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

Percentage Accurate: 85.2% → 97.9%

Time: 6.3s

Alternatives: 10

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: 85.2% 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: 97.9% 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 87.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 99.2

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

4. Applied rewrites 99.2%

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

Alternative 2: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (<= t_1 -5e+66)
     (fma (- 1.0 (/ t z)) y x)
     (if (<= t_1 2e+35) (fma (/ z (- z a)) y x) (* (/ y (- z a)) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if (t_1 <= -5e+66) {
		tmp = fma((1.0 - (t / z)), y, x);
	} else if (t_1 <= 2e+35) {
		tmp = fma((z / (z - a)), y, x);
	} else {
		tmp = (y / (z - a)) * (z - t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+66)
		tmp = fma(Float64(1.0 - Float64(t / z)), y, x);
	elseif (t_1 <= 2e+35)
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	else
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(z - t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+66], N[(N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+35], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -4.99999999999999991e66

   1. Initial program 69.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. *-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 78.7

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

   5. Applied rewrites 78.7%

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

   7. Applied rewrites 78.8%

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

   if -4.99999999999999991e66 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.9999999999999999e35

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 92.1

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

   5. Applied rewrites 92.1%

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

   if 1.9999999999999999e35 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 75.7%

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

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

      2. fp-cancel-sub-sign N/A

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

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

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-out N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 88.6

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

   5. Applied rewrites 88.6%

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

Alternative 3: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+90}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t) z) y x)))
   (if (<= z -1.5e+90)
     (+ y x)
     (if (<= z -1.9e-30)
       t_1
       (if (<= z 1.15e+35)
         (fma (/ t a) y x)
         (if (<= z 7.5e+164) t_1 (+ y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((-t / z), y, x);
	double tmp;
	if (z <= -1.5e+90) {
		tmp = y + x;
	} else if (z <= -1.9e-30) {
		tmp = t_1;
	} else if (z <= 1.15e+35) {
		tmp = fma((t / a), y, x);
	} else if (z <= 7.5e+164) {
		tmp = t_1;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(-t) / z), y, x)
	tmp = 0.0
	if (z <= -1.5e+90)
		tmp = Float64(y + x);
	elseif (z <= -1.9e-30)
		tmp = t_1;
	elseif (z <= 1.15e+35)
		tmp = fma(Float64(t / a), y, x);
	elseif (z <= 7.5e+164)
		tmp = t_1;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-t) / z), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -1.5e+90], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.9e-30], t$95$1, If[LessEqual[z, 1.15e+35], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 7.5e+164], t$95$1, N[(y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999989e90 or 7.49999999999999976e164 < z

   1. Initial program 70.2%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 91.3

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

   5. Applied rewrites 91.3%

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

   if -1.49999999999999989e90 < z < -1.9000000000000002e-30 or 1.1499999999999999e35 < z < 7.49999999999999976e164

   1. Initial program 89.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.6%

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

   if -1.9000000000000002e-30 < z < 1.1499999999999999e35

   1. Initial program 97.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 98.5

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

   4. Applied rewrites 98.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 79.4

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

   7. Applied rewrites 79.4%

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

Alternative 4: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -60000000000 \lor \neg \left(a \leq 4.9 \cdot 10^{-33}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -60000000000.0) (not (<= a 4.9e-33)))
   (fma (/ t a) y x)
   (fma (- 1.0 (/ t z)) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -60000000000.0) || !(a <= 4.9e-33)) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = fma((1.0 - (t / z)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -60000000000.0) || !(a <= 4.9e-33))
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = fma(Float64(1.0 - Float64(t / z)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -60000000000.0], N[Not[LessEqual[a, 4.9e-33]], $MachinePrecision]], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6e10 or 4.8999999999999998e-33 < a

   1. Initial program 87.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 82.7

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

   7. Applied rewrites 82.7%

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

   if -6e10 < a < 4.8999999999999998e-33

   1. Initial program 87.9%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. *-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 89.1

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

   5. Applied rewrites 89.1%

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

   7. Applied rewrites 89.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -60000000000 \lor \neg \left(a \leq 4.9 \cdot 10^{-33}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -60000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-35}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -60000000000.0)
   (fma (/ t a) y x)
   (if (<= a 1.45e-35) (fma (- 1.0 (/ t z)) y x) (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -60000000000.0) {
		tmp = fma((t / a), y, x);
	} else if (a <= 1.45e-35) {
		tmp = fma((1.0 - (t / z)), y, x);
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -60000000000.0)
		tmp = fma(Float64(t / a), y, x);
	elseif (a <= 1.45e-35)
		tmp = fma(Float64(1.0 - Float64(t / z)), y, x);
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -60000000000.0], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[a, 1.45e-35], N[(N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6e10

   1. Initial program 88.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 86.2

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

   7. Applied rewrites 86.2%

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

   if -6e10 < a < 1.4500000000000001e-35

   1. Initial program 87.8%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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. *-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 89.0

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

   5. Applied rewrites 89.0%

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

   7. Applied rewrites 89.0%

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

   if 1.4500000000000001e-35 < a

   1. Initial program 87.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 83.6

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

   5. Applied rewrites 83.6%

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

Alternative 6: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.8e+33) (not (<= z 3.4e+50))) (+ y x) (fma (/ t a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.8e+33) || !(z <= 3.4e+50)) {
		tmp = y + x;
	} else {
		tmp = fma((t / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.8e+33) || !(z <= 3.4e+50))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.8e+33], N[Not[LessEqual[z, 3.4e+50]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.80000000000000027e33 or 3.3999999999999998e50 < z

   1. Initial program 75.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 79.9

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

   5. Applied rewrites 79.9%

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

   if -9.80000000000000027e33 < z < 3.3999999999999998e50

   1. Initial program 97.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 98.6

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 78.3

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

   7. Applied rewrites 78.3%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 3.4 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 3.3 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.8e+33) (not (<= z 3.3e+50))) (+ y x) (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.8e+33) || !(z <= 3.3e+50)) {
		tmp = y + x;
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.8e+33) || !(z <= 3.3e+50))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.8e+33], N[Not[LessEqual[z, 3.3e+50]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.80000000000000027e33 or 3.3e50 < z

   1. Initial program 75.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 79.9

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

   5. Applied rewrites 79.9%

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

   if -9.80000000000000027e33 < z < 3.3e50

   1. Initial program 97.4%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 77.6

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

   5. Applied rewrites 77.6%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 3.3 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{+132} \lor \neg \left(y \leq 1.22 \cdot 10^{+260}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y 2.45e+132) (not (<= y 1.22e+260))) (+ y x) (* (/ t a) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= 2.45e+132) || !(y <= 1.22e+260)) {
		tmp = y + x;
	} else {
		tmp = (t / a) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= 2.45d+132) .or. (.not. (y <= 1.22d+260))) then
        tmp = y + x
    else
        tmp = (t / a) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= 2.45e+132) || !(y <= 1.22e+260)) {
		tmp = y + x;
	} else {
		tmp = (t / a) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= 2.45e+132) or not (y <= 1.22e+260):
		tmp = y + x
	else:
		tmp = (t / a) * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= 2.45e+132) || !(y <= 1.22e+260))
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(t / a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= 2.45e+132) || ~((y <= 1.22e+260)))
		tmp = y + x;
	else
		tmp = (t / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, 2.45e+132], N[Not[LessEqual[y, 1.22e+260]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4500000000000001e132 or 1.22e260 < y

   1. Initial program 87.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 64.5

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

   5. Applied rewrites 64.5%

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

   if 2.4500000000000001e132 < y < 1.22e260

   1. Initial program 95.8%

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

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

      2. fp-cancel-sub-sign N/A

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

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

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-out N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 62.5%

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

   13. Applied rewrites 62.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{+132} \lor \neg \left(y \leq 1.22 \cdot 10^{+260}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{+132} \lor \neg \left(y \leq 3.8 \cdot 10^{+259}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y 2.45e+132) (not (<= y 3.8e+259))) (+ y x) (* t (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= 2.45e+132) || !(y <= 3.8e+259)) {
		tmp = y + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= 2.45d+132) .or. (.not. (y <= 3.8d+259))) then
        tmp = y + x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= 2.45e+132) || !(y <= 3.8e+259)) {
		tmp = y + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= 2.45e+132) or not (y <= 3.8e+259):
		tmp = y + x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= 2.45e+132) || !(y <= 3.8e+259))
		tmp = Float64(y + x);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= 2.45e+132) || ~((y <= 3.8e+259)))
		tmp = y + x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, 2.45e+132], N[Not[LessEqual[y, 3.8e+259]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4500000000000001e132 or 3.8e259 < y

   1. Initial program 87.1%

      \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
   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 64.5

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

   5. Applied rewrites 64.5%

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

   if 2.4500000000000001e132 < y < 3.8e259

   1. Initial program 95.8%

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

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

      2. fp-cancel-sub-sign N/A

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

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

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-out N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 79.3

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

   5. Applied rewrites 79.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 62.5%

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

   13. Applied rewrites 62.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.45 \cdot 10^{+132} \lor \neg \left(y \leq 3.8 \cdot 10^{+259}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.1% 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 87.9%

   \[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
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 60.6

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

5. Applied rewrites 60.6%

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

Developer Target 1: 98.0% 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 2024339 
(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))))