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

Percentage Accurate: 85.3% → 99.4%

Time: 10.2s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{\frac{a - z}{t}} + x\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+218}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (- y z) (/ (- a z) t)) x)) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 1e+218) (+ t_2 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) / ((a - z) / t)) + x;
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+218) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) / ((a - z) / t)) + x;
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 1e+218) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) / ((a - z) / t)) + x
	t_2 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 1e+218:
		tmp = t_2 + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) / Float64(Float64(a - z) / t)) + x)
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+218)
		tmp = Float64(t_2 + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) / ((a - z) / t)) + x;
	t_2 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 1e+218)
		tmp = t_2 + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1e+218], N[(t$95$2 + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 1.00000000000000008e218 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 47.3%

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

      1. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - z\right) \cdot t}{a - z}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{a - z}{t}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - z}{\frac{a - z}{t}}\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(a - z\right), t\right)\right), x\right) \]

      9. --lowering--.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), t\right)\right), x\right) \]

   4. Applied egg-rr 100.0%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1.00000000000000008e218

   1. Initial program 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}} + x\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+218}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t}} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+223}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ t (- a z))))) (t_2 (/ (* (- y z) t) (- a z))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 5e+223) (+ t_2 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+223) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / (a - z)));
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 5e+223) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	t_2 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 5e+223:
		tmp = t_2 + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+223)
		tmp = Float64(t_2 + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	t_2 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 5e+223)
		tmp = t_2 + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+223], N[(t$95$2 + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 4.99999999999999985e223 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 46.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a - z} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t}{a - z}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(a - z\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \left(y - z\right)\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.99999999999999985e223

   1. Initial program 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 5 \cdot 10^{+223}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4400000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (+ -1.0 (/ y z))))))
   (if (<= z -4400000000000.0)
     t_1
     (if (<= z 1.1e+27) (+ x (/ y (/ (- a z) t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (-1.0 + (y / z)));
	double tmp;
	if (z <= -4400000000000.0) {
		tmp = t_1;
	} else if (z <= 1.1e+27) {
		tmp = x + (y / ((a - z) / t));
	} 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) :: tmp
    t_1 = x - (t * ((-1.0d0) + (y / z)))
    if (z <= (-4400000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.1d+27) then
        tmp = x + (y / ((a - z) / t))
    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 = x - (t * (-1.0 + (y / z)));
	double tmp;
	if (z <= -4400000000000.0) {
		tmp = t_1;
	} else if (z <= 1.1e+27) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (-1.0 + (y / z)))
	tmp = 0
	if z <= -4400000000000.0:
		tmp = t_1
	elif z <= 1.1e+27:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(-1.0 + Float64(y / z))))
	tmp = 0.0
	if (z <= -4400000000000.0)
		tmp = t_1;
	elseif (z <= 1.1e+27)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (-1.0 + (y / z)));
	tmp = 0.0;
	if (z <= -4400000000000.0)
		tmp = t_1;
	elseif (z <= 1.1e+27)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4400000000000.0], t$95$1, If[LessEqual[z, 1.1e+27], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e12 or 1.0999999999999999e27 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{t \cdot \left(y - z\right)}{z}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \color{blue}{\frac{y - z}{z}}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y - z}{z}\right)}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{z}\right)\right)}\right)\right)\right) \]

      8. *-inverses N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(\frac{y}{z} + -1\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \left(-1 + \color{blue}{\frac{y}{z}}\right)\right)\right) \]

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

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(-1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right)\right) \]

      12. /-lowering-/.f64 91.4%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(-1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   5. Simplified 91.4%

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

   if -4.4e12 < z < 1.0999999999999999e27

   1. Initial program 96.2%

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

      1. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - z\right) \cdot t}{a - z}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{a - z}{t}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - z}{\frac{a - z}{t}}\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(a - z\right), t\right)\right), x\right) \]

      9. --lowering--.f64 96.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), t\right)\right), x\right) \]

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), t\right)\right), x\right) \]
   6. Step-by-step derivation

   7. Simplified 88.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000000:\\ \;\;\;\;x - t \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+18}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e+18)
   (+ t x)
   (if (<= z 7.5e+75) (+ x (/ y (/ (- a z) t))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+18) {
		tmp = t + x;
	} else if (z <= 7.5e+75) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.6d+18)) then
        tmp = t + x
    else if (z <= 7.5d+75) then
        tmp = x + (y / ((a - z) / t))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+18) {
		tmp = t + x;
	} else if (z <= 7.5e+75) {
		tmp = x + (y / ((a - z) / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e+18:
		tmp = t + x
	elif z <= 7.5e+75:
		tmp = x + (y / ((a - z) / t))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e+18)
		tmp = Float64(t + x);
	elseif (z <= 7.5e+75)
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / t)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e+18)
		tmp = t + x;
	elseif (z <= 7.5e+75)
		tmp = x + (y / ((a - z) / t));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e+18], N[(t + x), $MachinePrecision], If[LessEqual[z, 7.5e+75], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6e18 or 7.4999999999999995e75 < z

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 85.3%

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

   if -5.6e18 < z < 7.4999999999999995e75

   1. Initial program 96.0%

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

      1. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - z\right) \cdot t}{a - z}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{a - z}{t}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - z}{\frac{a - z}{t}}\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(a - z\right), t\right)\right), x\right) \]

      9. --lowering--.f64 96.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), t\right)\right), x\right) \]

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), t\right)\right), x\right) \]
   6. Step-by-step derivation

   7. Simplified 87.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+18}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+75}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-15}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.75e-15)
   (+ t x)
   (if (<= z 4.1e+21) (+ x (/ (* (- y z) t) a)) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-15) {
		tmp = t + x;
	} else if (z <= 4.1e+21) {
		tmp = x + (((y - z) * t) / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.75d-15)) then
        tmp = t + x
    else if (z <= 4.1d+21) then
        tmp = x + (((y - z) * t) / a)
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.75e-15) {
		tmp = t + x;
	} else if (z <= 4.1e+21) {
		tmp = x + (((y - z) * t) / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.75e-15:
		tmp = t + x
	elif z <= 4.1e+21:
		tmp = x + (((y - z) * t) / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.75e-15)
		tmp = Float64(t + x);
	elseif (z <= 4.1e+21)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / a));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.75e-15)
		tmp = t + x;
	elseif (z <= 4.1e+21)
		tmp = x + (((y - z) * t) / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.75e-15], N[(t + x), $MachinePrecision], If[LessEqual[z, 4.1e+21], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e-15 or 4.1e21 < z

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 82.6%

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

   if -1.75e-15 < z < 4.1e21

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right), \color{blue}{a}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 80.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-15}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e-16)
   (+ t x)
   (if (<= z 2.25e+22) (+ x (/ y (/ a t))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e-16) {
		tmp = t + x;
	} else if (z <= 2.25e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.65d-16)) then
        tmp = t + x
    else if (z <= 2.25d+22) then
        tmp = x + (y / (a / t))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e-16) {
		tmp = t + x;
	} else if (z <= 2.25e+22) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e-16:
		tmp = t + x
	elif z <= 2.25e+22:
		tmp = x + (y / (a / t))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e-16)
		tmp = Float64(t + x);
	elseif (z <= 2.25e+22)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e-16)
		tmp = t + x;
	elseif (z <= 2.25e+22)
		tmp = x + (y / (a / t));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e-16], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.25e+22], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999994e-16 or 2.2499999999999999e22 < z

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 82.6%

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

   if -1.64999999999999994e-16 < z < 2.2499999999999999e22

   1. Initial program 96.1%

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

      1. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - z\right) \cdot t}{a - z}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{a - z}{t}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - z}{\frac{a - z}{t}}\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(a - z\right), t\right)\right), x\right) \]

      9. --lowering--.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), t\right)\right), x\right) \]

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \color{blue}{\left(\frac{a}{t}\right)}\right), x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 83.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(a, t\right)\right), x\right) \]

   7. Simplified 83.4%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, \mathsf{/.f64}\left(a, t\right)\right), x\right) \]
   9. Step-by-step derivation

   10. Simplified 78.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-16}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-15) (+ t x) (if (<= z 4.4e+18) (+ x (* y (/ t a))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-15) {
		tmp = t + x;
	} else if (z <= 4.4e+18) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-15)) then
        tmp = t + x
    else if (z <= 4.4d+18) then
        tmp = x + (y * (t / a))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-15) {
		tmp = t + x;
	} else if (z <= 4.4e+18) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-15:
		tmp = t + x
	elif z <= 4.4e+18:
		tmp = x + (y * (t / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-15)
		tmp = Float64(t + x);
	elseif (z <= 4.4e+18)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-15)
		tmp = t + x;
	elseif (z <= 4.4e+18)
		tmp = x + (y * (t / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-15], N[(t + x), $MachinePrecision], If[LessEqual[z, 4.4e+18], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000002e-15 or 4.4e18 < z

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 82.6%

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

   if -5.5000000000000002e-15 < z < 4.4e18

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 76.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   5. Simplified 76.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot t}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{t}{a}}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      4. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   7. Applied egg-rr 78.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-80}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-163}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.25e-80)
   (+ t x)
   (if (<= x 1.12e-163) (* t (/ y (- a z))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.25e-80) {
		tmp = t + x;
	} else if (x <= 1.12e-163) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.25d-80)) then
        tmp = t + x
    else if (x <= 1.12d-163) then
        tmp = t * (y / (a - z))
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.25e-80) {
		tmp = t + x;
	} else if (x <= 1.12e-163) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.25e-80:
		tmp = t + x
	elif x <= 1.12e-163:
		tmp = t * (y / (a - z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.25e-80)
		tmp = Float64(t + x);
	elseif (x <= 1.12e-163)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.25e-80)
		tmp = t + x;
	elseif (x <= 1.12e-163)
		tmp = t * (y / (a - z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.25e-80], N[(t + x), $MachinePrecision], If[LessEqual[x, 1.12e-163], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-80 or 1.12e-163 < x

   1. Initial program 85.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 76.6%

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

   if -1.25e-80 < x < 1.12e-163

   1. Initial program 87.9%

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

      1. +-commutative N/A

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

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\left(y - z\right) \cdot t}{a - z}\right), \color{blue}{x}\right) \]

      3. associate-/l* N/A

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

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(y - z\right) \cdot \frac{1}{\frac{a - z}{t}}\right), x\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y - z}{\frac{a - z}{t}}\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{a - z}{t}\right)\right), x\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\left(a - z\right), t\right)\right), x\right) \]

      9. --lowering--.f64 91.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(a, z\right), t\right)\right), x\right) \]

   4. Applied egg-rr 91.3%

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

   5. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a - z}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{\left(a - z\right)}\right)\right) \]

      4. --lowering--.f64 54.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 54.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-80}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-163}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1500000000000:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1500000000000.0) (+ t x) (if (<= z 4.8e-234) x (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1500000000000.0) {
		tmp = t + x;
	} else if (z <= 4.8e-234) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1500000000000.0d0)) then
        tmp = t + x
    else if (z <= 4.8d-234) then
        tmp = x
    else
        tmp = t + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1500000000000.0) {
		tmp = t + x;
	} else if (z <= 4.8e-234) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1500000000000.0:
		tmp = t + x
	elif z <= 4.8e-234:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1500000000000.0)
		tmp = Float64(t + x);
	elseif (z <= 4.8e-234)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1500000000000.0)
		tmp = t + x;
	elseif (z <= 4.8e-234)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1500000000000.0], N[(t + x), $MachinePrecision], If[LessEqual[z, 4.8e-234], x, N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e12 or 4.7999999999999998e-234 < z

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 74.1%

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

   if -1.5e12 < z < 4.7999999999999998e-234

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.4%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1500000000000:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.3e+91) t (if (<= t 7.2e+130) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.3e+91) {
		tmp = t;
	} else if (t <= 7.2e+130) {
		tmp = x;
	} else {
		tmp = t;
	}
	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 <= (-6.3d+91)) then
        tmp = t
    else if (t <= 7.2d+130) then
        tmp = x
    else
        tmp = t
    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 <= -6.3e+91) {
		tmp = t;
	} else if (t <= 7.2e+130) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.3e+91:
		tmp = t
	elif t <= 7.2e+130:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.3e+91)
		tmp = t;
	elseif (t <= 7.2e+130)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.3e+91)
		tmp = t;
	elseif (t <= 7.2e+130)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.3e+91], t, If[LessEqual[t, 7.2e+130], x, t]]

Derivation

1. Split input into 2 regimes

2. if t < -6.3e91 or 7.2000000000000002e130 < t

   1. Initial program 66.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 45.0%

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

   6. Taylor expanded in x around 0

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

   8. Simplified 38.3%

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

   if -6.3e91 < t < 7.2000000000000002e130

   1. Initial program 96.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 69.6%

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

Alternative 11: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.4%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - z\right) \cdot \color{blue}{\frac{t}{a - z}}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t}{a - z} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t}{a - z}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(a - z\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \left(y - z\right)\right)\right) \]

   6. --lowering--.f64 95.8%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(a, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

4. Applied egg-rr 95.8%

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

5. Final simplification 95.8%

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

Alternative 12: 61.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+227}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 4.8e+227) (+ t x) (/ (* y t) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.8e+227) {
		tmp = t + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 4.8d+227) then
        tmp = t + x
    else
        tmp = (y * t) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.8e+227) {
		tmp = t + x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 4.8e+227:
		tmp = t + x
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.8e+227)
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 4.8e+227)
		tmp = t + x;
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.8e+227], N[(t + x), $MachinePrecision], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.7999999999999996e227

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 65.7%

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

   if 4.7999999999999996e227 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{t \cdot y}{a}\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right)\right) \]

      3. *-lowering-*.f64 75.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right)\right) \]

   5. Simplified 75.4%

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

   6. Taylor expanded in x around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, y\right), a\right) \]

   8. Simplified 70.5%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.8 \cdot 10^{+227}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+227}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 5.5e+227) (+ t x) (* t (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.5e+227) {
		tmp = t + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 5.5d+227) then
        tmp = t + x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.5e+227) {
		tmp = t + x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 5.5e+227:
		tmp = t + x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 5.5e+227)
		tmp = Float64(t + x);
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 5.5e+227)
		tmp = t + x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 5.5e+227], N[(t + x), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.5000000000000001e227

   1. Initial program 86.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
   4. Step-by-step derivation

   5. Simplified 65.7%

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

   if 5.5000000000000001e227 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right), \color{blue}{a}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 75.8%

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

   6. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y - z}{a}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{a}\right)\right) \]

      4. --lowering--.f64 70.8%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), a\right)\right) \]

   8. Simplified 70.8%

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

   9. Taylor expanded in y around inf

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

       1. associate-/l* N/A

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

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

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{y}{a}\right)}\right) \]

       3. /-lowering-/.f64 70.3%

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{a}\right)\right) \]

   11. Simplified 70.3%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+227}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 19.0% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return 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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 86.4%

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

3. Taylor expanded in z around inf

   \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{t}\right) \]
4. Step-by-step derivation

5. Simplified 61.6%

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

6. Taylor expanded in x around 0

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

8. Simplified 18.7%

   \[\leadsto \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} 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) :: tmp
    t_1 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    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 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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