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

Percentage Accurate: 85.4% → 98.0%

Time: 10.4s

Alternatives: 13

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% 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]

Derivation

1. Initial program 85.4%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 97.8

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

4. Applied egg-rr 97.8%

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

Alternative 2: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+138}:\\ \;\;\;\;y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+194}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (<= t_1 -2e+138) y (if (<= t_1 5e+194) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_1 <= -2e+138) {
		tmp = y;
	} else if (t_1 <= 5e+194) {
		tmp = x;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (a - t)
    if (t_1 <= (-2d+138)) then
        tmp = y
    else if (t_1 <= 5d+194) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_1 <= -2e+138) {
		tmp = y;
	} else if (t_1 <= 5e+194) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if t_1 <= -2e+138:
		tmp = y
	elif t_1 <= 5e+194:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -2e+138)
		tmp = y;
	elseif (t_1 <= 5e+194)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if (t_1 <= -2e+138)
		tmp = y;
	elseif (t_1 <= 5e+194)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+138], y, If[LessEqual[t$95$1, 5e+194], x, y]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -2.0000000000000001e138 or 4.99999999999999989e194 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 52.4%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. --lowering--.f64 51.1

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

   5. Simplified 51.1%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 31.2%

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

   if -2.0000000000000001e138 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.99999999999999989e194

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 71.0%

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

Alternative 3: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+111}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{-t}, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+111)
   (+ x y)
   (if (<= t -2.1e-22)
     (fma z (/ y (- t)) x)
     (if (<= t 5e+109) (+ x (/ (* y z) a)) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+111) {
		tmp = x + y;
	} else if (t <= -2.1e-22) {
		tmp = fma(z, (y / -t), x);
	} else if (t <= 5e+109) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+111)
		tmp = Float64(x + y);
	elseif (t <= -2.1e-22)
		tmp = fma(z, Float64(y / Float64(-t)), x);
	elseif (t <= 5e+109)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+111], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.1e-22], N[(z * N[(y / (-t)), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 5e+109], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2999999999999999e111 or 5.0000000000000001e109 < t

   1. Initial program 60.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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. +-lowering-+.f64 79.6

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

   5. Simplified 79.6%

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

   if -1.2999999999999999e111 < t < -2.10000000000000008e-22

   1. Initial program 96.8%

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

      1. +-commutative N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*l* N/A

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

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

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

      8. --lowering--.f64 N/A

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

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

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

      10. neg-lowering-neg.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. neg-sub0 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. associate--r+ N/A

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

      16. neg-sub0 N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

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

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

      3. /-lowering-/.f64 81.0

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

   7. Simplified 81.0%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 83.8%

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

   if -2.10000000000000008e-22 < t < 5.0000000000000001e109

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 79.7

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

   5. Simplified 79.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+111}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{-t}, x\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;a \leq 3.45 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e-65)
   (fma y (/ (- z t) a) x)
   (if (<= a 3.45e+19) (fma y (- 1.0 (/ z t)) x) (fma (- z t) (/ y a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e-65) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (a <= 3.45e+19) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = fma((z - t), (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e-65)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (a <= 3.45e+19)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = fma(Float64(z - t), Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e-65], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 3.45e+19], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6999999999999999e-65

   1. Initial program 88.2%

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

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

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

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

      5. --lowering--.f64 86.1

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

   5. Simplified 86.1%

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

   if -2.6999999999999999e-65 < a < 3.45e19

   1. Initial program 83.5%

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. /-lowering-/.f64 85.1

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

   5. Simplified 85.1%

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

   if 3.45e19 < a

   1. Initial program 86.2%

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

      1. +-commutative N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*l* N/A

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

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

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

      8. --lowering--.f64 N/A

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

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

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

      10. neg-lowering-neg.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. neg-sub0 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. associate--r+ N/A

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

      16. neg-sub0 N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 96.4

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 86.6

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

   7. Simplified 86.6%

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

Alternative 5: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{if}\;a \leq -5.7 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (- z t) a) x)))
   (if (<= a -5.7e-64) t_1 (if (<= a 7.2e+18) (fma y (- 1.0 (/ z t)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((z - t) / a), x);
	double tmp;
	if (a <= -5.7e-64) {
		tmp = t_1;
	} else if (a <= 7.2e+18) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(z - t) / a), x)
	tmp = 0.0
	if (a <= -5.7e-64)
		tmp = t_1;
	elseif (a <= 7.2e+18)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5.7e-64], t$95$1, If[LessEqual[a, 7.2e+18], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.7000000000000003e-64 or 7.2e18 < a

   1. Initial program 87.3%

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

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

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

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

      5. --lowering--.f64 86.2

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

   5. Simplified 86.2%

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

   if -5.7000000000000003e-64 < a < 7.2e18

   1. Initial program 83.5%

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. /-lowering-/.f64 85.1

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

   5. Simplified 85.1%

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

Alternative 6: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{t - a}, x\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e-85)
   (fma y (/ t (- t a)) x)
   (if (<= a 2.95e+49) (fma y (- 1.0 (/ z t)) x) (fma y (/ z a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e-85) {
		tmp = fma(y, (t / (t - a)), x);
	} else if (a <= 2.95e+49) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else {
		tmp = fma(y, (z / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e-85)
		tmp = fma(y, Float64(t / Float64(t - a)), x);
	elseif (a <= 2.95e+49)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	else
		tmp = fma(y, Float64(z / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e-85], N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 2.95e+49], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.2000000000000001e-85

   1. Initial program 89.1%

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

      1. +-commutative N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*l* N/A

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

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

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

      8. --lowering--.f64 N/A

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

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

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

      10. neg-lowering-neg.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. neg-sub0 N/A

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

      13. sub-neg N/A

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

      14. +-commutative N/A

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

      15. associate--r+ N/A

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

      16. neg-sub0 N/A

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

      17. remove-double-neg N/A

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

      18. --lowering--.f64 92.4

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

   4. Applied egg-rr 92.4%

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

   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. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

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

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

      6. --lowering--.f64 81.5

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

   7. Simplified 81.5%

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

   if -9.2000000000000001e-85 < a < 2.9500000000000001e49

   1. Initial program 82.2%

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. /-lowering-/.f64 84.7

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

   5. Simplified 84.7%

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

   if 2.9500000000000001e49 < a

   1. Initial program 87.9%

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

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

      4. /-lowering-/.f64 84.6

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

   5. Simplified 84.6%

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

Alternative 7: 78.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+109}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ z t)) x)))
   (if (<= t -6.5e-24) t_1 (if (<= t 5e+109) (+ x (/ (* y z) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (z / t)), x);
	double tmp;
	if (t <= -6.5e-24) {
		tmp = t_1;
	} else if (t <= 5e+109) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(z / t)), x)
	tmp = 0.0
	if (t <= -6.5e-24)
		tmp = t_1;
	elseif (t <= 5e+109)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	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[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -6.5e-24], t$95$1, If[LessEqual[t, 5e+109], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5e-24 or 5.0000000000000001e109 < t

   1. Initial program 70.6%

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

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

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

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

      6. neg-sub0 N/A

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

      7. div-sub N/A

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

      8. *-inverses N/A

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

      9. associate-+l- N/A

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

      10. neg-sub0 N/A

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

      11. mul-1-neg N/A

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

      12. +-commutative N/A

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

      13. mul-1-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 N/A

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

      16. /-lowering-/.f64 87.3

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

   5. Simplified 87.3%

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

   if -6.5e-24 < t < 5.0000000000000001e109

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 79.7

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

   5. Simplified 79.7%

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

Alternative 8: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.6e+45) (+ x y) (if (<= t 1.4e+114) (+ x (/ (* y z) a)) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.6e+45) {
		tmp = x + y;
	} else if (t <= 1.4e+114) {
		tmp = x + ((y * z) / a);
	} 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 (t <= (-5.6d+45)) then
        tmp = x + y
    else if (t <= 1.4d+114) then
        tmp = x + ((y * z) / a)
    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 (t <= -5.6e+45) {
		tmp = x + y;
	} else if (t <= 1.4e+114) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.6e+45:
		tmp = x + y
	elif t <= 1.4e+114:
		tmp = x + ((y * z) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.6e+45)
		tmp = Float64(x + y);
	elseif (t <= 1.4e+114)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.6e+45)
		tmp = x + y;
	elseif (t <= 1.4e+114)
		tmp = x + ((y * z) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.6e+45], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.4e+114], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5999999999999999e45 or 1.4e114 < t

   1. Initial program 65.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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. +-lowering-+.f64 80.4

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

   5. Simplified 80.4%

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

   if -5.5999999999999999e45 < t < 1.4e114

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0

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

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

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

      2. *-lowering-*.f64 77.0

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

   5. Simplified 77.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e+45) (+ x y) (if (<= t 5e+109) (fma y (/ z a) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e+45) {
		tmp = x + y;
	} else if (t <= 5e+109) {
		tmp = fma(y, (z / a), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e+45)
		tmp = Float64(x + y);
	elseif (t <= 5e+109)
		tmp = fma(y, Float64(z / a), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e+45], N[(x + y), $MachinePrecision], If[LessEqual[t, 5e+109], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7999999999999994e45 or 5.0000000000000001e109 < t

   1. Initial program 65.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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. +-lowering-+.f64 80.4

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

   5. Simplified 80.4%

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

   if -5.7999999999999994e45 < t < 5.0000000000000001e109

   1. Initial program 96.9%

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

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

      4. /-lowering-/.f64 74.8

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

   5. Simplified 74.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+45}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+109}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

   1. +-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-commutative N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 97.2

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

4. Applied egg-rr 97.2%

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

Alternative 11: 96.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

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

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

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

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

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

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

   8. --lowering--.f64 94.7

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

4. Applied egg-rr 94.7%

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

Alternative 12: 63.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+129) x (if (<= a 2.4e+139) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+129) {
		tmp = x;
	} else if (a <= 2.4e+139) {
		tmp = x + 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 (a <= (-1.2d+129)) then
        tmp = x
    else if (a <= 2.4d+139) then
        tmp = x + 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 (a <= -1.2e+129) {
		tmp = x;
	} else if (a <= 2.4e+139) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+129:
		tmp = x
	elif a <= 2.4e+139:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+129)
		tmp = x;
	elseif (a <= 2.4e+139)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+129)
		tmp = x;
	elseif (a <= 2.4e+139)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+129], x, If[LessEqual[a, 2.4e+139], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1999999999999999e129 or 2.40000000000000008e139 < a

   1. Initial program 85.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 71.9%

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

   if -1.1999999999999999e129 < a < 2.40000000000000008e139

   1. Initial program 85.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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. +-lowering-+.f64 64.2

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

   5. Simplified 64.2%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+139}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.9% 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 85.4%

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

3. Taylor expanded in x around inf

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

5. Simplified 53.9%

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

Developer Target 1: 98.0% 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 2024198 
(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))))