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

Percentage Accurate: 98.1% → 98.1%

Time: 8.8s

Alternatives: 10

Speedup: 1.0×

Specification

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]

Initial Program: 98.1% 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]

Alternative 1: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. +-commutative 98.6%

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

   2. fma-def 98.6%

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

3. Simplified 98.6%

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

4. Final simplification 98.6%

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

Alternative 2: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 6200000:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{1 - \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y t) (- t z)))))
   (if (<= t -6.5e+76)
     t_1
     (if (<= t 1.15e-89)
       (+ x (* z (/ y (- a t))))
       (if (<= t 6200000.0)
         (- x (* y (/ (- t z) a)))
         (if (<= t 4.3e+81)
           t_1
           (if (<= t 1.45e+115) (/ y (- 1.0 (/ a t))) (+ y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / t) * (t - z));
	double tmp;
	if (t <= -6.5e+76) {
		tmp = t_1;
	} else if (t <= 1.15e-89) {
		tmp = x + (z * (y / (a - t)));
	} else if (t <= 6200000.0) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 4.3e+81) {
		tmp = t_1;
	} else if (t <= 1.45e+115) {
		tmp = y / (1.0 - (a / t));
	} else {
		tmp = y + 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / t) * (t - z))
    if (t <= (-6.5d+76)) then
        tmp = t_1
    else if (t <= 1.15d-89) then
        tmp = x + (z * (y / (a - t)))
    else if (t <= 6200000.0d0) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 4.3d+81) then
        tmp = t_1
    else if (t <= 1.45d+115) then
        tmp = y / (1.0d0 - (a / t))
    else
        tmp = y + x
    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 / t) * (t - z));
	double tmp;
	if (t <= -6.5e+76) {
		tmp = t_1;
	} else if (t <= 1.15e-89) {
		tmp = x + (z * (y / (a - t)));
	} else if (t <= 6200000.0) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 4.3e+81) {
		tmp = t_1;
	} else if (t <= 1.45e+115) {
		tmp = y / (1.0 - (a / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / t) * (t - z))
	tmp = 0
	if t <= -6.5e+76:
		tmp = t_1
	elif t <= 1.15e-89:
		tmp = x + (z * (y / (a - t)))
	elif t <= 6200000.0:
		tmp = x - (y * ((t - z) / a))
	elif t <= 4.3e+81:
		tmp = t_1
	elif t <= 1.45e+115:
		tmp = y / (1.0 - (a / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / t) * Float64(t - z)))
	tmp = 0.0
	if (t <= -6.5e+76)
		tmp = t_1;
	elseif (t <= 1.15e-89)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	elseif (t <= 6200000.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 4.3e+81)
		tmp = t_1;
	elseif (t <= 1.45e+115)
		tmp = Float64(y / Float64(1.0 - Float64(a / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / t) * (t - z));
	tmp = 0.0;
	if (t <= -6.5e+76)
		tmp = t_1;
	elseif (t <= 1.15e-89)
		tmp = x + (z * (y / (a - t)));
	elseif (t <= 6200000.0)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 4.3e+81)
		tmp = t_1;
	elseif (t <= 1.45e+115)
		tmp = y / (1.0 - (a / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+76], t$95$1, If[LessEqual[t, 1.15e-89], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6200000.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e+81], t$95$1, If[LessEqual[t, 1.45e+115], N[(y / N[(1.0 - N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.5000000000000005e76 or 6.2e6 < t < 4.3000000000000001e81

   1. Initial program 99.9%

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

   2. Taylor expanded in a around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. unsub-neg 73.1%

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

      3. associate-/l* 92.6%

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

      4. associate-/r/ 88.1%

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

   4. Simplified 88.1%

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

   if -6.5000000000000005e76 < t < 1.15e-89

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. associate-/l* 91.4%

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

      2. associate-/r/ 92.0%

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

   4. Simplified 92.0%

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

   if 1.15e-89 < t < 6.2e6

   1. Initial program 99.6%

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

   2. Taylor expanded in a around inf 99.6%

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

   if 4.3000000000000001e81 < t < 1.45000000000000002e115

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 62.3%

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

      1. mul-1-neg 62.3%

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

      2. unsub-neg 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-/l* 99.4%

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

   4. Simplified 99.4%

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

      1. div-inv 99.7%

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

      2. div-sub 99.7%

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

      3. pow1 99.7%

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

      4. pow1 99.7%

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

      5. pow-div 99.7%

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

      6. metadata-eval 99.7%

         \[\leadsto x - y \cdot \frac{1}{\frac{a}{t} - {t}^{\color{blue}{0}}} \]

      7. metadata-eval 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0 89.7%

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

      1. metadata-eval 89.7%

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

      2. sub-neg 89.7%

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

      3. metadata-eval 89.7%

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

      4. times-frac 89.7%

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

      5. *-lft-identity 89.7%

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

      6. neg-mul-1 89.7%

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

      7. neg-sub0 89.7%

         \[\leadsto \frac{y}{\color{blue}{0 - \left(\frac{a}{t} + -1\right)}} \]

      8. +-commutative 89.7%

         \[\leadsto \frac{y}{0 - \color{blue}{\left(-1 + \frac{a}{t}\right)}} \]

      9. associate--r+ 89.7%

         \[\leadsto \frac{y}{\color{blue}{\left(0 - -1\right) - \frac{a}{t}}} \]

      10. metadata-eval 89.7%

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

   9. Simplified 89.7%

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

   if 1.45000000000000002e115 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 87.9%

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

      1. +-commutative 87.9%

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

   4. Simplified 87.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 6200000:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{1 - \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3300000:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+29}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+77)
   (+ y x)
   (if (<= t 5.6e-89)
     (+ x (* z (/ y (- a t))))
     (if (<= t 3300000.0)
       (- x (* y (/ (- t z) a)))
       (if (<= t 3e+29) (- x (* z (/ y t))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+77) {
		tmp = y + x;
	} else if (t <= 5.6e-89) {
		tmp = x + (z * (y / (a - t)));
	} else if (t <= 3300000.0) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 3e+29) {
		tmp = x - (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d+77)) then
        tmp = y + x
    else if (t <= 5.6d-89) then
        tmp = x + (z * (y / (a - t)))
    else if (t <= 3300000.0d0) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 3d+29) then
        tmp = x - (z * (y / t))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+77) {
		tmp = y + x;
	} else if (t <= 5.6e-89) {
		tmp = x + (z * (y / (a - t)));
	} else if (t <= 3300000.0) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 3e+29) {
		tmp = x - (z * (y / t));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+77:
		tmp = y + x
	elif t <= 5.6e-89:
		tmp = x + (z * (y / (a - t)))
	elif t <= 3300000.0:
		tmp = x - (y * ((t - z) / a))
	elif t <= 3e+29:
		tmp = x - (z * (y / t))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+77)
		tmp = Float64(y + x);
	elseif (t <= 5.6e-89)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	elseif (t <= 3300000.0)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 3e+29)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+77)
		tmp = y + x;
	elseif (t <= 5.6e-89)
		tmp = x + (z * (y / (a - t)));
	elseif (t <= 3300000.0)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 3e+29)
		tmp = x - (z * (y / t));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+77], N[(y + x), $MachinePrecision], If[LessEqual[t, 5.6e-89], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3300000.0], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+29], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.14999999999999997e77 or 2.9999999999999999e29 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.3%

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

      1. +-commutative 82.3%

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

   4. Simplified 82.3%

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

   if -1.14999999999999997e77 < t < 5.5999999999999998e-89

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. associate-/l* 91.4%

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

      2. associate-/r/ 92.0%

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

   4. Simplified 92.0%

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

   if 5.5999999999999998e-89 < t < 3.3e6

   1. Initial program 99.6%

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

   2. Taylor expanded in a around inf 99.6%

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

   if 3.3e6 < t < 2.9999999999999999e29

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

      3. associate-/l* 84.4%

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

      4. associate-/r/ 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in t around 0 67.8%

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

      1. associate-/l* 67.8%

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

   7. Simplified 67.8%

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

      1. associate-/r/ 68.0%

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

   9. Applied egg-rr 68.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 3300000:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+29}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 4: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+79)
   (+ y x)
   (if (<= t 8e+29) (+ x (* y (/ z (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+79) {
		tmp = y + x;
	} else if (t <= 8e+29) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.05d+79)) then
        tmp = y + x
    else if (t <= 8d+29) then
        tmp = x + (y * (z / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+79) {
		tmp = y + x;
	} else if (t <= 8e+29) {
		tmp = x + (y * (z / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+79:
		tmp = y + x
	elif t <= 8e+29:
		tmp = x + (y * (z / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+79)
		tmp = Float64(y + x);
	elseif (t <= 8e+29)
		tmp = Float64(x + Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+79)
		tmp = y + x;
	elseif (t <= 8e+29)
		tmp = x + (y * (z / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+79], N[(y + x), $MachinePrecision], If[LessEqual[t, 8e+29], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05000000000000004e79 or 7.99999999999999931e29 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.3%

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

      1. +-commutative 82.3%

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

   4. Simplified 82.3%

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

   if -1.05000000000000004e79 < t < 7.99999999999999931e29

   1. Initial program 97.8%

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

      1. clear-num 97.4%

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

      2. associate-/r/ 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around inf 88.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 5: 87.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+84}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.7e+84)
   (+ x (* z (/ y (- a t))))
   (if (<= z 5.6e-46) (- x (/ y (/ (- a t) t))) (+ x (* y (/ z (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.7e+84) {
		tmp = x + (z * (y / (a - t)));
	} else if (z <= 5.6e-46) {
		tmp = x - (y / ((a - t) / t));
	} 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 (z <= (-5.7d+84)) then
        tmp = x + (z * (y / (a - t)))
    else if (z <= 5.6d-46) then
        tmp = x - (y / ((a - t) / t))
    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 (z <= -5.7e+84) {
		tmp = x + (z * (y / (a - t)));
	} else if (z <= 5.6e-46) {
		tmp = x - (y / ((a - t) / t));
	} else {
		tmp = x + (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.7e+84:
		tmp = x + (z * (y / (a - t)))
	elif z <= 5.6e-46:
		tmp = x - (y / ((a - t) / t))
	else:
		tmp = x + (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.7e+84)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	elseif (z <= 5.6e-46)
		tmp = Float64(x - Float64(y / Float64(Float64(a - t) / t)));
	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 (z <= -5.7e+84)
		tmp = x + (z * (y / (a - t)));
	elseif (z <= 5.6e-46)
		tmp = x - (y / ((a - t) / t));
	else
		tmp = x + (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.7e+84], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-46], N[(x - N[(y / N[(N[(a - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6999999999999997e84

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 71.8%

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

      1. associate-/l* 82.1%

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

      2. associate-/r/ 87.0%

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

   4. Simplified 87.0%

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

   if -5.6999999999999997e84 < z < 5.5999999999999997e-46

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. unsub-neg 76.3%

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

      3. *-commutative 76.3%

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

      4. associate-/l* 91.1%

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

   4. Simplified 91.1%

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

   if 5.5999999999999997e-46 < z

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 90.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+84}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-46}:\\ \;\;\;\;x - \frac{y}{\frac{a - t}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a - t}\\ \end{array} \]

Alternative 6: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.8e+76) (+ y x) (if (<= t 1.06e-5) (+ x (* y (/ z a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+76) {
		tmp = y + x;
	} else if (t <= 1.06e-5) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.8d+76)) then
        tmp = y + x
    else if (t <= 1.06d-5) then
        tmp = x + (y * (z / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e+76) {
		tmp = y + x;
	} else if (t <= 1.06e-5) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.8e+76:
		tmp = y + x
	elif t <= 1.06e-5:
		tmp = x + (y * (z / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.8e+76)
		tmp = Float64(y + x);
	elseif (t <= 1.06e-5)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.8e+76)
		tmp = y + x;
	elseif (t <= 1.06e-5)
		tmp = x + (y * (z / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.8e+76], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.06e-5], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8e76 or 1.06e-5 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.4%

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

      1. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   if -4.8e76 < t < 1.06e-5

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 79.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 7: 77.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+76) (+ y x) (if (<= t 8.5e-6) (+ x (* z (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+76) {
		tmp = y + x;
	} else if (t <= 8.5e-6) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-7d+76)) then
        tmp = y + x
    else if (t <= 8.5d-6) then
        tmp = x + (z * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+76) {
		tmp = y + x;
	} else if (t <= 8.5e-6) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+76:
		tmp = y + x
	elif t <= 8.5e-6:
		tmp = x + (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+76)
		tmp = Float64(y + x);
	elseif (t <= 8.5e-6)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e+76)
		tmp = y + x;
	elseif (t <= 8.5e-6)
		tmp = x + (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+76], N[(y + x), $MachinePrecision], If[LessEqual[t, 8.5e-6], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000001e76 or 8.4999999999999999e-6 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 80.4%

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

      1. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   if -7.00000000000000001e76 < t < 8.4999999999999999e-6

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-/l* 79.8%

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

      3. associate-/r/ 79.9%

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

   4. Simplified 79.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 8: 98.1% 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 98.6%

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

2. Final simplification 98.6%

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

Alternative 9: 62.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+77) (+ y x) (if (<= t 5e-100) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+77) {
		tmp = y + x;
	} else if (t <= 5e-100) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.5d+77)) then
        tmp = y + x
    else if (t <= 5d-100) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+77) {
		tmp = y + x;
	} else if (t <= 5e-100) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+77:
		tmp = y + x
	elif t <= 5e-100:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+77)
		tmp = Float64(y + x);
	elseif (t <= 5e-100)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+77)
		tmp = y + x;
	elseif (t <= 5e-100)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+77], N[(y + x), $MachinePrecision], If[LessEqual[t, 5e-100], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4999999999999999e77 or 5.0000000000000001e-100 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 75.5%

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

      1. +-commutative 75.5%

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

   4. Simplified 75.5%

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

   if -1.4999999999999999e77 < t < 5.0000000000000001e-100

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 57.0%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 50.1% 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 98.6%

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

2. Taylor expanded in x around inf 51.0%

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

3. Final simplification 51.0%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))))
   (if (< y -8.508084860551241e-17)
     t_1
     (if (< y 2.894426862792089e-49)
       (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	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 - t) / (a - t)))
    if (y < (-8.508084860551241d-17)) then
        tmp = t_1
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) * (1.0d0 / (a - t)))
    else
        tmp = t_1
    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 - t) / (a - t)));
	double tmp;
	if (y < -8.508084860551241e-17) {
		tmp = t_1;
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if y < -8.508084860551241e-17:
		tmp = t_1
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) * Float64(1.0 / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (y < -8.508084860551241e-17)
		tmp = t_1;
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) * (1.0 / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -8.508084860551241e-17], t$95$1, If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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