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

Percentage Accurate: 85.9% → 99.3%

Time: 6.9s

Alternatives: 13

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: 85.9% 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: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t\_1 \leq 10^{+198}:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- y z) t) (- a z))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- y z) (/ t (- a z))))
     (if (<= t_1 1e+198)
       (- x (/ (* t (- z y)) (- a z)))
       (+ x (/ (- y z) (/ (- a z) t)))))))

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) * (t / (a - z)));
	} else if (t_1 <= 1e+198) {
		tmp = x - ((t * (z - y)) / (a - z));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	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) * (t / (a - z)));
	} else if (t_1 <= 1e+198) {
		tmp = x - ((t * (z - y)) / (a - z));
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	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) * (t / (a - z)))
	elif t_1 <= 1e+198:
		tmp = x - ((t * (z - y)) / (a - z))
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	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(t / Float64(a - z))));
	elseif (t_1 <= 1e+198)
		tmp = Float64(x - Float64(Float64(t * Float64(z - y)) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	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) * (t / (a - z)));
	elseif (t_1 <= 1e+198)
		tmp = x - ((t * (z - y)) / (a - z));
	else
		tmp = x + ((y - z) / ((a - z) / t));
	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[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+198], N[(x - N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $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 29.8%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 1.00000000000000002e198

   1. Initial program 99.9%

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

   if 1.00000000000000002e198 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 31.6%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq 10^{+198}:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+167}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a - z}\\ \end{array} \end{array} \]

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 5e+167)))
     (+ x (* (- y z) (/ t (- a z))))
     (- x (/ (* t (- z y)) (- 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)) || !(t_1 <= 5e+167)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x - ((t * (z - y)) / (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) || !(t_1 <= 5e+167)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x - ((t * (z - y)) / (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) or not (t_1 <= 5e+167):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = x - ((t * (z - y)) / (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)) || !(t_1 <= 5e+167))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x - Float64(Float64(t * Float64(z - y)) / 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) || ~((t_1 <= 5e+167)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = x - ((t * (z - y)) / (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[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+167]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 4.9999999999999997e167 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 33.1%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.9999999999999997e167

   1. Initial program 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 81.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - t \cdot \frac{y}{z}\right)\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-89}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (- t (* t (/ y z))))) (t_2 (+ x (* t (/ (- y z) a)))))
   (if (<= a -1.3e-41)
     t_2
     (if (<= a 2.3e-193)
       t_1
       (if (<= a 6e-89)
         (+ x (* y (/ t (- a z))))
         (if (<= a 9.5e+81) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - (t * (y / z)));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.3e-41) {
		tmp = t_2;
	} else if (a <= 2.3e-193) {
		tmp = t_1;
	} else if (a <= 6e-89) {
		tmp = x + (y * (t / (a - z)));
	} else if (a <= 9.5e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t - (t * (y / z)))
    t_2 = x + (t * ((y - z) / a))
    if (a <= (-1.3d-41)) then
        tmp = t_2
    else if (a <= 2.3d-193) then
        tmp = t_1
    else if (a <= 6d-89) then
        tmp = x + (y * (t / (a - z)))
    else if (a <= 9.5d+81) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - (t * (y / z)));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.3e-41) {
		tmp = t_2;
	} else if (a <= 2.3e-193) {
		tmp = t_1;
	} else if (a <= 6e-89) {
		tmp = x + (y * (t / (a - z)));
	} else if (a <= 9.5e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - (t * (y / z)))
	t_2 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -1.3e-41:
		tmp = t_2
	elif a <= 2.3e-193:
		tmp = t_1
	elif a <= 6e-89:
		tmp = x + (y * (t / (a - z)))
	elif a <= 9.5e+81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - Float64(t * Float64(y / z))))
	t_2 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -1.3e-41)
		tmp = t_2;
	elseif (a <= 2.3e-193)
		tmp = t_1;
	elseif (a <= 6e-89)
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	elseif (a <= 9.5e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t - (t * (y / z)));
	t_2 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -1.3e-41)
		tmp = t_2;
	elseif (a <= 2.3e-193)
		tmp = t_1;
	elseif (a <= 6e-89)
		tmp = x + (y * (t / (a - z)));
	elseif (a <= 9.5e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.3e-41], t$95$2, If[LessEqual[a, 2.3e-193], t$95$1, If[LessEqual[a, 6e-89], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+81], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3e-41 or 9.50000000000000083e81 < a

   1. Initial program 79.5%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 76.8%

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

      1. associate-/l* 88.7%

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

   7. Simplified 88.7%

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

   if -1.3e-41 < a < 2.30000000000000009e-193 or 5.9999999999999999e-89 < a < 9.50000000000000083e81

   1. Initial program 87.0%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in a around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-/l* 85.4%

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

      3. distribute-lft-neg-in 85.4%

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

      4. div-sub 85.4%

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

      5. sub-neg 85.4%

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

      6. *-inverses 85.4%

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

      7. metadata-eval 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in y around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. associate-*r/ 85.5%

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

      3. unsub-neg 85.5%

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

   10. Simplified 85.5%

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

   if 2.30000000000000009e-193 < a < 5.9999999999999999e-89

   1. Initial program 91.4%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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. Taylor expanded in y around inf 95.5%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

   7. Simplified 99.8%

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

Alternative 4: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -1.46 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-264}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-145}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 100:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ (- y z) a)))))
   (if (<= a -1.46e-52)
     t_1
     (if (<= a -2.5e-264)
       (+ t x)
       (if (<= a 4.6e-145)
         (- x (* y (/ t z)))
         (if (<= a 100.0) (+ t x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.46e-52) {
		tmp = t_1;
	} else if (a <= -2.5e-264) {
		tmp = t + x;
	} else if (a <= 4.6e-145) {
		tmp = x - (y * (t / z));
	} else if (a <= 100.0) {
		tmp = t + x;
	} 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 + (t * ((y - z) / a))
    if (a <= (-1.46d-52)) then
        tmp = t_1
    else if (a <= (-2.5d-264)) then
        tmp = t + x
    else if (a <= 4.6d-145) then
        tmp = x - (y * (t / z))
    else if (a <= 100.0d0) then
        tmp = t + x
    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 + (t * ((y - z) / a));
	double tmp;
	if (a <= -1.46e-52) {
		tmp = t_1;
	} else if (a <= -2.5e-264) {
		tmp = t + x;
	} else if (a <= 4.6e-145) {
		tmp = x - (y * (t / z));
	} else if (a <= 100.0) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -1.46e-52:
		tmp = t_1
	elif a <= -2.5e-264:
		tmp = t + x
	elif a <= 4.6e-145:
		tmp = x - (y * (t / z))
	elif a <= 100.0:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -1.46e-52)
		tmp = t_1;
	elseif (a <= -2.5e-264)
		tmp = Float64(t + x);
	elseif (a <= 4.6e-145)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (a <= 100.0)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -1.46e-52)
		tmp = t_1;
	elseif (a <= -2.5e-264)
		tmp = t + x;
	elseif (a <= 4.6e-145)
		tmp = x - (y * (t / z));
	elseif (a <= 100.0)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.46e-52], t$95$1, If[LessEqual[a, -2.5e-264], N[(t + x), $MachinePrecision], If[LessEqual[a, 4.6e-145], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 100.0], N[(t + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.46000000000000003e-52 or 100 < a

   1. Initial program 80.4%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in a around inf 75.4%

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

      1. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   if -1.46000000000000003e-52 < a < -2.5e-264 or 4.60000000000000014e-145 < a < 100

   1. Initial program 87.9%

      \[x + \frac{\left(y - z\right) \cdot t}{a - z} \]
   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 z around inf 79.5%

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

   if -2.5e-264 < a < 4.60000000000000014e-145

   1. Initial program 89.6%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in a around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-/l* 81.6%

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

      3. distribute-lft-neg-in 81.6%

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

      4. div-sub 81.6%

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

      5. sub-neg 81.6%

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

      6. *-inverses 81.6%

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

      7. metadata-eval 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in y around inf 76.9%

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

      1. associate-*l/ 77.2%

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

      2. associate-*l* 77.2%

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

      3. *-commutative 77.2%

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

      4. mul-1-neg 77.2%

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

      5. distribute-neg-frac2 77.2%

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

   10. Simplified 77.2%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{-52}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-264}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-145}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 100:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+109}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-77}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+109)
   (+ t x)
   (if (<= z -1.6e-77)
     (- x (* y (/ t z)))
     (if (<= z 1.12e+95) (+ x (/ (* y t) a)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+109) {
		tmp = t + x;
	} else if (z <= -1.6e-77) {
		tmp = x - (y * (t / z));
	} else if (z <= 1.12e+95) {
		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 <= (-1d+109)) then
        tmp = t + x
    else if (z <= (-1.6d-77)) then
        tmp = x - (y * (t / z))
    else if (z <= 1.12d+95) 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 <= -1e+109) {
		tmp = t + x;
	} else if (z <= -1.6e-77) {
		tmp = x - (y * (t / z));
	} else if (z <= 1.12e+95) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+109:
		tmp = t + x
	elif z <= -1.6e-77:
		tmp = x - (y * (t / z))
	elif z <= 1.12e+95:
		tmp = x + ((y * t) / a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+109)
		tmp = Float64(t + x);
	elseif (z <= -1.6e-77)
		tmp = Float64(x - Float64(y * Float64(t / z)));
	elseif (z <= 1.12e+95)
		tmp = Float64(x + Float64(Float64(y * 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 <= -1e+109)
		tmp = t + x;
	elseif (z <= -1.6e-77)
		tmp = x - (y * (t / z));
	elseif (z <= 1.12e+95)
		tmp = x + ((y * t) / a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+109], N[(t + x), $MachinePrecision], If[LessEqual[z, -1.6e-77], N[(x - N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+95], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999982e108 or 1.11999999999999999e95 < z

   1. Initial program 57.6%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 81.9%

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

   if -9.99999999999999982e108 < z < -1.6e-77

   1. Initial program 93.7%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in a around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-/l* 75.4%

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

      3. distribute-lft-neg-in 75.4%

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

      4. div-sub 75.4%

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

      5. sub-neg 75.4%

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

      6. *-inverses 75.4%

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

      7. metadata-eval 75.4%

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

   7. Simplified 75.4%

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

   8. Taylor expanded in y around inf 74.1%

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

      1. associate-*l/ 74.2%

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

      2. associate-*l* 74.2%

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

      3. *-commutative 74.2%

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

      4. mul-1-neg 74.2%

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

      5. distribute-neg-frac2 74.2%

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

   10. Simplified 74.2%

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

   if -1.6e-77 < z < 1.11999999999999999e95

   1. Initial program 95.1%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 79.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+109}:\\ \;\;\;\;t + x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-77}:\\ \;\;\;\;x - y \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-20} \lor \neg \left(z \leq 3.6 \cdot 10^{+59}\right):\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e-20) (not (<= z 3.6e+59)))
   (+ x (* z (/ t (- z a))))
   (+ x (/ (* y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e-20) || !(z <= 3.6e+59)) {
		tmp = x + (z * (t / (z - a)));
	} else {
		tmp = x + ((y * t) / (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 ((z <= (-4.4d-20)) .or. (.not. (z <= 3.6d+59))) then
        tmp = x + (z * (t / (z - a)))
    else
        tmp = x + ((y * t) / (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 ((z <= -4.4e-20) || !(z <= 3.6e+59)) {
		tmp = x + (z * (t / (z - a)));
	} else {
		tmp = x + ((y * t) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e-20) or not (z <= 3.6e+59):
		tmp = x + (z * (t / (z - a)))
	else:
		tmp = x + ((y * t) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e-20) || !(z <= 3.6e+59))
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y * t) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.4e-20) || ~((z <= 3.6e+59)))
		tmp = x + (z * (t / (z - a)));
	else
		tmp = x + ((y * t) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e-20], N[Not[LessEqual[z, 3.6e+59]], $MachinePrecision]], N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999982e-20 or 3.5999999999999999e59 < z

   1. Initial program 68.8%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. associate-*l/ 85.8%

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

      3. distribute-rgt-neg-out 85.8%

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

   7. Simplified 85.8%

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

   if -4.39999999999999982e-20 < z < 3.5999999999999999e59

   1. Initial program 96.5%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 90.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-20} \lor \neg \left(z \leq 3.6 \cdot 10^{+59}\right):\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+131} \lor \neg \left(z \leq 3 \cdot 10^{+98}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+131) (not (<= z 3e+98)))
   (+ t x)
   (+ x (* y (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+131) || !(z <= 3e+98)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / (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 ((z <= (-3.8d+131)) .or. (.not. (z <= 3d+98))) then
        tmp = t + x
    else
        tmp = x + (y * (t / (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 ((z <= -3.8e+131) || !(z <= 3e+98)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+131) or not (z <= 3e+98):
		tmp = t + x
	else:
		tmp = x + (y * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+131) || !(z <= 3e+98))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(y * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.8e+131) || ~((z <= 3e+98)))
		tmp = t + x;
	else
		tmp = x + (y * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+131], N[Not[LessEqual[z, 3e+98]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000004e131 or 3.0000000000000001e98 < z

   1. Initial program 59.2%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -3.8000000000000004e131 < z < 3.0000000000000001e98

   1. Initial program 93.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 84.4%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

   7. Simplified 86.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+131} \lor \neg \left(z \leq 3 \cdot 10^{+98}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-53} \lor \neg \left(z \leq 1.2 \cdot 10^{+97}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.9e-53) (not (<= z 1.2e+97))) (+ t x) (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.9e-53) || !(z <= 1.2e+97)) {
		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 <= (-3.9d-53)) .or. (.not. (z <= 1.2d+97))) 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 <= -3.9e-53) || !(z <= 1.2e+97)) {
		tmp = t + x;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.9e-53) or not (z <= 1.2e+97):
		tmp = t + x
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.9e-53) || !(z <= 1.2e+97))
		tmp = Float64(t + x);
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.9e-53) || ~((z <= 1.2e+97)))
		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, -3.9e-53], N[Not[LessEqual[z, 1.2e+97]], $MachinePrecision]], N[(t + x), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9000000000000002e-53 or 1.2e97 < z

   1. Initial program 69.4%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around inf 76.9%

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

   if -3.9000000000000002e-53 < z < 1.2e97

   1. Initial program 95.2%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0 77.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-53} \lor \neg \left(z \leq 1.2 \cdot 10^{+97}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+130} \lor \neg \left(z \leq 1.45 \cdot 10^{+95}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+130) (not (<= z 1.45e+95))) (+ t x) (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+130) || !(z <= 1.45e+95)) {
		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 <= (-1.85d+130)) .or. (.not. (z <= 1.45d+95))) 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 <= -1.85e+130) || !(z <= 1.45e+95)) {
		tmp = t + x;
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+130) or not (z <= 1.45e+95):
		tmp = t + x
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+130) || !(z <= 1.45e+95))
		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 <= -1.85e+130) || ~((z <= 1.45e+95)))
		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, -1.85e+130], N[Not[LessEqual[z, 1.45e+95]], $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 < -1.8500000000000001e130 or 1.45000000000000007e95 < z

   1. Initial program 59.2%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -1.8500000000000001e130 < z < 1.45000000000000007e95

   1. Initial program 93.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+130} \lor \neg \left(z \leq 1.45 \cdot 10^{+95}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+122} \lor \neg \left(z \leq 1.12 \cdot 10^{+95}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e+122) (not (<= z 1.12e+95))) (+ t x) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+122) || !(z <= 1.12e+95)) {
		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 <= (-6.4d+122)) .or. (.not. (z <= 1.12d+95))) 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 <= -6.4e+122) || !(z <= 1.12e+95)) {
		tmp = t + x;
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e+122) or not (z <= 1.12e+95):
		tmp = t + x
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e+122) || !(z <= 1.12e+95))
		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 <= -6.4e+122) || ~((z <= 1.12e+95)))
		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, -6.4e+122], N[Not[LessEqual[z, 1.12e+95]], $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 < -6.40000000000000024e122 or 1.11999999999999999e95 < z

   1. Initial program 59.2%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -6.40000000000000024e122 < z < 1.11999999999999999e95

   1. Initial program 93.3%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0 72.9%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+122} \lor \neg \left(z \leq 1.12 \cdot 10^{+95}\right):\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+93}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.6e+161) x (if (<= a 9.2e+93) (+ t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e+161) {
		tmp = x;
	} else if (a <= 9.2e+93) {
		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 <= (-8.6d+161)) then
        tmp = x
    else if (a <= 9.2d+93) 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 <= -8.6e+161) {
		tmp = x;
	} else if (a <= 9.2e+93) {
		tmp = t + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.6e+161:
		tmp = x
	elif a <= 9.2e+93:
		tmp = t + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e+161)
		tmp = x;
	elseif (a <= 9.2e+93)
		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 <= -8.6e+161)
		tmp = x;
	elseif (a <= 9.2e+93)
		tmp = t + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e+161], x, If[LessEqual[a, 9.2e+93], N[(t + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.6e161 or 9.2000000000000006e93 < a

   1. Initial program 76.9%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in a around inf 76.7%

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

      1. *-commutative 76.7%

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

      2. associate-/l* 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in y around 0 66.4%

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

      1. associate-*r/ 66.4%

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

      2. mul-1-neg 66.4%

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

      3. distribute-rgt-neg-out 66.4%

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

      4. associate-/l* 75.6%

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

   10. Simplified 75.6%

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

   11. Taylor expanded in x around inf 65.2%

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

   if -8.6e161 < a < 9.2000000000000006e93

   1. Initial program 87.4%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around inf 64.0%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+93}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 96.3% 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 83.7%

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

   1. associate-/l* 95.5%

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

3. Simplified 95.5%

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

Alternative 13: 50.8% 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 83.7%

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

   1. associate-/l* 95.5%

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

3. Simplified 95.5%

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

5. Taylor expanded in a around inf 61.5%

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

   1. *-commutative 61.5%

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

   2. associate-/l* 65.9%

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

7. Simplified 65.9%

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

8. Taylor expanded in y around 0 48.1%

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

   1. associate-*r/ 48.1%

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

   2. mul-1-neg 48.1%

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

   3. distribute-rgt-neg-out 48.1%

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

   4. associate-/l* 51.3%

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

10. Simplified 51.3%

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

11. Taylor expanded in x around inf 54.2%

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

Developer target: 99.1% 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 2024101 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (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))))