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

Percentage Accurate: 85.6% → 98.1%

Time: 8.8s

Alternatives: 10

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: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

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 88.2%

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

   1. associate-/l* 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a}{t} + -1}\\ t_2 := x + \frac{y \cdot z}{a - t}\\ \mathbf{if}\;t \leq -1.28 \cdot 10^{+66}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (+ (/ a t) -1.0))) (t_2 (+ x (/ (* y z) (- a t)))))
   (if (<= t -1.28e+66)
     (+ x y)
     (if (<= t 7.5e-34)
       t_2
       (if (<= t 1.4e-28)
         t_1
         (if (<= t 5.5e+102)
           t_2
           (if (<= t 5e+118) t_1 (if (<= t 7e+155) t_2 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a / t) + -1.0);
	double t_2 = x + ((y * z) / (a - t));
	double tmp;
	if (t <= -1.28e+66) {
		tmp = x + y;
	} else if (t <= 7.5e-34) {
		tmp = t_2;
	} else if (t <= 1.4e-28) {
		tmp = t_1;
	} else if (t <= 5.5e+102) {
		tmp = t_2;
	} else if (t <= 5e+118) {
		tmp = t_1;
	} else if (t <= 7e+155) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = -y / ((a / t) + (-1.0d0))
    t_2 = x + ((y * z) / (a - t))
    if (t <= (-1.28d+66)) then
        tmp = x + y
    else if (t <= 7.5d-34) then
        tmp = t_2
    else if (t <= 1.4d-28) then
        tmp = t_1
    else if (t <= 5.5d+102) then
        tmp = t_2
    else if (t <= 5d+118) then
        tmp = t_1
    else if (t <= 7d+155) then
        tmp = t_2
    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 = -y / ((a / t) + -1.0);
	double t_2 = x + ((y * z) / (a - t));
	double tmp;
	if (t <= -1.28e+66) {
		tmp = x + y;
	} else if (t <= 7.5e-34) {
		tmp = t_2;
	} else if (t <= 1.4e-28) {
		tmp = t_1;
	} else if (t <= 5.5e+102) {
		tmp = t_2;
	} else if (t <= 5e+118) {
		tmp = t_1;
	} else if (t <= 7e+155) {
		tmp = t_2;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((a / t) + -1.0)
	t_2 = x + ((y * z) / (a - t))
	tmp = 0
	if t <= -1.28e+66:
		tmp = x + y
	elif t <= 7.5e-34:
		tmp = t_2
	elif t <= 1.4e-28:
		tmp = t_1
	elif t <= 5.5e+102:
		tmp = t_2
	elif t <= 5e+118:
		tmp = t_1
	elif t <= 7e+155:
		tmp = t_2
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(a / t) + -1.0))
	t_2 = Float64(x + Float64(Float64(y * z) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.28e+66)
		tmp = Float64(x + y);
	elseif (t <= 7.5e-34)
		tmp = t_2;
	elseif (t <= 1.4e-28)
		tmp = t_1;
	elseif (t <= 5.5e+102)
		tmp = t_2;
	elseif (t <= 5e+118)
		tmp = t_1;
	elseif (t <= 7e+155)
		tmp = t_2;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((a / t) + -1.0);
	t_2 = x + ((y * z) / (a - t));
	tmp = 0.0;
	if (t <= -1.28e+66)
		tmp = x + y;
	elseif (t <= 7.5e-34)
		tmp = t_2;
	elseif (t <= 1.4e-28)
		tmp = t_1;
	elseif (t <= 5.5e+102)
		tmp = t_2;
	elseif (t <= 5e+118)
		tmp = t_1;
	elseif (t <= 7e+155)
		tmp = t_2;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.28e+66], N[(x + y), $MachinePrecision], If[LessEqual[t, 7.5e-34], t$95$2, If[LessEqual[t, 1.4e-28], t$95$1, If[LessEqual[t, 5.5e+102], t$95$2, If[LessEqual[t, 5e+118], t$95$1, If[LessEqual[t, 7e+155], t$95$2, N[(x + y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.28000000000000003e66 or 6.99999999999999969e155 < t

   1. Initial program 72.9%

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

      1. +-commutative 72.9%

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

      2. associate-*l/ 95.4%

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

      3. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in t around inf 88.5%

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

      1. +-commutative 88.5%

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

   6. Simplified 88.5%

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

   if -1.28000000000000003e66 < t < 7.5000000000000004e-34 or 1.3999999999999999e-28 < t < 5.49999999999999981e102 or 4.99999999999999972e118 < t < 6.99999999999999969e155

   1. Initial program 96.8%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around inf 88.4%

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

   if 7.5000000000000004e-34 < t < 1.3999999999999999e-28 or 5.49999999999999981e102 < t < 4.99999999999999972e118

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-*l/ 91.8%

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

      3. fma-def 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

      3. *-commutative 91.7%

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

      4. associate-/l* 99.9%

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

      5. div-sub 99.9%

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

      6. sub-neg 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. neg-mul-1 99.9%

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

      5. +-commutative 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{+66}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-28}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+118}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+155}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{a}{t} + -1}\\ t_2 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (+ (/ a t) -1.0))) (t_2 (+ x (/ (* y z) a))))
   (if (<= t -7.4e+33)
     (+ x y)
     (if (<= t 4.8e-55)
       (+ x (/ y (/ a z)))
       (if (<= t 4.8e-24)
         t_1
         (if (<= t 1.65e+102)
           t_2
           (if (<= t 6e+118) t_1 (if (<= t 3.4e+142) t_2 (+ x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((a / t) + -1.0);
	double t_2 = x + ((y * z) / a);
	double tmp;
	if (t <= -7.4e+33) {
		tmp = x + y;
	} else if (t <= 4.8e-55) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.8e-24) {
		tmp = t_1;
	} else if (t <= 1.65e+102) {
		tmp = t_2;
	} else if (t <= 6e+118) {
		tmp = t_1;
	} else if (t <= 3.4e+142) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = -y / ((a / t) + (-1.0d0))
    t_2 = x + ((y * z) / a)
    if (t <= (-7.4d+33)) then
        tmp = x + y
    else if (t <= 4.8d-55) then
        tmp = x + (y / (a / z))
    else if (t <= 4.8d-24) then
        tmp = t_1
    else if (t <= 1.65d+102) then
        tmp = t_2
    else if (t <= 6d+118) then
        tmp = t_1
    else if (t <= 3.4d+142) then
        tmp = t_2
    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 = -y / ((a / t) + -1.0);
	double t_2 = x + ((y * z) / a);
	double tmp;
	if (t <= -7.4e+33) {
		tmp = x + y;
	} else if (t <= 4.8e-55) {
		tmp = x + (y / (a / z));
	} else if (t <= 4.8e-24) {
		tmp = t_1;
	} else if (t <= 1.65e+102) {
		tmp = t_2;
	} else if (t <= 6e+118) {
		tmp = t_1;
	} else if (t <= 3.4e+142) {
		tmp = t_2;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((a / t) + -1.0)
	t_2 = x + ((y * z) / a)
	tmp = 0
	if t <= -7.4e+33:
		tmp = x + y
	elif t <= 4.8e-55:
		tmp = x + (y / (a / z))
	elif t <= 4.8e-24:
		tmp = t_1
	elif t <= 1.65e+102:
		tmp = t_2
	elif t <= 6e+118:
		tmp = t_1
	elif t <= 3.4e+142:
		tmp = t_2
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(a / t) + -1.0))
	t_2 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (t <= -7.4e+33)
		tmp = Float64(x + y);
	elseif (t <= 4.8e-55)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 4.8e-24)
		tmp = t_1;
	elseif (t <= 1.65e+102)
		tmp = t_2;
	elseif (t <= 6e+118)
		tmp = t_1;
	elseif (t <= 3.4e+142)
		tmp = t_2;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((a / t) + -1.0);
	t_2 = x + ((y * z) / a);
	tmp = 0.0;
	if (t <= -7.4e+33)
		tmp = x + y;
	elseif (t <= 4.8e-55)
		tmp = x + (y / (a / z));
	elseif (t <= 4.8e-24)
		tmp = t_1;
	elseif (t <= 1.65e+102)
		tmp = t_2;
	elseif (t <= 6e+118)
		tmp = t_1;
	elseif (t <= 3.4e+142)
		tmp = t_2;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+33], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.8e-55], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-24], t$95$1, If[LessEqual[t, 1.65e+102], t$95$2, If[LessEqual[t, 6e+118], t$95$1, If[LessEqual[t, 3.4e+142], t$95$2, N[(x + y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.3999999999999997e33 or 3.3999999999999998e142 < t

   1. Initial program 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-*l/ 95.4%

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

      3. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around inf 85.6%

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

      1. +-commutative 85.6%

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

   6. Simplified 85.6%

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

   if -7.3999999999999997e33 < t < 4.79999999999999983e-55

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-*l/ 97.2%

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

      3. fma-def 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-/l* 86.0%

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

   6. Simplified 86.0%

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

   if 4.79999999999999983e-55 < t < 4.7999999999999996e-24 or 1.64999999999999999e102 < t < 6e118

   1. Initial program 93.9%

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

      1. +-commutative 93.9%

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

      2. associate-*l/ 94.0%

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

      3. fma-def 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. unsub-neg 74.7%

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

      3. *-commutative 74.7%

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

      4. associate-/l* 80.6%

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

      5. div-sub 80.6%

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

      6. sub-neg 80.6%

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

      7. *-inverses 80.6%

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

      8. metadata-eval 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in x around 0 80.6%

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

      1. sub-neg 80.6%

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

      2. metadata-eval 80.6%

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

      3. associate-*r/ 80.6%

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

      4. neg-mul-1 80.6%

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

      5. +-commutative 80.6%

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

   9. Simplified 80.6%

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

   if 4.7999999999999996e-24 < t < 1.64999999999999999e102 or 6e118 < t < 3.3999999999999998e142

   1. Initial program 92.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 69.4%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+118}:\\ \;\;\;\;\frac{-y}{\frac{a}{t} + -1}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) a))))
   (if (<= t -3.1e+34)
     (+ x y)
     (if (<= t 4.8e-55)
       t_1
       (if (<= t 1.08e-23)
         (* y (- 1.0 (/ z t)))
         (if (<= t 6e+99) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double tmp;
	if (t <= -3.1e+34) {
		tmp = x + y;
	} else if (t <= 4.8e-55) {
		tmp = t_1;
	} else if (t <= 1.08e-23) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 6e+99) {
		tmp = t_1;
	} 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 + ((y * z) / a)
    if (t <= (-3.1d+34)) then
        tmp = x + y
    else if (t <= 4.8d-55) then
        tmp = t_1
    else if (t <= 1.08d-23) then
        tmp = y * (1.0d0 - (z / t))
    else if (t <= 6d+99) then
        tmp = t_1
    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 + ((y * z) / a);
	double tmp;
	if (t <= -3.1e+34) {
		tmp = x + y;
	} else if (t <= 4.8e-55) {
		tmp = t_1;
	} else if (t <= 1.08e-23) {
		tmp = y * (1.0 - (z / t));
	} else if (t <= 6e+99) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / a)
	tmp = 0
	if t <= -3.1e+34:
		tmp = x + y
	elif t <= 4.8e-55:
		tmp = t_1
	elif t <= 1.08e-23:
		tmp = y * (1.0 - (z / t))
	elif t <= 6e+99:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / a))
	tmp = 0.0
	if (t <= -3.1e+34)
		tmp = Float64(x + y);
	elseif (t <= 4.8e-55)
		tmp = t_1;
	elseif (t <= 1.08e-23)
		tmp = Float64(y * Float64(1.0 - Float64(z / t)));
	elseif (t <= 6e+99)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / a);
	tmp = 0.0;
	if (t <= -3.1e+34)
		tmp = x + y;
	elseif (t <= 4.8e-55)
		tmp = t_1;
	elseif (t <= 1.08e-23)
		tmp = y * (1.0 - (z / t));
	elseif (t <= 6e+99)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e+34], N[(x + y), $MachinePrecision], If[LessEqual[t, 4.8e-55], t$95$1, If[LessEqual[t, 1.08e-23], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+99], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.09999999999999977e34 or 6.00000000000000029e99 < t

   1. Initial program 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-*l/ 95.7%

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

      3. fma-def 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in t around inf 82.0%

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

      1. +-commutative 82.0%

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

   6. Simplified 82.0%

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

   if -3.09999999999999977e34 < t < 4.79999999999999983e-55 or 1.08000000000000003e-23 < t < 6.00000000000000029e99

   1. Initial program 96.5%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in t around 0 81.8%

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

   if 4.79999999999999983e-55 < t < 1.08000000000000003e-23

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l/ 90.1%

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

      3. fma-def 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in a around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

      3. associate-/l* 67.4%

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

   6. Simplified 67.4%

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

   7. Taylor expanded in y around inf 67.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+34}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+99}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 5: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+41} \lor \neg \left(z \leq 2.3 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+41) (not (<= z 2.3e+39)))
   (+ x (/ (* y z) (- a t)))
   (- x (/ t (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+41) || !(z <= 2.3e+39)) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (t / ((a - t) / 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 ((z <= (-1.4d+41)) .or. (.not. (z <= 2.3d+39))) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x - (t / ((a - t) / 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 ((z <= -1.4e+41) || !(z <= 2.3e+39)) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (t / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+41) or not (z <= 2.3e+39):
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x - (t / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+41) || !(z <= 2.3e+39))
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+41) || ~((z <= 2.3e+39)))
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x - (t / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+41], N[Not[LessEqual[z, 2.3e+39]], $MachinePrecision]], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e41 or 2.30000000000000012e39 < z

   1. Initial program 92.0%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around inf 82.5%

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

   if -1.4e41 < z < 2.30000000000000012e39

   1. Initial program 85.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around 0 81.5%

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

      1. mul-1-neg 81.5%

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

      2. associate-/l* 92.9%

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

   8. Simplified 92.9%

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

   9. Taylor expanded in x around 0 81.5%

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

       1. mul-1-neg 81.5%

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

       2. unsub-neg 81.5%

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

       3. associate-/l* 92.9%

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

   11. Simplified 92.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+41} \lor \neg \left(z \leq 2.3 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 6: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+40} \lor \neg \left(z \leq 4.9 \cdot 10^{+38}\right):\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e+40) (not (<= z 4.9e+38)))
   (+ x (/ (* y z) (- 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 <= -4.8e+40) || !(z <= 4.9e+38)) {
		tmp = x + ((y * z) / (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 <= (-4.8d+40)) .or. (.not. (z <= 4.9d+38))) then
        tmp = x + ((y * z) / (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 <= -4.8e+40) || !(z <= 4.9e+38)) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x - (y / ((a / t) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e+40) or not (z <= 4.9e+38):
		tmp = x + ((y * z) / (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 <= -4.8e+40) || !(z <= 4.9e+38))
		tmp = Float64(x + Float64(Float64(y * z) / 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 <= -4.8e+40) || ~((z <= 4.9e+38)))
		tmp = x + ((y * z) / (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, -4.8e+40], N[Not[LessEqual[z, 4.9e+38]], $MachinePrecision]], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $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 < -4.8e40 or 4.90000000000000002e38 < z

   1. Initial program 92.0%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around inf 82.5%

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

   if -4.8e40 < z < 4.90000000000000002e38

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-*l/ 97.3%

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

      3. fma-def 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 81.5%

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

      1. mul-1-neg 81.5%

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

      2. unsub-neg 81.5%

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

      3. *-commutative 81.5%

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

      4. associate-/l* 95.4%

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

      5. div-sub 95.4%

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

      6. sub-neg 95.4%

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

      7. *-inverses 95.4%

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

      8. metadata-eval 95.4%

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

   6. Simplified 95.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+40} \lor \neg \left(z \leq 4.9 \cdot 10^{+38}\right):\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\ \end{array} \]

Alternative 7: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0061 \lor \neg \left(a \leq 1.7 \cdot 10^{+93}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.0061) (not (<= a 1.7e+93))) (+ x (/ y (/ a z))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.0061) || !(a <= 1.7e+93)) {
		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 ((a <= (-0.0061d0)) .or. (.not. (a <= 1.7d+93))) 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 ((a <= -0.0061) || !(a <= 1.7e+93)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.0061) or not (a <= 1.7e+93):
		tmp = x + (y / (a / z))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.0061) || !(a <= 1.7e+93))
		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 ((a <= -0.0061) || ~((a <= 1.7e+93)))
		tmp = x + (y / (a / z));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.0061], N[Not[LessEqual[a, 1.7e+93]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.00610000000000000039 or 1.7e93 < a

   1. Initial program 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-*l/ 98.2%

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

      3. fma-def 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-/l* 82.8%

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

   6. Simplified 82.8%

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

   if -0.00610000000000000039 < a < 1.7e93

   1. Initial program 86.9%

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

      1. +-commutative 86.9%

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

      2. associate-*l/ 95.0%

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

      3. fma-def 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around inf 71.9%

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

      1. +-commutative 71.9%

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

   6. Simplified 71.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0061 \lor \neg \left(a \leq 1.7 \cdot 10^{+93}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 8: 96.2% 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 88.2%

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

   1. associate-/l* 99.2%

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

3. Simplified 99.2%

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

   1. associate-/r/ 96.6%

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

5. Applied egg-rr 96.6%

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

6. Final simplification 96.6%

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

Alternative 9: 60.5% 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 88.2%

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

   1. +-commutative 88.2%

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

   2. associate-*l/ 96.6%

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

   3. fma-def 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in t around inf 66.3%

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

   1. +-commutative 66.3%

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

6. Simplified 66.3%

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

7. Final simplification 66.3%

   \[\leadsto x + y \]

Alternative 10: 51.5% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 88.2%

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

   1. +-commutative 88.2%

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

   2. associate-*l/ 96.6%

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

   3. fma-def 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in y around 0 52.9%

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

5. Final simplification 52.9%

   \[\leadsto x \]

Developer target: 98.1% 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 2023322 
(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))))