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

Percentage Accurate: 98.1% → 98.1%

Time: 7.6s

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: 98.1% 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: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Final simplification 98.0%

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

Alternative 2: 80.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{-a}, y, x\right)\\ \mathbf{elif}\;t\_1 \leq 5000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))))
   (if (<= t_1 -5e-90)
     (fma (/ y a) t x)
     (if (<= t_1 4e-18)
       (fma (/ z (- a)) y x)
       (if (<= t_1 5000000.0) (+ y x) (fma (/ t a) 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 <= -5e-90) {
		tmp = fma((y / a), t, x);
	} else if (t_1 <= 4e-18) {
		tmp = fma((z / -a), y, x);
	} else if (t_1 <= 5000000.0) {
		tmp = y + x;
	} else {
		tmp = fma((t / a), 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 <= -5e-90)
		tmp = fma(Float64(y / a), t, x);
	elseif (t_1 <= 4e-18)
		tmp = fma(Float64(z / Float64(-a)), y, x);
	elseif (t_1 <= 5000000.0)
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-90], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 4e-18], N[(N[(z / (-a)), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[t$95$1, 5000000.0], N[(y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5.00000000000000019e-90

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 65.4

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

   5. Applied rewrites 65.4%

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

   if -5.00000000000000019e-90 < (/.f64 (-.f64 z t) (-.f64 z a)) < 4.0000000000000003e-18

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 87.8%

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

   if 4.0000000000000003e-18 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5e6

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if 5e6 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 67.8

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

   5. Applied rewrites 67.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.8

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

   7. Applied rewrites 67.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq -5 \cdot 10^{-90}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{-a}, y, x\right)\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 5000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot y}{a}\\ t_2 := \frac{t - z}{a - z} \cdot y\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1.8 \cdot 10^{+282}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t y) a)) (t_2 (* (/ (- t z) (- a z)) y)))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 1.8e+282) (+ y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = ((t - z) / (a - z)) * y;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1.8e+282) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / a;
	double t_2 = ((t - z) / (a - z)) * y;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 1.8e+282) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / a
	t_2 = ((t - z) / (a - z)) * y
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 1.8e+282:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / a)
	t_2 = Float64(Float64(Float64(t - z) / Float64(a - z)) * y)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1.8e+282)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / a;
	t_2 = ((t - z) / (a - z)) * y;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 1.8e+282)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1.8e+282], N[(y + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < -inf.0 or 1.79999999999999993e282 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

   1. Initial program 85.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 67.5

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

   7. Applied rewrites 67.5%

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

   8. Taylor expanded in a around 0

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

   10. Applied rewrites 64.4%

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

   if -inf.0 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < 1.79999999999999993e282

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 67.1

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

   5. Applied rewrites 67.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \cdot y \leq -\infty:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;\frac{t - z}{a - z} \cdot y \leq 1.8 \cdot 10^{+282}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))))
   (if (<= t_1 0.2)
     (fma (- t z) (/ y a) x)
     (if (<= t_1 4e+162) (fma (- 1.0 (/ t z)) y x) (* (/ y (- a z)) t)))))

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 <= 0.2) {
		tmp = fma((t - z), (y / a), x);
	} else if (t_1 <= 4e+162) {
		tmp = fma((1.0 - (t / z)), y, x);
	} else {
		tmp = (y / (a - z)) * t;
	}
	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 <= 0.2)
		tmp = fma(Float64(t - z), Float64(y / a), x);
	elseif (t_1 <= 4e+162)
		tmp = fma(Float64(1.0 - Float64(t / z)), y, x);
	else
		tmp = Float64(Float64(y / Float64(a - z)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.2], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 4e+162], N[(N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 0.20000000000000001

   1. Initial program 96.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if 0.20000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 3.9999999999999998e162

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. *-inverses N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 90.6

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

   5. Applied rewrites 90.6%

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

   7. Applied rewrites 90.6%

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

   if 3.9999999999999998e162 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. metadata-eval N/A

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

      7. sub-neg N/A

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

      8. lower-*.f64 N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. metadata-eval N/A

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

      14. unsub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 95.1

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

   5. Applied rewrites 95.1%

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

   6. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

      4. lower-*.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 90.9

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

   8. Applied rewrites 90.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{a}, x\right)\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 4 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))))
   (if (<= t_1 0.2)
     (fma (- t z) (/ y a) x)
     (if (<= t_1 1e+39) (fma (- 1.0 (/ t z)) y x) (fma (/ t a) 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 <= 0.2) {
		tmp = fma((t - z), (y / a), x);
	} else if (t_1 <= 1e+39) {
		tmp = fma((1.0 - (t / z)), y, x);
	} else {
		tmp = fma((t / a), 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 <= 0.2)
		tmp = fma(Float64(t - z), Float64(y / a), x);
	elseif (t_1 <= 1e+39)
		tmp = fma(Float64(1.0 - Float64(t / z)), y, x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.2], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1e+39], N[(N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 0.20000000000000001

   1. Initial program 96.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

      6. mul-1-neg N/A

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

      7. lower-fma.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. unsub-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-/.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if 0.20000000000000001 < (/.f64 (-.f64 z t) (-.f64 z a)) < 9.9999999999999994e38

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. *-inverses N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 97.1

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

   5. Applied rewrites 97.1%

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

   7. Applied rewrites 97.1%

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

   if 9.9999999999999994e38 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 69.6

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

   5. Applied rewrites 69.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 69.6

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

   7. Applied rewrites 69.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq 0.2:\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{a}, x\right)\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ \mathbf{if}\;t\_1 \leq 3 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;t\_1 \leq 5000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))))
   (if (<= t_1 3e-42)
     (fma (/ y a) t x)
     (if (<= t_1 5000000.0) (+ y x) (fma (/ t a) 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 <= 3e-42) {
		tmp = fma((y / a), t, x);
	} else if (t_1 <= 5000000.0) {
		tmp = y + x;
	} else {
		tmp = fma((t / a), 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 <= 3e-42)
		tmp = fma(Float64(y / a), t, x);
	elseif (t_1 <= 5000000.0)
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 3e-42], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[t$95$1, 5000000.0], N[(y + x), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 3.00000000000000027e-42

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 79.0

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

   5. Applied rewrites 79.0%

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

   if 3.00000000000000027e-42 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5e6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if 5e6 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 67.8

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

   5. Applied rewrites 67.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.8

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

   7. Applied rewrites 67.8%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq 3 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 5000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a - z}\\ t_2 := \mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{if}\;t\_1 \leq 3 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) (- a z))) (t_2 (fma (/ y a) t x)))
   (if (<= t_1 3e-42) t_2 (if (<= t_1 5000000.0) (+ 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 = fma((y / a), t, x);
	double tmp;
	if (t_1 <= 3e-42) {
		tmp = t_2;
	} else if (t_1 <= 5000000.0) {
		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 = fma(Float64(y / a), t, x)
	tmp = 0.0
	if (t_1 <= 3e-42)
		tmp = t_2;
	elseif (t_1 <= 5000000.0)
		tmp = Float64(y + x);
	else
		tmp = t_2;
	end
	return 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 / a), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[t$95$1, 3e-42], t$95$2, If[LessEqual[t$95$1, 5000000.0], N[(y + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 3.00000000000000027e-42 or 5e6 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 75.2

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

   5. Applied rewrites 75.2%

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

   if 3.00000000000000027e-42 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5e6

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 88.9

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

   5. Applied rewrites 88.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - z}{a - z} \leq 3 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{elif}\;\frac{t - z}{a - z} \leq 5000000:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma z (/ y (- z a)) x)))
   (if (<= z -3.8e+24)
     t_1
     (if (<= z -2.05e-78)
       (fma (/ (- t) z) y x)
       (if (<= z 4.5e-66) (+ (/ (* t y) a) x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(z, (y / (z - a)), x);
	double tmp;
	if (z <= -3.8e+24) {
		tmp = t_1;
	} else if (z <= -2.05e-78) {
		tmp = fma((-t / z), y, x);
	} else if (z <= 4.5e-66) {
		tmp = ((t * y) / a) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(z, Float64(y / Float64(z - a)), x)
	tmp = 0.0
	if (z <= -3.8e+24)
		tmp = t_1;
	elseif (z <= -2.05e-78)
		tmp = fma(Float64(Float64(-t) / z), y, x);
	elseif (z <= 4.5e-66)
		tmp = Float64(Float64(Float64(t * y) / a) + x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -3.8e+24], t$95$1, If[LessEqual[z, -2.05e-78], N[(N[((-t) / z), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[z, 4.5e-66], N[(N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000015e24 or 4.4999999999999998e-66 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.2

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

   5. Applied rewrites 85.2%

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

   7. Applied rewrites 82.2%

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

   if -3.80000000000000015e24 < z < -2.0499999999999999e-78

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. *-inverses N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 94.7

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

   5. Applied rewrites 94.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 83.9%

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

   if -2.0499999999999999e-78 < z < 4.4999999999999998e-66

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 88.2

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

   5. Applied rewrites 88.2%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-78}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{z}, y, x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{t \cdot y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(1 - \frac{t}{z}, y, x\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- 1.0 (/ t z)) y x)))
   (if (<= z -5.8e-79) t_1 (if (<= z 2.8e-29) (fma (/ t a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((1.0 - (t / z)), y, x);
	double tmp;
	if (z <= -5.8e-79) {
		tmp = t_1;
	} else if (z <= 2.8e-29) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(1.0 - Float64(t / z)), y, x)
	tmp = 0.0
	if (z <= -5.8e-79)
		tmp = t_1;
	elseif (z <= 2.8e-29)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -5.8e-79], t$95$1, If[LessEqual[z, 2.8e-29], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000001e-79 or 2.8000000000000002e-29 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. *-inverses N/A

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

      10. mul-1-neg N/A

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

      11. sub-neg N/A

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

      12. div-sub N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 85.0

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

   5. Applied rewrites 85.0%

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

   7. Applied rewrites 85.0%

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

   if -5.8000000000000001e-79 < z < 2.8000000000000002e-29

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 85.3

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

   5. Applied rewrites 85.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 85.3

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

   7. Applied rewrites 85.3%

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

Alternative 10: 59.6% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 61.2

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

5. Applied rewrites 61.2%

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

Developer Target 1: 98.3% accurate, 0.8× 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 2024243 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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