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

Percentage Accurate: 85.1% → 96.1%

Time: 7.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 82.1%

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

   1. +-commutative 82.1%

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

   2. associate-*l/ 98.5%

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

   3. fma-def 98.5%

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

3. Simplified 98.5%

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

4. Final simplification 98.5%

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

Alternative 2: 92.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ y (/ (- a t) z)))
     (if (<= t_1 5e+292) (+ x t_1) (- x (/ y (/ t (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (y / ((a - t) / z));
	} else if (t_1 <= 5e+292) {
		tmp = x + t_1;
	} else {
		tmp = x - (y / (t / (z - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y / ((a - t) / z));
	} else if (t_1 <= 5e+292) {
		tmp = x + t_1;
	} else {
		tmp = x - (y / (t / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y / ((a - t) / z))
	elif t_1 <= 5e+292:
		tmp = x + t_1
	else:
		tmp = x - (y / (t / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	elseif (t_1 <= 5e+292)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (y / ((a - t) / z));
	elseif (t_1 <= 5e+292)
		tmp = x + t_1;
	else
		tmp = x - (y / (t / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+292], N[(x + t$95$1), $MachinePrecision], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0

   1. Initial program 36.6%

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

      1. +-commutative 36.6%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-*l/ 36.6%

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

      3. associate-/l* 99.9%

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

      4. div-inv 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 43.4%

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

      1. associate-/l* 73.2%

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

   8. Simplified 73.2%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.9999999999999996e292

   1. Initial program 99.9%

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

   if 4.9999999999999996e292 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 32.4%

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

   2. Taylor expanded in a around 0 22.4%

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

      1. mul-1-neg 22.4%

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

      2. unsub-neg 22.4%

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

      3. associate-/l* 74.6%

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

   4. Simplified 74.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+292}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \end{array} \]

Alternative 3: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+139}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{-287}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ (- a t) z)))))
   (if (<= t -1.75e+139)
     (+ y x)
     (if (<= t -1.6e-165)
       t_1
       (if (<= t 7.3e-287)
         (+ x (/ (- z t) (/ a y)))
         (if (<= t 2.25e+73) t_1 (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / ((a - t) / z));
	double tmp;
	if (t <= -1.75e+139) {
		tmp = y + x;
	} else if (t <= -1.6e-165) {
		tmp = t_1;
	} else if (t <= 7.3e-287) {
		tmp = x + ((z - t) / (a / y));
	} else if (t <= 2.25e+73) {
		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 / ((a - t) / z))
    if (t <= (-1.75d+139)) then
        tmp = y + x
    else if (t <= (-1.6d-165)) then
        tmp = t_1
    else if (t <= 7.3d-287) then
        tmp = x + ((z - t) / (a / y))
    else if (t <= 2.25d+73) 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 / ((a - t) / z));
	double tmp;
	if (t <= -1.75e+139) {
		tmp = y + x;
	} else if (t <= -1.6e-165) {
		tmp = t_1;
	} else if (t <= 7.3e-287) {
		tmp = x + ((z - t) / (a / y));
	} else if (t <= 2.25e+73) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / ((a - t) / z))
	tmp = 0
	if t <= -1.75e+139:
		tmp = y + x
	elif t <= -1.6e-165:
		tmp = t_1
	elif t <= 7.3e-287:
		tmp = x + ((z - t) / (a / y))
	elif t <= 2.25e+73:
		tmp = t_1
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(Float64(a - t) / z)))
	tmp = 0.0
	if (t <= -1.75e+139)
		tmp = Float64(y + x);
	elseif (t <= -1.6e-165)
		tmp = t_1;
	elseif (t <= 7.3e-287)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	elseif (t <= 2.25e+73)
		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 / ((a - t) / z));
	tmp = 0.0;
	if (t <= -1.75e+139)
		tmp = y + x;
	elseif (t <= -1.6e-165)
		tmp = t_1;
	elseif (t <= 7.3e-287)
		tmp = x + ((z - t) / (a / y));
	elseif (t <= 2.25e+73)
		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[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+139], N[(y + x), $MachinePrecision], If[LessEqual[t, -1.6e-165], t$95$1, If[LessEqual[t, 7.3e-287], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+73], t$95$1, N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.74999999999999989e139 or 2.24999999999999992e73 < t

   1. Initial program 62.2%

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

   2. Taylor expanded in t around inf 88.0%

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

      1. +-commutative 88.0%

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

   4. Simplified 88.0%

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

   if -1.74999999999999989e139 < t < -1.60000000000000006e-165 or 7.29999999999999982e-287 < t < 2.24999999999999992e73

   1. Initial program 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-*l/ 98.5%

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

      3. fma-def 98.5%

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

   3. Simplified 98.5%

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

      1. fma-udef 98.5%

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

      2. associate-*l/ 88.6%

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

      3. associate-/l* 98.5%

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

      4. div-inv 98.5%

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

      5. clear-num 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in z around inf 79.4%

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

      1. associate-/l* 88.5%

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

   8. Simplified 88.5%

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

   if -1.60000000000000006e-165 < t < 7.29999999999999982e-287

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 97.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+139}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-165}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{-287}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+73}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-16} \lor \neg \left(t \leq 1.7 \cdot 10^{+71}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e-16) (not (<= t 1.7e+71)))
   (+ y x)
   (+ x (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-16) || !(t <= 1.7e+71)) {
		tmp = y + x;
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.8d-16)) .or. (.not. (t <= 1.7d+71))) then
        tmp = y + x
    else
        tmp = x + ((z - t) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-16) || !(t <= 1.7e+71)) {
		tmp = y + x;
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e-16) or not (t <= 1.7e+71):
		tmp = y + x
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e-16) || !(t <= 1.7e+71))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e-16) || ~((t <= 1.7e+71)))
		tmp = y + x;
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e-16], N[Not[LessEqual[t, 1.7e+71]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999991e-16 or 1.6999999999999999e71 < t

   1. Initial program 68.8%

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

   2. Taylor expanded in t around inf 83.3%

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

      1. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -1.79999999999999991e-16 < t < 1.6999999999999999e71

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*l/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

      1. fma-udef 98.6%

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

      2. associate-*l/ 92.5%

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

      3. associate-/l* 94.5%

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

      4. div-inv 93.9%

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

      5. clear-num 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in a around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*r/ 85.7%

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

   8. Simplified 85.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-16} \lor \neg \left(t \leq 1.7 \cdot 10^{+71}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-16} \lor \neg \left(t \leq 2.25 \cdot 10^{+72}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.75e-16) (not (<= t 2.25e+72)))
   (- x (* y (/ t (- a t))))
   (+ x (/ y (/ (- a t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e-16) || !(t <= 2.25e+72)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.75d-16)) .or. (.not. (t <= 2.25d+72))) then
        tmp = x - (y * (t / (a - t)))
    else
        tmp = x + (y / ((a - t) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e-16) || !(t <= 2.25e+72)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + (y / ((a - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.75e-16) or not (t <= 2.25e+72):
		tmp = x - (y * (t / (a - t)))
	else:
		tmp = x + (y / ((a - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.75e-16) || !(t <= 2.25e+72))
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.75e-16) || ~((t <= 2.25e+72)))
		tmp = x - (y * (t / (a - t)));
	else
		tmp = x + (y / ((a - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.75e-16], N[Not[LessEqual[t, 2.25e+72]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75000000000000009e-16 or 2.2499999999999999e72 < t

   1. Initial program 68.8%

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

   2. Taylor expanded in z around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. associate-*l/ 90.9%

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

      3. unsub-neg 90.9%

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

      4. *-commutative 90.9%

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

   4. Simplified 90.9%

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

   if -1.75000000000000009e-16 < t < 2.2499999999999999e72

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*l/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

      1. fma-udef 98.6%

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

      2. associate-*l/ 92.5%

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

      3. associate-/l* 94.5%

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

      4. div-inv 93.9%

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

      5. clear-num 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in z around inf 85.7%

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

      1. associate-/l* 89.9%

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

   8. Simplified 89.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-16} \lor \neg \left(t \leq 2.25 \cdot 10^{+72}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \end{array} \]

Alternative 6: 78.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e-16)
   (+ y x)
   (if (<= t 5.6e+69) (+ x (/ (- z t) (/ a y))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-16) {
		tmp = y + x;
	} else if (t <= 5.6e+69) {
		tmp = x + ((z - t) / (a / y));
	} 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 (t <= (-1.6d-16)) then
        tmp = y + x
    else if (t <= 5.6d+69) then
        tmp = x + ((z - t) / (a / y))
    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 (t <= -1.6e-16) {
		tmp = y + x;
	} else if (t <= 5.6e+69) {
		tmp = x + ((z - t) / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e-16:
		tmp = y + x
	elif t <= 5.6e+69:
		tmp = x + ((z - t) / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e-16)
		tmp = Float64(y + x);
	elseif (t <= 5.6e+69)
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e-16)
		tmp = y + x;
	elseif (t <= 5.6e+69)
		tmp = x + ((z - t) / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e-16], N[(y + x), $MachinePrecision], If[LessEqual[t, 5.6e+69], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000011e-16 or 5.59999999999999964e69 < t

   1. Initial program 68.8%

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

   2. Taylor expanded in t around inf 83.3%

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

      1. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -1.60000000000000011e-16 < t < 5.59999999999999964e69

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in a around inf 85.7%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-16} \lor \neg \left(t \leq 4.9 \cdot 10^{+69}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e-16) (not (<= t 4.9e+69))) (+ y x) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-16) || !(t <= 4.9e+69)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.45d-16)) .or. (.not. (t <= 4.9d+69))) then
        tmp = y + x
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e-16) || !(t <= 4.9e+69)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.45e-16) or not (t <= 4.9e+69):
		tmp = y + x
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e-16) || !(t <= 4.9e+69))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45e-16) || ~((t <= 4.9e+69)))
		tmp = y + x;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e-16], N[Not[LessEqual[t, 4.9e+69]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4499999999999999e-16 or 4.9e69 < t

   1. Initial program 68.8%

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

   2. Taylor expanded in t around inf 83.3%

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

      1. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -1.4499999999999999e-16 < t < 4.9e69

   1. Initial program 92.5%

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

   2. Taylor expanded in t around 0 77.5%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-16} \lor \neg \left(t \leq 4.9 \cdot 10^{+69}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 8: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-16} \lor \neg \left(t \leq 6.5 \cdot 10^{+69}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e-16) (not (<= t 6.5e+69))) (+ y x) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-16) || !(t <= 6.5e+69)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.8d-16)) .or. (.not. (t <= 6.5d+69))) then
        tmp = y + x
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e-16) || !(t <= 6.5e+69)) {
		tmp = y + x;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e-16) or not (t <= 6.5e+69):
		tmp = y + x
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e-16) || !(t <= 6.5e+69))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e-16) || ~((t <= 6.5e+69)))
		tmp = y + x;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e-16], N[Not[LessEqual[t, 6.5e+69]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.79999999999999991e-16 or 6.5000000000000001e69 < t

   1. Initial program 68.8%

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

   2. Taylor expanded in t around inf 83.3%

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

      1. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -1.79999999999999991e-16 < t < 6.5000000000000001e69

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*l/ 98.6%

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

      3. fma-def 98.6%

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

   3. Simplified 98.6%

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

      1. fma-udef 98.6%

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

      2. associate-*l/ 92.5%

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

      3. associate-/l* 94.5%

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

      4. div-inv 93.9%

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

      5. clear-num 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in t around 0 77.5%

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

      1. associate-*r/ 81.7%

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

   8. Simplified 81.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-16} \lor \neg \left(t \leq 6.5 \cdot 10^{+69}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 9: 76.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e-16) (+ y x) (if (<= t 5.6e+69) (+ x (* z (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e-16) {
		tmp = y + x;
	} else if (t <= 5.6e+69) {
		tmp = x + (z * (y / a));
	} 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 (t <= (-1.7d-16)) then
        tmp = y + x
    else if (t <= 5.6d+69) then
        tmp = x + (z * (y / a))
    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 (t <= -1.7e-16) {
		tmp = y + x;
	} else if (t <= 5.6e+69) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e-16:
		tmp = y + x
	elif t <= 5.6e+69:
		tmp = x + (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e-16)
		tmp = Float64(y + x);
	elseif (t <= 5.6e+69)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e-16)
		tmp = y + x;
	elseif (t <= 5.6e+69)
		tmp = x + (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e-16], N[(y + x), $MachinePrecision], If[LessEqual[t, 5.6e+69], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7e-16 or 5.59999999999999964e69 < t

   1. Initial program 68.8%

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

   2. Taylor expanded in t around inf 83.3%

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

      1. +-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -1.7e-16 < t < 5.59999999999999964e69

   1. Initial program 92.5%

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

   2. Taylor expanded in t around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. associate-/l* 81.7%

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

   4. Simplified 81.7%

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

      1. associate-/r/ 83.5%

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

   6. Applied egg-rr 83.5%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+69}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{z - t}{\frac{a - t}{y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.1%

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

   1. *-commutative 82.1%

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

   2. associate-/l* 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

   \[\leadsto x + \frac{z - t}{\frac{a - t}{y}} \]

Alternative 11: 63.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e+149) x (if (<= a 1.6e+71) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e+149) {
		tmp = x;
	} else if (a <= 1.6e+71) {
		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 (a <= (-1.4d+149)) then
        tmp = x
    else if (a <= 1.6d+71) 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 (a <= -1.4e+149) {
		tmp = x;
	} else if (a <= 1.6e+71) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e+149:
		tmp = x
	elif a <= 1.6e+71:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e+149)
		tmp = x;
	elseif (a <= 1.6e+71)
		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 (a <= -1.4e+149)
		tmp = x;
	elseif (a <= 1.6e+71)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e+149], x, If[LessEqual[a, 1.6e+71], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4e149 or 1.60000000000000012e71 < a

   1. Initial program 78.1%

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

   2. Taylor expanded in x around inf 66.0%

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

   if -1.4e149 < a < 1.60000000000000012e71

   1. Initial program 84.3%

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

   2. Taylor expanded in t around inf 70.3%

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

      1. +-commutative 70.3%

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

   4. Simplified 70.3%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+71}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 50.8% accurate, 11.0× 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 82.1%

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

2. Taylor expanded in x around inf 53.8%

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

3. Final simplification 53.8%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023291 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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