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

Percentage Accurate: 98.0% → 97.1%

Time: 9.8s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t\_1 \leq 20000000000:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))) (t_2 (+ x (* t (/ y (- a z))))))
   (if (<= t_1 -1e+16)
     t_2
     (if (<= t_1 0.02)
       (- x (* y (/ (- z t) a)))
       (if (<= t_1 20000000000.0) (+ x (* y (- 1.0 (/ t z)))) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (a - z);
	double t_2 = x + (t * (y / (a - z)));
	double tmp;
	if (t_1 <= -1e+16) {
		tmp = t_2;
	} else if (t_1 <= 0.02) {
		tmp = x - (y * ((z - t) / a));
	} else if (t_1 <= 20000000000.0) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - z) / (a - z)
    t_2 = x + (t * (y / (a - z)))
    if (t_1 <= (-1d+16)) then
        tmp = t_2
    else if (t_1 <= 0.02d0) then
        tmp = x - (y * ((z - t) / a))
    else if (t_1 <= 20000000000.0d0) then
        tmp = x + (y * (1.0d0 - (t / z)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (a - z);
	double t_2 = x + (t * (y / (a - z)));
	double tmp;
	if (t_1 <= -1e+16) {
		tmp = t_2;
	} else if (t_1 <= 0.02) {
		tmp = x - (y * ((z - t) / a));
	} else if (t_1 <= 20000000000.0) {
		tmp = x + (y * (1.0 - (t / z)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) / (a - z)
	t_2 = x + (t * (y / (a - z)))
	tmp = 0
	if t_1 <= -1e+16:
		tmp = t_2
	elif t_1 <= 0.02:
		tmp = x - (y * ((z - t) / a))
	elif t_1 <= 20000000000.0:
		tmp = x + (y * (1.0 - (t / z)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(a - z))
	t_2 = Float64(x + Float64(t * Float64(y / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e+16)
		tmp = t_2;
	elseif (t_1 <= 0.02)
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / a)));
	elseif (t_1 <= 20000000000.0)
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) / (a - z);
	t_2 = x + (t * (y / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e+16)
		tmp = t_2;
	elseif (t_1 <= 0.02)
		tmp = x - (y * ((z - t) / a));
	elseif (t_1 <= 20000000000.0)
		tmp = x + (y * (1.0 - (t / z)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+16], t$95$2, If[LessEqual[t$95$1, 0.02], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20000000000.0], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -1e16 or 2e10 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 93.2%

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

      1. associate-*r/ 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. associate-/l* 98.6%

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

      3. distribute-rgt-neg-in 98.6%

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

      4. distribute-neg-frac2 98.6%

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

      5. neg-sub0 98.6%

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

      6. sub-neg 98.6%

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

      7. +-commutative 98.6%

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

      8. associate--r+ 98.6%

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

      9. neg-sub0 98.6%

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

      10. remove-double-neg 98.6%

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

   7. Simplified 98.6%

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

   if -1e16 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.0200000000000000004

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in a around inf 95.4%

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

      1. +-commutative 95.4%

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

      2. mul-1-neg 95.4%

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

      3. associate-/l* 98.5%

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

      4. distribute-rgt-neg-in 98.5%

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

      5. distribute-frac-neg 98.5%

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

      6. neg-sub0 98.5%

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

      7. sub-neg 98.5%

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

      8. +-commutative 98.5%

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

      9. associate--r+ 98.5%

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

      10. neg-sub0 98.5%

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

      11. remove-double-neg 98.5%

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

   7. Simplified 98.5%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e10

   1. Initial program 100.0%

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

      1. associate-*r/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in a around 0 71.2%

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

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq -1 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 0.02:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 20000000000:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 97.6%

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

3. Simplified 97.6%

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

5. Final simplification 97.6%

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

Alternative 3: 82.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ t_2 := \frac{y \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 0.02:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+94}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))) (t_2 (/ (* y t) (- a z))))
   (if (<= t_1 -4e+124)
     t_2
     (if (<= t_1 -1e+15)
       (- x (* y (/ t z)))
       (if (<= t_1 0.02)
         (+ x (* t (/ y a)))
         (if (<= t_1 1e+94) (+ y x) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (a - z);
	double t_2 = (y * t) / (a - z);
	double tmp;
	if (t_1 <= -4e+124) {
		tmp = t_2;
	} else if (t_1 <= -1e+15) {
		tmp = x - (y * (t / z));
	} else if (t_1 <= 0.02) {
		tmp = x + (t * (y / a));
	} else if (t_1 <= 1e+94) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - z) / (a - z)
    t_2 = (y * t) / (a - z)
    if (t_1 <= (-4d+124)) then
        tmp = t_2
    else if (t_1 <= (-1d+15)) then
        tmp = x - (y * (t / z))
    else if (t_1 <= 0.02d0) then
        tmp = x + (t * (y / a))
    else if (t_1 <= 1d+94) then
        tmp = y + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (a - z);
	double t_2 = (y * t) / (a - z);
	double tmp;
	if (t_1 <= -4e+124) {
		tmp = t_2;
	} else if (t_1 <= -1e+15) {
		tmp = x - (y * (t / z));
	} else if (t_1 <= 0.02) {
		tmp = x + (t * (y / a));
	} else if (t_1 <= 1e+94) {
		tmp = y + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) / (a - z)
	t_2 = (y * t) / (a - z)
	tmp = 0
	if t_1 <= -4e+124:
		tmp = t_2
	elif t_1 <= -1e+15:
		tmp = x - (y * (t / z))
	elif t_1 <= 0.02:
		tmp = x + (t * (y / a))
	elif t_1 <= 1e+94:
		tmp = y + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(a - z))
	t_2 = Float64(Float64(y * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -4e+124)
		tmp = t_2;
	elseif (t_1 <= -1e+15)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (t_1 <= 0.02)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (t_1 <= 1e+94)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) / (a - z);
	t_2 = (y * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -4e+124)
		tmp = t_2;
	elseif (t_1 <= -1e+15)
		tmp = x - (y * (t / z));
	elseif (t_1 <= 0.02)
		tmp = x + (t * (y / a));
	elseif (t_1 <= 1e+94)
		tmp = y + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+124], t$95$2, If[LessEqual[t$95$1, -1e+15], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.02], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+94], N[(y + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -3.99999999999999979e124 or 1e94 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. fma-define 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around inf 83.0%

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

      1. associate--l+ 83.0%

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

      2. div-sub 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in t around inf 85.1%

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

      1. associate-*r/ 85.1%

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

      2. mul-1-neg 85.1%

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

      3. *-commutative 85.1%

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

   10. Simplified 85.1%

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

   if -3.99999999999999979e124 < (/.f64 (-.f64 z t) (-.f64 z a)) < -1e15

   1. Initial program 99.9%

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

      1. associate-*r/ 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in t around inf 82.0%

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

      1. associate-*r/ 82.0%

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

      2. mul-1-neg 82.0%

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

      3. distribute-lft-neg-out 82.0%

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

      4. *-commutative 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in z around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-/l* 77.7%

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

      3. distribute-rgt-neg-in 77.7%

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

   10. Simplified 77.7%

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

       1. *-commutative 77.7%

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

       2. distribute-neg-frac 77.7%

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

       3. associate-*l/ 68.5%

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

   12. Applied egg-rr 68.5%

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

   13. Taylor expanded in x around 0 68.5%

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

       1. mul-1-neg 68.5%

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

       2. associate-*l/ 81.9%

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

       3. distribute-lft-neg-in 81.9%

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

       4. cancel-sign-sub-inv 81.9%

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

       5. *-commutative 81.9%

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

   15. Simplified 81.9%

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

   if -1e15 < (/.f64 (-.f64 z t) (-.f64 z a)) < 0.0200000000000000004

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. associate-/l* 87.0%

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

   7. Simplified 87.0%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e94

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. +-commutative 93.9%

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

   7. Simplified 93.9%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq -4 \cdot 10^{+124}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 0.02:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 10^{+94}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq 0.02 \lor \neg \left(t\_1 \leq 20000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))))
   (if (or (<= t_1 0.02) (not (<= t_1 20000000000.0)))
     (+ x (* t (/ y (- a z))))
     (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (a - z);
	double tmp;
	if ((t_1 <= 0.02) || !(t_1 <= 20000000000.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	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 = (t - z) / (a - z)
    if ((t_1 <= 0.02d0) .or. (.not. (t_1 <= 20000000000.0d0))) then
        tmp = x + (t * (y / (a - z)))
    else
        tmp = x + (y * (1.0d0 - (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (a - z);
	double tmp;
	if ((t_1 <= 0.02) || !(t_1 <= 20000000000.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) / (a - z)
	tmp = 0
	if (t_1 <= 0.02) or not (t_1 <= 20000000000.0):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= 0.02) || !(t_1 <= 20000000000.0))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) / (a - z);
	tmp = 0.0;
	if ((t_1 <= 0.02) || ~((t_1 <= 20000000000.0)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 0.02], N[Not[LessEqual[t$95$1, 20000000000.0]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 0.0200000000000000004 or 2e10 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 96.1%

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

      1. associate-*r/ 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 91.7%

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

      3. distribute-rgt-neg-in 91.7%

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

      4. distribute-neg-frac2 91.7%

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

      5. neg-sub0 91.7%

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

      6. sub-neg 91.7%

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

      7. +-commutative 91.7%

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

      8. associate--r+ 91.7%

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

      9. neg-sub0 91.7%

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

      10. remove-double-neg 91.7%

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

   7. Simplified 91.7%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e10

   1. Initial program 100.0%

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

      1. associate-*r/ 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in a around 0 71.2%

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

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq 0.02 \lor \neg \left(\frac{t - z}{a - z} \leq 20000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq 0.02 \lor \neg \left(t\_1 \leq 20000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))))
   (if (or (<= t_1 0.02) (not (<= t_1 20000000000.0)))
     (+ x (* t (/ y (- a z))))
     (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / (a - z);
	double tmp;
	if ((t_1 <= 0.02) || !(t_1 <= 20000000000.0)) {
		tmp = x + (t * (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) :: t_1
    real(8) :: tmp
    t_1 = (t - z) / (a - z)
    if ((t_1 <= 0.02d0) .or. (.not. (t_1 <= 20000000000.0d0))) then
        tmp = x + (t * (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 t_1 = (t - z) / (a - z);
	double tmp;
	if ((t_1 <= 0.02) || !(t_1 <= 20000000000.0)) {
		tmp = x + (t * (y / (a - z)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) / (a - z)
	tmp = 0
	if (t_1 <= 0.02) or not (t_1 <= 20000000000.0):
		tmp = x + (t * (y / (a - z)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= 0.02) || !(t_1 <= 20000000000.0))
		tmp = Float64(x + Float64(t * Float64(y / Float64(a - z))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) / (a - z);
	tmp = 0.0;
	if ((t_1 <= 0.02) || ~((t_1 <= 20000000000.0)))
		tmp = x + (t * (y / (a - z)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 0.02], N[Not[LessEqual[t$95$1, 20000000000.0]], $MachinePrecision]], N[(x + N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 0.0200000000000000004 or 2e10 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 96.1%

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

      1. associate-*r/ 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in t around inf 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 91.7%

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

      3. distribute-rgt-neg-in 91.7%

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

      4. distribute-neg-frac2 91.7%

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

      5. neg-sub0 91.7%

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

      6. sub-neg 91.7%

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

      7. +-commutative 91.7%

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

      8. associate--r+ 91.7%

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

      9. neg-sub0 91.7%

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

      10. remove-double-neg 91.7%

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

   7. Simplified 91.7%

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

   if 0.0200000000000000004 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2e10

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. +-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq 0.02 \lor \neg \left(\frac{t - z}{a - z} \leq 20000000000\right):\\ \;\;\;\;x + t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+21} \lor \neg \left(z \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.82e+21) (not (<= z 4.1e+34))) (+ y x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.82e+21) || !(z <= 4.1e+34)) {
		tmp = y + x;
	} else {
		tmp = x + (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 ((z <= (-1.82d+21)) .or. (.not. (z <= 4.1d+34))) then
        tmp = y + x
    else
        tmp = x + (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 ((z <= -1.82e+21) || !(z <= 4.1e+34)) {
		tmp = y + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.82e+21) or not (z <= 4.1e+34):
		tmp = y + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.82e+21) || !(z <= 4.1e+34))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.82e+21) || ~((z <= 4.1e+34)))
		tmp = y + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.82e+21], N[Not[LessEqual[z, 4.1e+34]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.82e21 or 4.0999999999999998e34 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.8%

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

      1. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   if -1.82e21 < z < 4.0999999999999998e34

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. fma-define 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+21} \lor \neg \left(z \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+21} \lor \neg \left(z \leq 3.85 \cdot 10^{+34}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+21) (not (<= z 3.85e+34))) (+ y x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+21) || !(z <= 3.85e+34)) {
		tmp = y + x;
	} else {
		tmp = x + ((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 ((z <= (-1.95d+21)) .or. (.not. (z <= 3.85d+34))) then
        tmp = y + x
    else
        tmp = x + ((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 ((z <= -1.95e+21) || !(z <= 3.85e+34)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+21) or not (z <= 3.85e+34):
		tmp = y + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+21) || !(z <= 3.85e+34))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+21) || ~((z <= 3.85e+34)))
		tmp = y + x;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+21], N[Not[LessEqual[z, 3.85e+34]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e21 or 3.8499999999999999e34 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.8%

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

      1. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   if -1.95e21 < z < 3.8499999999999999e34

   1. Initial program 95.1%

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

      1. associate-*r/ 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around 0 80.9%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+21} \lor \neg \left(z \leq 3.85 \cdot 10^{+34}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Final simplification 97.6%

   \[\leadsto x + y \cdot \frac{t - z}{a - z} \]
4. Add Preprocessing

Alternative 9: 61.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 9.2e+48) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 9.2e+48) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 9.2d+48) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 9.2e+48) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 9.2e+48:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 9.2e+48)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 9.2e+48)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 9.2e+48], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 9.2000000000000001e48

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. fma-define 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. +-commutative 65.0%

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

   7. Simplified 65.0%

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

   if 9.2000000000000001e48 < a

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 74.2%

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

Alternative 10: 51.1% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-define 97.6%

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

3. Simplified 97.6%

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

5. Taylor expanded in y around 0 51.2%

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

Developer target: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (+ x (/ y (/ (- z a) (- z t))))

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