= 52.0) {
		tmp = y - (z / (a / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e+57:
		tmp = x + y
	elif a <= 1.48e-37:
		tmp = x + ((y * (z - a)) / t)
	elif a <= 52.0:
		tmp = y - (z / (a / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e+57)
		tmp = Float64(x + y);
	elseif (a <= 1.48e-37)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	elseif (a <= 52.0)
		tmp = Float64(y - Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e+57)
		tmp = x + y;
	elseif (a <= 1.48e-37)
		tmp = x + ((y * (z - a)) / t);
	elseif (a <= 52.0)
		tmp = y - (z / (a / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e+57], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.48e-37], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 52.0], N[(y - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3499999999999999e57 or 52 < a

   1. Initial program 76.2%

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

      1. associate--l+ 76.9%

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

      2. sub-neg 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-/l* 93.8%

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

      5. distribute-neg-frac 93.8%

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

      6. associate-/r/ 94.5%

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

      7. fma-def 94.5%

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

      8. sub-neg 94.5%

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

      9. +-commutative 94.5%

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

      10. distribute-neg-in 94.5%

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

      11. unsub-neg 94.5%

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

      12. remove-double-neg 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in a around inf 82.4%

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

   if -1.3499999999999999e57 < a < 1.48e-37

   1. Initial program 78.0%

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

      1. associate--l+ 82.3%

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

      2. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around -inf 82.5%

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

      1. +-commutative 82.5%

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

      2. sub-neg 82.5%

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

      3. mul-1-neg 82.5%

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

      4. mul-1-neg 82.5%

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

      5. unsub-neg 82.5%

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

      6. mul-1-neg 82.5%

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

      7. sub-neg 82.5%

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

      8. distribute-lft-out-- 82.5%

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

   6. Simplified 82.5%

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

   if 1.48e-37 < a < 52

   1. Initial program 99.6%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around 0 99.6%

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

   5. Taylor expanded in x around 0 78.4%

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

      1. associate-*r/ 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-/r/ 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+57}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;a \leq 52:\\ \;\;\;\;y - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 7: 82.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-30} \lor \neg \left(a \leq 1.14 \cdot 10^{-57}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.12e-30) (not (<= a 1.14e-57)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.12e-30) || !(a <= 1.14e-57)) {
		tmp = (x + y) - (y * (z / 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) :: tmp
    if ((a <= (-1.12d-30)) .or. (.not. (a <= 1.14d-57))) then
        tmp = (x + y) - (y * (z / 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 tmp;
	if ((a <= -1.12e-30) || !(a <= 1.14e-57)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.12e-30) or not (a <= 1.14e-57):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.12e-30) || !(a <= 1.14e-57))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / 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)
	tmp = 0.0;
	if ((a <= -1.12e-30) || ~((a <= 1.14e-57)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.12e-30], N[Not[LessEqual[a, 1.14e-57]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $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 a < -1.12e-30 or 1.14000000000000006e-57 < a

   1. Initial program 79.2%

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

      1. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in t around 0 89.0%

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

   if -1.12e-30 < a < 1.14000000000000006e-57

   1. Initial program 76.0%

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

      1. associate--l+ 81.2%

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

      2. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in t around -inf 86.9%

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

      1. +-commutative 86.9%

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

      2. sub-neg 86.9%

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

      3. mul-1-neg 86.9%

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

      4. mul-1-neg 86.9%

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

      5. unsub-neg 86.9%

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

      6. mul-1-neg 86.9%

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

      7. sub-neg 86.9%

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

      8. distribute-lft-out-- 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-30} \lor \neg \left(a \leq 1.14 \cdot 10^{-57}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]

Alternative 8: 76.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e+60) (+ x y) (if (<= a 1.1e+108) (+ x (/ y (/ t z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e+60) {
		tmp = x + y;
	} else if (a <= 1.1e+108) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	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 <= (-3.2d+60)) then
        tmp = x + y
    else if (a <= 1.1d+108) then
        tmp = x + (y / (t / z))
    else
        tmp = x + y
    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 <= -3.2e+60) {
		tmp = x + y;
	} else if (a <= 1.1e+108) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e+60:
		tmp = x + y
	elif a <= 1.1e+108:
		tmp = x + (y / (t / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e+60)
		tmp = Float64(x + y);
	elseif (a <= 1.1e+108)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e+60)
		tmp = x + y;
	elseif (a <= 1.1e+108)
		tmp = x + (y / (t / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e+60], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.1e+108], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.19999999999999991e60 or 1.1000000000000001e108 < a

   1. Initial program 75.3%

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

      1. associate--l+ 75.2%

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

      2. sub-neg 75.2%

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

      3. +-commutative 75.2%

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

      4. associate-/l* 94.0%

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

      5. distribute-neg-frac 94.0%

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

      6. associate-/r/ 93.8%

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

      7. fma-def 93.8%

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

      8. sub-neg 93.8%

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

      9. +-commutative 93.8%

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

      10. distribute-neg-in 93.8%

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

      11. unsub-neg 93.8%

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

      12. remove-double-neg 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in a around inf 85.5%

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

   if -3.19999999999999991e60 < a < 1.1000000000000001e108

   1. Initial program 79.3%

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

      1. associate--l+ 83.4%

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

      2. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in t around inf 74.3%

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

      1. sub-neg 74.3%

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

      2. +-commutative 74.3%

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

      3. mul-1-neg 74.3%

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

      4. unsub-neg 74.3%

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

      5. associate-/l* 73.8%

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

      6. mul-1-neg 73.8%

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

      7. remove-double-neg 73.8%

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

      8. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in y around 0 77.0%

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

   8. Taylor expanded in z around inf 75.0%

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

      1. associate-/l* 75.6%

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

   10. Simplified 75.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+60}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 60.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+259}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+259) (* y (/ (- z) a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+259) {
		tmp = y * (-z / a);
	} else {
		tmp = x + y;
	}
	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 (z <= (-1.8d+259)) then
        tmp = y * (-z / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+259) {
		tmp = y * (-z / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+259:
		tmp = y * (-z / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+259)
		tmp = Float64(y * Float64(Float64(-z) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+259)
		tmp = y * (-z / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+259], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e259

   1. Initial program 87.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in t around 0 69.8%

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

   5. Taylor expanded in z around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-*r/ 57.5%

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

      3. distribute-rgt-neg-in 57.5%

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

      4. distribute-neg-frac 57.5%

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

   7. Simplified 57.5%

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

   if -1.8000000000000001e259 < z

   1. Initial program 77.2%

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

      1. associate--l+ 79.9%

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

      2. sub-neg 79.9%

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

      3. +-commutative 79.9%

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

      4. associate-/l* 88.9%

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

      5. distribute-neg-frac 88.9%

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

      6. associate-/r/ 90.7%

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

      7. fma-def 90.7%

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

      8. sub-neg 90.7%

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

      9. +-commutative 90.7%

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

      10. distribute-neg-in 90.7%

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

      11. unsub-neg 90.7%

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

      12. remove-double-neg 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around inf 63.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+259}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 10: 60.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+255}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+255) (* z (/ (- y) a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+255) {
		tmp = z * (-y / a);
	} else {
		tmp = x + y;
	}
	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 (z <= (-5.5d+255)) then
        tmp = z * (-y / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+255) {
		tmp = z * (-y / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+255:
		tmp = z * (-y / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+255)
		tmp = Float64(z * Float64(Float64(-y) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+255)
		tmp = z * (-y / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+255], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999998e255

   1. Initial program 87.6%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

      1. associate-/r/ 99.8%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around inf 81.6%

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

   7. Taylor expanded in z around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. associate-*l/ 69.2%

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

      3. *-commutative 69.2%

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

      4. distribute-rgt-neg-in 69.2%

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

   9. Simplified 69.2%

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

   if -5.4999999999999998e255 < z

   1. Initial program 77.2%

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

      1. associate--l+ 79.9%

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

      2. sub-neg 79.9%

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

      3. +-commutative 79.9%

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

      4. associate-/l* 88.9%

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

      5. distribute-neg-frac 88.9%

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

      6. associate-/r/ 90.7%

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

      7. fma-def 90.7%

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

      8. sub-neg 90.7%

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

      9. +-commutative 90.7%

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

      10. distribute-neg-in 90.7%

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

      11. unsub-neg 90.7%

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

      12. remove-double-neg 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in a around inf 63.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+255}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 11: 52.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+211}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.02e+211) y (if (<= y 3.4e+119) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.02e+211) {
		tmp = y;
	} else if (y <= 3.4e+119) {
		tmp = x;
	} else {
		tmp = y;
	}
	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 (y <= (-1.02d+211)) then
        tmp = y
    else if (y <= 3.4d+119) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.02e+211) {
		tmp = y;
	} else if (y <= 3.4e+119) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.02e+211:
		tmp = y
	elif y <= 3.4e+119:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.02e+211)
		tmp = y;
	elseif (y <= 3.4e+119)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.02e+211)
		tmp = y;
	elseif (y <= 3.4e+119)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.02e+211], y, If[LessEqual[y, 3.4e+119], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e211 or 3.40000000000000013e119 < y

   1. Initial program 56.3%

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

      1. associate-*l/ 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in t around 0 64.7%

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

   5. Taylor expanded in x around 0 50.5%

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

      1. associate-*r/ 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-/r/ 62.3%

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

   7. Simplified 62.3%

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

   8. Taylor expanded in z around 0 35.1%

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

   if -1.02e211 < y < 3.40000000000000013e119

   1. Initial program 84.4%

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

      1. associate--l+ 87.8%

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

      2. sub-neg 87.8%

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

      3. +-commutative 87.8%

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

      4. associate-/l* 92.6%

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

      5. distribute-neg-frac 92.6%

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

      6. associate-/r/ 92.1%

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

      7. fma-def 92.1%

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

      8. sub-neg 92.1%

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

      9. +-commutative 92.1%

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

      10. distribute-neg-in 92.1%

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

      11. unsub-neg 92.1%

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

      12. remove-double-neg 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in x around inf 67.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+211}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 12: 60.1% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.8%

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

   1. associate--l+ 80.4%

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

   2. sub-neg 80.4%

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

   3. +-commutative 80.4%

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

   4. associate-/l* 89.6%

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

   5. distribute-neg-frac 89.6%

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

   6. associate-/r/ 89.8%

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

   7. fma-def 89.8%

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

   8. sub-neg 89.8%

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

   9. +-commutative 89.8%

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

   10. distribute-neg-in 89.8%

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

   11. unsub-neg 89.8%

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

   12. remove-double-neg 89.8%

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

3. Simplified 89.8%

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

4. Taylor expanded in a around inf 60.5%

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

5. Final simplification 60.5%

   \[\leadsto x + y \]

Alternative 13: 50.9% 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 77.8%

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

   1. associate--l+ 80.4%

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

   2. sub-neg 80.4%

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

   3. +-commutative 80.4%

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

   4. associate-/l* 89.6%

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

   5. distribute-neg-frac 89.6%

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

   6. associate-/r/ 89.8%

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

   7. fma-def 89.8%

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

   8. sub-neg 89.8%

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

   9. +-commutative 89.8%

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

   10. distribute-neg-in 89.8%

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

   11. unsub-neg 89.8%

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

   12. remove-double-neg 89.8%

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

3. Simplified 89.8%

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

4. Taylor expanded in x around inf 53.9%

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

5. Final simplification 53.9%

   \[\leadsto x \]

Developer target: 87.6% 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 2023257 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (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))))