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

Percentage Accurate: 98.3% → 98.3%

Time: 9.5s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

   \[x + y \cdot \frac{z - t}{a - t} \]
2. Step-by-step derivation

   1. +-commutative 99.2%

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

   2. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+111}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-91}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e+111)
   (+ y x)
   (if (<= t -2.6e-91)
     (- x (/ y (/ t z)))
     (if (<= t 8.5e-17) (+ x (/ y (/ a z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+111) {
		tmp = y + x;
	} else if (t <= -2.6e-91) {
		tmp = x - (y / (t / z));
	} else if (t <= 8.5e-17) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.5d+111)) then
        tmp = y + x
    else if (t <= (-2.6d-91)) then
        tmp = x - (y / (t / z))
    else if (t <= 8.5d-17) then
        tmp = x + (y / (a / z))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+111) {
		tmp = y + x;
	} else if (t <= -2.6e-91) {
		tmp = x - (y / (t / z));
	} else if (t <= 8.5e-17) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e+111:
		tmp = y + x
	elif t <= -2.6e-91:
		tmp = x - (y / (t / z))
	elif t <= 8.5e-17:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e+111)
		tmp = Float64(y + x);
	elseif (t <= -2.6e-91)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif (t <= 8.5e-17)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e+111)
		tmp = y + x;
	elseif (t <= -2.6e-91)
		tmp = x - (y / (t / z));
	elseif (t <= 8.5e-17)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e+111], N[(y + x), $MachinePrecision], If[LessEqual[t, -2.6e-91], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-17], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.50000000000000019e111 or 8.5e-17 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 85.5%

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

   if -9.50000000000000019e111 < t < -2.60000000000000014e-91

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.2%

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

   3. Taylor expanded in a around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. mul-1-neg 68.5%

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

      3. unsub-neg 68.5%

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

      4. associate-/l* 70.2%

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

   5. Simplified 70.2%

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

   if -2.60000000000000014e-91 < t < 8.5e-17

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 78.9%

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

      1. associate-/l* 81.8%

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

   4. Simplified 81.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+111}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-91}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-94}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.6e+112)
   (+ y x)
   (if (<= t -1e-94)
     (- x (* y (/ z t)))
     (if (<= t 4.5e-17) (+ x (/ y (/ a z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.6e+112) {
		tmp = y + x;
	} else if (t <= -1e-94) {
		tmp = x - (y * (z / t));
	} else if (t <= 4.5e-17) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.6d+112)) then
        tmp = y + x
    else if (t <= (-1d-94)) then
        tmp = x - (y * (z / t))
    else if (t <= 4.5d-17) then
        tmp = x + (y / (a / z))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.6e+112) {
		tmp = y + x;
	} else if (t <= -1e-94) {
		tmp = x - (y * (z / t));
	} else if (t <= 4.5e-17) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.6e+112:
		tmp = y + x
	elif t <= -1e-94:
		tmp = x - (y * (z / t))
	elif t <= 4.5e-17:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.6e+112)
		tmp = Float64(y + x);
	elseif (t <= -1e-94)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	elseif (t <= 4.5e-17)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.6e+112)
		tmp = y + x;
	elseif (t <= -1e-94)
		tmp = x - (y * (z / t));
	elseif (t <= 4.5e-17)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.6e+112], N[(y + x), $MachinePrecision], If[LessEqual[t, -1e-94], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-17], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.60000000000000015e112 or 4.49999999999999978e-17 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 85.5%

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

   if -7.60000000000000015e112 < t < -9.9999999999999996e-95

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 80.2%

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

   3. Taylor expanded in a around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. neg-mul-1 70.3%

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

   5. Simplified 70.3%

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

   if -9.9999999999999996e-95 < t < 4.49999999999999978e-17

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 78.9%

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

      1. associate-/l* 81.8%

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

   4. Simplified 81.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+112}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-94}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+17}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.2e+93)
   (+ y x)
   (if (<= t -3e+17)
     (* (- t z) (/ y (- t a)))
     (if (<= t 7e-18) (+ x (/ y (/ a z))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+93) {
		tmp = y + x;
	} else if (t <= -3e+17) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 7e-18) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.2d+93)) then
        tmp = y + x
    else if (t <= (-3d+17)) then
        tmp = (t - z) * (y / (t - a))
    else if (t <= 7d-18) then
        tmp = x + (y / (a / z))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.2e+93) {
		tmp = y + x;
	} else if (t <= -3e+17) {
		tmp = (t - z) * (y / (t - a));
	} else if (t <= 7e-18) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.2e+93:
		tmp = y + x
	elif t <= -3e+17:
		tmp = (t - z) * (y / (t - a))
	elif t <= 7e-18:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.2e+93)
		tmp = Float64(y + x);
	elseif (t <= -3e+17)
		tmp = Float64(Float64(t - z) * Float64(y / Float64(t - a)));
	elseif (t <= 7e-18)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.2e+93)
		tmp = y + x;
	elseif (t <= -3e+17)
		tmp = (t - z) * (y / (t - a));
	elseif (t <= 7e-18)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.2e+93], N[(y + x), $MachinePrecision], If[LessEqual[t, -3e+17], N[(N[(t - z), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-18], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.19999999999999999e93 or 6.9999999999999997e-18 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 85.4%

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

   if -5.19999999999999999e93 < t < -3e17

   1. Initial program 100.0%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l/ 78.6%

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

      4. sub-neg 78.6%

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

      5. +-commutative 78.6%

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

      6. neg-sub0 78.6%

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

      7. associate-+l- 78.6%

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

      8. sub0-neg 78.6%

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

      9. neg-mul-1 78.6%

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

      10. times-frac 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. neg-sub0 99.7%

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

      15. associate-+l- 99.7%

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

      16. sub0-neg 99.7%

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

      17. neg-mul-1 99.7%

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

      18. *-commutative 99.7%

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

      19. associate-/l* 99.7%

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

      20. metadata-eval 99.7%

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

      21. /-rgt-identity 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around -inf 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*r/ 82.8%

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

   6. Simplified 82.8%

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

   if -3e17 < t < 6.9999999999999997e-18

   1. Initial program 98.4%

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

   2. Taylor expanded in t around 0 77.0%

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

      1. associate-/l* 79.1%

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

   4. Simplified 79.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+17}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+64} \lor \neg \left(t \leq 8.5 \cdot 10^{-18}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+64) (not (<= t 8.5e-18)))
   (- x (/ y (+ (/ a t) -1.0)))
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+64) || !(t <= 8.5e-18)) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y * (z / (a - 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 <= (-1.15d+64)) .or. (.not. (t <= 8.5d-18))) then
        tmp = x - (y / ((a / t) + (-1.0d0)))
    else
        tmp = x + (y * (z / (a - 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 <= -1.15e+64) || !(t <= 8.5e-18)) {
		tmp = x - (y / ((a / t) + -1.0));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.15e+64) or not (t <= 8.5e-18):
		tmp = x - (y / ((a / t) + -1.0))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+64) || !(t <= 8.5e-18))
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.15e+64) || ~((t <= 8.5e-18)))
		tmp = x - (y / ((a / t) + -1.0));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+64], N[Not[LessEqual[t, 8.5e-18]], $MachinePrecision]], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e64 or 8.4999999999999995e-18 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 66.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{a - t} + x} \]
   3. Step-by-step derivation

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. associate-/l* 89.5%

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

      5. div-sub 89.5%

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

      6. *-inverses 89.5%

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

   4. Simplified 89.5%

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

   if -1.15e64 < t < 8.4999999999999995e-18

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 91.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+64} \lor \neg \left(t \leq 8.5 \cdot 10^{-18}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 6: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.4e+178)
   (+ y x)
   (if (<= t 9.2e-17) (+ x (* y (/ z (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e+178) {
		tmp = y + x;
	} else if (t <= 9.2e-17) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.4d+178)) then
        tmp = y + x
    else if (t <= 9.2d-17) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e+178) {
		tmp = y + x;
	} else if (t <= 9.2e-17) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.4e+178:
		tmp = y + x
	elif t <= 9.2e-17:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.4e+178)
		tmp = Float64(y + x);
	elseif (t <= 9.2e-17)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.4e+178)
		tmp = y + x;
	elseif (t <= 9.2e-17)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.4e+178], N[(y + x), $MachinePrecision], If[LessEqual[t, 9.2e-17], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.39999999999999997e178 or 9.20000000000000035e-17 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 89.7%

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

   if -1.39999999999999997e178 < t < 9.20000000000000035e-17

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 87.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+178}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 10^{-18}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.7e-14)
   (+ x (/ (- t z) (/ t y)))
   (if (<= t 1e-18) (+ x (* y (/ z (- a t)))) (- x (/ y (+ (/ a t) -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7e-14) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 1e-18) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	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 <= (-2.7d-14)) then
        tmp = x + ((t - z) / (t / y))
    else if (t <= 1d-18) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = x - (y / ((a / t) + (-1.0d0)))
    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 <= -2.7e-14) {
		tmp = x + ((t - z) / (t / y));
	} else if (t <= 1e-18) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7e-14:
		tmp = x + ((t - z) / (t / y))
	elif t <= 1e-18:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7e-14)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(t / y)));
	elseif (t <= 1e-18)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7e-14)
		tmp = x + ((t - z) / (t / y));
	elseif (t <= 1e-18)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7e-14], N[(x + N[(N[(t - z), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-18], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999999e-14

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. unsub-neg 62.6%

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

      4. associate-/l* 84.3%

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

   4. Simplified 84.3%

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

   if -2.6999999999999999e-14 < t < 1.0000000000000001e-18

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 93.5%

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

   if 1.0000000000000001e-18 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{a - t} + x} \]
   3. Step-by-step derivation

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. associate-/l* 95.8%

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

      5. div-sub 95.8%

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

      6. *-inverses 95.8%

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

   4. Simplified 95.8%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{t} - 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t - z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 10^{-18}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 8: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e-47) (+ y x) (if (<= t 7.6e-17) (+ x (* y (/ z a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e-47) {
		tmp = y + x;
	} else if (t <= 7.6e-17) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.5d-47)) then
        tmp = y + x
    else if (t <= 7.6d-17) then
        tmp = x + (y * (z / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e-47) {
		tmp = y + x;
	} else if (t <= 7.6e-17) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e-47:
		tmp = y + x
	elif t <= 7.6e-17:
		tmp = x + (y * (z / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e-47)
		tmp = Float64(y + x);
	elseif (t <= 7.6e-17)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e-47)
		tmp = y + x;
	elseif (t <= 7.6e-17)
		tmp = x + (y * (z / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e-47], N[(y + x), $MachinePrecision], If[LessEqual[t, 7.6e-17], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5000000000000004e-47 or 7.6000000000000002e-17 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.0%

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

   if -6.5000000000000004e-47 < t < 7.6000000000000002e-17

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 81.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.8e-47) (+ y x) (if (<= t 6.5e-17) (+ x (/ y (/ a z))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e-47) {
		tmp = y + x;
	} else if (t <= 6.5e-17) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7.8d-47)) then
        tmp = y + x
    else if (t <= 6.5d-17) then
        tmp = x + (y / (a / z))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.8e-47) {
		tmp = y + x;
	} else if (t <= 6.5e-17) {
		tmp = x + (y / (a / z));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.8e-47:
		tmp = y + x
	elif t <= 6.5e-17:
		tmp = x + (y / (a / z))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.8e-47)
		tmp = Float64(y + x);
	elseif (t <= 6.5e-17)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.8e-47)
		tmp = y + x;
	elseif (t <= 6.5e-17)
		tmp = x + (y / (a / z));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.8e-47], N[(y + x), $MachinePrecision], If[LessEqual[t, 6.5e-17], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.79999999999999956e-47 or 6.4999999999999996e-17 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.0%

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

   if -7.79999999999999956e-47 < t < 6.4999999999999996e-17

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0 79.7%

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

      1. associate-/l* 81.4%

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

   4. Simplified 81.4%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-47}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 98.3% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 11: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+264}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+201}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+264)
   (/ (* y z) a)
   (if (<= z 1.2e+201) (+ y x) (* (- z) (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.65e+264) {
		tmp = (y * z) / a;
	} else if (z <= 1.2e+201) {
		tmp = y + x;
	} else {
		tmp = -z * (y / 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 (z <= (-1.65d+264)) then
        tmp = (y * z) / a
    else if (z <= 1.2d+201) then
        tmp = y + x
    else
        tmp = -z * (y / 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 (z <= -1.65e+264) {
		tmp = (y * z) / a;
	} else if (z <= 1.2e+201) {
		tmp = y + x;
	} else {
		tmp = -z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.65e+264:
		tmp = (y * z) / a
	elif z <= 1.2e+201:
		tmp = y + x
	else:
		tmp = -z * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.65e+264)
		tmp = Float64(Float64(y * z) / a);
	elseif (z <= 1.2e+201)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(-z) * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.65e+264)
		tmp = (y * z) / a;
	elseif (z <= 1.2e+201)
		tmp = y + x;
	else
		tmp = -z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.65e+264], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.2e+201], N[(y + x), $MachinePrecision], N[((-z) * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e264

   1. Initial program 89.3%

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

   2. Taylor expanded in t around 0 77.9%

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

   3. Taylor expanded in y around inf 77.9%

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

   if -1.65e264 < z < 1.19999999999999996e201

   1. Initial program 99.5%

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

   2. Taylor expanded in t around inf 68.8%

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

   if 1.19999999999999996e201 < z

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 76.3%

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

      4. sub-neg 76.3%

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

      5. +-commutative 76.3%

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

      6. neg-sub0 76.3%

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

      7. associate-+l- 76.3%

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

      8. sub0-neg 76.3%

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

      9. neg-mul-1 76.3%

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

      10. times-frac 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. +-commutative 99.8%

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

      14. neg-sub0 99.8%

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

      15. associate-+l- 99.8%

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

      16. sub0-neg 99.8%

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

      17. neg-mul-1 99.8%

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

      18. *-commutative 99.8%

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

      19. associate-/l* 99.8%

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

      20. metadata-eval 99.8%

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

      21. /-rgt-identity 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 66.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 66.6%

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

      2. associate-*r* 66.6%

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

      3. neg-mul-1 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in t around inf 51.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 51.7%

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

      2. associate-/l* 60.8%

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

      3. distribute-neg-frac 60.8%

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

   9. Simplified 60.8%

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

   10. Taylor expanded in y around 0 51.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 51.7%

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

       2. associate-*l/ 60.9%

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

       3. *-commutative 60.9%

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

       4. distribute-rgt-neg-in 60.9%

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

       5. distribute-neg-frac 60.9%

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

   12. Simplified 60.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+264}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+201}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{t}\\ \end{array} \]

Alternative 12: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+266}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+203}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.06e+266)
   (/ (* y z) a)
   (if (<= z 8e+203) (+ y x) (* y (- (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.06e+266) {
		tmp = (y * z) / a;
	} else if (z <= 8e+203) {
		tmp = y + x;
	} else {
		tmp = y * -(z / 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 (z <= (-1.06d+266)) then
        tmp = (y * z) / a
    else if (z <= 8d+203) then
        tmp = y + x
    else
        tmp = y * -(z / 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 (z <= -1.06e+266) {
		tmp = (y * z) / a;
	} else if (z <= 8e+203) {
		tmp = y + x;
	} else {
		tmp = y * -(z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.06e+266:
		tmp = (y * z) / a
	elif z <= 8e+203:
		tmp = y + x
	else:
		tmp = y * -(z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.06e+266)
		tmp = Float64(Float64(y * z) / a);
	elseif (z <= 8e+203)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(-Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.06e+266)
		tmp = (y * z) / a;
	elseif (z <= 8e+203)
		tmp = y + x;
	else
		tmp = y * -(z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.06e+266], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 8e+203], N[(y + x), $MachinePrecision], N[(y * (-N[(z / t), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06000000000000007e266

   1. Initial program 89.3%

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

   2. Taylor expanded in t around 0 77.9%

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

   3. Taylor expanded in y around inf 77.9%

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

   if -1.06000000000000007e266 < z < 7.9999999999999999e203

   1. Initial program 99.5%

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

   2. Taylor expanded in t around inf 68.8%

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

   if 7.9999999999999999e203 < z

   1. Initial program 99.8%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 76.3%

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

      4. sub-neg 76.3%

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

      5. +-commutative 76.3%

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

      6. neg-sub0 76.3%

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

      7. associate-+l- 76.3%

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

      8. sub0-neg 76.3%

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

      9. neg-mul-1 76.3%

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

      10. times-frac 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. +-commutative 99.8%

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

      14. neg-sub0 99.8%

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

      15. associate-+l- 99.8%

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

      16. sub0-neg 99.8%

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

      17. neg-mul-1 99.8%

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

      18. *-commutative 99.8%

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

      19. associate-/l* 99.8%

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

      20. metadata-eval 99.8%

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

      21. /-rgt-identity 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 66.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a}} \]
   5. Step-by-step derivation

      1. associate-*r/ 66.6%

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

      2. associate-*r* 66.6%

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

      3. neg-mul-1 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in y around 0 66.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{t - a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 66.6%

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

      2. associate-*r/ 85.5%

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

      3. *-commutative 85.5%

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

      4. distribute-rgt-neg-in 85.5%

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

   9. Simplified 85.5%

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

   10. Taylor expanded in t around inf 61.0%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+266}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+203}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z}{t}\right)\\ \end{array} \]

Alternative 13: 63.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-51}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e-51) (+ y x) (if (<= t 2.8e-21) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e-51) {
		tmp = y + x;
	} else if (t <= 2.8e-21) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.5d-51)) then
        tmp = y + x
    else if (t <= 2.8d-21) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e-51) {
		tmp = y + x;
	} else if (t <= 2.8e-21) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e-51:
		tmp = y + x
	elif t <= 2.8e-21:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e-51)
		tmp = Float64(y + x);
	elseif (t <= 2.8e-21)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e-51)
		tmp = y + x;
	elseif (t <= 2.8e-21)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e-51], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.8e-21], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.49999999999999974e-51 or 2.80000000000000004e-21 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 77.3%

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

   if -4.49999999999999974e-51 < t < 2.80000000000000004e-21

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf 56.0%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-51}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 14: 52.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.15e+86) y (if (<= y 3.3e+121) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.15e+86) {
		tmp = y;
	} else if (y <= 3.3e+121) {
		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) :: tmp
    if (y <= (-1.15d+86)) then
        tmp = y
    else if (y <= 3.3d+121) 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 tmp;
	if (y <= -1.15e+86) {
		tmp = y;
	} else if (y <= 3.3e+121) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.15e+86:
		tmp = y
	elif y <= 3.3e+121:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.15e+86)
		tmp = y;
	elseif (y <= 3.3e+121)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.15e+86)
		tmp = y;
	elseif (y <= 3.3e+121)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.15e+86], y, If[LessEqual[y, 3.3e+121], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999995e86 or 3.29999999999999979e121 < y

   1. Initial program 99.9%

      \[x + y \cdot \frac{z - t}{a - t} \]
   2. Step-by-step derivation

      1. associate-*r/ 58.6%

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

      2. clear-num 58.5%

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

   3. Applied egg-rr 58.5%

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

   4. Taylor expanded in z around 0 30.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{a - t} + x} \]
   5. Step-by-step derivation

      1. +-commutative 30.3%

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

      2. mul-1-neg 30.3%

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

      3. unsub-neg 30.3%

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

      4. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

   7. Taylor expanded in x around 0 14.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot t}{a - t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 14.6%

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

      2. associate-*l/ 48.4%

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

      3. *-commutative 48.4%

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

      4. distribute-rgt-neg-in 48.4%

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

      5. distribute-neg-frac 48.4%

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

   9. Simplified 48.4%

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

   10. Taylor expanded in t around inf 39.0%

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

   if -1.14999999999999995e86 < y < 3.29999999999999979e121

   1. Initial program 98.8%

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

   2. Taylor expanded in x around inf 65.1%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+86}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+121}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15: 50.8% accurate, 11.0× 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 99.2%

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

2. Taylor expanded in x around inf 50.6%

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

3. Final simplification 50.6%

   \[\leadsto x \]

Developer target: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - 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 + (y * ((z - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - 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 + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	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 - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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