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

Percentage Accurate: 85.1% → 96.6%

Time: 8.2s

Alternatives: 9

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - t} \cdot \left(z - t\right)\\ t_2 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+290}:\\ \;\;\;\;x + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- a t)) (- z t))) (t_2 (/ (* (- z t) y) (- a t))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 4e+290) (+ x t_2) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (a - t)) * (z - t);
	double t_2 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 4e+290) {
		tmp = x + t_2;
	} 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 / (a - t)) * (z - t);
	double t_2 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 4e+290) {
		tmp = x + t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (a - t)) * (z - t)
	t_2 = ((z - t) * y) / (a - t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 4e+290:
		tmp = x + t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(a - t)) * Float64(z - t))
	t_2 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 4e+290)
		tmp = Float64(x + t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (a - t)) * (z - t);
	t_2 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 4e+290)
		tmp = x + t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 4e+290], N[(x + t$95$2), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -inf.0 or 4.00000000000000025e290 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 34.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 92.1

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

   5. Applied rewrites 92.1%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.00000000000000025e290

   1. Initial program 99.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -\infty:\\ \;\;\;\;\frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq 4 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - t} \cdot \left(z - t\right)\\ t_2 := \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+207}:\\ \;\;\;\;\frac{z \cdot y}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- a t)) (- z t))) (t_2 (/ (* (- z t) y) (- a t))))
   (if (<= t_2 -5e+185)
     t_1
     (if (<= t_2 5e+207) (+ (/ (* z y) (- a t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (a - t)) * (z - t);
	double t_2 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_2 <= -5e+185) {
		tmp = t_1;
	} else if (t_2 <= 5e+207) {
		tmp = ((z * y) / (a - t)) + 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 / (a - t)) * (z - t)
    t_2 = ((z - t) * y) / (a - t)
    if (t_2 <= (-5d+185)) then
        tmp = t_1
    else if (t_2 <= 5d+207) then
        tmp = ((z * y) / (a - t)) + 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 / (a - t)) * (z - t);
	double t_2 = ((z - t) * y) / (a - t);
	double tmp;
	if (t_2 <= -5e+185) {
		tmp = t_1;
	} else if (t_2 <= 5e+207) {
		tmp = ((z * y) / (a - t)) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (a - t)) * (z - t)
	t_2 = ((z - t) * y) / (a - t)
	tmp = 0
	if t_2 <= -5e+185:
		tmp = t_1
	elif t_2 <= 5e+207:
		tmp = ((z * y) / (a - t)) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(a - t)) * Float64(z - t))
	t_2 = Float64(Float64(Float64(z - t) * y) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= -5e+185)
		tmp = t_1;
	elseif (t_2 <= 5e+207)
		tmp = Float64(Float64(Float64(z * y) / Float64(a - t)) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (a - t)) * (z - t);
	t_2 = ((z - t) * y) / (a - t);
	tmp = 0.0;
	if (t_2 <= -5e+185)
		tmp = t_1;
	elseif (t_2 <= 5e+207)
		tmp = ((z * y) / (a - t)) + 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[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+185], t$95$1, If[LessEqual[t$95$2, 5e+207], N[(N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -4.9999999999999999e185 or 4.9999999999999999e207 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 41.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 88.1

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

   5. Applied rewrites 88.1%

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

   if -4.9999999999999999e185 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.9999999999999999e207

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.4

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

   5. Applied rewrites 91.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq -5 \cdot 10^{+185}:\\ \;\;\;\;\frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a - t} \leq 5 \cdot 10^{+207}:\\ \;\;\;\;\frac{z \cdot y}{a - t} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1360000000:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-61}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t - a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1360000000.0)
   (fma (- 1.0 (/ z t)) y x)
   (if (<= t 2.9e-61) (fma (/ (- z t) a) y x) (fma (/ y (- t a)) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1360000000.0) {
		tmp = fma((1.0 - (z / t)), y, x);
	} else if (t <= 2.9e-61) {
		tmp = fma(((z - t) / a), y, x);
	} else {
		tmp = fma((y / (t - a)), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1360000000.0)
		tmp = fma(Float64(1.0 - Float64(z / t)), y, x);
	elseif (t <= 2.9e-61)
		tmp = fma(Float64(Float64(z - t) / a), y, x);
	else
		tmp = fma(Float64(y / Float64(t - a)), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1360000000.0], N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t, 2.9e-61], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.36e9

   1. Initial program 72.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \frac{z - t}{t}}, y, x\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\frac{z}{t} - \frac{t}{t}\right)}, y, x\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{z}{t} - \color{blue}{1}\right), y, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{z}{t}\right) + 1}, y, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 84.5

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

   5. Applied rewrites 84.5%

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

   if -1.36e9 < t < 2.8999999999999999e-61

   1. Initial program 95.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if 2.8999999999999999e-61 < t

   1. Initial program 72.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. associate-/r/ N/A

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

      6. lower-fma.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. neg-sub0 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{0 - \left(a - t\right)}}, y \cdot \left(z - t\right), x\right) \]

      11. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{0 - \color{blue}{\left(a - t\right)}}, y \cdot \left(z - t\right), x\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(t\right)\right)\right)}}, y \cdot \left(z - t\right), x\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(t\right)\right) + a\right)}}, y \cdot \left(z - t\right), x\right) \]

      14. associate--r+ N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(t\right)\right)\right) - a}}, y \cdot \left(z - t\right), x\right) \]

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. lower--.f64 72.1

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. lower-*.f64 72.1

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

   4. Applied rewrites 72.1%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 87.7

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

   7. Applied rewrites 87.7%

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

Alternative 4: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)\\ \mathbf{if}\;t \leq -1360000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (/ z t)) y x)))
   (if (<= t -1360000000.0)
     t_1
     (if (<= t 5e-81) (fma (/ (- z t) a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((1.0 - (z / t)), y, x);
	double tmp;
	if (t <= -1360000000.0) {
		tmp = t_1;
	} else if (t <= 5e-81) {
		tmp = fma(((z - t) / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(1.0 - Float64(z / t)), y, x)
	tmp = 0.0
	if (t <= -1360000000.0)
		tmp = t_1;
	elseif (t <= 5e-81)
		tmp = fma(Float64(Float64(z - t) / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[t, -1360000000.0], t$95$1, If[LessEqual[t, 5e-81], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.36e9 or 4.99999999999999981e-81 < t

   1. Initial program 72.8%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \frac{z - t}{t}}, y, x\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\frac{z}{t} - \frac{t}{t}\right)}, y, x\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{z}{t} - \color{blue}{1}\right), y, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{z}{t}\right) + 1}, y, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -1.36e9 < t < 4.99999999999999981e-81

   1. Initial program 95.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 89.8

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

   5. Applied rewrites 89.8%

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

Alternative 5: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \frac{z}{t}, y, x\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (/ z t)) y x)))
   (if (<= t -3e-63) t_1 (if (<= t 5e-81) (fma (/ z a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((1.0 - (z / t)), y, x);
	double tmp;
	if (t <= -3e-63) {
		tmp = t_1;
	} else if (t <= 5e-81) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(1.0 - Float64(z / t)), y, x)
	tmp = 0.0
	if (t <= -3e-63)
		tmp = t_1;
	elseif (t <= 5e-81)
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[t, -3e-63], t$95$1, If[LessEqual[t, 5e-81], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999979e-63 or 4.99999999999999981e-81 < t

   1. Initial program 75.2%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \frac{z - t}{t}}, y, x\right) \]

      8. div-sub N/A

         \[\leadsto \mathsf{fma}\left(0 - \color{blue}{\left(\frac{z}{t} - \frac{t}{t}\right)}, y, x\right) \]

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{z}{t} - \color{blue}{1}\right), y, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{z}{t}\right) + 1}, y, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if -2.99999999999999979e-63 < t < 4.99999999999999981e-81

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 92.4

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

   5. Applied rewrites 92.4%

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

Alternative 6: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.26e+102) (+ x y) (if (<= t 3.6e+41) (fma (/ z a) y x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.26e+102) {
		tmp = x + y;
	} else if (t <= 3.6e+41) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.26e+102)
		tmp = Float64(x + y);
	elseif (t <= 3.6e+41)
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.26e+102], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.6e+41], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.26000000000000001e102 or 3.60000000000000025e41 < t

   1. Initial program 63.5%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -1.26000000000000001e102 < t < 3.60000000000000025e41

   1. Initial program 94.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 82.2

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

   5. Applied rewrites 82.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+102}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+41}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+204}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+204) (* (/ z a) y) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+204) {
		tmp = (z / a) * y;
	} else {
		tmp = x + 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 (z <= (-1.9d+204)) then
        tmp = (z / a) * y
    else
        tmp = x + 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 (z <= -1.9e+204) {
		tmp = (z / a) * y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+204:
		tmp = (z / a) * y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+204)
		tmp = Float64(Float64(z / a) * y);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+204)
		tmp = (z / a) * y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+204], N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e204

   1. Initial program 84.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 61.7%

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

   if -1.8999999999999999e204 < z

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 68.3

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

   5. Applied rewrites 68.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+204}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+204}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+204) (* (/ y a) z) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+204) {
		tmp = (y / a) * z;
	} else {
		tmp = x + 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 (z <= (-1.9d+204)) then
        tmp = (y / a) * z
    else
        tmp = x + 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 (z <= -1.9e+204) {
		tmp = (y / a) * z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+204:
		tmp = (y / a) * z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+204)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+204)
		tmp = (y / a) * z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+204], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e204

   1. Initial program 84.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 51.7%

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

   10. Applied rewrites 56.3%

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

   if -1.8999999999999999e204 < z

   1. Initial program 82.7%

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

   3. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 68.3

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

   5. Applied rewrites 68.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+204}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.8%

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

3. Taylor expanded in t around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 65.7

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

5. Applied rewrites 65.7%

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

6. Final simplification 65.7%

   \[\leadsto x + y \]
7. Add Preprocessing

Developer Target 1: 98.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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