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

Percentage Accurate: 85.2% → 98.1%

Time: 6.2s

Alternatives: 9

Speedup: 1.1×

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: 85.2% 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: 98.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 97.0

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

4. Applied rewrites 97.0%

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

Alternative 2: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+41} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (or (<= t_1 -1e+41) (not (<= t_1 5e+16)))
     (* (- z t) (/ y (- a t)))
     (- x (* y (/ t (- a 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 <= -1e+41) || !(t_1 <= 5e+16)) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (a - t)
    if ((t_1 <= (-1d+41)) .or. (.not. (t_1 <= 5d+16))) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = x - (y * (t / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -1e+41) || !(t_1 <= 5e+16)) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if (t_1 <= -1e+41) or not (t_1 <= 5e+16):
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = x - (y * (t / (a - 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 <= -1e+41) || !(t_1 <= 5e+16))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - 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 <= -1e+41) || ~((t_1 <= 5e+16)))
		tmp = (z - t) * (y / (a - t));
	else
		tmp = x - (y * (t / (a - 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[Or[LessEqual[t$95$1, -1e+41], N[Not[LessEqual[t$95$1, 5e+16]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -1.00000000000000001e41 or 5e16 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 74.2%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 80.4

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

   5. Applied rewrites 80.4%

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

   if -1.00000000000000001e41 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 5e16

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 91.5

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

   5. Applied rewrites 91.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{+41} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4500000000 \lor \neg \left(t \leq 3.8 \cdot 10^{+15}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4500000000.0) (not (<= t 3.8e+15)))
   (- x (* y (/ t (- a t))))
   (+ x (/ (* z y) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4500000000.0) || !(t <= 3.8e+15)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + ((z * y) / (a - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4500000000.0d0)) .or. (.not. (t <= 3.8d+15))) then
        tmp = x - (y * (t / (a - t)))
    else
        tmp = x + ((z * y) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4500000000.0) || !(t <= 3.8e+15)) {
		tmp = x - (y * (t / (a - t)));
	} else {
		tmp = x + ((z * y) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4500000000.0) or not (t <= 3.8e+15):
		tmp = x - (y * (t / (a - t)))
	else:
		tmp = x + ((z * y) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4500000000.0) || !(t <= 3.8e+15))
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	else
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4500000000.0) || ~((t <= 3.8e+15)))
		tmp = x - (y * (t / (a - t)));
	else
		tmp = x + ((z * y) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4500000000.0], N[Not[LessEqual[t, 3.8e+15]], $MachinePrecision]], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e9 or 3.8e15 < t

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   if -4.5e9 < t < 3.8e15

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 90.0

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

   5. Applied rewrites 90.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4500000000 \lor \neg \left(t \leq 3.8 \cdot 10^{+15}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{-t}, y, x\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+64)
   (fma (/ (- z t) (- t)) y x)
   (if (<= t 3.8e+15) (+ x (/ (* z y) (- a t))) (- x (* y (/ t (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+64) {
		tmp = fma(((z - t) / -t), y, x);
	} else if (t <= 3.8e+15) {
		tmp = x + ((z * y) / (a - t));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+64)
		tmp = fma(Float64(Float64(z - t) / Float64(-t)), y, x);
	elseif (t <= 3.8e+15)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+64], N[(N[(N[(z - t), $MachinePrecision] / (-t)), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 3.8e+15], N[(x + N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.9999999999999997e64

   1. Initial program 85.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 92.8

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

   7. Applied rewrites 92.8%

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

   if -6.9999999999999997e64 < t < 3.8e15

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 89.0

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

   5. Applied rewrites 89.0%

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

   if 3.8e15 < t

   1. Initial program 80.4%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 89.4

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

   5. Applied rewrites 89.4%

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

Alternative 5: 78.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+40} \lor \neg \left(t \leq 1.3 \cdot 10^{+73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45e+40) (not (<= t 1.3e+73)))
   (+ y x)
   (fma (- z t) (/ y a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.45e+40) || !(t <= 1.3e+73)) {
		tmp = y + x;
	} else {
		tmp = fma((z - t), (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.45e+40) || !(t <= 1.3e+73))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(z - t), Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.45e+40], N[Not[LessEqual[t, 1.3e+73]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.45000000000000009e40 or 1.3e73 < t

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 83.7

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

   5. Applied rewrites 83.7%

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

   if -1.45000000000000009e40 < t < 1.3e73

   1. Initial program 92.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+40} \lor \neg \left(t \leq 1.3 \cdot 10^{+73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+39} \lor \neg \left(t \leq 1.7 \cdot 10^{-46}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35e+39) (not (<= t 1.7e-46))) (+ y x) (fma (/ z a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e+39) || !(t <= 1.7e-46)) {
		tmp = y + x;
	} else {
		tmp = fma((z / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.35e+39) || !(t <= 1.7e-46))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(z / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.35e+39], N[Not[LessEqual[t, 1.7e-46]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35000000000000002e39 or 1.69999999999999998e-46 < t

   1. Initial program 85.0%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -1.35000000000000002e39 < t < 1.69999999999999998e-46

   1. Initial program 92.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 83.0

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

   5. Applied rewrites 83.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+39} \lor \neg \left(t \leq 1.7 \cdot 10^{-46}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-224}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.4e-224)
   (+ y x)
   (if (<= t -3.8e-296)
     (* y (/ z a))
     (if (<= t 7e-17) (* (- x) -1.0) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.4e-224) {
		tmp = y + x;
	} else if (t <= -3.8e-296) {
		tmp = y * (z / a);
	} else if (t <= 7e-17) {
		tmp = -x * -1.0;
	} 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 <= (-4.4d-224)) then
        tmp = y + x
    else if (t <= (-3.8d-296)) then
        tmp = y * (z / a)
    else if (t <= 7d-17) then
        tmp = -x * (-1.0d0)
    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 <= -4.4e-224) {
		tmp = y + x;
	} else if (t <= -3.8e-296) {
		tmp = y * (z / a);
	} else if (t <= 7e-17) {
		tmp = -x * -1.0;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.4e-224:
		tmp = y + x
	elif t <= -3.8e-296:
		tmp = y * (z / a)
	elif t <= 7e-17:
		tmp = -x * -1.0
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.4e-224)
		tmp = Float64(y + x);
	elseif (t <= -3.8e-296)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 7e-17)
		tmp = Float64(Float64(-x) * -1.0);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.4e-224)
		tmp = y + x;
	elseif (t <= -3.8e-296)
		tmp = y * (z / a);
	elseif (t <= 7e-17)
		tmp = -x * -1.0;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.4e-224], N[(y + x), $MachinePrecision], If[LessEqual[t, -3.8e-296], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-17], N[((-x) * -1.0), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4000000000000002e-224 or 7.0000000000000003e-17 < t

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 69.7

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

   5. Applied rewrites 69.7%

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

   if -4.4000000000000002e-224 < t < -3.8000000000000002e-296

   1. Initial program 85.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 78.1%

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

   if -3.8000000000000002e-296 < t < 7.0000000000000003e-17

   1. Initial program 92.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. distribute-lft-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 83.2

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

   7. Applied rewrites 83.2%

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

   8. Taylor expanded in x around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   9. Step-by-step derivation

   10. Applied rewrites 58.0%

       \[\leadsto \left(-x\right) \cdot -1 \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-224}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-15} \lor \neg \left(t \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.75e-15) (not (<= t 7e-17))) (+ y x) (* (- x) -1.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.75e-15) || !(t <= 7e-17)) {
		tmp = y + x;
	} else {
		tmp = -x * -1.0;
	}
	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-15)) .or. (.not. (t <= 7d-17))) then
        tmp = y + x
    else
        tmp = -x * (-1.0d0)
    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-15) || !(t <= 7e-17)) {
		tmp = y + x;
	} else {
		tmp = -x * -1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.75e-15) or not (t <= 7e-17):
		tmp = y + x
	else:
		tmp = -x * -1.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.75e-15) || !(t <= 7e-17))
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(-x) * -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.75e-15) || ~((t <= 7e-17)))
		tmp = y + x;
	else
		tmp = -x * -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.75e-15], N[Not[LessEqual[t, 7e-17]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[((-x) * -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e-15 or 7.0000000000000003e-17 < t

   1. Initial program 84.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 75.9

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

   5. Applied rewrites 75.9%

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

   if -1.75e-15 < t < 7.0000000000000003e-17

   1. Initial program 92.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 93.8

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

   4. Applied rewrites 93.8%

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

   5. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. associate-/l* N/A

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

      8. distribute-lft-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lower-neg.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower--.f64 81.2

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

   7. Applied rewrites 81.2%

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

   8. Taylor expanded in x around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   9. Step-by-step derivation

   10. Applied rewrites 53.6%

       \[\leadsto \left(-x\right) \cdot -1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-15} \lor \neg \left(t \leq 7 \cdot 10^{-17}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.5% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.6%

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

3. Taylor expanded in t around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 60.9

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

5. Applied rewrites 60.9%

   \[\leadsto \color{blue}{y + x} \]
6. Add Preprocessing

Developer Target 1: 98.3% accurate, 0.8× 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 2024320 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- a t) (- z t)))))

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