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

Percentage Accurate: 85.6% → 99.0%

Time: 10.5s

Alternatives: 16

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: 85.6% 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: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;t\_1 \leq 20000000:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- y z) (/ (- a z) t)))
     (if (<= t_1 20000000.0) (+ t_1 x) (fma (- y z) (/ t (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (t_1 <= 20000000.0) {
		tmp = t_1 + x;
	} else {
		tmp = fma((y - z), (t / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (t_1 <= 20000000.0)
		tmp = Float64(t_1 + x);
	else
		tmp = fma(Float64(y - z), Float64(t / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20000000.0], N[(t$95$1 + x), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0

   1. Initial program 45.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e7

   1. Initial program 99.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   if 2e7 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 65.0%

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

      1. +-commutative 65.0%

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

      2. associate-/l* 99.7%

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

      3. fma-define 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)} \]
   4. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 20000000:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 20000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 20000000.0)))
     (+ x (* (- y z) (/ t (- a z))))
     (+ t_1 x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 20000000.0)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 20000000.0)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 20000000.0):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = t_1 + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 20000000.0))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(t_1 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 20000000.0)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = t_1 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 20000000.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 2e7 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 58.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e7

   1. Initial program 99.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 20000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;t\_1 \leq 20000000:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- y z) (/ (- a z) t)))
     (if (<= t_1 20000000.0) (+ t_1 x) (+ x (* (- y z) (/ t (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (t_1 <= 20000000.0) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (t_1 <= 20000000.0) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y - z) / ((a - z) / t))
	elif t_1 <= 20000000.0:
		tmp = t_1 + x
	else:
		tmp = x + ((y - z) * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (t_1 <= 20000000.0)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (t_1 <= 20000000.0)
		tmp = t_1 + x;
	else
		tmp = x + ((y - z) * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20000000.0], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0

   1. Initial program 45.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e7

   1. Initial program 99.3%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   2. Add Preprocessing

   if 2e7 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 65.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 20000000:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+183}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ t (/ z y)))))
   (if (<= z -7.2e+183)
     (+ t x)
     (if (<= z -3.1e-7)
       t_1
       (if (<= z 4.4e-60)
         (+ x (* y (/ t a)))
         (if (<= z 3.55e+143) t_1 (+ t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -7.2e+183) {
		tmp = t + x;
	} else if (z <= -3.1e-7) {
		tmp = t_1;
	} else if (z <= 4.4e-60) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.55e+143) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (t / (z / y))
    if (z <= (-7.2d+183)) then
        tmp = t + x
    else if (z <= (-3.1d-7)) then
        tmp = t_1
    else if (z <= 4.4d-60) then
        tmp = x + (y * (t / a))
    else if (z <= 3.55d+143) then
        tmp = t_1
    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 t_1 = x - (t / (z / y));
	double tmp;
	if (z <= -7.2e+183) {
		tmp = t + x;
	} else if (z <= -3.1e-7) {
		tmp = t_1;
	} else if (z <= 4.4e-60) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.55e+143) {
		tmp = t_1;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t / (z / y))
	tmp = 0
	if z <= -7.2e+183:
		tmp = t + x
	elif z <= -3.1e-7:
		tmp = t_1
	elif z <= 4.4e-60:
		tmp = x + (y * (t / a))
	elif z <= 3.55e+143:
		tmp = t_1
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t / Float64(z / y)))
	tmp = 0.0
	if (z <= -7.2e+183)
		tmp = Float64(t + x);
	elseif (z <= -3.1e-7)
		tmp = t_1;
	elseif (z <= 4.4e-60)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 3.55e+143)
		tmp = t_1;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t / (z / y));
	tmp = 0.0;
	if (z <= -7.2e+183)
		tmp = t + x;
	elseif (z <= -3.1e-7)
		tmp = t_1;
	elseif (z <= 4.4e-60)
		tmp = x + (y * (t / a));
	elseif (z <= 3.55e+143)
		tmp = t_1;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+183], N[(t + x), $MachinePrecision], If[LessEqual[z, -3.1e-7], t$95$1, If[LessEqual[z, 4.4e-60], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.20000000000000046e183 or 3.55000000000000021e143 < z

   1. Initial program 56.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around inf 87.0%

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

   if -7.20000000000000046e183 < z < -3.1e-7 or 4.3999999999999998e-60 < z < 3.55000000000000021e143

   1. Initial program 83.5%

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

      1. +-commutative 83.5%

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

      2. associate-/l* 95.5%

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

      3. fma-define 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.2%

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

   9. Applied egg-rr 73.2%

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

   10. Taylor expanded in z around 0 62.8%

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

   if -3.1e-7 < z < 4.3999999999999998e-60

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 80.2%

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

      1. +-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-/l/ 82.6%

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

      4. associate-/r/ 82.6%

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

      5. clear-num 83.2%

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

   9. Applied egg-rr 83.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+183}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-7}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.24 \cdot 10^{+185}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y z)))))
   (if (<= z -1.24e+185)
     (+ t x)
     (if (<= z -2.35e-5)
       t_1
       (if (<= z 5.2e-60)
         (+ x (* y (/ t a)))
         (if (<= z 3.55e+143) t_1 (+ t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -1.24e+185) {
		tmp = t + x;
	} else if (z <= -2.35e-5) {
		tmp = t_1;
	} else if (z <= 5.2e-60) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.55e+143) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (y / z))
    if (z <= (-1.24d+185)) then
        tmp = t + x
    else if (z <= (-2.35d-5)) then
        tmp = t_1
    else if (z <= 5.2d-60) then
        tmp = x + (y * (t / a))
    else if (z <= 3.55d+143) then
        tmp = t_1
    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 t_1 = x - (t * (y / z));
	double tmp;
	if (z <= -1.24e+185) {
		tmp = t + x;
	} else if (z <= -2.35e-5) {
		tmp = t_1;
	} else if (z <= 5.2e-60) {
		tmp = x + (y * (t / a));
	} else if (z <= 3.55e+143) {
		tmp = t_1;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / z))
	tmp = 0
	if z <= -1.24e+185:
		tmp = t + x
	elif z <= -2.35e-5:
		tmp = t_1
	elif z <= 5.2e-60:
		tmp = x + (y * (t / a))
	elif z <= 3.55e+143:
		tmp = t_1
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / z)))
	tmp = 0.0
	if (z <= -1.24e+185)
		tmp = Float64(t + x);
	elseif (z <= -2.35e-5)
		tmp = t_1;
	elseif (z <= 5.2e-60)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 3.55e+143)
		tmp = t_1;
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / z));
	tmp = 0.0;
	if (z <= -1.24e+185)
		tmp = t + x;
	elseif (z <= -2.35e-5)
		tmp = t_1;
	elseif (z <= 5.2e-60)
		tmp = x + (y * (t / a));
	elseif (z <= 3.55e+143)
		tmp = t_1;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.24e+185], N[(t + x), $MachinePrecision], If[LessEqual[z, -2.35e-5], t$95$1, If[LessEqual[z, 5.2e-60], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.55e+143], t$95$1, N[(t + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2399999999999999e185 or 3.55000000000000021e143 < z

   1. Initial program 56.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around inf 87.0%

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

   if -1.2399999999999999e185 < z < -2.34999999999999986e-5 or 5.1999999999999995e-60 < z < 3.55000000000000021e143

   1. Initial program 83.5%

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

      1. +-commutative 83.5%

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

      2. associate-/l* 95.5%

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

      3. fma-define 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in a around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 62.8%

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

   10. Simplified 62.8%

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

   if -2.34999999999999986e-5 < z < 5.1999999999999995e-60

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 80.2%

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

      1. +-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-/l/ 82.6%

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

      4. associate-/r/ 82.6%

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

      5. clear-num 83.2%

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

   9. Applied egg-rr 83.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{+185}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-5}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-60}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+143}:\\ \;\;\;\;x - t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+97} \lor \neg \left(y \leq 7.2 \cdot 10^{-30}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{1 - \frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.55e+97) (not (<= y 7.2e-30)))
   (+ x (* y (/ t (- a z))))
   (+ x (/ t (- 1.0 (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.55e+97) || !(y <= 7.2e-30)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t / (1.0 - (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 <= (-1.55d+97)) .or. (.not. (y <= 7.2d-30))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (t / (1.0d0 - (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 <= -1.55e+97) || !(y <= 7.2e-30)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t / (1.0 - (a / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.55e+97) or not (y <= 7.2e-30):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (t / (1.0 - (a / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.55e+97) || !(y <= 7.2e-30))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t / Float64(1.0 - Float64(a / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.55e+97) || ~((y <= 7.2e-30)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (t / (1.0 - (a / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.55e+97], N[Not[LessEqual[y, 7.2e-30]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999991e97 or 7.2000000000000006e-30 < y

   1. Initial program 81.7%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in y around inf 89.3%

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

   if -1.54999999999999991e97 < y < 7.2000000000000006e-30

   1. Initial program 84.2%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. associate-/l* 92.8%

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

      3. distribute-rgt-neg-in 92.8%

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

      4. distribute-neg-frac2 92.8%

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

      5. neg-sub0 92.8%

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

      6. sub-neg 92.8%

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

      7. +-commutative 92.8%

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

      8. associate--r+ 92.8%

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

      9. neg-sub0 92.8%

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

      10. remove-double-neg 92.8%

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

   7. Simplified 92.8%

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

      1. +-commutative 92.8%

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

      2. *-un-lft-identity 92.8%

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

      3. fma-define 92.8%

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

      4. clear-num 92.7%

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

      5. un-div-inv 92.8%

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

      6. div-sub 92.8%

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

      7. *-inverses 92.8%

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

   9. Applied egg-rr 92.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1, \frac{t}{1 - \frac{a}{z}}, x\right)} \]
   10. Step-by-step derivation

       1. fma-undefine 92.8%

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

       2. *-lft-identity 92.8%

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

   11. Simplified 92.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+97} \lor \neg \left(y \leq 7.2 \cdot 10^{-30}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{1 - \frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+97} \lor \neg \left(y \leq 8 \cdot 10^{-30}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.55e+97) (not (<= y 8e-30)))
   (+ x (* y (/ t (- a z))))
   (+ x (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.55e+97) || !(y <= 8e-30)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.55d+97)) .or. (.not. (y <= 8d-30))) then
        tmp = x + (y * (t / (a - z)))
    else
        tmp = x + (t * (z / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.55e+97) || !(y <= 8e-30)) {
		tmp = x + (y * (t / (a - z)));
	} else {
		tmp = x + (t * (z / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.55e+97) or not (y <= 8e-30):
		tmp = x + (y * (t / (a - z)))
	else:
		tmp = x + (t * (z / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.55e+97) || !(y <= 8e-30))
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.55e+97) || ~((y <= 8e-30)))
		tmp = x + (y * (t / (a - z)));
	else
		tmp = x + (t * (z / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.55e+97], N[Not[LessEqual[y, 8e-30]], $MachinePrecision]], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.54999999999999991e97 or 8.000000000000001e-30 < y

   1. Initial program 81.7%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in y around inf 89.3%

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

   if -1.54999999999999991e97 < y < 8.000000000000001e-30

   1. Initial program 84.2%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. associate-/l* 92.8%

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

      3. distribute-rgt-neg-in 92.8%

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

      4. distribute-neg-frac2 92.8%

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

      5. neg-sub0 92.8%

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

      6. sub-neg 92.8%

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

      7. +-commutative 92.8%

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

      8. associate--r+ 92.8%

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

      9. neg-sub0 92.8%

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

      10. remove-double-neg 92.8%

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

   7. Simplified 92.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+97} \lor \neg \left(y \leq 8 \cdot 10^{-30}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e+131)
   (- x (/ t (/ z y)))
   (if (<= y 3.2e+16) (+ x (* t (/ z (- z a)))) (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+131) {
		tmp = x - (t / (z / y));
	} else if (y <= 3.2e+16) {
		tmp = x + (t * (z / (z - a)));
	} 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 (y <= (-1.05d+131)) then
        tmp = x - (t / (z / y))
    else if (y <= 3.2d+16) then
        tmp = x + (t * (z / (z - a)))
    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 (y <= -1.05e+131) {
		tmp = x - (t / (z / y));
	} else if (y <= 3.2e+16) {
		tmp = x + (t * (z / (z - a)));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+131:
		tmp = x - (t / (z / y))
	elif y <= 3.2e+16:
		tmp = x + (t * (z / (z - a)))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+131)
		tmp = Float64(x - Float64(t / Float64(z / y)));
	elseif (y <= 3.2e+16)
		tmp = Float64(x + Float64(t * Float64(z / Float64(z - a))));
	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 (y <= -1.05e+131)
		tmp = x - (t / (z / y));
	elseif (y <= 3.2e+16)
		tmp = x + (t * (z / (z - a)));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+131], N[(x - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+16], N[(x + N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04999999999999993e131

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

      1. clear-num 69.0%

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

      2. un-div-inv 69.0%

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

   9. Applied egg-rr 69.0%

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

   10. Taylor expanded in z around 0 64.0%

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

   if -1.04999999999999993e131 < y < 3.2e16

   1. Initial program 84.3%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-/l* 89.4%

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

      3. distribute-rgt-neg-in 89.4%

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

      4. distribute-neg-frac2 89.4%

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

      5. neg-sub0 89.4%

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

      6. sub-neg 89.4%

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

      7. +-commutative 89.4%

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

      8. associate--r+ 89.4%

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

      9. neg-sub0 89.4%

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

      10. remove-double-neg 89.4%

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

   7. Simplified 89.4%

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

   if 3.2e16 < y

   1. Initial program 83.0%

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

      1. +-commutative 83.0%

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

      2. associate-/l* 97.7%

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

      3. fma-define 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 54.8%

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

      1. +-commutative 54.8%

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

   7. Simplified 54.8%

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

      1. clear-num 54.8%

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

      2. *-commutative 54.8%

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

      3. associate-/l/ 66.2%

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

      4. associate-/r/ 66.2%

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

      5. clear-num 67.1%

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

   9. Applied egg-rr 67.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;x - \frac{t}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;x + t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+86} \lor \neg \left(z \leq 3.55 \cdot 10^{+143}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.12e+86) (not (<= z 3.55e+143))) (+ t x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.12e+86) || !(z <= 3.55e+143)) {
		tmp = t + x;
	} 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 <= (-1.12d+86)) .or. (.not. (z <= 3.55d+143))) then
        tmp = t + x
    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 <= -1.12e+86) || !(z <= 3.55e+143)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.12e+86) or not (z <= 3.55e+143):
		tmp = t + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.12e+86) || !(z <= 3.55e+143))
		tmp = Float64(t + x);
	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 <= -1.12e+86) || ~((z <= 3.55e+143)))
		tmp = t + x;
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.12e+86], N[Not[LessEqual[z, 3.55e+143]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e86 or 3.55000000000000021e143 < z

   1. Initial program 59.5%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around inf 78.9%

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

   if -1.12e86 < z < 3.55000000000000021e143

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-/l* 98.0%

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

      3. fma-define 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 66.6%

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

      1. +-commutative 66.6%

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

   7. Simplified 66.6%

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

      1. clear-num 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-/l/ 70.8%

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

      4. associate-/r/ 70.8%

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

      5. clear-num 71.2%

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

   9. Applied egg-rr 71.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+86} \lor \neg \left(z \leq 3.55 \cdot 10^{+143}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+85} \lor \neg \left(z \leq 3.55 \cdot 10^{+143}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+85) (not (<= z 3.55e+143))) (+ t x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+85) || !(z <= 3.55e+143)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.45d+85)) .or. (.not. (z <= 3.55d+143))) then
        tmp = t + x
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+85) || !(z <= 3.55e+143)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+85) or not (z <= 3.55e+143):
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+85) || !(z <= 3.55e+143))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+85) || ~((z <= 3.55e+143)))
		tmp = t + x;
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+85], N[Not[LessEqual[z, 3.55e+143]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.44999999999999999e85 or 3.55000000000000021e143 < z

   1. Initial program 59.5%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around inf 78.9%

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

   if -1.44999999999999999e85 < z < 3.55000000000000021e143

   1. Initial program 93.1%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 69.2%

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

   7. Simplified 69.2%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+85} \lor \neg \left(z \leq 3.55 \cdot 10^{+143}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+167} \lor \neg \left(t \leq 1.3 \cdot 10^{+97}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.7e+167) (not (<= t 1.3e+97))) (* t (- 1.0 (/ y z))) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.7e+167) || !(t <= 1.3e+97)) {
		tmp = t * (1.0 - (y / z));
	} 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 ((t <= (-4.7d+167)) .or. (.not. (t <= 1.3d+97))) then
        tmp = t * (1.0d0 - (y / z))
    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 ((t <= -4.7e+167) || !(t <= 1.3e+97)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.7e+167) or not (t <= 1.3e+97):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.7e+167) || !(t <= 1.3e+97))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.7e+167) || ~((t <= 1.3e+97)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.7e+167], N[Not[LessEqual[t, 1.3e+97]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.70000000000000013e167 or 1.3e97 < t

   1. Initial program 65.7%

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

      1. +-commutative 65.7%

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

      2. associate-/l* 97.6%

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

      3. fma-define 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in a around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. unsub-neg 40.2%

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

      3. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

      1. clear-num 63.4%

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

      2. un-div-inv 63.4%

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

   9. Applied egg-rr 63.4%

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

   10. Taylor expanded in t around inf 53.8%

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

   if -4.70000000000000013e167 < t < 1.3e97

   1. Initial program 91.5%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 69.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+167} \lor \neg \left(t \leq 1.3 \cdot 10^{+97}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{\frac{z}{-y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1e+131) (/ t (/ z (- y))) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e+131) {
		tmp = t / (z / -y);
	} 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 (y <= (-1d+131)) then
        tmp = t / (z / -y)
    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 (y <= -1e+131) {
		tmp = t / (z / -y);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1e+131:
		tmp = t / (z / -y)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1e+131)
		tmp = Float64(t / Float64(z / Float64(-y)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1e+131)
		tmp = t / (z / -y);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1e+131], N[(t / N[(z / (-y)), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999991e130

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

      1. clear-num 69.0%

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

      2. un-div-inv 69.0%

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

   9. Applied egg-rr 69.0%

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

   10. Taylor expanded in z around 0 38.8%

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

       1. mul-1-neg 38.8%

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

       2. associate-/l* 50.7%

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

       3. distribute-lft-neg-in 50.7%

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

   12. Simplified 50.7%

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

       1. clear-num 50.7%

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

       2. un-div-inv 50.8%

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

       3. distribute-neg-frac 50.8%

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

       4. distribute-neg-frac2 50.8%

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

       5. distribute-neg-frac2 50.8%

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

   14. Applied egg-rr 50.8%

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

   if -9.9999999999999991e130 < y

   1. Initial program 83.9%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 61.3%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+131}:\\ \;\;\;\;\frac{t}{\frac{z}{-y}}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e+131) (* t (/ y (- z))) (+ t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+131) {
		tmp = t * (y / -z);
	} 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 (y <= (-1.05d+131)) then
        tmp = t * (y / -z)
    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 (y <= -1.05e+131) {
		tmp = t * (y / -z);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+131:
		tmp = t * (y / -z)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+131)
		tmp = Float64(t * Float64(y / Float64(-z)));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e+131)
		tmp = t * (y / -z);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+131], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999993e131

   1. Initial program 77.7%

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

      1. +-commutative 77.7%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in y around inf 38.8%

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

      1. mul-1-neg 38.8%

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

      2. associate-/l* 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

      4. distribute-frac-neg2 50.7%

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

   10. Simplified 50.7%

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

   if -1.04999999999999993e131 < y

   1. Initial program 83.9%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 61.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 95.8% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.0%

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

   1. associate-/l* 96.0%

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

3. Simplified 96.0%

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

Alternative 15: 62.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.8 \cdot 10^{+159}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= a 2.8e+159) (+ t x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.8e+159) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= 2.8d+159) then
        tmp = t + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.8e+159) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 2.8e+159:
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.8e+159)
		tmp = Float64(t + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 2.8e+159)
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 2.8e+159], N[(t + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < 2.8000000000000001e159

   1. Initial program 83.3%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around inf 57.2%

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

   if 2.8000000000000001e159 < a

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 97.2%

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

      3. fma-define 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around 0 73.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.8 \cdot 10^{+159}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.2% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

   1. +-commutative 83.0%

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

   2. associate-/l* 96.0%

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

   3. fma-define 96.0%

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

3. Simplified 96.0%

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

5. Taylor expanded in t around 0 48.5%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.5× 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 2024163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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