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

Percentage Accurate: 86.2% → 98.1%

Time: 11.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 2: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-71}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+100}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e-71)
   (+ x y)
   (if (<= t 6.5e-84)
     (+ x (/ y (/ a z)))
     (if (<= t 1.2e+100) (- x (/ z (/ t y))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e-71) {
		tmp = x + y;
	} else if (t <= 6.5e-84) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.2e+100) {
		tmp = x - (z / (t / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7d-71)) then
        tmp = x + y
    else if (t <= 6.5d-84) then
        tmp = x + (y / (a / z))
    else if (t <= 1.2d+100) then
        tmp = x - (z / (t / y))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e-71) {
		tmp = x + y;
	} else if (t <= 6.5e-84) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.2e+100) {
		tmp = x - (z / (t / y));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e-71:
		tmp = x + y
	elif t <= 6.5e-84:
		tmp = x + (y / (a / z))
	elif t <= 1.2e+100:
		tmp = x - (z / (t / y))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e-71)
		tmp = Float64(x + y);
	elseif (t <= 6.5e-84)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.2e+100)
		tmp = Float64(x - Float64(z / Float64(t / y)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e-71)
		tmp = x + y;
	elseif (t <= 6.5e-84)
		tmp = x + (y / (a / z));
	elseif (t <= 1.2e+100)
		tmp = x - (z / (t / y));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e-71], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.5e-84], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+100], N[(x - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.9999999999999998e-71 or 1.20000000000000006e100 < t

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-/l* 94.2%

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

      4. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around inf 72.1%

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

      1. +-commutative 72.1%

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

   7. Simplified 72.1%

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

   if -6.9999999999999998e-71 < t < 6.50000000000000022e-84

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-/l* 93.0%

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

      4. fma-define 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.4%

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

   9. Applied egg-rr 85.4%

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

   if 6.50000000000000022e-84 < t < 1.20000000000000006e100

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. *-commutative 95.2%

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

      3. associate-/l* 99.7%

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

      4. fma-define 99.7%

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

   3. Simplified 99.7%

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

      1. fma-undefine 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 86.7%

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

   8. Taylor expanded in a around 0 79.4%

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

      1. neg-mul-1 79.4%

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

      2. distribute-neg-frac 79.4%

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

   10. Simplified 79.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-71}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-84}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+100}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e-70)
   (+ x y)
   (if (<= t 9e-82)
     (+ x (/ y (/ a z)))
     (if (<= t 3.8e+99) (- x (* y (/ z t))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e-70) {
		tmp = x + y;
	} else if (t <= 9e-82) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.8e+99) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.22d-70)) then
        tmp = x + y
    else if (t <= 9d-82) then
        tmp = x + (y / (a / z))
    else if (t <= 3.8d+99) then
        tmp = x - (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e-70) {
		tmp = x + y;
	} else if (t <= 9e-82) {
		tmp = x + (y / (a / z));
	} else if (t <= 3.8e+99) {
		tmp = x - (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e-70:
		tmp = x + y
	elif t <= 9e-82:
		tmp = x + (y / (a / z))
	elif t <= 3.8e+99:
		tmp = x - (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e-70)
		tmp = Float64(x + y);
	elseif (t <= 9e-82)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 3.8e+99)
		tmp = Float64(x - Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e-70)
		tmp = x + y;
	elseif (t <= 9e-82)
		tmp = x + (y / (a / z));
	elseif (t <= 3.8e+99)
		tmp = x - (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e-70], N[(x + y), $MachinePrecision], If[LessEqual[t, 9e-82], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+99], N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22e-70 or 3.8e99 < t

   1. Initial program 76.4%

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

      1. +-commutative 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-/l* 94.2%

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

      4. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around inf 72.1%

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

      1. +-commutative 72.1%

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

   7. Simplified 72.1%

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

   if -1.22e-70 < t < 8.9999999999999997e-82

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-/l* 93.0%

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

      4. fma-define 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.4%

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

   9. Applied egg-rr 85.4%

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

   if 8.9999999999999997e-82 < t < 3.8e99

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. *-commutative 95.2%

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

      3. associate-/l* 99.7%

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

      4. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. mul-1-neg 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in z around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-/l* 79.4%

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

      3. distribute-rgt-neg-in 79.4%

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

      4. distribute-neg-frac2 79.4%

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

   10. Simplified 79.4%

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

   11. Taylor expanded in y around 0 77.2%

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

       1. mul-1-neg 77.2%

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

       2. associate-*r/ 79.4%

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

       3. unsub-neg 79.4%

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

   13. Simplified 79.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+99}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+82} \lor \neg \left(t \leq 1.65 \cdot 10^{+181}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+82) (not (<= t 1.65e+181)))
   (+ x y)
   (- x (* y (/ z (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+82) || !(t <= 1.65e+181)) {
		tmp = x + y;
	} else {
		tmp = x - (y * (z / (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 ((t <= (-2.3d+82)) .or. (.not. (t <= 1.65d+181))) then
        tmp = x + y
    else
        tmp = x - (y * (z / (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 ((t <= -2.3e+82) || !(t <= 1.65e+181)) {
		tmp = x + y;
	} else {
		tmp = x - (y * (z / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+82) or not (t <= 1.65e+181):
		tmp = x + y
	else:
		tmp = x - (y * (z / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+82) || !(t <= 1.65e+181))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e+82) || ~((t <= 1.65e+181)))
		tmp = x + y;
	else
		tmp = x - (y * (z / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+82], N[Not[LessEqual[t, 1.65e+181]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.29999999999999988e82 or 1.65000000000000008e181 < t

   1. Initial program 71.5%

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

      1. +-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. associate-/l* 91.5%

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

      4. fma-define 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around inf 83.9%

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

      1. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   if -2.29999999999999988e82 < t < 1.65000000000000008e181

   1. Initial program 92.1%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 81.6%

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

      1. associate-/l* 84.8%

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

   7. Simplified 84.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+82} \lor \neg \left(t \leq 1.65 \cdot 10^{+181}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-45)
   (- x (/ z (/ (- t a) y)))
   (if (<= z 8.8e-48) (+ x (* y (/ t (- t a)))) (- x (* y (/ z (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-45) {
		tmp = x - (z / ((t - a) / y));
	} else if (z <= 8.8e-48) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x - (y * (z / (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 <= (-4.4d-45)) then
        tmp = x - (z / ((t - a) / y))
    else if (z <= 8.8d-48) then
        tmp = x + (y * (t / (t - a)))
    else
        tmp = x - (y * (z / (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 <= -4.4e-45) {
		tmp = x - (z / ((t - a) / y));
	} else if (z <= 8.8e-48) {
		tmp = x + (y * (t / (t - a)));
	} else {
		tmp = x - (y * (z / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-45:
		tmp = x - (z / ((t - a) / y))
	elif z <= 8.8e-48:
		tmp = x + (y * (t / (t - a)))
	else:
		tmp = x - (y * (z / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-45)
		tmp = Float64(x - Float64(z / Float64(Float64(t - a) / y)));
	elseif (z <= 8.8e-48)
		tmp = Float64(x + Float64(y * Float64(t / Float64(t - a))));
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e-45)
		tmp = x - (z / ((t - a) / y));
	elseif (z <= 8.8e-48)
		tmp = x + (y * (t / (t - a)));
	else
		tmp = x - (y * (z / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-45], N[(x - N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-48], N[(x + N[(y * N[(t / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999987e-45

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-/l* 95.2%

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

      4. fma-define 95.2%

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

   3. Simplified 95.2%

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

      1. fma-undefine 95.2%

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

      2. clear-num 95.3%

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

      3. un-div-inv 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in z around inf 88.7%

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

   if -4.39999999999999987e-45 < z < 8.8000000000000005e-48

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-/l* 93.3%

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

      4. fma-define 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. *-commutative 80.7%

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

      4. *-lft-identity 80.7%

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

      5. times-frac 92.5%

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

      6. /-rgt-identity 92.5%

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

   7. Simplified 92.5%

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

   if 8.8000000000000005e-48 < z

   1. Initial program 87.5%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 85.7%

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

      1. associate-/l* 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x - \frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-48}:\\ \;\;\;\;x + y \cdot \frac{t}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{-42}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e-46)
   (- x (/ z (/ (- t a) y)))
   (if (<= z 1.34e-42) (+ x (* t (/ y (- t a)))) (- x (* y (/ z (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e-46) {
		tmp = x - (z / ((t - a) / y));
	} else if (z <= 1.34e-42) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x - (y * (z / (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 <= (-7.5d-46)) then
        tmp = x - (z / ((t - a) / y))
    else if (z <= 1.34d-42) then
        tmp = x + (t * (y / (t - a)))
    else
        tmp = x - (y * (z / (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 <= -7.5e-46) {
		tmp = x - (z / ((t - a) / y));
	} else if (z <= 1.34e-42) {
		tmp = x + (t * (y / (t - a)));
	} else {
		tmp = x - (y * (z / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e-46:
		tmp = x - (z / ((t - a) / y))
	elif z <= 1.34e-42:
		tmp = x + (t * (y / (t - a)))
	else:
		tmp = x - (y * (z / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e-46)
		tmp = Float64(x - Float64(z / Float64(Float64(t - a) / y)));
	elseif (z <= 1.34e-42)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e-46)
		tmp = x - (z / ((t - a) / y));
	elseif (z <= 1.34e-42)
		tmp = x + (t * (y / (t - a)));
	else
		tmp = x - (y * (z / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e-46], N[(x - N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.34e-42], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000027e-46

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-/l* 95.2%

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

      4. fma-define 95.2%

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

   3. Simplified 95.2%

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

      1. fma-undefine 95.2%

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

      2. clear-num 95.3%

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

      3. un-div-inv 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in z around inf 88.7%

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

   if -7.50000000000000027e-46 < z < 1.34e-42

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-/l* 93.3%

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

      4. fma-define 93.3%

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

   3. Simplified 93.3%

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

      1. fma-undefine 93.3%

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

      2. clear-num 93.2%

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

      3. un-div-inv 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in z around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. associate-*r/ 90.7%

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

      3. unsub-neg 90.7%

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

   9. Simplified 90.7%

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

   if 1.34e-42 < z

   1. Initial program 87.5%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in z around inf 85.7%

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

      1. associate-/l* 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{-42}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-72} \lor \neg \left(t \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.85e-72) (not (<= t 5e-66))) (+ x y) (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e-72) || !(t <= 5e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / 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) :: tmp
    if ((t <= (-1.85d-72)) .or. (.not. (t <= 5d-66))) then
        tmp = x + y
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e-72) || !(t <= 5e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.85e-72) or not (t <= 5e-66):
		tmp = x + y
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.85e-72) || !(t <= 5e-66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.85e-72) || ~((t <= 5e-66)))
		tmp = x + y;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.85e-72], N[Not[LessEqual[t, 5e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8499999999999999e-72 or 4.99999999999999962e-66 < t

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-/l* 95.5%

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

      4. fma-define 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   7. Simplified 67.8%

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

   if -1.8499999999999999e-72 < t < 4.99999999999999962e-66

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-/l* 93.1%

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

      4. fma-define 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

      1. clear-num 84.6%

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

      2. un-div-inv 84.6%

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

   9. Applied egg-rr 84.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-72} \lor \neg \left(t \leq 5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-71} \lor \neg \left(t \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e-71) (not (<= t 3.4e-66))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e-71) || !(t <= 3.4e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / 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 ((t <= (-8.5d-71)) .or. (.not. (t <= 3.4d-66))) then
        tmp = x + y
    else
        tmp = x + (y * (z / 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 ((t <= -8.5e-71) || !(t <= 3.4e-66)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e-71) or not (t <= 3.4e-66):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e-71) || !(t <= 3.4e-66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e-71) || ~((t <= 3.4e-66)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e-71], N[Not[LessEqual[t, 3.4e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.49999999999999988e-71 or 3.39999999999999997e-66 < t

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-/l* 95.5%

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

      4. fma-define 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   7. Simplified 67.8%

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

   if -8.49999999999999988e-71 < t < 3.39999999999999997e-66

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-/l* 93.1%

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

      4. fma-define 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/l* 84.6%

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

   7. Simplified 84.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-71} \lor \neg \left(t \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-71} \lor \neg \left(t \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e-71) (not (<= t 4.5e-66))) (+ x y) (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e-71) || !(t <= 4.5e-66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / 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 ((t <= (-2.3d-71)) .or. (.not. (t <= 4.5d-66))) then
        tmp = x + y
    else
        tmp = x + ((y * z) / 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 ((t <= -2.3e-71) || !(t <= 4.5e-66)) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e-71) or not (t <= 4.5e-66):
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e-71) || !(t <= 4.5e-66))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.3e-71) || ~((t <= 4.5e-66)))
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e-71], N[Not[LessEqual[t, 4.5e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2999999999999998e-71 or 4.4999999999999998e-66 < t

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-/l* 95.5%

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

      4. fma-define 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   7. Simplified 67.8%

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

   if -2.2999999999999998e-71 < t < 4.4999999999999998e-66

   1. Initial program 95.6%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around 0 83.6%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-71} \lor \neg \left(t \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-71} \lor \neg \left(t \leq 3.6 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e-71) (not (<= t 3.6e-66))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-71) || !(t <= 3.6e-66)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-9.5d-71)) .or. (.not. (t <= 3.6d-66))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e-71) || !(t <= 3.6e-66)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e-71) or not (t <= 3.6e-66):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e-71) || !(t <= 3.6e-66))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -9.5e-71) || ~((t <= 3.6e-66)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -9.5e-71], N[Not[LessEqual[t, 3.6e-66]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999994e-71 or 3.60000000000000012e-66 < t

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-/l* 95.5%

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

      4. fma-define 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around inf 67.8%

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

      1. +-commutative 67.8%

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

   7. Simplified 67.8%

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

   if -9.4999999999999994e-71 < t < 3.60000000000000012e-66

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-/l* 93.1%

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

      4. fma-define 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in y around 0 54.2%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-71} \lor \neg \left(t \leq 3.6 \cdot 10^{-66}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% 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 86.6%

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

   1. +-commutative 86.6%

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

   2. *-commutative 86.6%

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

   3. associate-/l* 94.6%

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

   4. fma-define 94.6%

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

3. Simplified 94.6%

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

5. Taylor expanded in y around 0 52.5%

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

Developer Target 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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