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

Percentage Accurate: 85.4% → 98.3%

Time: 8.7s

Alternatives: 11

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 98.3

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

4. Applied rewrites 98.3%

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

5. Final simplification 98.3%

   \[\leadsto \frac{y}{\frac{z - a}{z - t}} + x \]
6. Add Preprocessing

Alternative 2: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{z - a}{z - t}}\\ t_2 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+205}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ (- z a) (- z t)))) (t_2 (/ (* (- z t) y) (- z a))))
   (if (<= t_2 -1e+205) t_1 (if (<= t_2 5e+278) (+ t_2 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / ((z - a) / (z - t));
	double t_2 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_2 <= -1e+205) {
		tmp = t_1;
	} else if (t_2 <= 5e+278) {
		tmp = t_2 + x;
	} 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 / ((z - a) / (z - t))
    t_2 = ((z - t) * y) / (z - a)
    if (t_2 <= (-1d+205)) then
        tmp = t_1
    else if (t_2 <= 5d+278) then
        tmp = t_2 + x
    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 / ((z - a) / (z - t));
	double t_2 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_2 <= -1e+205) {
		tmp = t_1;
	} else if (t_2 <= 5e+278) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / ((z - a) / (z - t))
	t_2 = ((z - t) * y) / (z - a)
	tmp = 0
	if t_2 <= -1e+205:
		tmp = t_1
	elif t_2 <= 5e+278:
		tmp = t_2 + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(Float64(z - a) / Float64(z - t)))
	t_2 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if (t_2 <= -1e+205)
		tmp = t_1;
	elseif (t_2 <= 5e+278)
		tmp = Float64(t_2 + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / ((z - a) / (z - t));
	t_2 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if (t_2 <= -1e+205)
		tmp = t_1;
	elseif (t_2 <= 5e+278)
		tmp = t_2 + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(N[(z - a), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+205], t$95$1, If[LessEqual[t$95$2, 5e+278], N[(t$95$2 + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -1.00000000000000002e205 or 5.00000000000000029e278 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 48.7%

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

   3. Taylor expanded in y around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 86.7

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

   5. Applied rewrites 86.7%

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

   7. Applied rewrites 91.0%

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

   if -1.00000000000000002e205 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.00000000000000029e278

   1. Initial program 99.4%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -1 \cdot 10^{+205}:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z - a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot \left(z - t\right)\\ t_2 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) (- z t))) (t_2 (/ (* (- z t) y) (- z a))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 5e+278) (+ t_2 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (z - t);
	double t_2 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+278) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * (z - t);
	double t_2 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 5e+278) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * (z - t)
	t_2 = ((z - t) * y) / (z - a)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 5e+278:
		tmp = t_2 + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * Float64(z - t))
	t_2 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+278)
		tmp = Float64(t_2 + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * (z - t);
	t_2 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 5e+278)
		tmp = t_2 + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+278], N[(t$95$2 + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 5.00000000000000029e278 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 42.5%

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

   3. Taylor expanded in y around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.00000000000000029e278

   1. Initial program 99.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -\infty:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z - a} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{\frac{a}{t}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e-87)
   (fma (/ (- z t) z) y x)
   (if (<= z 2.35e-53) (+ (/ y (/ a t)) x) (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-87) {
		tmp = fma(((z - t) / z), y, x);
	} else if (z <= 2.35e-53) {
		tmp = (y / (a / t)) + x;
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e-87)
		tmp = fma(Float64(Float64(z - t) / z), y, x);
	elseif (z <= 2.35e-53)
		tmp = Float64(Float64(y / Float64(a / t)) + x);
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e-87], N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 2.35e-53], N[(N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000004e-87

   1. Initial program 84.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if -2.00000000000000004e-87 < z < 2.35e-53

   1. Initial program 94.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.3

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

   4. Applied rewrites 95.3%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 81.9

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

   7. Applied rewrites 81.9%

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

   if 2.35e-53 < z

   1. Initial program 80.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 87.7

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

   5. Applied rewrites 87.7%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{\frac{a}{t}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e-87)
   (fma (/ (- z t) z) y x)
   (if (<= z 2.35e-53) (+ (/ (* t y) a) x) (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e-87) {
		tmp = fma(((z - t) / z), y, x);
	} else if (z <= 2.35e-53) {
		tmp = ((t * y) / a) + x;
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e-87)
		tmp = fma(Float64(Float64(z - t) / z), y, x);
	elseif (z <= 2.35e-53)
		tmp = Float64(Float64(Float64(t * y) / a) + x);
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e-87], N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 2.35e-53], N[(N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999996e-87

   1. Initial program 84.4%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if -1.79999999999999996e-87 < z < 2.35e-53

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 78.7

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

   5. Applied rewrites 78.7%

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

   if 2.35e-53 < z

   1. Initial program 80.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 87.7

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

   5. Applied rewrites 87.7%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- z a)) y x)))
   (if (<= z -5.2e-151) t_1 (if (<= z 2.35e-53) (+ (/ (* t y) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / (z - a)), y, x);
	double tmp;
	if (z <= -5.2e-151) {
		tmp = t_1;
	} else if (z <= 2.35e-53) {
		tmp = ((t * y) / a) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(z - a)), y, x)
	tmp = 0.0
	if (z <= -5.2e-151)
		tmp = t_1;
	elseif (z <= 2.35e-53)
		tmp = Float64(Float64(Float64(t * y) / a) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -5.2e-151], t$95$1, If[LessEqual[z, 2.35e-53], N[(N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000001e-151 or 2.35e-53 < z

   1. Initial program 83.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 83.5

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

   5. Applied rewrites 83.5%

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

   if -5.2000000000000001e-151 < z < 2.35e-53

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-151}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-53}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-55}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ y (- z a)) x)))
   (if (<= z -5.2e-151) t_1 (if (<= z 1.16e-55) (+ (/ (* t y) a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, (y / (z - a)), x);
	double tmp;
	if (z <= -5.2e-151) {
		tmp = t_1;
	} else if (z <= 1.16e-55) {
		tmp = ((t * y) / a) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(y / Float64(z - a)), x)
	tmp = 0.0
	if (z <= -5.2e-151)
		tmp = t_1;
	elseif (z <= 1.16e-55)
		tmp = Float64(Float64(Float64(t * y) / a) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -5.2e-151], t$95$1, If[LessEqual[z, 1.16e-55], N[(N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000001e-151 or 1.15999999999999996e-55 < z

   1. Initial program 83.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 83.5

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

   5. Applied rewrites 83.5%

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

   7. Applied rewrites 80.2%

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

   if -5.2000000000000001e-151 < z < 1.15999999999999996e-55

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-151}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-55}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-27}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.15e-27) (+ y x) (if (<= z 1.5e-50) (+ (/ (* t y) a) x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.15e-27) {
		tmp = y + x;
	} else if (z <= 1.5e-50) {
		tmp = ((t * y) / a) + x;
	} 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 (z <= (-3.15d-27)) then
        tmp = y + x
    else if (z <= 1.5d-50) then
        tmp = ((t * y) / a) + x
    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 (z <= -3.15e-27) {
		tmp = y + x;
	} else if (z <= 1.5e-50) {
		tmp = ((t * y) / a) + x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.15e-27:
		tmp = y + x
	elif z <= 1.5e-50:
		tmp = ((t * y) / a) + x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.15e-27)
		tmp = Float64(y + x);
	elseif (z <= 1.5e-50)
		tmp = Float64(Float64(Float64(t * y) / a) + x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.15e-27)
		tmp = y + x;
	elseif (z <= 1.5e-50)
		tmp = ((t * y) / a) + x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.15e-27], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.5e-50], N[(N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.15000000000000005e-27 or 1.49999999999999995e-50 < z

   1. Initial program 79.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.1

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

   5. Applied rewrites 79.1%

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

   if -3.15000000000000005e-27 < z < 1.49999999999999995e-50

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.2

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

   5. Applied rewrites 73.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{-27}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-87}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-57}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.8e-87) (+ y x) (if (<= z 2.9e-57) (fma (/ y a) t x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.8e-87) {
		tmp = y + x;
	} else if (z <= 2.9e-57) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.8e-87)
		tmp = Float64(y + x);
	elseif (z <= 2.9e-57)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.8e-87], N[(y + x), $MachinePrecision], If[LessEqual[z, 2.9e-57], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.7999999999999996e-87 or 2.90000000000000025e-57 < z

   1. Initial program 82.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 74.7

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

   5. Applied rewrites 74.7%

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

   if -7.7999999999999996e-87 < z < 2.90000000000000025e-57

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 78.7

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

   5. Applied rewrites 78.7%

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

Alternative 10: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-229}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e-229) (+ y x) (if (<= z 4.4e-128) (* (/ t a) y) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e-229) {
		tmp = y + x;
	} else if (z <= 4.4e-128) {
		tmp = (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 (z <= (-4.5d-229)) then
        tmp = y + x
    else if (z <= 4.4d-128) then
        tmp = (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 (z <= -4.5e-229) {
		tmp = y + x;
	} else if (z <= 4.4e-128) {
		tmp = (t / a) * y;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e-229:
		tmp = y + x
	elif z <= 4.4e-128:
		tmp = (t / a) * y
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e-229)
		tmp = Float64(y + x);
	elseif (z <= 4.4e-128)
		tmp = Float64(Float64(t / 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 (z <= -4.5e-229)
		tmp = y + x;
	elseif (z <= 4.4e-128)
		tmp = (t / a) * y;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e-229], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.4e-128], N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5000000000000002e-229 or 4.40000000000000019e-128 < z

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 69.8

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

   5. Applied rewrites 69.8%

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

   if -4.5000000000000002e-229 < z < 4.40000000000000019e-128

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf

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

      1. distribute-lft-out-- N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-out-- N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 57.5

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

   5. Applied rewrites 57.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 48.0%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 48.7%

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

   13. Applied rewrites 55.6%

       \[\leadsto \frac{t}{a} \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 60.3% 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 86.7%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 64.0

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

5. Applied rewrites 64.0%

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

Developer Target 1: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024268 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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