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

Percentage Accurate: 85.8% → 98.4%

Time: 9.2s

Alternatives: 10

Speedup: 1.0×

• could not determine a ground truth

  1. x = 8.488710148297956e-41
  2. y = 2.2410322822143822e-41
  3. z = -3.7862621114826064e-24
  4. t = -9.662351187983504e+213
  5. a = -8.626040502086168e+67

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: 85.8% 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: 98.4% 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 83.8%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

   1. clear-num 98.0%

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

   2. un-div-inv 98.2%

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

6. Applied egg-rr 98.2%

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

7. Final simplification 98.2%

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

Alternative 2: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-222}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+122}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.9e+119)
   (+ x y)
   (if (<= t -2.25e-222)
     (+ x (* z (/ y (- a t))))
     (if (<= t 2.75e-55)
       (+ x (* y (/ (- z t) a)))
       (if (<= t 1.12e+122) (+ x (* y (/ z (- a t)))) (+ x y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.9e+119) {
		tmp = x + y;
	} else if (t <= -2.25e-222) {
		tmp = x + (z * (y / (a - t)));
	} else if (t <= 2.75e-55) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 1.12e+122) {
		tmp = x + (y * (z / (a - 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 <= (-5.9d+119)) then
        tmp = x + y
    else if (t <= (-2.25d-222)) then
        tmp = x + (z * (y / (a - t)))
    else if (t <= 2.75d-55) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 1.12d+122) then
        tmp = x + (y * (z / (a - 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 <= -5.9e+119) {
		tmp = x + y;
	} else if (t <= -2.25e-222) {
		tmp = x + (z * (y / (a - t)));
	} else if (t <= 2.75e-55) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 1.12e+122) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.9e+119:
		tmp = x + y
	elif t <= -2.25e-222:
		tmp = x + (z * (y / (a - t)))
	elif t <= 2.75e-55:
		tmp = x + (y * ((z - t) / a))
	elif t <= 1.12e+122:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.9e+119)
		tmp = Float64(x + y);
	elseif (t <= -2.25e-222)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	elseif (t <= 2.75e-55)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 1.12e+122)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - 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 <= -5.9e+119)
		tmp = x + y;
	elseif (t <= -2.25e-222)
		tmp = x + (z * (y / (a - t)));
	elseif (t <= 2.75e-55)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 1.12e+122)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.9e+119], N[(x + y), $MachinePrecision], If[LessEqual[t, -2.25e-222], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.75e-55], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+122], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.9000000000000001e119 or 1.12000000000000002e122 < t

   1. Initial program 68.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 86.9%

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

   if -5.9000000000000001e119 < t < -2.25000000000000007e-222

   1. Initial program 92.7%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. clear-num 95.5%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in z around inf 87.5%

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

      1. associate-/r/ 89.8%

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

   9. Applied egg-rr 89.8%

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

   if -2.25000000000000007e-222 < t < 2.7499999999999999e-55

   1. Initial program 92.5%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in a around inf 86.6%

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

      1. associate-/l* 92.5%

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

   7. Simplified 92.5%

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

   if 2.7499999999999999e-55 < t < 1.12000000000000002e122

   1. Initial program 87.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 80.1%

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

      1. associate-/l* 88.7%

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

   7. Simplified 88.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-222}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+122}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a - t}\\ t_2 := x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+115}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- a t))))) (t_2 (- x (* y (+ (/ z t) -1.0)))))
   (if (<= t -1.55e+115)
     t_2
     (if (<= t -2.8e-226)
       t_1
       (if (<= t 2.5e-30)
         (+ x (* y (/ (- z t) a)))
         (if (<= t 2.3e+54) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double t_2 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -1.55e+115) {
		tmp = t_2;
	} else if (t <= -2.8e-226) {
		tmp = t_1;
	} else if (t <= 2.5e-30) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 2.3e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / (a - t)))
    t_2 = x - (y * ((z / t) + (-1.0d0)))
    if (t <= (-1.55d+115)) then
        tmp = t_2
    else if (t <= (-2.8d-226)) then
        tmp = t_1
    else if (t <= 2.5d-30) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 2.3d+54) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double t_2 = x - (y * ((z / t) + -1.0));
	double tmp;
	if (t <= -1.55e+115) {
		tmp = t_2;
	} else if (t <= -2.8e-226) {
		tmp = t_1;
	} else if (t <= 2.5e-30) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 2.3e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (a - t)))
	t_2 = x - (y * ((z / t) + -1.0))
	tmp = 0
	if t <= -1.55e+115:
		tmp = t_2
	elif t <= -2.8e-226:
		tmp = t_1
	elif t <= 2.5e-30:
		tmp = x + (y * ((z - t) / a))
	elif t <= 2.3e+54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(a - t))))
	t_2 = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)))
	tmp = 0.0
	if (t <= -1.55e+115)
		tmp = t_2;
	elseif (t <= -2.8e-226)
		tmp = t_1;
	elseif (t <= 2.5e-30)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 2.3e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (a - t)));
	t_2 = x - (y * ((z / t) + -1.0));
	tmp = 0.0;
	if (t <= -1.55e+115)
		tmp = t_2;
	elseif (t <= -2.8e-226)
		tmp = t_1;
	elseif (t <= 2.5e-30)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 2.3e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+115], t$95$2, If[LessEqual[t, -2.8e-226], t$95$1, If[LessEqual[t, 2.5e-30], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+54], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55000000000000002e115 or 2.29999999999999994e54 < t

   1. Initial program 68.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. associate-/l* 91.0%

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

      3. distribute-lft-neg-in 91.0%

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

      4. div-sub 91.0%

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

      5. sub-neg 91.0%

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

      6. *-inverses 91.0%

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

      7. metadata-eval 91.0%

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

   7. Simplified 91.0%

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

   if -1.55000000000000002e115 < t < -2.80000000000000008e-226 or 2.49999999999999986e-30 < t < 2.29999999999999994e54

   1. Initial program 93.4%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.5%

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

      2. un-div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in z around inf 87.3%

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

      1. associate-/r/ 89.1%

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

   9. Applied egg-rr 89.1%

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

   if -2.80000000000000008e-226 < t < 2.49999999999999986e-30

   1. Initial program 93.1%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in a around inf 87.7%

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

      1. associate-/l* 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+115}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-226}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+115}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y (- a t))))))
   (if (<= t -1.55e+115)
     (- x (* y (+ (/ z t) -1.0)))
     (if (<= t -4e-219)
       t_1
       (if (<= t 4.5e-30)
         (+ x (* y (/ (- z t) a)))
         (if (<= t 2e+54) t_1 (+ x (/ y (/ t (- t z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (t <= -1.55e+115) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= -4e-219) {
		tmp = t_1;
	} else if (t <= 4.5e-30) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 2e+54) {
		tmp = t_1;
	} else {
		tmp = x + (y / (t / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / (a - t)))
    if (t <= (-1.55d+115)) then
        tmp = x - (y * ((z / t) + (-1.0d0)))
    else if (t <= (-4d-219)) then
        tmp = t_1
    else if (t <= 4.5d-30) then
        tmp = x + (y * ((z - t) / a))
    else if (t <= 2d+54) then
        tmp = t_1
    else
        tmp = x + (y / (t / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / (a - t)));
	double tmp;
	if (t <= -1.55e+115) {
		tmp = x - (y * ((z / t) + -1.0));
	} else if (t <= -4e-219) {
		tmp = t_1;
	} else if (t <= 4.5e-30) {
		tmp = x + (y * ((z - t) / a));
	} else if (t <= 2e+54) {
		tmp = t_1;
	} else {
		tmp = x + (y / (t / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / (a - t)))
	tmp = 0
	if t <= -1.55e+115:
		tmp = x - (y * ((z / t) + -1.0))
	elif t <= -4e-219:
		tmp = t_1
	elif t <= 4.5e-30:
		tmp = x + (y * ((z - t) / a))
	elif t <= 2e+54:
		tmp = t_1
	else:
		tmp = x + (y / (t / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.55e+115)
		tmp = Float64(x - Float64(y * Float64(Float64(z / t) + -1.0)));
	elseif (t <= -4e-219)
		tmp = t_1;
	elseif (t <= 4.5e-30)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t <= 2e+54)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(t / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / (a - t)));
	tmp = 0.0;
	if (t <= -1.55e+115)
		tmp = x - (y * ((z / t) + -1.0));
	elseif (t <= -4e-219)
		tmp = t_1;
	elseif (t <= 4.5e-30)
		tmp = x + (y * ((z - t) / a));
	elseif (t <= 2e+54)
		tmp = t_1;
	else
		tmp = x + (y / (t / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+115], N[(x - N[(y * N[(N[(z / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-219], t$95$1, If[LessEqual[t, 4.5e-30], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+54], t$95$1, N[(x + N[(y / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.55000000000000002e115

   1. Initial program 68.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-in 87.5%

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

      4. div-sub 87.5%

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

      5. sub-neg 87.5%

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

      6. *-inverses 87.5%

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

      7. metadata-eval 87.5%

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

   7. Simplified 87.5%

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

   if -1.55000000000000002e115 < t < -4.0000000000000001e-219 or 4.49999999999999967e-30 < t < 2.0000000000000002e54

   1. Initial program 93.4%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.5%

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

      2. un-div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

   7. Taylor expanded in z around inf 87.3%

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

      1. associate-/r/ 89.1%

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

   9. Applied egg-rr 89.1%

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

   if -4.0000000000000001e-219 < t < 4.49999999999999967e-30

   1. Initial program 93.1%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in a around inf 87.7%

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

      1. associate-/l* 93.1%

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

   7. Simplified 93.1%

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

   if 2.0000000000000002e54 < t

   1. Initial program 68.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in a around 0 93.3%

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

      1. neg-mul-1 93.3%

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

      2. distribute-neg-frac2 93.3%

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

      3. neg-sub0 93.3%

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

      4. associate--r- 93.3%

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

      5. neg-sub0 93.3%

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

   9. Simplified 93.3%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{t}{\left(-z\right) + t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+115}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{t} + -1\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-219}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-30}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+54}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+116} \lor \neg \left(t \leq 2 \cdot 10^{+122}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.52e+116) (not (<= t 2e+122)))
   (+ x y)
   (+ x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.52e+116) || !(t <= 2e+122)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.52d+116)) .or. (.not. (t <= 2d+122))) then
        tmp = x + y
    else
        tmp = x + (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.52e+116) || !(t <= 2e+122)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.52e+116) or not (t <= 2e+122):
		tmp = x + y
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.52e+116) || !(t <= 2e+122))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.52e+116) || ~((t <= 2e+122)))
		tmp = x + y;
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.52e+116], N[Not[LessEqual[t, 2e+122]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.52e116 or 2.00000000000000003e122 < t

   1. Initial program 68.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 86.9%

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

   if -1.52e116 < t < 2.00000000000000003e122

   1. Initial program 91.2%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 83.0%

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

      1. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+116} \lor \neg \left(t \leq 2 \cdot 10^{+122}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-32} \lor \neg \left(t \leq 980000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e-32) (not (<= t 980000000.0)))
   (+ x y)
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e-32) || !(t <= 980000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.6d-32)) .or. (.not. (t <= 980000000.0d0))) then
        tmp = x + y
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e-32) || !(t <= 980000000.0)) {
		tmp = x + y;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e-32) or not (t <= 980000000.0):
		tmp = x + y
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e-32) || !(t <= 980000000.0))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e-32) || ~((t <= 980000000.0)))
		tmp = x + y;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e-32], N[Not[LessEqual[t, 980000000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6000000000000001e-32 or 9.8e8 < t

   1. Initial program 74.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 74.6%

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

   if -4.6000000000000001e-32 < t < 9.8e8

   1. Initial program 95.0%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in a around inf 84.4%

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

   6. Taylor expanded in z around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. distribute-lft-neg-out 53.8%

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

      3. *-commutative 53.8%

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

   8. Simplified 53.8%

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

      1. div-inv 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-*l* 55.1%

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

      4. add-sqr-sqrt 23.4%

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

      5. sqrt-unprod 47.9%

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

      6. sqr-neg 47.9%

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

      7. sqrt-unprod 27.8%

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

      8. add-sqr-sqrt 53.2%

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

      9. div-inv 53.2%

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

   10. Applied egg-rr 53.2%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-32} \lor \neg \left(t \leq 980000000\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+103} \lor \neg \left(t \leq 6.5 \cdot 10^{+40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.8e+103) (not (<= t 6.5e+40))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.8e+103) || !(t <= 6.5e+40)) {
		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 <= (-8.8d+103)) .or. (.not. (t <= 6.5d+40))) 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 <= -8.8e+103) || !(t <= 6.5e+40)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.8e+103) or not (t <= 6.5e+40):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.8e+103) || !(t <= 6.5e+40))
		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 <= -8.8e+103) || ~((t <= 6.5e+40)))
		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, -8.8e+103], N[Not[LessEqual[t, 6.5e+40]], $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 < -8.7999999999999997e103 or 6.5000000000000001e40 < t

   1. Initial program 69.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 81.6%

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

   if -8.7999999999999997e103 < t < 6.5000000000000001e40

   1. Initial program 94.1%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 74.2%

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

      1. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+103} \lor \neg \left(t \leq 6.5 \cdot 10^{+40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e+37) x (if (<= a 1.7e+93) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+37) {
		tmp = x;
	} else if (a <= 1.7e+93) {
		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 (a <= (-5.2d+37)) then
        tmp = x
    else if (a <= 1.7d+93) 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 (a <= -5.2e+37) {
		tmp = x;
	} else if (a <= 1.7e+93) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.2e+37:
		tmp = x
	elif a <= 1.7e+93:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e+37)
		tmp = x;
	elseif (a <= 1.7e+93)
		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 (a <= -5.2e+37)
		tmp = x;
	elseif (a <= 1.7e+93)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e+37], x, If[LessEqual[a, 1.7e+93], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.1999999999999998e37 or 1.7e93 < a

   1. Initial program 84.8%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around 0 79.4%

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

   6. Taylor expanded in x around inf 65.3%

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

   if -5.1999999999999998e37 < a < 1.7e93

   1. Initial program 83.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   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 t around inf 61.5%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+93}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 10: 52.0% 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 83.8%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Taylor expanded in t around 0 60.5%

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

6. Taylor expanded in x around inf 49.3%

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

7. Final simplification 49.3%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 98.4% 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 2024074 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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