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

Percentage Accurate: 76.9% → 90.7%

Time: 10.7s

Alternatives: 17

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: 76.9% 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: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+114} \lor \neg \left(t \leq 1.32 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+114) (not (<= t 1.32e+41)))
   (+ x (- (* y (/ z t)) (* a (/ y t))))
   (fma (- z t) (/ y (- t a)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+114) || !(t <= 1.32e+41)) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else {
		tmp = fma((z - t), (y / (t - a)), (x + y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+114) || !(t <= 1.32e+41))
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) - Float64(a * Float64(y / t))));
	else
		tmp = fma(Float64(z - t), Float64(y / Float64(t - a)), Float64(x + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+114], N[Not[LessEqual[t, 1.32e+41]], $MachinePrecision]], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3e114 or 1.3199999999999999e41 < t

   1. Initial program 49.3%

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

      1. sub-neg 49.3%

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

      2. +-commutative 49.3%

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

      3. distribute-frac-neg 49.3%

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

      4. distribute-rgt-neg-out 49.3%

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

      5. associate-/l* 58.8%

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

      6. fma-define 59.2%

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

      7. distribute-frac-neg 59.2%

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

      8. distribute-neg-frac2 59.2%

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

      9. sub-neg 59.2%

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

      10. distribute-neg-in 59.2%

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

      11. remove-double-neg 59.2%

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

      12. +-commutative 59.2%

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

      13. sub-neg 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in t around inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. associate-+r+ 73.7%

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

      3. distribute-rgt1-in 73.7%

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

      4. metadata-eval 73.7%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      5. mul0-lft 73.7%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      6. associate-/l* 82.7%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      7. associate-/l* 89.8%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 89.8%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]

   if -2.3e114 < t < 1.3199999999999999e41

   1. Initial program 91.4%

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

      1. sub-neg 91.4%

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

      2. +-commutative 91.4%

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

      3. distribute-frac-neg 91.4%

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

      4. distribute-rgt-neg-out 91.4%

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

      5. associate-/l* 92.0%

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

      6. fma-define 92.3%

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

      7. distribute-frac-neg 92.3%

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

      8. distribute-neg-frac2 92.3%

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

      9. sub-neg 92.3%

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

      10. distribute-neg-in 92.3%

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

      11. remove-double-neg 92.3%

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

      12. +-commutative 92.3%

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

      13. sub-neg 92.3%

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

   3. Simplified 92.3%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+114} \lor \neg \left(t \leq 1.32 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{t - a}, x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-238} \lor \neg \left(t\_1 \leq 10^{-196}\right):\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (/ (* y (- t z)) (- a t)))))
   (if (or (<= t_1 -2e-238) (not (<= t_1 1e-196)))
     (+ (+ x y) (* (- 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 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-238) || !(t_1 <= 1e-196)) {
		tmp = (x + y) + ((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 = (x + y) + ((y * (t - z)) / (a - t))
    if ((t_1 <= (-2d-238)) .or. (.not. (t_1 <= 1d-196))) then
        tmp = (x + y) + ((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 = (x + y) + ((y * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-238) || !(t_1 <= 1e-196)) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x + ((y * (z - 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 <= -2e-238) or not (t_1 <= 1e-196):
		tmp = (x + y) + ((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(x + y) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-238) || !(t_1 <= 1e-196))
		tmp = Float64(Float64(x + y) + 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 = (x + y) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -2e-238) || ~((t_1 <= 1e-196)))
		tmp = (x + y) + ((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[(x + y), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-238], N[Not[LessEqual[t$95$1, 1e-196]], $MachinePrecision]], N[(N[(x + y), $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))) < -2e-238 or 1e-196 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 83.6%

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

      1. associate-/l* 88.2%

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

      2. *-commutative 88.2%

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

   4. Applied egg-rr 88.2%

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

   if -2e-238 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1e-196

   1. Initial program 10.8%

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

   3. Taylor expanded in t around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. distribute-lft-out-- 99.9%

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

      3. div-sub 99.8%

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

      4. mul-1-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. *-commutative 99.8%

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

      7. distribute-lft-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -2 \cdot 10^{-238} \lor \neg \left(\left(x + y\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 10^{-196}\right):\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-144}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(\frac{z}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -3.4e+112)
     t_1
     (if (<= t -7e-144)
       (+ x y)
       (if (<= t -1.02e-269)
         (* y (+ (/ z (- t a)) 1.0))
         (if (<= t 5.8e+80) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -3.4e+112) {
		tmp = t_1;
	} else if (t <= -7e-144) {
		tmp = x + y;
	} else if (t <= -1.02e-269) {
		tmp = y * ((z / (t - a)) + 1.0);
	} else if (t <= 5.8e+80) {
		tmp = x + y;
	} 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) :: tmp
    t_1 = x - (a * (y / t))
    if (t <= (-3.4d+112)) then
        tmp = t_1
    else if (t <= (-7d-144)) then
        tmp = x + y
    else if (t <= (-1.02d-269)) then
        tmp = y * ((z / (t - a)) + 1.0d0)
    else if (t <= 5.8d+80) then
        tmp = x + y
    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 = x - (a * (y / t));
	double tmp;
	if (t <= -3.4e+112) {
		tmp = t_1;
	} else if (t <= -7e-144) {
		tmp = x + y;
	} else if (t <= -1.02e-269) {
		tmp = y * ((z / (t - a)) + 1.0);
	} else if (t <= 5.8e+80) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -3.4e+112:
		tmp = t_1
	elif t <= -7e-144:
		tmp = x + y
	elif t <= -1.02e-269:
		tmp = y * ((z / (t - a)) + 1.0)
	elif t <= 5.8e+80:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -3.4e+112)
		tmp = t_1;
	elseif (t <= -7e-144)
		tmp = Float64(x + y);
	elseif (t <= -1.02e-269)
		tmp = Float64(y * Float64(Float64(z / Float64(t - a)) + 1.0));
	elseif (t <= 5.8e+80)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -3.4e+112)
		tmp = t_1;
	elseif (t <= -7e-144)
		tmp = x + y;
	elseif (t <= -1.02e-269)
		tmp = y * ((z / (t - a)) + 1.0);
	elseif (t <= 5.8e+80)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+112], t$95$1, If[LessEqual[t, -7e-144], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.02e-269], N[(y * N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+80], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999993e112 or 5.79999999999999971e80 < t

   1. Initial program 46.7%

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

   3. Taylor expanded in z around 0 42.2%

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

      1. associate--l+ 52.0%

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

      2. sub-neg 52.0%

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

      3. mul-1-neg 52.0%

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

      4. remove-double-neg 52.0%

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

      5. associate-/l* 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in x around inf 45.1%

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

      1. associate-+r+ 40.5%

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

      2. associate-/l* 48.3%

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

      3. associate-/r* 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in t around inf 58.2%

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

       1. +-commutative 58.2%

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

       2. mul-1-neg 58.2%

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

       3. unsub-neg 58.2%

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

       4. distribute-lft1-in 58.2%

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

       5. metadata-eval 58.2%

          \[\leadsto x \cdot \left(1 + \color{blue}{0} \cdot \frac{y}{x}\right) - \frac{a \cdot y}{t} \]

       6. mul0-lft 63.1%

          \[\leadsto x \cdot \left(1 + \color{blue}{0}\right) - \frac{a \cdot y}{t} \]

       7. metadata-eval 63.1%

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

       8. *-rgt-identity 63.1%

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

       9. associate-/l* 71.1%

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

   11. Simplified 71.1%

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

   if -3.39999999999999993e112 < t < -6.9999999999999997e-144 or -1.02000000000000002e-269 < t < 5.79999999999999971e80

   1. Initial program 89.1%

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

   3. Taylor expanded in a around inf 73.2%

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

      1. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -6.9999999999999997e-144 < t < -1.02000000000000002e-269

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 96.4%

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

      1. associate-/l* 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in x around 0 82.1%

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

      1. associate-/l* 82.2%

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

      2. cancel-sign-sub-inv 82.2%

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

      3. *-rgt-identity 82.2%

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

      4. distribute-lft-neg-in 82.2%

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

      5. distribute-rgt-neg-in 82.2%

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

      6. distribute-lft-in 82.2%

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

      7. sub-neg 82.2%

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

   8. Simplified 82.2%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+112}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-144}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(\frac{z}{t - a} + 1\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - a \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* a (/ y t)))))
   (if (<= t -1.9e+105)
     t_1
     (if (<= t -3.1e-142)
       (+ x y)
       (if (<= t -3.1e-268)
         (* y (- 1.0 (/ z a)))
         (if (<= t 5.8e+80) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (a * (y / t));
	double tmp;
	if (t <= -1.9e+105) {
		tmp = t_1;
	} else if (t <= -3.1e-142) {
		tmp = x + y;
	} else if (t <= -3.1e-268) {
		tmp = y * (1.0 - (z / a));
	} else if (t <= 5.8e+80) {
		tmp = x + y;
	} 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) :: tmp
    t_1 = x - (a * (y / t))
    if (t <= (-1.9d+105)) then
        tmp = t_1
    else if (t <= (-3.1d-142)) then
        tmp = x + y
    else if (t <= (-3.1d-268)) then
        tmp = y * (1.0d0 - (z / a))
    else if (t <= 5.8d+80) then
        tmp = x + y
    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 = x - (a * (y / t));
	double tmp;
	if (t <= -1.9e+105) {
		tmp = t_1;
	} else if (t <= -3.1e-142) {
		tmp = x + y;
	} else if (t <= -3.1e-268) {
		tmp = y * (1.0 - (z / a));
	} else if (t <= 5.8e+80) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (a * (y / t))
	tmp = 0
	if t <= -1.9e+105:
		tmp = t_1
	elif t <= -3.1e-142:
		tmp = x + y
	elif t <= -3.1e-268:
		tmp = y * (1.0 - (z / a))
	elif t <= 5.8e+80:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(a * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.9e+105)
		tmp = t_1;
	elseif (t <= -3.1e-142)
		tmp = Float64(x + y);
	elseif (t <= -3.1e-268)
		tmp = Float64(y * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5.8e+80)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (a * (y / t));
	tmp = 0.0;
	if (t <= -1.9e+105)
		tmp = t_1;
	elseif (t <= -3.1e-142)
		tmp = x + y;
	elseif (t <= -3.1e-268)
		tmp = y * (1.0 - (z / a));
	elseif (t <= 5.8e+80)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+105], t$95$1, If[LessEqual[t, -3.1e-142], N[(x + y), $MachinePrecision], If[LessEqual[t, -3.1e-268], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+80], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e105 or 5.79999999999999971e80 < t

   1. Initial program 46.7%

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

   3. Taylor expanded in z around 0 42.2%

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

      1. associate--l+ 52.0%

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

      2. sub-neg 52.0%

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

      3. mul-1-neg 52.0%

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

      4. remove-double-neg 52.0%

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

      5. associate-/l* 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in x around inf 45.1%

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

      1. associate-+r+ 40.5%

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

      2. associate-/l* 48.3%

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

      3. associate-/r* 48.5%

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

   8. Simplified 48.5%

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

   9. Taylor expanded in t around inf 58.2%

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

       1. +-commutative 58.2%

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

       2. mul-1-neg 58.2%

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

       3. unsub-neg 58.2%

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

       4. distribute-lft1-in 58.2%

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

       5. metadata-eval 58.2%

          \[\leadsto x \cdot \left(1 + \color{blue}{0} \cdot \frac{y}{x}\right) - \frac{a \cdot y}{t} \]

       6. mul0-lft 63.1%

          \[\leadsto x \cdot \left(1 + \color{blue}{0}\right) - \frac{a \cdot y}{t} \]

       7. metadata-eval 63.1%

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

       8. *-rgt-identity 63.1%

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

       9. associate-/l* 71.1%

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

   11. Simplified 71.1%

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

   if -1.9e105 < t < -3.1e-142 or -3.0999999999999998e-268 < t < 5.79999999999999971e80

   1. Initial program 89.1%

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

   3. Taylor expanded in a around inf 73.2%

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

      1. +-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -3.1e-142 < t < -3.0999999999999998e-268

   1. Initial program 96.2%

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

   3. Taylor expanded in t around 0 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-/l* 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around inf 78.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+105}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-142}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-268}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+80}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+114} \lor \neg \left(t \leq 1.26 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.1e+114) (not (<= t 1.26e+41)))
   (+ x (- (* y (/ z t)) (* a (/ y t))))
   (+ (+ x y) (* (- z t) (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.1e+114) || !(t <= 1.26e+41)) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else {
		tmp = (x + y) + ((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 <= (-3.1d+114)) .or. (.not. (t <= 1.26d+41))) then
        tmp = x + ((y * (z / t)) - (a * (y / t)))
    else
        tmp = (x + y) + ((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 <= -3.1e+114) || !(t <= 1.26e+41)) {
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.1e+114) or not (t <= 1.26e+41):
		tmp = x + ((y * (z / t)) - (a * (y / t)))
	else:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.1e+114) || !(t <= 1.26e+41))
		tmp = Float64(x + Float64(Float64(y * Float64(z / t)) - Float64(a * Float64(y / t))));
	else
		tmp = Float64(Float64(x + y) + 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 <= -3.1e+114) || ~((t <= 1.26e+41)))
		tmp = x + ((y * (z / t)) - (a * (y / t)));
	else
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.1e+114], N[Not[LessEqual[t, 1.26e+41]], $MachinePrecision]], N[(x + N[(N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $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 < -3.1e114 or 1.26000000000000001e41 < t

   1. Initial program 49.3%

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

      1. sub-neg 49.3%

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

      2. +-commutative 49.3%

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

      3. distribute-frac-neg 49.3%

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

      4. distribute-rgt-neg-out 49.3%

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

      5. associate-/l* 58.8%

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

      6. fma-define 59.2%

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

      7. distribute-frac-neg 59.2%

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

      8. distribute-neg-frac2 59.2%

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

      9. sub-neg 59.2%

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

      10. distribute-neg-in 59.2%

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

      11. remove-double-neg 59.2%

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

      12. +-commutative 59.2%

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

      13. sub-neg 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in t around inf 67.1%

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

      1. associate--l+ 67.1%

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

      2. associate-+r+ 73.7%

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

      3. distribute-rgt1-in 73.7%

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

      4. metadata-eval 73.7%

         \[\leadsto x + \left(\left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      5. mul0-lft 73.7%

         \[\leadsto x + \left(\left(\color{blue}{0} + \frac{y \cdot z}{t}\right) - \frac{a \cdot y}{t}\right) \]

      6. associate-/l* 82.7%

         \[\leadsto x + \left(\left(0 + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t}\right) \]

      7. associate-/l* 89.8%

         \[\leadsto x + \left(\left(0 + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}}\right) \]

   7. Simplified 89.8%

      \[\leadsto \color{blue}{x + \left(\left(0 + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\right)} \]

   if -3.1e114 < t < 1.26000000000000001e41

   1. Initial program 91.4%

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

      1. associate-/l* 92.0%

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

      2. *-commutative 92.0%

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

   4. Applied egg-rr 92.0%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+114} \lor \neg \left(t \leq 1.26 \cdot 10^{+41}\right):\\ \;\;\;\;x + \left(y \cdot \frac{z}{t} - a \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e-102)
   (+ x y)
   (if (<= a 1.2e-250) x (if (<= a 5.1e-102) (* y (/ z (- t a))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-102) {
		tmp = x + y;
	} else if (a <= 1.2e-250) {
		tmp = x;
	} else if (a <= 5.1e-102) {
		tmp = y * (z / (t - 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 (a <= (-2.3d-102)) then
        tmp = x + y
    else if (a <= 1.2d-250) then
        tmp = x
    else if (a <= 5.1d-102) then
        tmp = y * (z / (t - 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 (a <= -2.3e-102) {
		tmp = x + y;
	} else if (a <= 1.2e-250) {
		tmp = x;
	} else if (a <= 5.1e-102) {
		tmp = y * (z / (t - a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e-102:
		tmp = x + y
	elif a <= 1.2e-250:
		tmp = x
	elif a <= 5.1e-102:
		tmp = y * (z / (t - a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e-102)
		tmp = Float64(x + y);
	elseif (a <= 1.2e-250)
		tmp = x;
	elseif (a <= 5.1e-102)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e-102)
		tmp = x + y;
	elseif (a <= 1.2e-250)
		tmp = x;
	elseif (a <= 5.1e-102)
		tmp = y * (z / (t - a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e-102], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.2e-250], x, If[LessEqual[a, 5.1e-102], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.29999999999999987e-102 or 5.09999999999999999e-102 < a

   1. Initial program 79.6%

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

   3. Taylor expanded in a around inf 72.7%

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

      1. +-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -2.29999999999999987e-102 < a < 1.1999999999999999e-250

   1. Initial program 71.9%

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

   3. Taylor expanded in x around inf 67.9%

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

   if 1.1999999999999999e-250 < a < 5.09999999999999999e-102

   1. Initial program 63.4%

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

      1. sub-neg 63.4%

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

      2. +-commutative 63.4%

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

      3. distribute-frac-neg 63.4%

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

      4. distribute-rgt-neg-out 63.4%

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

      5. associate-/l* 65.3%

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

      6. fma-define 65.8%

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

      7. distribute-frac-neg 65.8%

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

      8. distribute-neg-frac2 65.8%

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

      9. sub-neg 65.8%

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

      10. distribute-neg-in 65.8%

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

      11. remove-double-neg 65.8%

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

      12. +-commutative 65.8%

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

      13. sub-neg 65.8%

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

   3. Simplified 65.8%

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

   5. Taylor expanded in z around inf 55.5%

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

      1. associate-/l* 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-250}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-102}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+161}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+40}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e+161)
   (- x (* a (/ y t)))
   (if (<= t 6e+40)
     (+ (+ x y) (* y (/ z (- t a))))
     (+ x (/ (* y (- z a)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e+161) {
		tmp = x - (a * (y / t));
	} else if (t <= 6e+40) {
		tmp = (x + y) + (y * (z / (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) :: tmp
    if (t <= (-4.4d+161)) then
        tmp = x - (a * (y / t))
    else if (t <= 6d+40) then
        tmp = (x + y) + (y * (z / (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 tmp;
	if (t <= -4.4e+161) {
		tmp = x - (a * (y / t));
	} else if (t <= 6e+40) {
		tmp = (x + y) + (y * (z / (t - a)));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e+161:
		tmp = x - (a * (y / t))
	elif t <= 6e+40:
		tmp = (x + y) + (y * (z / (t - a)))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e+161)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif (t <= 6e+40)
		tmp = Float64(Float64(x + y) + Float64(y * Float64(z / 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)
	tmp = 0.0;
	if (t <= -4.4e+161)
		tmp = x - (a * (y / t));
	elseif (t <= 6e+40)
		tmp = (x + y) + (y * (z / (t - a)));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e+161], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+40], N[(N[(x + y), $MachinePrecision] + N[(y * N[(z / 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 3 regimes

2. if t < -4.4e161

   1. Initial program 25.3%

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

   3. Taylor expanded in z around 0 29.0%

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

      1. associate--l+ 40.1%

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

      2. sub-neg 40.1%

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

      3. mul-1-neg 40.1%

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

      4. remove-double-neg 40.1%

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

      5. associate-/l* 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in x around inf 34.9%

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

      1. associate-+r+ 27.6%

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

      2. associate-/l* 39.9%

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

      3. associate-/r* 39.8%

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

   8. Simplified 39.8%

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

   9. Taylor expanded in t around inf 54.8%

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

       1. +-commutative 54.8%

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

       2. mul-1-neg 54.8%

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

       3. unsub-neg 54.8%

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

       4. distribute-lft1-in 54.8%

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

       5. metadata-eval 54.8%

          \[\leadsto x \cdot \left(1 + \color{blue}{0} \cdot \frac{y}{x}\right) - \frac{a \cdot y}{t} \]

       6. mul0-lft 62.5%

          \[\leadsto x \cdot \left(1 + \color{blue}{0}\right) - \frac{a \cdot y}{t} \]

       7. metadata-eval 62.5%

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

       8. *-rgt-identity 62.5%

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

       9. associate-/l* 84.5%

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

   11. Simplified 84.5%

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

   if -4.4e161 < t < 6.0000000000000004e40

   1. Initial program 90.1%

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

   3. Taylor expanded in z around inf 88.9%

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

      1. associate-/l* 87.8%

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

   5. Simplified 87.8%

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

   if 6.0000000000000004e40 < t

   1. Initial program 56.7%

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

   3. Taylor expanded in t around inf 76.5%

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

      1. associate--l+ 76.5%

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

      2. distribute-lft-out-- 76.5%

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

      3. div-sub 76.5%

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

      4. mul-1-neg 76.5%

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

      5. unsub-neg 76.5%

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

      6. *-commutative 76.5%

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

      7. distribute-lft-out-- 76.5%

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

   5. Simplified 76.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+161}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+40}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-88} \lor \neg \left(a \leq 105000000\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.3e-88) (not (<= a 105000000.0)))
   (- (+ 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 <= -4.3e-88) || !(a <= 105000000.0)) {
		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 <= (-4.3d-88)) .or. (.not. (a <= 105000000.0d0))) 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 <= -4.3e-88) || !(a <= 105000000.0)) {
		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 <= -4.3e-88) or not (a <= 105000000.0):
		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 <= -4.3e-88) || !(a <= 105000000.0))
		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 <= -4.3e-88) || ~((a <= 105000000.0)))
		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, -4.3e-88], N[Not[LessEqual[a, 105000000.0]], $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 < -4.2999999999999997e-88 or 1.05e8 < a

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 81.7%

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

      1. +-commutative 81.7%

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

      2. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   if -4.2999999999999997e-88 < a < 1.05e8

   1. Initial program 66.4%

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

   3. Taylor expanded in t around inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. distribute-lft-out-- 78.0%

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

      3. div-sub 79.0%

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

      4. mul-1-neg 79.0%

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

      5. unsub-neg 79.0%

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

      6. *-commutative 79.0%

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

      7. distribute-lft-out-- 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{-88} \lor \neg \left(a \leq 105000000\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+20} \lor \neg \left(a \leq 10^{+111}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.5e+20) (not (<= a 1e+111)))
   (+ x y)
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e+20) || !(a <= 1e+111)) {
		tmp = x + y;
	} 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 <= (-2.5d+20)) .or. (.not. (a <= 1d+111))) then
        tmp = x + y
    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 <= -2.5e+20) || !(a <= 1e+111)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.5e+20) or not (a <= 1e+111):
		tmp = x + y
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.5e+20) || !(a <= 1e+111))
		tmp = Float64(x + y);
	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 <= -2.5e+20) || ~((a <= 1e+111)))
		tmp = x + y;
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.5e+20], N[Not[LessEqual[a, 1e+111]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5e20 or 9.99999999999999957e110 < a

   1. Initial program 82.0%

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

   3. Taylor expanded in a around inf 86.0%

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

      1. +-commutative 86.0%

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

   5. Simplified 86.0%

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

   if -2.5e20 < a < 9.99999999999999957e110

   1. Initial program 71.5%

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

   3. Taylor expanded in t around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. distribute-lft-out-- 72.7%

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

      3. div-sub 74.1%

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

      4. mul-1-neg 74.1%

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

      5. unsub-neg 74.1%

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

      6. *-commutative 74.1%

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

      7. distribute-lft-out-- 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+20} \lor \neg \left(a \leq 10^{+111}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-69}:\\ \;\;\;\;x + \left(y + t \cdot \frac{y}{a - t}\right)\\ \mathbf{elif}\;a \leq 105000000:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e-69)
   (+ x (+ y (* t (/ y (- a t)))))
   (if (<= a 105000000.0)
     (+ x (/ (* y (- z a)) t))
     (- (+ x y) (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e-69) {
		tmp = x + (y + (t * (y / (a - t))));
	} else if (a <= 105000000.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (y * (z / 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 (a <= (-2d-69)) then
        tmp = x + (y + (t * (y / (a - t))))
    else if (a <= 105000000.0d0) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = (x + y) - (y * (z / 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 (a <= -2e-69) {
		tmp = x + (y + (t * (y / (a - t))));
	} else if (a <= 105000000.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e-69:
		tmp = x + (y + (t * (y / (a - t))))
	elif a <= 105000000.0:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = (x + y) - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e-69)
		tmp = Float64(x + Float64(y + Float64(t * Float64(y / Float64(a - t)))));
	elseif (a <= 105000000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e-69)
		tmp = x + (y + (t * (y / (a - t))));
	elseif (a <= 105000000.0)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = (x + y) - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e-69], N[(x + N[(y + N[(t * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 105000000.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.9999999999999999e-69

   1. Initial program 80.4%

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

   3. Taylor expanded in z around 0 78.2%

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

      1. associate--l+ 80.4%

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

      2. sub-neg 80.4%

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

      3. mul-1-neg 80.4%

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

      4. remove-double-neg 80.4%

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

      5. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

   if -1.9999999999999999e-69 < a < 1.05e8

   1. Initial program 68.3%

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

   3. Taylor expanded in t around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. distribute-lft-out-- 77.1%

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

      3. div-sub 78.1%

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

      4. mul-1-neg 78.1%

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

      5. unsub-neg 78.1%

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

      6. *-commutative 78.1%

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

      7. distribute-lft-out-- 78.1%

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

   5. Simplified 78.1%

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

   if 1.05e8 < a

   1. Initial program 83.5%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-69}:\\ \;\;\;\;x + \left(y + t \cdot \frac{y}{a - t}\right)\\ \mathbf{elif}\;a \leq 105000000:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+274}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+274)
   (/ (* y (- z)) a)
   (if (<= z 5.3e+171) (+ x y) (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+274) {
		tmp = (y * -z) / a;
	} else if (z <= 5.3e+171) {
		tmp = x + y;
	} 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 (z <= (-2d+274)) then
        tmp = (y * -z) / a
    else if (z <= 5.3d+171) then
        tmp = x + y
    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 (z <= -2e+274) {
		tmp = (y * -z) / a;
	} else if (z <= 5.3e+171) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+274:
		tmp = (y * -z) / a
	elif z <= 5.3e+171:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+274)
		tmp = Float64(Float64(y * Float64(-z)) / a);
	elseif (z <= 5.3e+171)
		tmp = Float64(x + y);
	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 (z <= -2e+274)
		tmp = (y * -z) / a;
	elseif (z <= 5.3e+171)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+274], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 5.3e+171], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999984e274

   1. Initial program 79.3%

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

      1. sub-neg 79.3%

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

      2. +-commutative 79.3%

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

      3. distribute-frac-neg 79.3%

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

      4. distribute-rgt-neg-out 79.3%

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

      5. associate-/l* 99.7%

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

      6. fma-define 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-frac2 99.7%

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

      9. sub-neg 99.7%

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

      10. distribute-neg-in 99.7%

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

      11. remove-double-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 79.3%

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

   6. Taylor expanded in t around 0 66.8%

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

      1. associate-*r/ 66.8%

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

      2. associate-*r* 66.8%

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

      3. neg-mul-1 66.8%

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

   8. Simplified 66.8%

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

   if -1.99999999999999984e274 < z < 5.29999999999999982e171

   1. Initial program 76.2%

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

   3. Taylor expanded in a around inf 67.3%

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

      1. +-commutative 67.3%

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

   5. Simplified 67.3%

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

   if 5.29999999999999982e171 < z

   1. Initial program 71.8%

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

      1. sub-neg 71.8%

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

      2. +-commutative 71.8%

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

      3. distribute-frac-neg 71.8%

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

      4. distribute-rgt-neg-out 71.8%

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

      5. associate-/l* 80.6%

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

      6. fma-define 80.4%

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

      7. distribute-frac-neg 80.4%

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

      8. distribute-neg-frac2 80.4%

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

      9. sub-neg 80.4%

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

      10. distribute-neg-in 80.4%

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

      11. remove-double-neg 80.4%

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

      12. +-commutative 80.4%

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

      13. sub-neg 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   6. Taylor expanded in t around inf 54.7%

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

      1. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+274}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+171}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+277}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.25e+277)
   (* y (/ (- z) a))
   (if (<= z 4.45e+170) (+ x y) (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.25e+277) {
		tmp = y * (-z / a);
	} else if (z <= 4.45e+170) {
		tmp = x + y;
	} 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 (z <= (-1.25d+277)) then
        tmp = y * (-z / a)
    else if (z <= 4.45d+170) then
        tmp = x + y
    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 (z <= -1.25e+277) {
		tmp = y * (-z / a);
	} else if (z <= 4.45e+170) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.25e+277:
		tmp = y * (-z / a)
	elif z <= 4.45e+170:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.25e+277)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (z <= 4.45e+170)
		tmp = Float64(x + y);
	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 (z <= -1.25e+277)
		tmp = y * (-z / a);
	elseif (z <= 4.45e+170)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.25e+277], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.45e+170], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999995e277

   1. Initial program 79.3%

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

   3. Taylor expanded in x around inf 68.8%

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

   4. Taylor expanded in z around inf 68.8%

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

      1. associate-*r/ 68.8%

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

      2. associate-*r* 68.8%

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

      3. *-commutative 68.8%

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

      4. times-frac 58.0%

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

      5. neg-mul-1 58.0%

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

      6. distribute-neg-frac 58.0%

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

      7. distribute-neg-frac2 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in a around inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-/l* 56.2%

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

      3. distribute-rgt-neg-in 56.2%

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

   9. Simplified 56.2%

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

   if -1.24999999999999995e277 < z < 4.45e170

   1. Initial program 76.2%

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

   3. Taylor expanded in a around inf 67.3%

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

      1. +-commutative 67.3%

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

   5. Simplified 67.3%

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

   if 4.45e170 < z

   1. Initial program 71.8%

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

      1. sub-neg 71.8%

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

      2. +-commutative 71.8%

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

      3. distribute-frac-neg 71.8%

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

      4. distribute-rgt-neg-out 71.8%

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

      5. associate-/l* 80.6%

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

      6. fma-define 80.4%

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

      7. distribute-frac-neg 80.4%

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

      8. distribute-neg-frac2 80.4%

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

      9. sub-neg 80.4%

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

      10. distribute-neg-in 80.4%

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

      11. remove-double-neg 80.4%

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

      12. +-commutative 80.4%

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

      13. sub-neg 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   6. Taylor expanded in t around inf 54.7%

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

      1. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+277}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-100} \lor \neg \left(a \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.05e-100) (not (<= a 9.5e-8))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e-100) || !(a <= 9.5e-8)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	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 <= (-1.05d-100)) .or. (.not. (a <= 9.5d-8))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e-100) || !(a <= 9.5e-8)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.05e-100) or not (a <= 9.5e-8):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.05e-100) || !(a <= 9.5e-8))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.05e-100) || ~((a <= 9.5e-8)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.05e-100], N[Not[LessEqual[a, 9.5e-8]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.05000000000000005e-100 or 9.50000000000000036e-8 < a

   1. Initial program 80.3%

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

   3. Taylor expanded in a around inf 75.1%

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

      1. +-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -1.05000000000000005e-100 < a < 9.50000000000000036e-8

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 52.6%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-100} \lor \neg \left(a \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{-154}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-147}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5.9e-154) x (if (<= x 2.6e-147) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.9e-154) {
		tmp = x;
	} else if (x <= 2.6e-147) {
		tmp = y;
	} else {
		tmp = x;
	}
	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 <= (-5.9d-154)) then
        tmp = x
    else if (x <= 2.6d-147) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.9e-154) {
		tmp = x;
	} else if (x <= 2.6e-147) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.9e-154:
		tmp = x
	elif x <= 2.6e-147:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.9e-154)
		tmp = x;
	elseif (x <= 2.6e-147)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.9e-154)
		tmp = x;
	elseif (x <= 2.6e-147)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.9e-154], x, If[LessEqual[x, 2.6e-147], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9000000000000003e-154 or 2.5999999999999999e-147 < x

   1. Initial program 81.1%

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

   3. Taylor expanded in x around inf 60.1%

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

   if -5.9000000000000003e-154 < x < 2.5999999999999999e-147

   1. Initial program 62.7%

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

   3. Taylor expanded in x around inf 38.0%

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

   4. Taylor expanded in a around inf 31.9%

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

   5. Taylor expanded in x around 0 41.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 60.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.3 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 5.3e+170) (+ x y) (* y (/ z t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 5.3e+170) {
		tmp = x + y;
	} 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 (z <= 5.3d+170) then
        tmp = x + y
    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 (z <= 5.3e+170) {
		tmp = x + y;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 5.3e+170:
		tmp = x + y
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 5.3e+170)
		tmp = Float64(x + y);
	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 (z <= 5.3e+170)
		tmp = x + y;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 5.3e+170], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.30000000000000003e170

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 64.9%

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

      1. +-commutative 64.9%

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

   5. Simplified 64.9%

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

   if 5.30000000000000003e170 < z

   1. Initial program 71.8%

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

      1. sub-neg 71.8%

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

      2. +-commutative 71.8%

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

      3. distribute-frac-neg 71.8%

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

      4. distribute-rgt-neg-out 71.8%

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

      5. associate-/l* 80.6%

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

      6. fma-define 80.4%

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

      7. distribute-frac-neg 80.4%

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

      8. distribute-neg-frac2 80.4%

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

      9. sub-neg 80.4%

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

      10. distribute-neg-in 80.4%

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

      11. remove-double-neg 80.4%

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

      12. +-commutative 80.4%

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

      13. sub-neg 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   6. Taylor expanded in t around inf 54.7%

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

      1. associate-/l* 63.6%

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

   8. Simplified 63.6%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.3 \cdot 10^{+170}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.0% 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 75.9%

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

3. Taylor expanded in x around inf 47.9%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Alternative 17: 2.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 75.9%

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

3. Taylor expanded in z around 0 61.7%

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

   1. associate--l+ 65.7%

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

   2. sub-neg 65.7%

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

   3. mul-1-neg 65.7%

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

   4. remove-double-neg 65.7%

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

   5. associate-/l* 68.5%

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

5. Simplified 68.5%

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

6. Taylor expanded in x around 0 23.7%

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

7. Taylor expanded in t around inf 2.8%

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

   1. distribute-rgt1-in 2.8%

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

   2. metadata-eval 2.8%

      \[\leadsto \color{blue}{0} \cdot y \]

   3. mul0-lft 2.8%

      \[\leadsto \color{blue}{0} \]

9. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]
10. Add Preprocessing

Developer target: 87.9% 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 2024103 
(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))))