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

Percentage Accurate: 77.0% → 90.1%

Time: 11.9s

Alternatives: 13

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% 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: 90.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-224}:\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \left(\left(z - t\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -2e-224)
     (+ (+ x y) (/ (- z t) (/ (- t a) y)))
     (if (<= t_1 0.0)
       (- x (/ (* y (- a z)) t))
       (- (+ x y) (* y (* (- z t) (/ -1.0 (- t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-224) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) - (y * ((z - t) * (-1.0 / (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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-2d-224)) then
        tmp = (x + y) + ((z - t) / ((t - a) / y))
    else if (t_1 <= 0.0d0) then
        tmp = x - ((y * (a - z)) / t)
    else
        tmp = (x + y) - (y * ((z - t) * ((-1.0d0) / (t - a))))
    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 * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-224) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) - (y * ((z - t) * (-1.0 / (t - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -2e-224:
		tmp = (x + y) + ((z - t) / ((t - a) / y))
	elif t_1 <= 0.0:
		tmp = x - ((y * (a - z)) / t)
	else:
		tmp = (x + y) - (y * ((z - t) * (-1.0 / (t - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -2e-224)
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) / Float64(Float64(t - a) / y)));
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(y * Float64(Float64(z - t) * Float64(-1.0 / Float64(t - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -2e-224)
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	elseif (t_1 <= 0.0)
		tmp = x - ((y * (a - z)) / t);
	else
		tmp = (x + y) - (y * ((z - t) * (-1.0 / (t - a))));
	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[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-224], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(y * N[(N[(z - t), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-224

   1. Initial program 82.9%

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

      1. clear-num 82.9%

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

      2. inv-pow 82.9%

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

      3. *-commutative 82.9%

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

      4. associate-/r* 90.1%

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

   4. Applied egg-rr 90.1%

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

      1. unpow-1 90.1%

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

      2. clear-num 90.1%

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

      3. div-sub 90.0%

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

   6. Applied egg-rr 90.0%

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

      1. div-sub 90.1%

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

   8. Simplified 90.1%

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

   if -2e-224 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 8.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-lft-out-- 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 81.3%

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

      1. div-inv 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l* 92.8%

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

   4. Applied egg-rr 92.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-224}:\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \left(\left(z - t\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ t_2 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-224}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ x y) (* (- z t) (/ y (- t a)))))
        (t_2 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_2 -2e-224)
     t_1
     (if (<= t_2 0.0)
       (- x (/ (* y (- a z)) t))
       (if (<= t_2 2e+303) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) + ((z - t) * (y / (t - a)));
	double t_2 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-224) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t_2 <= 2e+303) {
		tmp = t_2;
	} 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 = (x + y) + ((z - t) * (y / (t - a)))
    t_2 = (x + y) - ((y * (z - t)) / (a - t))
    if (t_2 <= (-2d-224)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = x - ((y * (a - z)) / t)
    else if (t_2 <= 2d+303) then
        tmp = t_2
    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 + y) + ((z - t) * (y / (t - a)));
	double t_2 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -2e-224) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t_2 <= 2e+303) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) + ((z - t) * (y / (t - a)))
	t_2 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -2e-224:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = x - ((y * (a - z)) / t)
	elif t_2 <= 2e+303:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -2e-224)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	elseif (t_2 <= 2e+303)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) + ((z - t) * (y / (t - a)));
	t_2 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -2e-224)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = x - ((y * (a - z)) / t);
	elseif (t_2 <= 2e+303)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-224], t$95$1, If[LessEqual[t$95$2, 0.0], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+303], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2e-224 or 2e303 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 72.1%

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

   3. Taylor expanded in y around 0 72.1%

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

      1. associate-*l/ 87.7%

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

   5. Simplified 87.7%

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

   if -2e-224 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 8.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. *-commutative 99.9%

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

      7. distribute-lft-out-- 99.9%

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

   5. Simplified 99.9%

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

   if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 2e303

   1. Initial program 96.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-224}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-224} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (or (<= t_1 -2e-224) (not (<= t_1 0.0)))
     (+ (+ x y) (/ (- z t) (/ (- t a) y)))
     (- x (/ (* y (- a z)) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-224) || !(t_1 <= 0.0)) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else {
		tmp = x - ((y * (a - 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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - ((y * (z - t)) / (a - t))
    if ((t_1 <= (-2d-224)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = (x + y) + ((z - t) / ((t - a) / y))
    else
        tmp = x - ((y * (a - z)) / 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 * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -2e-224) || !(t_1 <= 0.0)) {
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -2e-224) or not (t_1 <= 0.0):
		tmp = (x + y) + ((z - t) / ((t - a) / y))
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= -2e-224) || !(t_1 <= 0.0))
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) / Float64(Float64(t - a) / y)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -2e-224) || ~((t_1 <= 0.0)))
		tmp = (x + y) + ((z - t) / ((t - a) / y));
	else
		tmp = x - ((y * (a - z)) / 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[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-224], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $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-224 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 82.1%

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

      1. clear-num 82.0%

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

      2. inv-pow 82.0%

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

      3. *-commutative 82.0%

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

      4. associate-/r* 90.2%

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

   4. Applied egg-rr 90.2%

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

      1. unpow-1 90.2%

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

      2. clear-num 90.3%

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

      3. div-sub 90.2%

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

   6. Applied egg-rr 90.2%

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

      1. div-sub 90.3%

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

   8. Simplified 90.3%

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

   if -2e-224 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 8.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 99.9%

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

      4. mul-1-neg 99.9%

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

      5. unsub-neg 99.9%

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

      6. *-commutative 99.9%

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

      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 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-224} \lor \neg \left(\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\left(x + y\right) + \frac{z - t}{\frac{t - a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;a \leq -6.3 \cdot 10^{-195}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= a -6.3e-195)
     (+ x y)
     (if (<= a 9.5e-271)
       t_1
       (if (<= a 3.1e-213) x (if (<= a 5e-113) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (a <= -6.3e-195) {
		tmp = x + y;
	} else if (a <= 9.5e-271) {
		tmp = t_1;
	} else if (a <= 3.1e-213) {
		tmp = x;
	} else if (a <= 5e-113) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (a <= (-6.3d-195)) then
        tmp = x + y
    else if (a <= 9.5d-271) then
        tmp = t_1
    else if (a <= 3.1d-213) then
        tmp = x
    else if (a <= 5d-113) then
        tmp = t_1
    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 t_1 = y * (z / (t - a));
	double tmp;
	if (a <= -6.3e-195) {
		tmp = x + y;
	} else if (a <= 9.5e-271) {
		tmp = t_1;
	} else if (a <= 3.1e-213) {
		tmp = x;
	} else if (a <= 5e-113) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if a <= -6.3e-195:
		tmp = x + y
	elif a <= 9.5e-271:
		tmp = t_1
	elif a <= 3.1e-213:
		tmp = x
	elif a <= 5e-113:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (a <= -6.3e-195)
		tmp = Float64(x + y);
	elseif (a <= 9.5e-271)
		tmp = t_1;
	elseif (a <= 3.1e-213)
		tmp = x;
	elseif (a <= 5e-113)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (a <= -6.3e-195)
		tmp = x + y;
	elseif (a <= 9.5e-271)
		tmp = t_1;
	elseif (a <= 3.1e-213)
		tmp = x;
	elseif (a <= 5e-113)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.3e-195], N[(x + y), $MachinePrecision], If[LessEqual[a, 9.5e-271], t$95$1, If[LessEqual[a, 3.1e-213], x, If[LessEqual[a, 5e-113], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.3e-195 or 4.9999999999999997e-113 < a

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -6.3e-195 < a < 9.50000000000000103e-271 or 3.0999999999999998e-213 < a < 4.9999999999999997e-113

   1. Initial program 66.6%

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

      1. sub-neg 66.6%

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

      2. +-commutative 66.6%

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

      3. distribute-frac-neg 66.6%

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

      4. distribute-rgt-neg-out 66.6%

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

      5. associate-/l* 75.4%

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

      6. fma-define 75.4%

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

      7. distribute-frac-neg 75.4%

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

      8. distribute-neg-frac2 75.4%

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

      9. sub-neg 75.4%

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

      10. distribute-neg-in 75.4%

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

      11. remove-double-neg 75.4%

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

      12. +-commutative 75.4%

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

      13. sub-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around inf 58.9%

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

      1. associate-/l* 67.2%

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

   7. Simplified 67.2%

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

   if 9.50000000000000103e-271 < a < 3.0999999999999998e-213

   1. Initial program 66.0%

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

   3. Taylor expanded in x around inf 70.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.3 \cdot 10^{-195}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-177}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-177)
   (+ x y)
   (if (<= a 8.6e-271)
     (* y (/ z (- t a)))
     (if (<= a 8.5e-213) x (if (<= a 5.5e-113) (* y (/ (- z a) t)) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-177) {
		tmp = x + y;
	} else if (a <= 8.6e-271) {
		tmp = y * (z / (t - a));
	} else if (a <= 8.5e-213) {
		tmp = x;
	} else if (a <= 5.5e-113) {
		tmp = y * ((z - a) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.8d-177)) then
        tmp = x + y
    else if (a <= 8.6d-271) then
        tmp = y * (z / (t - a))
    else if (a <= 8.5d-213) then
        tmp = x
    else if (a <= 5.5d-113) then
        tmp = y * ((z - a) / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-177) {
		tmp = x + y;
	} else if (a <= 8.6e-271) {
		tmp = y * (z / (t - a));
	} else if (a <= 8.5e-213) {
		tmp = x;
	} else if (a <= 5.5e-113) {
		tmp = y * ((z - a) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e-177:
		tmp = x + y
	elif a <= 8.6e-271:
		tmp = y * (z / (t - a))
	elif a <= 8.5e-213:
		tmp = x
	elif a <= 5.5e-113:
		tmp = y * ((z - a) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e-177)
		tmp = Float64(x + y);
	elseif (a <= 8.6e-271)
		tmp = Float64(y * Float64(z / Float64(t - a)));
	elseif (a <= 8.5e-213)
		tmp = x;
	elseif (a <= 5.5e-113)
		tmp = Float64(y * Float64(Float64(z - a) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e-177)
		tmp = x + y;
	elseif (a <= 8.6e-271)
		tmp = y * (z / (t - a));
	elseif (a <= 8.5e-213)
		tmp = x;
	elseif (a <= 5.5e-113)
		tmp = y * ((z - a) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e-177], N[(x + y), $MachinePrecision], If[LessEqual[a, 8.6e-271], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-213], x, If[LessEqual[a, 5.5e-113], N[(y * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.79999999999999991e-177 or 5.50000000000000053e-113 < a

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -1.79999999999999991e-177 < a < 8.6e-271

   1. Initial program 65.9%

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

      1. sub-neg 65.9%

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

      2. +-commutative 65.9%

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

      3. distribute-frac-neg 65.9%

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

      4. distribute-rgt-neg-out 65.9%

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

      5. associate-/l* 75.1%

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

      6. fma-define 75.3%

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

      7. distribute-frac-neg 75.3%

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

      8. distribute-neg-frac2 75.3%

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

      9. sub-neg 75.3%

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

      10. distribute-neg-in 75.3%

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

      11. remove-double-neg 75.3%

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

      12. +-commutative 75.3%

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

      13. sub-neg 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

   if 8.6e-271 < a < 8.49999999999999994e-213

   1. Initial program 66.0%

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

   3. Taylor expanded in x around inf 70.3%

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

   if 8.49999999999999994e-213 < a < 5.50000000000000053e-113

   1. Initial program 67.5%

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

      1. sub-neg 67.5%

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

      2. +-commutative 67.5%

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

      3. distribute-frac-neg 67.5%

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

      4. distribute-rgt-neg-out 67.5%

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

      5. associate-/l* 75.8%

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

      6. fma-define 75.6%

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

      7. distribute-frac-neg 75.6%

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

      8. distribute-neg-frac2 75.6%

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

      9. sub-neg 75.6%

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

      10. distribute-neg-in 75.6%

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

      11. remove-double-neg 75.6%

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

      12. +-commutative 75.6%

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

      13. sub-neg 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in t around inf 75.8%

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

      1. associate-+r+ 83.8%

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

      2. distribute-rgt1-in 83.8%

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

      3. metadata-eval 83.8%

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

      4. mul0-lft 83.8%

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

      5. associate-+r+ 83.8%

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

      6. associate-/l* 95.3%

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

      7. associate-/l* 91.1%

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

   7. Simplified 91.1%

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

   8. Taylor expanded in y around inf 64.7%

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

      1. div-sub 64.7%

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

   10. Simplified 64.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-177}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-213}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -5 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-212}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= a -5e-187)
     (+ x y)
     (if (<= a 7e-271)
       t_1
       (if (<= a 6e-212) x (if (<= a 4.9e-113) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / t);
	double tmp;
	if (a <= -5e-187) {
		tmp = x + y;
	} else if (a <= 7e-271) {
		tmp = t_1;
	} else if (a <= 6e-212) {
		tmp = x;
	} else if (a <= 4.9e-113) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if (a <= (-5d-187)) then
        tmp = x + y
    else if (a <= 7d-271) then
        tmp = t_1
    else if (a <= 6d-212) then
        tmp = x
    else if (a <= 4.9d-113) then
        tmp = t_1
    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 t_1 = y * (z / t);
	double tmp;
	if (a <= -5e-187) {
		tmp = x + y;
	} else if (a <= 7e-271) {
		tmp = t_1;
	} else if (a <= 6e-212) {
		tmp = x;
	} else if (a <= 4.9e-113) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / t)
	tmp = 0
	if a <= -5e-187:
		tmp = x + y
	elif a <= 7e-271:
		tmp = t_1
	elif a <= 6e-212:
		tmp = x
	elif a <= 4.9e-113:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (a <= -5e-187)
		tmp = Float64(x + y);
	elseif (a <= 7e-271)
		tmp = t_1;
	elseif (a <= 6e-212)
		tmp = x;
	elseif (a <= 4.9e-113)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / t);
	tmp = 0.0;
	if (a <= -5e-187)
		tmp = x + y;
	elseif (a <= 7e-271)
		tmp = t_1;
	elseif (a <= 6e-212)
		tmp = x;
	elseif (a <= 4.9e-113)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e-187], N[(x + y), $MachinePrecision], If[LessEqual[a, 7e-271], t$95$1, If[LessEqual[a, 6e-212], x, If[LessEqual[a, 4.9e-113], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.9999999999999996e-187 or 4.9000000000000003e-113 < a

   1. Initial program 79.2%

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

   3. Taylor expanded in a around inf 71.3%

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

      1. +-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -4.9999999999999996e-187 < a < 6.9999999999999999e-271 or 6.0000000000000005e-212 < a < 4.9000000000000003e-113

   1. Initial program 66.6%

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

      1. sub-neg 66.6%

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

      2. +-commutative 66.6%

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

      3. distribute-frac-neg 66.6%

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

      4. distribute-rgt-neg-out 66.6%

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

      5. associate-/l* 75.4%

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

      6. fma-define 75.4%

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

      7. distribute-frac-neg 75.4%

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

      8. distribute-neg-frac2 75.4%

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

      9. sub-neg 75.4%

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

      10. distribute-neg-in 75.4%

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

      11. remove-double-neg 75.4%

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

      12. +-commutative 75.4%

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

      13. sub-neg 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in z around inf 58.9%

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

   6. Taylor expanded in t around inf 55.3%

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

      1. associate-*r/ 63.6%

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

   8. Simplified 63.6%

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

   if 6.9999999999999999e-271 < a < 6.0000000000000005e-212

   1. Initial program 66.0%

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

   3. Taylor expanded in x around inf 70.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-187}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-212}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-69} \lor \neg \left(a \leq 7.2 \cdot 10^{-124}\right):\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.3e-69) (not (<= a 7.2e-124)))
   (+ (+ x y) (* (- z t) (/ y (- t a))))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e-69) || !(a <= 7.2e-124)) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x - ((y * (a - 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 ((a <= (-2.3d-69)) .or. (.not. (a <= 7.2d-124))) then
        tmp = (x + y) + ((z - t) * (y / (t - a)))
    else
        tmp = x - ((y * (a - 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 ((a <= -2.3e-69) || !(a <= 7.2e-124)) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.3e-69) or not (a <= 7.2e-124):
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.3e-69) || !(a <= 7.2e-124))
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.3e-69) || ~((a <= 7.2e-124)))
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.3e-69], N[Not[LessEqual[a, 7.2e-124]], $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[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3000000000000001e-69 or 7.20000000000000019e-124 < a

   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 y around 0 80.4%

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

      1. associate-*l/ 88.9%

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

   5. Simplified 88.9%

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

   if -2.3000000000000001e-69 < a < 7.20000000000000019e-124

   1. Initial program 67.5%

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

   3. Taylor expanded in t around inf 82.1%

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

      1. associate--l+ 82.1%

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

      2. distribute-lft-out-- 82.1%

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

      3. div-sub 83.2%

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

      4. mul-1-neg 83.2%

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

      5. unsub-neg 83.2%

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

      6. *-commutative 83.2%

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

      7. distribute-lft-out-- 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-69} \lor \neg \left(a \leq 7.2 \cdot 10^{-124}\right):\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-56} \lor \neg \left(a \leq 1.75 \cdot 10^{+48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e-56) (not (<= a 1.75e+48)))
   (+ x y)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-56) || !(a <= 1.75e+48)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - 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 ((a <= (-1.8d-56)) .or. (.not. (a <= 1.75d+48))) then
        tmp = x + y
    else
        tmp = x - ((y * (a - 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 ((a <= -1.8e-56) || !(a <= 1.75e+48)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e-56) or not (a <= 1.75e+48):
		tmp = x + y
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e-56) || !(a <= 1.75e+48))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e-56) || ~((a <= 1.75e+48)))
		tmp = x + y;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e-56], N[Not[LessEqual[a, 1.75e+48]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999989e-56 or 1.7499999999999999e48 < a

   1. Initial program 79.8%

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

   3. Taylor expanded in a around inf 81.4%

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

      1. +-commutative 81.4%

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

   5. Simplified 81.4%

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

   if -1.79999999999999989e-56 < a < 1.7499999999999999e48

   1. Initial program 72.3%

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

   3. Taylor expanded in t around inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. distribute-lft-out-- 76.1%

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

      3. div-sub 77.6%

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

      4. mul-1-neg 77.6%

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

      5. unsub-neg 77.6%

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

      6. *-commutative 77.6%

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

      7. distribute-lft-out-- 77.6%

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

   5. Simplified 77.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-56} \lor \neg \left(a \leq 1.75 \cdot 10^{+48}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{-65} \lor \neg \left(a \leq 1.35 \cdot 10^{-65}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.56e-65) (not (<= a 1.35e-65)))
   (- (+ x y) (* y (/ z a)))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.56e-65) || !(a <= 1.35e-65)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - 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 ((a <= (-1.56d-65)) .or. (.not. (a <= 1.35d-65))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x - ((y * (a - 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 ((a <= -1.56e-65) || !(a <= 1.35e-65)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.56e-65) or not (a <= 1.35e-65):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.56e-65) || !(a <= 1.35e-65))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.56e-65) || ~((a <= 1.35e-65)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.56e-65], N[Not[LessEqual[a, 1.35e-65]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55999999999999993e-65 or 1.3499999999999999e-65 < a

   1. Initial program 79.2%

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

   3. Taylor expanded in t around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. associate-/l* 84.4%

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

   5. Simplified 84.4%

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

   if -1.55999999999999993e-65 < a < 1.3499999999999999e-65

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 80.3%

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

      1. associate--l+ 80.3%

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

      2. distribute-lft-out-- 80.3%

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

      3. div-sub 82.0%

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

      4. mul-1-neg 82.0%

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

      5. unsub-neg 82.0%

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

      6. *-commutative 82.0%

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

      7. distribute-lft-out-- 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{-65} \lor \neg \left(a \leq 1.35 \cdot 10^{-65}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-55} \lor \neg \left(a \leq 3.65 \cdot 10^{-65}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e-55) (not (<= a 3.65e-65))) (+ x y) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e-55) || !(a <= 3.65e-65)) {
		tmp = x + y;
	} else {
		tmp = x + ((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 ((a <= (-2.2d-55)) .or. (.not. (a <= 3.65d-65))) then
        tmp = x + y
    else
        tmp = x + ((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 ((a <= -2.2e-55) || !(a <= 3.65e-65)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e-55) or not (a <= 3.65e-65):
		tmp = x + y
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e-55) || !(a <= 3.65e-65))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e-55) || ~((a <= 3.65e-65)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.2e-55], N[Not[LessEqual[a, 3.65e-65]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2e-55 or 3.6499999999999999e-65 < a

   1. Initial program 79.0%

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

   3. Taylor expanded in a around inf 77.7%

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

      1. +-commutative 77.7%

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

   5. Simplified 77.7%

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

   if -2.2e-55 < a < 3.6499999999999999e-65

   1. Initial program 71.6%

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

      1. sub-neg 71.6%

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

      2. +-commutative 71.6%

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

      3. distribute-frac-neg 71.6%

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

      4. distribute-rgt-neg-out 71.6%

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

      5. associate-/l* 75.9%

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

      6. fma-define 76.1%

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

      7. distribute-frac-neg 76.1%

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

      8. distribute-neg-frac2 76.1%

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

      9. sub-neg 76.1%

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

      10. distribute-neg-in 76.1%

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

      11. remove-double-neg 76.1%

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

      12. +-commutative 76.1%

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

      13. sub-neg 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in t around inf 73.5%

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

      1. associate-+r+ 79.6%

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

      2. distribute-rgt1-in 79.6%

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

      3. metadata-eval 79.6%

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

      4. mul0-lft 79.6%

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

      5. associate-+r+ 79.6%

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

      6. associate-/l* 85.9%

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

      7. associate-/l* 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in a around 0 76.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{-55} \lor \neg \left(a \leq 3.65 \cdot 10^{-65}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-5} \lor \neg \left(a \leq 1.8 \cdot 10^{-199}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.4e-5) (not (<= a 1.8e-199))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.4e-5) || !(a <= 1.8e-199)) {
		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 <= (-3.4d-5)) .or. (.not. (a <= 1.8d-199))) 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 <= -3.4e-5) || !(a <= 1.8e-199)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.4e-5) or not (a <= 1.8e-199):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.4e-5) || !(a <= 1.8e-199))
		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 <= -3.4e-5) || ~((a <= 1.8e-199)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.4e-5], N[Not[LessEqual[a, 1.8e-199]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.4e-5 or 1.8000000000000001e-199 < a

   1. Initial program 79.0%

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

   3. Taylor expanded in a around inf 71.5%

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

      1. +-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -3.4e-5 < a < 1.8000000000000001e-199

   1. Initial program 69.3%

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

   3. Taylor expanded in x around inf 43.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-5} \lor \neg \left(a \leq 1.8 \cdot 10^{-199}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 75.7%

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

3. Taylor expanded in x around 0 36.8%

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

   1. associate-*r/ 42.9%

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

5. Simplified 42.9%

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

6. Taylor expanded in z around 0 17.6%

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

   1. sub-neg 17.6%

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

   2. mul-1-neg 17.6%

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

   3. remove-double-neg 17.6%

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

   4. associate-/l* 20.3%

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

8. Simplified 20.3%

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

9. Taylor expanded in t around inf 2.7%

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

    1. distribute-rgt1-in 2.7%

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

    2. metadata-eval 2.7%

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

    3. mul0-lft 2.7%

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

11. Simplified 2.7%

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

12. Final simplification 2.7%

    \[\leadsto 0 \]
13. Add Preprocessing

Alternative 13: 50.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.7%

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

3. Taylor expanded in x around inf 47.9%

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

4. Final simplification 47.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 88.3% 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 2024066 
(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))))