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

Percentage Accurate: 77.9% → 93.8%

Time: 8.9s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.9% 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: 93.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x - y \cdot \left(\frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (* y (+ (/ z (- a t)) (- -1.0 (/ t (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	return x - (y * ((z / (a - t)) + (-1.0 - (t / (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 / (a - t)) + ((-1.0d0) - (t / (a - t)))))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - (y * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
}

Python

def code(x, y, z, t, a):
	return x - (y * ((z / (a - t)) + (-1.0 - (t / (a - t)))))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(y * Float64(Float64(z / Float64(a - t)) + Float64(-1.0 - Float64(t / Float64(a - t))))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - (y * ((z / (a - t)) + (-1.0 - (t / (a - t)))));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(y * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.5%

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

   1. associate-*l/ 84.5%

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

3. Simplified 84.5%

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

4. Taylor expanded in y around 0 95.4%

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

5. Final simplification 95.4%

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

Alternative 2: 92.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-272}:\\ \;\;\;\;x + \left(y - \left(z - t\right) \cdot \frac{y}{a - t}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (+ y x) (/ (* y (- t z)) (- a t)))))
   (if (<= t_1 -5e-272)
     (+ x (- y (* (- z t) (/ y (- a t)))))
     (if (<= t_1 0.0)
       (- x (/ (* y (- a z)) t))
       (+ x (+ y (/ (- t z) (/ (- a t) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = x + (y - ((z - t) * (y / (a - t))));
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / 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 + x) + ((y * (t - z)) / (a - t))
    if (t_1 <= (-5d-272)) then
        tmp = x + (y - ((z - t) * (y / (a - t))))
    else if (t_1 <= 0.0d0) then
        tmp = x - ((y * (a - z)) / t)
    else
        tmp = x + (y + ((t - z) / ((a - t) / 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 + x) + ((y * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = x + (y - ((z - t) * (y / (a - t))));
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) + ((y * (t - z)) / (a - t))
	tmp = 0
	if t_1 <= -5e-272:
		tmp = x + (y - ((z - t) * (y / (a - t))))
	elif t_1 <= 0.0:
		tmp = x - ((y * (a - z)) / t)
	else:
		tmp = x + (y + ((t - z) / ((a - t) / y)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) + Float64(Float64(y * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e-272)
		tmp = Float64(x + Float64(y - Float64(Float64(z - t) * Float64(y / Float64(a - t)))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = Float64(x + Float64(y + Float64(Float64(t - z) / Float64(Float64(a - t) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) + ((y * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -5e-272)
		tmp = x + (y - ((z - t) * (y / (a - t))));
	elseif (t_1 <= 0.0)
		tmp = x - ((y * (a - z)) / t);
	else
		tmp = x + (y + ((t - z) / ((a - t) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-272], N[(x + N[(y - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y + N[(N[(t - z), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / y), $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))) < -4.99999999999999982e-272

   1. Initial program 75.3%

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

      1. associate--l+ 75.3%

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

      2. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. div-inv 91.6%

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

      2. clear-num 92.5%

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

   5. Applied egg-rr 92.5%

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

   if -4.99999999999999982e-272 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.1%

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

      1. associate-*l/ 4.1%

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

   3. Simplified 4.1%

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

   4. Taylor expanded in t around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. distribute-lft-out-- 99.7%

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

   6. Simplified 99.7%

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

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

   1. Initial program 80.6%

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

      1. associate--l+ 80.6%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq -5 \cdot 10^{-272}:\\ \;\;\;\;x + \left(y - \left(z - t\right) \cdot \frac{y}{a - t}\right)\\ \mathbf{elif}\;\left(y + x\right) + \frac{y \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y + \frac{t - z}{\frac{a - t}{y}}\right)\\ \end{array} \]

Alternative 3: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-22}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+45}:\\ \;\;\;\;y - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= a -8.8e+101)
     (+ y x)
     (if (<= a -3.7e-22)
       (- x (* z (/ y a)))
       (if (<= a 1.02e+18)
         t_1
         (if (<= a 1.02e+45)
           (- y (/ (* y z) a))
           (if (<= a 1.2e+51) t_1 (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (a <= -8.8e+101) {
		tmp = y + x;
	} else if (a <= -3.7e-22) {
		tmp = x - (z * (y / a));
	} else if (a <= 1.02e+18) {
		tmp = t_1;
	} else if (a <= 1.02e+45) {
		tmp = y - ((y * z) / a);
	} else if (a <= 1.2e+51) {
		tmp = t_1;
	} else {
		tmp = y + 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (a <= (-8.8d+101)) then
        tmp = y + x
    else if (a <= (-3.7d-22)) then
        tmp = x - (z * (y / a))
    else if (a <= 1.02d+18) then
        tmp = t_1
    else if (a <= 1.02d+45) then
        tmp = y - ((y * z) / a)
    else if (a <= 1.2d+51) then
        tmp = t_1
    else
        tmp = y + x
    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));
	double tmp;
	if (a <= -8.8e+101) {
		tmp = y + x;
	} else if (a <= -3.7e-22) {
		tmp = x - (z * (y / a));
	} else if (a <= 1.02e+18) {
		tmp = t_1;
	} else if (a <= 1.02e+45) {
		tmp = y - ((y * z) / a);
	} else if (a <= 1.2e+51) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / t))
	tmp = 0
	if a <= -8.8e+101:
		tmp = y + x
	elif a <= -3.7e-22:
		tmp = x - (z * (y / a))
	elif a <= 1.02e+18:
		tmp = t_1
	elif a <= 1.02e+45:
		tmp = y - ((y * z) / a)
	elif a <= 1.2e+51:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (a <= -8.8e+101)
		tmp = Float64(y + x);
	elseif (a <= -3.7e-22)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (a <= 1.02e+18)
		tmp = t_1;
	elseif (a <= 1.02e+45)
		tmp = Float64(y - Float64(Float64(y * z) / a));
	elseif (a <= 1.2e+51)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (a <= -8.8e+101)
		tmp = y + x;
	elseif (a <= -3.7e-22)
		tmp = x - (z * (y / a));
	elseif (a <= 1.02e+18)
		tmp = t_1;
	elseif (a <= 1.02e+45)
		tmp = y - ((y * z) / a);
	elseif (a <= 1.2e+51)
		tmp = t_1;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.8e+101], N[(y + x), $MachinePrecision], If[LessEqual[a, -3.7e-22], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+18], t$95$1, If[LessEqual[a, 1.02e+45], N[(y - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e+51], t$95$1, N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.8000000000000003e101 or 1.1999999999999999e51 < a

   1. Initial program 74.5%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around inf 87.3%

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

   if -8.8000000000000003e101 < a < -3.7e-22

   1. Initial program 69.0%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 99.7%

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

   5. Taylor expanded in t around inf 88.5%

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

   6. Taylor expanded in a around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. associate-/l* 82.3%

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

      4. unsub-neg 82.3%

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

      5. associate-/r/ 82.3%

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

      6. *-commutative 82.3%

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

   8. Simplified 82.3%

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

   if -3.7e-22 < a < 1.02e18 or 1.02e45 < a < 1.1999999999999999e51

   1. Initial program 70.0%

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

      1. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in y around 0 93.4%

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

   5. Taylor expanded in t around inf 90.2%

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

   6. Taylor expanded in a around 0 76.2%

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

      1. associate-*r/ 81.2%

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

   8. Simplified 81.2%

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

   if 1.02e18 < a < 1.02e45

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   5. Taylor expanded in x around 0 85.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-22}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+45}:\\ \;\;\;\;y - \frac{y \cdot z}{a}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 89.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-120} \lor \neg \left(a \leq 750000\right):\\ \;\;\;\;x + \left(y + \frac{y}{a - t} \cdot \left(t - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e-120) (not (<= a 750000.0)))
   (+ x (+ y (* (/ y (- a t)) (- t z))))
   (- x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-120) || !(a <= 750000.0)) {
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	} else {
		tmp = x - (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.6d-120)) .or. (.not. (a <= 750000.0d0))) then
        tmp = x + (y + ((y / (a - t)) * (t - z)))
    else
        tmp = x - (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-120) || !(a <= 750000.0)) {
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	} else {
		tmp = x - (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e-120) or not (a <= 750000.0):
		tmp = x + (y + ((y / (a - t)) * (t - z)))
	else:
		tmp = x - (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e-120) || !(a <= 750000.0))
		tmp = Float64(x + Float64(y + Float64(Float64(y / Float64(a - t)) * Float64(t - z))));
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.6e-120) || ~((a <= 750000.0)))
		tmp = x + (y + ((y / (a - t)) * (t - z)));
	else
		tmp = x - (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e-120], N[Not[LessEqual[a, 750000.0]], $MachinePrecision]], N[(x + N[(y + N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e-120 or 7.5e5 < a

   1. Initial program 74.4%

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

      1. associate--l+ 77.3%

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

      2. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

      1. div-inv 93.8%

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

      2. clear-num 93.7%

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

   5. Applied egg-rr 93.7%

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

   if -1.6e-120 < a < 7.5e5

   1. Initial program 69.3%

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

      1. associate-*l/ 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in y around 0 91.3%

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

   5. Taylor expanded in t around inf 89.9%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. sub-neg 86.7%

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

      4. associate-*r/ 89.9%

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

   8. Simplified 89.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-120} \lor \neg \left(a \leq 750000\right):\\ \;\;\;\;x + \left(y + \frac{y}{a - t} \cdot \left(t - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 5: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-22}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.45e+101)
   (+ y x)
   (if (<= a -1.1e-22)
     (- x (* z (/ y a)))
     (if (<= a 6.5e+16) (+ x (* y (/ z t))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.45e+101) {
		tmp = y + x;
	} else if (a <= -1.1e-22) {
		tmp = x - (z * (y / a));
	} else if (a <= 6.5e+16) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + 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 <= (-2.45d+101)) then
        tmp = y + x
    else if (a <= (-1.1d-22)) then
        tmp = x - (z * (y / a))
    else if (a <= 6.5d+16) then
        tmp = x + (y * (z / t))
    else
        tmp = y + 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 <= -2.45e+101) {
		tmp = y + x;
	} else if (a <= -1.1e-22) {
		tmp = x - (z * (y / a));
	} else if (a <= 6.5e+16) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.45e+101:
		tmp = y + x
	elif a <= -1.1e-22:
		tmp = x - (z * (y / a))
	elif a <= 6.5e+16:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.45e+101)
		tmp = Float64(y + x);
	elseif (a <= -1.1e-22)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (a <= 6.5e+16)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.45e+101)
		tmp = y + x;
	elseif (a <= -1.1e-22)
		tmp = x - (z * (y / a));
	elseif (a <= 6.5e+16)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.45e+101], N[(y + x), $MachinePrecision], If[LessEqual[a, -1.1e-22], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+16], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.44999999999999991e101 or 6.5e16 < a

   1. Initial program 75.6%

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

      1. associate-*l/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in a around inf 83.5%

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

   if -2.44999999999999991e101 < a < -1.1e-22

   1. Initial program 69.0%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 99.7%

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

   5. Taylor expanded in t around inf 88.5%

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

   6. Taylor expanded in a around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. associate-/l* 82.3%

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

      4. unsub-neg 82.3%

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

      5. associate-/r/ 82.3%

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

      6. *-commutative 82.3%

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

   8. Simplified 82.3%

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

   if -1.1e-22 < a < 6.5e16

   1. Initial program 70.2%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around 0 93.1%

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

   5. Taylor expanded in t around inf 89.8%

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

   6. Taylor expanded in a around 0 76.1%

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

      1. associate-*r/ 80.6%

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

   8. Simplified 80.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+101}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-22}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-23} \lor \neg \left(a \leq 4.4 \cdot 10^{+17}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.8e-23) (not (<= a 4.4e+17)))
   (+ x (* y (- 1.0 (/ z a))))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e-23) || !(a <= 4.4e+17)) {
		tmp = x + (y * (1.0 - (z / a)));
	} 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 <= (-5.8d-23)) .or. (.not. (a <= 4.4d+17))) then
        tmp = x + (y * (1.0d0 - (z / a)))
    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 <= -5.8e-23) || !(a <= 4.4e+17)) {
		tmp = x + (y * (1.0 - (z / a)));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.8e-23) or not (a <= 4.4e+17):
		tmp = x + (y * (1.0 - (z / a)))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.8e-23) || !(a <= 4.4e+17))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.8e-23) || ~((a <= 4.4e+17)))
		tmp = x + (y * (1.0 - (z / a)));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.8e-23], N[Not[LessEqual[a, 4.4e+17]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.8000000000000003e-23 or 4.4e17 < a

   1. Initial program 74.8%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around 0 97.7%

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

   5. Taylor expanded in t around 0 89.8%

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

   if -5.8000000000000003e-23 < a < 4.4e17

   1. Initial program 70.2%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around 0 93.1%

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

   5. Taylor expanded in t around inf 89.8%

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

   6. Taylor expanded in a around 0 76.1%

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

      1. associate-*r/ 80.6%

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

   8. Simplified 80.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-23} \lor \neg \left(a \leq 4.4 \cdot 10^{+17}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+43} \lor \neg \left(a \leq 4.5 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e+43) (not (<= a 4.5e+15)))
   (+ x (* y (- 1.0 (/ z a))))
   (- x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e+43) || !(a <= 4.5e+15)) {
		tmp = x + (y * (1.0 - (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 <= (-2.8d+43)) .or. (.not. (a <= 4.5d+15))) then
        tmp = x + (y * (1.0d0 - (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 <= -2.8e+43) || !(a <= 4.5e+15)) {
		tmp = x + (y * (1.0 - (z / a)));
	} else {
		tmp = x - (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e+43) or not (a <= 4.5e+15):
		tmp = x + (y * (1.0 - (z / a)))
	else:
		tmp = x - (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e+43) || !(a <= 4.5e+15))
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(z / a))));
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e+43) || ~((a <= 4.5e+15)))
		tmp = x + (y * (1.0 - (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, -2.8e+43], N[Not[LessEqual[a, 4.5e+15]], $MachinePrecision]], N[(x + N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.80000000000000019e43 or 4.5e15 < a

   1. Initial program 73.9%

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

      1. associate-*l/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around 0 97.6%

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

   5. Taylor expanded in t around 0 89.1%

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

   if -2.80000000000000019e43 < a < 4.5e15

   1. Initial program 71.3%

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

      1. associate-*l/ 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in y around 0 93.5%

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

   5. Taylor expanded in t around inf 90.4%

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

   6. Taylor expanded in y around 0 85.4%

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

      1. +-commutative 85.4%

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

      2. mul-1-neg 85.4%

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

      3. sub-neg 85.4%

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

      4. associate-*r/ 90.4%

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

   8. Simplified 90.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+43} \lor \neg \left(a \leq 4.5 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 8: 76.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e-21) (+ y x) (if (<= a 3.2e+17) (+ x (* y (/ z t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-21) {
		tmp = y + x;
	} else if (a <= 3.2e+17) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + 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 <= (-1.65d-21)) then
        tmp = y + x
    else if (a <= 3.2d+17) then
        tmp = x + (y * (z / t))
    else
        tmp = y + 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 <= -1.65e-21) {
		tmp = y + x;
	} else if (a <= 3.2e+17) {
		tmp = x + (y * (z / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e-21:
		tmp = y + x
	elif a <= 3.2e+17:
		tmp = x + (y * (z / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e-21)
		tmp = Float64(y + x);
	elseif (a <= 3.2e+17)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.65e-21)
		tmp = y + x;
	elseif (a <= 3.2e+17)
		tmp = x + (y * (z / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e-21], N[(y + x), $MachinePrecision], If[LessEqual[a, 3.2e+17], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65000000000000004e-21 or 3.2e17 < a

   1. Initial program 74.8%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in a around inf 78.9%

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

   if -1.65000000000000004e-21 < a < 3.2e17

   1. Initial program 70.2%

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

      1. associate-*l/ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around 0 93.1%

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

   5. Taylor expanded in t around inf 89.8%

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

   6. Taylor expanded in a around 0 76.1%

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

      1. associate-*r/ 80.6%

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

   8. Simplified 80.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-21}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 62.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+218}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{+195}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e+218) x (if (<= t 1.76e+195) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e+218) {
		tmp = x;
	} else if (t <= 1.76e+195) {
		tmp = y + x;
	} 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 (t <= (-6.8d+218)) then
        tmp = x
    else if (t <= 1.76d+195) then
        tmp = y + x
    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 (t <= -6.8e+218) {
		tmp = x;
	} else if (t <= 1.76e+195) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e+218:
		tmp = x
	elif t <= 1.76e+195:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e+218)
		tmp = x;
	elseif (t <= 1.76e+195)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.8e+218)
		tmp = x;
	elseif (t <= 1.76e+195)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e+218], x, If[LessEqual[t, 1.76e+195], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -6.80000000000000017e218 or 1.7600000000000001e195 < t

   1. Initial program 43.3%

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

      1. associate-*l/ 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in x around inf 77.8%

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

   if -6.80000000000000017e218 < t < 1.7600000000000001e195

   1. Initial program 78.4%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in a around inf 62.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+218}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.76 \cdot 10^{+195}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 50.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.5%

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

   1. associate-*l/ 84.5%

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

3. Simplified 84.5%

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

4. Taylor expanded in x around inf 49.6%

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

5. Final simplification 49.6%

   \[\leadsto x \]

Developer target: 88.1% 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 2023185 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

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

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