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

Percentage Accurate: 85.2% → 98.3%

Time: 8.2s

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: 85.2% 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: 98.3% 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]

Derivation

1. Initial program 85.5%

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

   1. associate-/l* 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-111}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ z (/ t y)))))
   (if (<= t -2.1e+136)
     (+ x y)
     (if (<= t -6.8e-44)
       t_1
       (if (<= t -2.1e-111)
         (+ x (* y (/ z a)))
         (if (<= t -2.2e-174)
           t_1
           (if (<= t -4.5e-272)
             (+ x (/ (* y z) a))
             (if (<= t 1.36e-34) (+ x (/ y (/ a z))) (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z / (t / y));
	double tmp;
	if (t <= -2.1e+136) {
		tmp = x + y;
	} else if (t <= -6.8e-44) {
		tmp = t_1;
	} else if (t <= -2.1e-111) {
		tmp = x + (y * (z / a));
	} else if (t <= -2.2e-174) {
		tmp = t_1;
	} else if (t <= -4.5e-272) {
		tmp = x + ((y * z) / a);
	} else if (t <= 1.36e-34) {
		tmp = x + (y / (a / z));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (z / (t / y))
    if (t <= (-2.1d+136)) then
        tmp = x + y
    else if (t <= (-6.8d-44)) then
        tmp = t_1
    else if (t <= (-2.1d-111)) then
        tmp = x + (y * (z / a))
    else if (t <= (-2.2d-174)) then
        tmp = t_1
    else if (t <= (-4.5d-272)) then
        tmp = x + ((y * z) / a)
    else if (t <= 1.36d-34) then
        tmp = x + (y / (a / z))
    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 t_1 = x - (z / (t / y));
	double tmp;
	if (t <= -2.1e+136) {
		tmp = x + y;
	} else if (t <= -6.8e-44) {
		tmp = t_1;
	} else if (t <= -2.1e-111) {
		tmp = x + (y * (z / a));
	} else if (t <= -2.2e-174) {
		tmp = t_1;
	} else if (t <= -4.5e-272) {
		tmp = x + ((y * z) / a);
	} else if (t <= 1.36e-34) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z / (t / y))
	tmp = 0
	if t <= -2.1e+136:
		tmp = x + y
	elif t <= -6.8e-44:
		tmp = t_1
	elif t <= -2.1e-111:
		tmp = x + (y * (z / a))
	elif t <= -2.2e-174:
		tmp = t_1
	elif t <= -4.5e-272:
		tmp = x + ((y * z) / a)
	elif t <= 1.36e-34:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z / Float64(t / y)))
	tmp = 0.0
	if (t <= -2.1e+136)
		tmp = Float64(x + y);
	elseif (t <= -6.8e-44)
		tmp = t_1;
	elseif (t <= -2.1e-111)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -2.2e-174)
		tmp = t_1;
	elseif (t <= -4.5e-272)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 1.36e-34)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z / (t / y));
	tmp = 0.0;
	if (t <= -2.1e+136)
		tmp = x + y;
	elseif (t <= -6.8e-44)
		tmp = t_1;
	elseif (t <= -2.1e-111)
		tmp = x + (y * (z / a));
	elseif (t <= -2.2e-174)
		tmp = t_1;
	elseif (t <= -4.5e-272)
		tmp = x + ((y * z) / a);
	elseif (t <= 1.36e-34)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+136], N[(x + y), $MachinePrecision], If[LessEqual[t, -6.8e-44], t$95$1, If[LessEqual[t, -2.1e-111], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.2e-174], t$95$1, If[LessEqual[t, -4.5e-272], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e-34], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.0999999999999999e136 or 1.3600000000000001e-34 < t

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 84.4%

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

   if -2.0999999999999999e136 < t < -6.80000000000000033e-44 or -2.0999999999999999e-111 < t < -2.20000000000000022e-174

   1. Initial program 94.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

   6. Simplified 89.7%

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

   7. Taylor expanded in a around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. unsub-neg 77.0%

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

      4. associate-*l/ 78.7%

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

      5. *-commutative 78.7%

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

   9. Simplified 78.7%

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

       1. clear-num 78.7%

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

       2. un-div-inv 80.5%

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

   11. Applied egg-rr 80.5%

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

   if -6.80000000000000033e-44 < t < -2.0999999999999999e-111

   1. Initial program 86.3%

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

      1. +-commutative 86.3%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 78.7%

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

   if -2.20000000000000022e-174 < t < -4.4999999999999998e-272

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. associate-*r/ 95.3%

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

      3. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around 0 77.4%

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

   if -4.4999999999999998e-272 < t < 1.3600000000000001e-34

   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. associate-*r/ 93.8%

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

      3. fma-def 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. associate-/l* 83.2%

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

   6. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}} + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-44}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-111}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;x - \frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 77.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-43}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+136)
   (+ x y)
   (if (<= t -1.3e-43)
     (- x (* z (/ y t)))
     (if (<= t 1.06e-34) (+ x (/ y (/ a z))) (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+136) {
		tmp = x + y;
	} else if (t <= -1.3e-43) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.06e-34) {
		tmp = x + (y / (a / z));
	} 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 <= (-3.4d+136)) then
        tmp = x + y
    else if (t <= (-1.3d-43)) then
        tmp = x - (z * (y / t))
    else if (t <= 1.06d-34) then
        tmp = x + (y / (a / z))
    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 <= -3.4e+136) {
		tmp = x + y;
	} else if (t <= -1.3e-43) {
		tmp = x - (z * (y / t));
	} else if (t <= 1.06e-34) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+136:
		tmp = x + y
	elif t <= -1.3e-43:
		tmp = x - (z * (y / t))
	elif t <= 1.06e-34:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+136)
		tmp = Float64(x + y);
	elseif (t <= -1.3e-43)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 1.06e-34)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+136)
		tmp = x + y;
	elseif (t <= -1.3e-43)
		tmp = x - (z * (y / t));
	elseif (t <= 1.06e-34)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+136], N[(x + y), $MachinePrecision], If[LessEqual[t, -1.3e-43], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e-34], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999997e136 or 1.06000000000000006e-34 < t

   1. Initial program 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 84.4%

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

   if -3.39999999999999997e136 < t < -1.3e-43

   1. Initial program 93.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 81.5%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in a around 0 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. associate-*l/ 78.5%

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

      5. *-commutative 78.5%

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

   9. Simplified 78.5%

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

   if -1.3e-43 < t < 1.06000000000000006e-34

   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. associate-*r/ 92.9%

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

      3. fma-def 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around 0 74.9%

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

      1. associate-/l* 76.8%

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

   6. Simplified 76.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+136}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-43}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+137} \lor \neg \left(t \leq 1.15 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e+137) (not (<= t 1.15e-9)))
   (+ x y)
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+137) || !(t <= 1.15e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.6d+137)) .or. (.not. (t <= 1.15d-9))) then
        tmp = x + y
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+137) || !(t <= 1.15e-9)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e+137) or not (t <= 1.15e-9):
		tmp = x + y
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e+137) || !(t <= 1.15e-9))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e+137) || ~((t <= 1.15e-9)))
		tmp = x + y;
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e+137], N[Not[LessEqual[t, 1.15e-9]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999999e137 or 1.15e-9 < t

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 84.9%

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

   if -4.59999999999999999e137 < t < 1.15e-9

   1. Initial program 95.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around inf 86.0%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

   6. Simplified 88.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+137} \lor \neg \left(t \leq 1.15 \cdot 10^{-9}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 5: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+40} \lor \neg \left(t \leq 9.5 \cdot 10^{-36}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.05e+40) (not (<= t 9.5e-36)))
   (+ x (- y (* z (/ y t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.05e+40) || !(t <= 9.5e-36)) {
		tmp = x + (y - (z * (y / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.05d+40)) .or. (.not. (t <= 9.5d-36))) then
        tmp = x + (y - (z * (y / t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.05e+40) || !(t <= 9.5e-36)) {
		tmp = x + (y - (z * (y / t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.05e+40) or not (t <= 9.5e-36):
		tmp = x + (y - (z * (y / t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.05e+40) || !(t <= 9.5e-36))
		tmp = Float64(x + Float64(y - Float64(z * Float64(y / t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.05e+40) || ~((t <= 9.5e-36)))
		tmp = x + (y - (z * (y / t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.05e+40], N[Not[LessEqual[t, 9.5e-36]], $MachinePrecision]], N[(x + N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.0500000000000001e40 or 9.5000000000000003e-36 < t

   1. Initial program 77.1%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around 0 86.4%

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

      1. associate-*r/ 86.4%

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

      2. neg-mul-1 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in t around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. mul-1-neg 84.9%

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

      3. unsub-neg 84.9%

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

      4. associate-*l/ 91.0%

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

      5. *-commutative 91.0%

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

   9. Simplified 91.0%

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

   if -2.0500000000000001e40 < t < 9.5000000000000003e-36

   1. Initial program 95.5%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around inf 88.2%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   6. Simplified 90.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+40} \lor \neg \left(t \leq 9.5 \cdot 10^{-36}\right):\\ \;\;\;\;x + \left(y - z \cdot \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]

Alternative 6: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+20} \lor \neg \left(z \leq 7.6 \cdot 10^{-31}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.42e+20) (not (<= z 7.6e-31)))
   (+ x (* z (/ y (- a t))))
   (- x (/ y (+ (/ a t) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.42e+20) || !(z <= 7.6e-31)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.42d+20)) .or. (.not. (z <= 7.6d-31))) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x - (y / ((a / t) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.42e+20) || !(z <= 7.6e-31)) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.42e+20) or not (z <= 7.6e-31):
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x - (y / ((a / t) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.42e+20) || !(z <= 7.6e-31))
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.42e+20) || ~((z <= 7.6e-31)))
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x - (y / ((a / t) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.42e+20], N[Not[LessEqual[z, 7.6e-31]], $MachinePrecision]], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.42e20 or 7.5999999999999999e-31 < z

   1. Initial program 85.4%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in z around inf 81.7%

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

      1. associate-*l/ 90.4%

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

      2. *-commutative 90.4%

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

   6. Simplified 90.4%

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

   if -1.42e20 < z < 7.5999999999999999e-31

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

      4. associate-/l* 91.2%

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

      5. div-sub 91.2%

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

      6. sub-neg 91.2%

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

      7. *-inverses 91.2%

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

      8. metadata-eval 91.2%

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

   6. Simplified 91.2%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{a}{t} + -1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+20} \lor \neg \left(z \leq 7.6 \cdot 10^{-31}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 7: 77.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+39} \lor \neg \left(t \leq 1.45 \cdot 10^{-36}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -9.5e+39) (not (<= t 1.45e-36))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -9.5e+39) || !(t <= 1.45e-36)) {
		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 <= (-9.5d+39)) .or. (.not. (t <= 1.45d-36))) 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 <= -9.5e+39) || !(t <= 1.45e-36)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -9.5e+39) or not (t <= 1.45e-36):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -9.5e+39) || !(t <= 1.45e-36))
		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 <= -9.5e+39) || ~((t <= 1.45e-36)))
		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, -9.5e+39], N[Not[LessEqual[t, 1.45e-36]], $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 < -9.50000000000000011e39 or 1.45000000000000006e-36 < t

   1. Initial program 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 80.1%

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

   if -9.50000000000000011e39 < t < 1.45000000000000006e-36

   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. associate-*r/ 94.1%

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

      3. fma-def 94.1%

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

   3. Simplified 94.1%

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

      1. fma-udef 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in t around 0 74.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+39} \lor \neg \left(t \leq 1.45 \cdot 10^{-36}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 8: 78.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.35e+42)
   (+ x y)
   (if (<= t 1.56e-34) (+ x (/ y (/ a z))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.35e+42) {
		tmp = x + y;
	} else if (t <= 1.56e-34) {
		tmp = x + (y / (a / z));
	} 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 <= (-1.35d+42)) then
        tmp = x + y
    else if (t <= 1.56d-34) then
        tmp = x + (y / (a / z))
    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 <= -1.35e+42) {
		tmp = x + y;
	} else if (t <= 1.56e-34) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.35e+42:
		tmp = x + y
	elif t <= 1.56e-34:
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.35e+42)
		tmp = Float64(x + y);
	elseif (t <= 1.56e-34)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.35e+42)
		tmp = x + y;
	elseif (t <= 1.56e-34)
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.35e+42], N[(x + y), $MachinePrecision], If[LessEqual[t, 1.56e-34], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e42 or 1.55999999999999992e-34 < t

   1. Initial program 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 80.1%

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

   if -1.35e42 < t < 1.55999999999999992e-34

   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. associate-*r/ 94.1%

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

      3. fma-def 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. associate-/l* 74.9%

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

   6. Simplified 74.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+42}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 9: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.5%

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

   1. associate-*l/ 96.3%

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

3. Simplified 96.3%

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

4. Final simplification 96.3%

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

Alternative 10: 61.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.5%

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

   1. +-commutative 85.5%

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

   2. associate-*r/ 97.3%

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

   3. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in t around inf 63.0%

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

5. Final simplification 63.0%

   \[\leadsto x + y \]

Alternative 11: 51.9% 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 85.5%

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

   1. +-commutative 85.5%

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

   2. associate-*r/ 97.3%

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

   3. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in y around 0 48.5%

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

5. Final simplification 48.5%

   \[\leadsto x \]

Developer target: 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 2023224 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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