Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.7% → 98.2%

Time: 8.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. +-commutative 86.0%

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

   2. associate-*l/ 98.7%

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

   3. fma-def 98.7%

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

3. Simplified 98.7%

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

4. Final simplification 98.7%

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

Alternative 2: 82.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-23} \lor \neg \left(z \leq 2.4 \cdot 10^{-54}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e-23) (not (<= z 2.4e-54)))
   (+ x (- t (* t (/ y z))))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-23) || !(z <= 2.4e-54)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d-23)) .or. (.not. (z <= 2.4d-54))) then
        tmp = x + (t - (t * (y / z)))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e-23) || !(z <= 2.4e-54)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e-23) or not (z <= 2.4e-54):
		tmp = x + (t - (t * (y / z)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e-23) || !(z <= 2.4e-54))
		tmp = Float64(x + Float64(t - Float64(t * Float64(y / z))));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e-23) || ~((z <= 2.4e-54)))
		tmp = x + (t - (t * (y / z)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e-23], N[Not[LessEqual[z, 2.4e-54]], $MachinePrecision]], N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-23 or 2.40000000000000013e-54 < z

   1. Initial program 82.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 93.0%

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

   5. Applied egg-rr 93.0%

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

   6. Taylor expanded in a around 0 78.4%

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

      1. neg-mul-1 78.4%

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

      2. distribute-neg-frac 78.4%

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

   8. Simplified 78.4%

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

   9. Taylor expanded in y around 0 77.4%

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

       1. mul-1-neg 77.4%

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

       2. unsub-neg 77.4%

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

       3. *-commutative 77.4%

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

       4. associate-*l/ 83.1%

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

       5. *-commutative 83.1%

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

   11. Simplified 83.1%

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

   if -1.7e-23 < z < 2.40000000000000013e-54

   1. Initial program 90.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

      1. associate-/r/ 84.1%

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

   8. Applied egg-rr 84.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-23} \lor \neg \left(z \leq 2.4 \cdot 10^{-54}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 3: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-23} \lor \neg \left(z \leq 7.5 \cdot 10^{+86}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.35e-23) (not (<= z 7.5e+86)))
   (+ x (- t (* t (/ y z))))
   (+ x (/ t (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.35e-23) || !(z <= 7.5e+86)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + (t / ((a - z) / 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 <= (-2.35d-23)) .or. (.not. (z <= 7.5d+86))) then
        tmp = x + (t - (t * (y / z)))
    else
        tmp = x + (t / ((a - z) / 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 <= -2.35e-23) || !(z <= 7.5e+86)) {
		tmp = x + (t - (t * (y / z)));
	} else {
		tmp = x + (t / ((a - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.35e-23) or not (z <= 7.5e+86):
		tmp = x + (t - (t * (y / z)))
	else:
		tmp = x + (t / ((a - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.35e-23) || !(z <= 7.5e+86))
		tmp = Float64(x + Float64(t - Float64(t * Float64(y / z))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.35e-23) || ~((z <= 7.5e+86)))
		tmp = x + (t - (t * (y / z)));
	else
		tmp = x + (t / ((a - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.35e-23], N[Not[LessEqual[z, 7.5e+86]], $MachinePrecision]], N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.35e-23 or 7.4999999999999997e86 < z

   1. Initial program 78.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in a around 0 78.6%

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

      1. neg-mul-1 78.6%

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

      2. distribute-neg-frac 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in y around 0 77.3%

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

       1. mul-1-neg 77.3%

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

       2. unsub-neg 77.3%

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

       3. *-commutative 77.3%

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

       4. associate-*l/ 84.3%

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

       5. *-commutative 84.3%

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

   11. Simplified 84.3%

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

   if -2.35e-23 < z < 7.4999999999999997e86

   1. Initial program 91.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 80.5%

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

      1. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-23} \lor \neg \left(z \leq 7.5 \cdot 10^{+86}\right):\\ \;\;\;\;x + \left(t - t \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 4: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-31} \lor \neg \left(y \leq 1350\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.1e-31) (not (<= y 1350.0)))
   (+ x (/ t (/ (- a z) y)))
   (- x (* t (/ z (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e-31) || !(y <= 1350.0)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.1d-31)) .or. (.not. (y <= 1350.0d0))) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x - (t * (z / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.1e-31) || !(y <= 1350.0)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (t * (z / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.1e-31) or not (y <= 1350.0):
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x - (t * (z / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.1e-31) || !(y <= 1350.0))
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x - Float64(t * Float64(z / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.1e-31) || ~((y <= 1350.0)))
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x - (t * (z / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.1e-31], N[Not[LessEqual[y, 1350.0]], $MachinePrecision]], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999991e-31 or 1350 < y

   1. Initial program 80.4%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. associate-/l* 88.1%

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

   6. Simplified 88.1%

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

   if -2.09999999999999991e-31 < y < 1350

   1. Initial program 92.2%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

      3. *-commutative 86.5%

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

      4. associate-*l/ 94.2%

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

   6. Simplified 94.2%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-31} \lor \neg \left(y \leq 1350\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{z}{a - z}\\ \end{array} \]

Alternative 5: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-33} \lor \neg \left(y \leq 88\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.25e-33) (not (<= y 88.0)))
   (+ x (/ t (/ (- a z) y)))
   (- x (/ t (+ (/ a z) -1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.25e-33) || !(y <= 88.0)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (t / ((a / z) + -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 ((y <= (-1.25d-33)) .or. (.not. (y <= 88.0d0))) then
        tmp = x + (t / ((a - z) / y))
    else
        tmp = x - (t / ((a / z) + (-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 ((y <= -1.25e-33) || !(y <= 88.0)) {
		tmp = x + (t / ((a - z) / y));
	} else {
		tmp = x - (t / ((a / z) + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.25e-33) or not (y <= 88.0):
		tmp = x + (t / ((a - z) / y))
	else:
		tmp = x - (t / ((a / z) + -1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.25e-33) || !(y <= 88.0))
		tmp = Float64(x + Float64(t / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(x - Float64(t / Float64(Float64(a / z) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.25e-33) || ~((y <= 88.0)))
		tmp = x + (t / ((a - z) / y));
	else
		tmp = x - (t / ((a / z) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.25e-33], N[Not[LessEqual[y, 88.0]], $MachinePrecision]], N[(x + N[(t / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000007e-33 or 88 < y

   1. Initial program 80.4%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. associate-/l* 88.1%

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

   6. Simplified 88.1%

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

   if -1.25000000000000007e-33 < y < 88

   1. Initial program 92.2%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

      3. *-commutative 86.5%

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

      4. associate-*l/ 94.2%

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

   6. Simplified 94.2%

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

      1. *-commutative 94.2%

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

      2. clear-num 94.2%

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

      3. div-inv 94.2%

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

      4. div-sub 94.2%

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

      5. *-inverses 94.2%

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

      6. sub-neg 94.2%

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

      7. metadata-eval 94.2%

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

   8. Applied egg-rr 94.2%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-33} \lor \neg \left(y \leq 88\right):\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z} + -1}\\ \end{array} \]

Alternative 6: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e-23) (+ t x) (if (<= z 1.45e+59) (+ x (* t (/ y a))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-23) {
		tmp = t + x;
	} else if (z <= 1.45e+59) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + 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 (z <= (-9.5d-23)) then
        tmp = t + x
    else if (z <= 1.45d+59) then
        tmp = x + (t * (y / a))
    else
        tmp = t + 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 (z <= -9.5e-23) {
		tmp = t + x;
	} else if (z <= 1.45e+59) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e-23:
		tmp = t + x
	elif z <= 1.45e+59:
		tmp = x + (t * (y / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e-23)
		tmp = Float64(t + x);
	elseif (z <= 1.45e+59)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e-23)
		tmp = t + x;
	elseif (z <= 1.45e+59)
		tmp = x + (t * (y / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e-23], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.45e+59], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000058e-23 or 1.44999999999999995e59 < z

   1. Initial program 79.3%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 73.3%

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

   if -9.50000000000000058e-23 < z < 1.44999999999999995e59

   1. Initial program 91.0%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around 0 79.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 7: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-21}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e-21) (+ t x) (if (<= z 1.75e-53) (+ x (/ y (/ a t))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e-21) {
		tmp = t + x;
	} else if (z <= 1.75e-53) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + 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 (z <= (-3.6d-21)) then
        tmp = t + x
    else if (z <= 1.75d-53) then
        tmp = x + (y / (a / t))
    else
        tmp = t + 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 (z <= -3.6e-21) {
		tmp = t + x;
	} else if (z <= 1.75e-53) {
		tmp = x + (y / (a / t));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e-21:
		tmp = t + x
	elif z <= 1.75e-53:
		tmp = x + (y / (a / t))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e-21)
		tmp = Float64(t + x);
	elseif (z <= 1.75e-53)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e-21)
		tmp = t + x;
	elseif (z <= 1.75e-53)
		tmp = x + (y / (a / t));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e-21], N[(t + x), $MachinePrecision], If[LessEqual[z, 1.75e-53], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999989e-21 or 1.74999999999999997e-53 < z

   1. Initial program 82.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.6%

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

   if -3.59999999999999989e-21 < z < 1.74999999999999997e-53

   1. Initial program 90.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around inf 81.5%

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

      1. associate-/l* 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in a around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/l* 83.8%

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

   9. Simplified 83.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-21}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-53}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 8: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-54}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e-23) (+ t x) (if (<= z 2.45e-54) (+ x (* y (/ t a))) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e-23) {
		tmp = t + x;
	} else if (z <= 2.45e-54) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + 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 (z <= (-6.8d-23)) then
        tmp = t + x
    else if (z <= 2.45d-54) then
        tmp = x + (y * (t / a))
    else
        tmp = t + 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 (z <= -6.8e-23) {
		tmp = t + x;
	} else if (z <= 2.45e-54) {
		tmp = x + (y * (t / a));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e-23:
		tmp = t + x
	elif z <= 2.45e-54:
		tmp = x + (y * (t / a))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e-23)
		tmp = Float64(t + x);
	elseif (z <= 2.45e-54)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e-23)
		tmp = t + x;
	elseif (z <= 2.45e-54)
		tmp = x + (y * (t / a));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e-23], N[(t + x), $MachinePrecision], If[LessEqual[z, 2.45e-54], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000001e-23 or 2.4500000000000001e-54 < z

   1. Initial program 82.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.6%

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

   if -6.8000000000000001e-23 < z < 2.4500000000000001e-54

   1. Initial program 90.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-/l* 82.2%

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

   6. Simplified 82.2%

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

      1. associate-/r/ 84.1%

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

   8. Applied egg-rr 84.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-54}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 9: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-*l/ 98.7%

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

3. Simplified 98.7%

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

4. Final simplification 98.7%

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

Alternative 10: 64.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e-24) (+ t x) (if (<= z 5.5e-54) x (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e-24) {
		tmp = t + x;
	} else if (z <= 5.5e-54) {
		tmp = x;
	} else {
		tmp = t + 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 (z <= (-1.35d-24)) then
        tmp = t + x
    else if (z <= 5.5d-54) then
        tmp = x
    else
        tmp = t + 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 (z <= -1.35e-24) {
		tmp = t + x;
	} else if (z <= 5.5e-54) {
		tmp = x;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e-24:
		tmp = t + x
	elif z <= 5.5e-54:
		tmp = x
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e-24)
		tmp = Float64(t + x);
	elseif (z <= 5.5e-54)
		tmp = x;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.35e-24)
		tmp = t + x;
	elseif (z <= 5.5e-54)
		tmp = x;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e-24], N[(t + x), $MachinePrecision], If[LessEqual[z, 5.5e-54], x, N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000003e-24 or 5.50000000000000046e-54 < z

   1. Initial program 82.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.6%

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

   if -1.35000000000000003e-24 < z < 5.50000000000000046e-54

   1. Initial program 90.2%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in x around inf 53.7%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-24}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

Alternative 11: 50.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. associate-*l/ 98.7%

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

3. Simplified 98.7%

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

4. Taylor expanded in x around inf 49.0%

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

5. Final simplification 49.0%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} 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) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    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) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

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

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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