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

Percentage Accurate: 85.1% → 98.1%

Time: 10.2s

Alternatives: 11

Speedup: 1.1×

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: 85.1% 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: 98.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. +-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 N/A

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

   7. --lowering--.f64 98.8

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

4. Applied egg-rr 98.8%

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

Alternative 2: 80.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)\\ t_2 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+288}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ t z)) x)) (t_2 (/ (* (- z t) y) (- z a))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-7)
       t_2
       (if (<= t_2 4e+71)
         (fma y (/ z (- z a)) x)
         (if (<= t_2 2e+288) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (t / z)), x);
	double t_2 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-7) {
		tmp = t_2;
	} else if (t_2 <= 4e+71) {
		tmp = fma(y, (z / (z - a)), x);
	} else if (t_2 <= 2e+288) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(t / z)), x)
	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 <= -1e-7)
		tmp = t_2;
	elseif (t_2 <= 4e+71)
		tmp = fma(y, Float64(z / Float64(z - a)), x);
	elseif (t_2 <= 2e+288)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] + x), $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, -1e-7], t$95$2, If[LessEqual[t$95$2, 4e+71], N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 2e+288], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 2e288 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 41.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

      6. --lowering--.f64 N/A

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

      7. /-lowering-/.f64 82.4

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

   5. Simplified 82.4%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -9.9999999999999995e-8 or 4.0000000000000002e71 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 2e288

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. --lowering--.f64 90.8

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

   5. Simplified 90.8%

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

   if -9.9999999999999995e-8 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.0000000000000002e71

   1. Initial program 100.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 92.5

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

   5. Simplified 92.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -1 \cdot 10^{-7}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 4 \cdot 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 2 \cdot 10^{+288}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+34}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+34)
   (+ y x)
   (if (<= z -1.16e-291) x (if (<= z 1.5e-260) (/ (* t y) a) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+34) {
		tmp = y + x;
	} else if (z <= -1.16e-291) {
		tmp = x;
	} else if (z <= 1.5e-260) {
		tmp = (t * 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 (z <= (-2.4d+34)) then
        tmp = y + x
    else if (z <= (-1.16d-291)) then
        tmp = x
    else if (z <= 1.5d-260) then
        tmp = (t * 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 (z <= -2.4e+34) {
		tmp = y + x;
	} else if (z <= -1.16e-291) {
		tmp = x;
	} else if (z <= 1.5e-260) {
		tmp = (t * y) / a;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+34:
		tmp = y + x
	elif z <= -1.16e-291:
		tmp = x
	elif z <= 1.5e-260:
		tmp = (t * y) / a
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+34)
		tmp = Float64(y + x);
	elseif (z <= -1.16e-291)
		tmp = x;
	elseif (z <= 1.5e-260)
		tmp = Float64(Float64(t * 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 (z <= -2.4e+34)
		tmp = y + x;
	elseif (z <= -1.16e-291)
		tmp = x;
	elseif (z <= 1.5e-260)
		tmp = (t * y) / a;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+34], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.16e-291], x, If[LessEqual[z, 1.5e-260], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999987e34 or 1.5e-260 < z

   1. Initial program 80.6%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. +-lowering-+.f64 75.9

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

   5. Simplified 75.9%

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

   if -2.39999999999999987e34 < z < -1.15999999999999997e-291

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 56.8%

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

   if -1.15999999999999997e-291 < z < 1.5e-260

   1. Initial program 99.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 90.2

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

   5. Simplified 90.2%

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

   6. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 79.6

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

   8. Simplified 79.6%

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

Alternative 4: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-105}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ t z)) x)))
   (if (<= z -1.3e-16) t_1 (if (<= z 5e-105) (fma (/ (- t z) a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (t / z)), x);
	double tmp;
	if (z <= -1.3e-16) {
		tmp = t_1;
	} else if (z <= 5e-105) {
		tmp = fma(((t - z) / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(t / z)), x)
	tmp = 0.0
	if (z <= -1.3e-16)
		tmp = t_1;
	elseif (z <= 5e-105)
		tmp = fma(Float64(Float64(t - z) / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.3e-16], t$95$1, If[LessEqual[z, 5e-105], N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2999999999999999e-16 or 4.99999999999999963e-105 < z

   1. Initial program 79.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

      6. --lowering--.f64 N/A

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

      7. /-lowering-/.f64 85.6

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

   5. Simplified 85.6%

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

   if -1.2999999999999999e-16 < z < 4.99999999999999963e-105

   1. Initial program 97.8%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 97.9

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

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. unsub-neg N/A

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

      8. remove-double-neg N/A

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

      9. --lowering--.f64 83.6

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

   7. Simplified 83.6%

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

Alternative 5: 78.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ z (- z a)) x)))
   (if (<= a -2.3e+19) t_1 (if (<= a 6.8e+89) (fma y (- 1.0 (/ t z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (z / (z - a)), x);
	double tmp;
	if (a <= -2.3e+19) {
		tmp = t_1;
	} else if (a <= 6.8e+89) {
		tmp = fma(y, (1.0 - (t / z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(z / Float64(z - a)), x)
	tmp = 0.0
	if (a <= -2.3e+19)
		tmp = t_1;
	elseif (a <= 6.8e+89)
		tmp = fma(y, Float64(1.0 - Float64(t / z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.3e+19], t$95$1, If[LessEqual[a, 6.8e+89], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3e19 or 6.8000000000000004e89 < a

   1. Initial program 84.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 86.3

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

   5. Simplified 86.3%

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

   if -2.3e19 < a < 6.8000000000000004e89

   1. Initial program 86.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

      6. --lowering--.f64 N/A

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

      7. /-lowering-/.f64 83.5

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

   5. Simplified 83.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-105}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ t z)) x)))
   (if (<= z -3.8e-103) t_1 (if (<= z 5.1e-105) (fma y (/ t a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (t / z)), x);
	double tmp;
	if (z <= -3.8e-103) {
		tmp = t_1;
	} else if (z <= 5.1e-105) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(t / z)), x)
	tmp = 0.0
	if (z <= -3.8e-103)
		tmp = t_1;
	elseif (z <= 5.1e-105)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -3.8e-103], t$95$1, If[LessEqual[z, 5.1e-105], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000001e-103 or 5.10000000000000007e-105 < z

   1. Initial program 81.7%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

      6. --lowering--.f64 N/A

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

      7. /-lowering-/.f64 82.8

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

   5. Simplified 82.8%

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

   if -3.8000000000000001e-103 < z < 5.10000000000000007e-105

   1. Initial program 97.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 89.6

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

   5. Simplified 89.6%

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

Alternative 7: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+67}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+67) (+ y x) (if (<= z 6.2e+38) (fma y (/ t a) x) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+67) {
		tmp = y + x;
	} else if (z <= 6.2e+38) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+67)
		tmp = Float64(y + x);
	elseif (z <= 6.2e+38)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+67], N[(y + x), $MachinePrecision], If[LessEqual[z, 6.2e+38], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000002e67 or 6.20000000000000035e38 < z

   1. Initial program 74.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. +-lowering-+.f64 85.6

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

   5. Simplified 85.6%

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

   if -2.40000000000000002e67 < z < 6.20000000000000035e38

   1. Initial program 97.0%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 75.1

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

   5. Simplified 75.1%

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

Alternative 8: 96.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+197}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+197)
   (fma y (- 1.0 (/ t z)) x)
   (fma (/ y (- z a)) (- z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+197) {
		tmp = fma(y, (1.0 - (t / z)), x);
	} else {
		tmp = fma((y / (z - a)), (z - t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+197)
		tmp = fma(y, Float64(1.0 - Float64(t / z)), x);
	else
		tmp = fma(Float64(y / Float64(z - a)), Float64(z - t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+197], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e197

   1. Initial program 67.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. accelerator-lowering-fma.f64 N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

      6. --lowering--.f64 N/A

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

      7. /-lowering-/.f64 98.6

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

   5. Simplified 98.6%

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

   if -1.15e197 < z

   1. Initial program 88.2%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. --lowering--.f64 97.3

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

   4. Applied egg-rr 97.3%

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

Alternative 9: 63.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+38}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+38) (+ y x) (if (<= z 4.9e-141) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+38) {
		tmp = y + x;
	} else if (z <= 4.9e-141) {
		tmp = 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 <= (-2.5d+38)) then
        tmp = y + x
    else if (z <= 4.9d-141) then
        tmp = 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 <= -2.5e+38) {
		tmp = y + x;
	} else if (z <= 4.9e-141) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+38:
		tmp = y + x
	elif z <= 4.9e-141:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+38)
		tmp = Float64(y + x);
	elseif (z <= 4.9e-141)
		tmp = 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 <= -2.5e+38)
		tmp = y + x;
	elseif (z <= 4.9e-141)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+38], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.9e-141], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999985e38 or 4.90000000000000006e-141 < z

   1. Initial program 78.5%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. +-lowering-+.f64 80.1

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

   5. Simplified 80.1%

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

   if -2.49999999999999985e38 < z < 4.90000000000000006e-141

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 51.3%

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

Alternative 10: 53.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-200}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.25e-162) x (if (<= x 2.6e-200) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.25e-162) {
		tmp = x;
	} else if (x <= 2.6e-200) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.25d-162)) then
        tmp = x
    else if (x <= 2.6d-200) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.25e-162) {
		tmp = x;
	} else if (x <= 2.6e-200) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.25e-162:
		tmp = x
	elif x <= 2.6e-200:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.25e-162)
		tmp = x;
	elseif (x <= 2.6e-200)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.25e-162)
		tmp = x;
	elseif (x <= 2.6e-200)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.25e-162], x, If[LessEqual[x, 2.6e-200], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000004e-162 or 2.5999999999999999e-200 < x

   1. Initial program 85.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 64.3%

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

   if -1.25000000000000004e-162 < x < 2.5999999999999999e-200

   1. Initial program 86.2%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. --lowering--.f64 75.7

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

   5. Simplified 75.7%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 45.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 50.7% accurate, 26.0× 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 85.8%

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

3. Taylor expanded in x around inf

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

5. Simplified 53.0%

   \[\leadsto \color{blue}{x} \]
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 2024195 
(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))))