Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.5% → 98.3%

Time: 5.9s

Alternatives: 12

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.2%

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

   2. Taylor expanded in z around inf 97.6%

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

   3. Taylor expanded in y around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. distribute-frac-neg 97.6%

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

      3. +-commutative 97.6%

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

      4. distribute-frac-neg 97.6%

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

      5. sub-neg 97.6%

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

      6. div-sub 100.0%

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

   5. Simplified 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 98.4%

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

4. Final simplification 98.7%

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

Alternative 2: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+216}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -5e-29)
     t_1
     (if (<= (/ z t) 5e-5) x (if (<= (/ z t) 1e+216) (* z (/ (- x) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e-29) {
		tmp = t_1;
	} else if ((z / t) <= 5e-5) {
		tmp = x;
	} else if ((z / t) <= 1e+216) {
		tmp = z * (-x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-5d-29)) then
        tmp = t_1
    else if ((z / t) <= 5d-5) then
        tmp = x
    else if ((z / t) <= 1d+216) then
        tmp = z * (-x / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e-29) {
		tmp = t_1;
	} else if ((z / t) <= 5e-5) {
		tmp = x;
	} else if ((z / t) <= 1e+216) {
		tmp = z * (-x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e-29:
		tmp = t_1
	elif (z / t) <= 5e-5:
		tmp = x
	elif (z / t) <= 1e+216:
		tmp = z * (-x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e-29)
		tmp = t_1;
	elseif (Float64(z / t) <= 5e-5)
		tmp = x;
	elseif (Float64(z / t) <= 1e+216)
		tmp = Float64(z * Float64(Float64(-x) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e-29)
		tmp = t_1;
	elseif ((z / t) <= 5e-5)
		tmp = x;
	elseif ((z / t) <= 1e+216)
		tmp = z * (-x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e-29], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 5e-5], x, If[LessEqual[N[(z / t), $MachinePrecision], 1e+216], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.99999999999999986e-29 or 1e216 < (/.f64 z t)

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 89.4%

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

   3. Taylor expanded in y around inf 56.1%

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

      1. associate-*l/ 54.6%

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

      2. associate-/l* 62.6%

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

   5. Applied egg-rr 62.6%

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

      1. clear-num 62.5%

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

      2. associate-/r/ 62.6%

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

      3. clear-num 62.7%

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

   7. Applied egg-rr 62.7%

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

   if -4.99999999999999986e-29 < (/.f64 z t) < 5.00000000000000024e-5

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 76.6%

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

   if 5.00000000000000024e-5 < (/.f64 z t) < 1e216

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 84.9%

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

   3. Taylor expanded in y around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. distribute-frac-neg 63.1%

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

   5. Simplified 63.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{+216}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 3: 83.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+15} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -4e+15) (not (<= (/ z t) 5e+19)))
   (* z (/ (- y x) t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e+15) || !((z / t) <= 5e+19)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-4d+15)) .or. (.not. ((z / t) <= 5d+19))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e+15) || !((z / t) <= 5e+19)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -4e+15) or not ((z / t) <= 5e+19):
		tmp = z * ((y - x) / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -4e+15) || !(Float64(z / t) <= 5e+19))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -4e+15) || ~(((z / t) <= 5e+19)))
		tmp = z * ((y - x) / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -4e+15], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e+19]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4e15 or 5e19 < (/.f64 z t)

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 92.9%

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

   3. Taylor expanded in y around 0 92.9%

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

      1. mul-1-neg 92.9%

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

      2. distribute-frac-neg 92.9%

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

      3. +-commutative 92.9%

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

      4. distribute-frac-neg 92.9%

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

      5. sub-neg 92.9%

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

      6. div-sub 93.8%

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

   5. Simplified 93.8%

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

   if -4e15 < (/.f64 z t) < 5e19

   1. Initial program 98.4%

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

   2. Taylor expanded in z around -inf 94.2%

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

   3. Taylor expanded in x around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

   5. Simplified 76.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+15} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+19}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 4: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+40} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+40) (not (<= (/ z t) 5e-5)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+40) || !((z / t) <= 5e-5)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1d+40)) .or. (.not. ((z / t) <= 5d-5))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+40) || !((z / t) <= 5e-5)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e+40) or not ((z / t) <= 5e-5):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+40) || !(Float64(z / t) <= 5e-5))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1e+40) || ~(((z / t) <= 5e-5)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+40], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-5]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.00000000000000003e40 or 5.00000000000000024e-5 < (/.f64 z t)

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 92.5%

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

   3. Taylor expanded in y around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. distribute-frac-neg 92.5%

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

      3. +-commutative 92.5%

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

      4. distribute-frac-neg 92.5%

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

      5. sub-neg 92.5%

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

      6. div-sub 93.3%

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

   5. Simplified 93.3%

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

   if -1.00000000000000003e40 < (/.f64 z t) < 5.00000000000000024e-5

   1. Initial program 98.4%

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

   2. Taylor expanded in y around inf 91.7%

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

      1. associate-*r/ 93.9%

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

   4. Simplified 93.9%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+40} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 94.6% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -10.0) (not (<= (/ z t) 5e-5)))
   (/ (* (- y x) z) t)
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10.0) || !((z / t) <= 5e-5)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-10.0d0)) .or. (.not. ((z / t) <= 5d-5))) then
        tmp = ((y - x) * z) / t
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10.0) || !((z / t) <= 5e-5)) {
		tmp = ((y - x) * z) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -10.0) or not ((z / t) <= 5e-5):
		tmp = ((y - x) * z) / t
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -10.0) || !(Float64(z / t) <= 5e-5))
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -10.0) || ~(((z / t) <= 5e-5)))
		tmp = ((y - x) * z) / t;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -10.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-5]], $MachinePrecision]], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -10 or 5.00000000000000024e-5 < (/.f64 z t)

   1. Initial program 95.6%

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

   2. Taylor expanded in z around inf 88.5%

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

   3. Taylor expanded in t around inf 91.7%

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

   if -10 < (/.f64 z t) < 5.00000000000000024e-5

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 95.1%

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

      1. associate-*r/ 97.4%

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

   4. Simplified 97.4%

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

4. Final simplification 94.4%

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

Alternative 6: 95.5% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -10.0)
   (/ (* (- y x) z) t)
   (if (<= (/ z t) 5e-5) (+ x (* y (/ z t))) (/ (- y x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -10.0) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 5e-5) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-10.0d0)) then
        tmp = ((y - x) * z) / t
    else if ((z / t) <= 5d-5) then
        tmp = x + (y * (z / t))
    else
        tmp = (y - x) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -10.0) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 5e-5) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -10.0:
		tmp = ((y - x) * z) / t
	elif (z / t) <= 5e-5:
		tmp = x + (y * (z / t))
	else:
		tmp = (y - x) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -10.0)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	elseif (Float64(z / t) <= 5e-5)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y - x) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -10.0)
		tmp = ((y - x) * z) / t;
	elseif ((z / t) <= 5e-5)
		tmp = x + (y * (z / t));
	else
		tmp = (y - x) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -10.0], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 5e-5], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -10

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 86.5%

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

   3. Taylor expanded in t around inf 91.3%

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

   if -10 < (/.f64 z t) < 5.00000000000000024e-5

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 95.1%

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

      1. associate-*r/ 97.4%

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

   4. Simplified 97.4%

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

   if 5.00000000000000024e-5 < (/.f64 z t)

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 90.1%

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

      1. sub-div 91.6%

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

      2. associate-/r/ 96.2%

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

   4. Applied egg-rr 96.2%

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

4. Final simplification 95.6%

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

Alternative 7: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-29} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-29) (not (<= (/ z t) 4e-23))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-29) || !((z / t) <= 4e-23)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-5d-29)) .or. (.not. ((z / t) <= 4d-23))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-29) || !((z / t) <= 4e-23)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-29) or not ((z / t) <= 4e-23):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-29) || !(Float64(z / t) <= 4e-23))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e-29) || ~(((z / t) <= 4e-23)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-29], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e-23]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.99999999999999986e-29 or 3.99999999999999984e-23 < (/.f64 z t)

   1. Initial program 95.8%

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

   2. Taylor expanded in z around inf 85.7%

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

   3. Taylor expanded in y around inf 46.3%

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

      1. associate-*l/ 47.3%

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

      2. associate-/l* 53.4%

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

   5. Applied egg-rr 53.4%

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

      1. clear-num 53.3%

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

      2. associate-/r/ 53.3%

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

      3. clear-num 53.4%

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

   7. Applied egg-rr 53.4%

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

   if -4.99999999999999986e-29 < (/.f64 z t) < 3.99999999999999984e-23

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 78.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-29} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -5e-29)
   (* y (/ z t))
   (if (<= (/ z t) 4e-23) x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-29) {
		tmp = y * (z / t);
	} else if ((z / t) <= 4e-23) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-5d-29)) then
        tmp = y * (z / t)
    else if ((z / t) <= 4d-23) then
        tmp = x
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -5e-29) {
		tmp = y * (z / t);
	} else if ((z / t) <= 4e-23) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -5e-29:
		tmp = y * (z / t)
	elif (z / t) <= 4e-23:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -5e-29)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 4e-23)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -5e-29)
		tmp = y * (z / t);
	elseif ((z / t) <= 4e-23)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -5e-29], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e-23], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.99999999999999986e-29

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 85.7%

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

   3. Taylor expanded in y around inf 53.7%

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

      1. associate-*l/ 51.4%

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

      2. associate-/l* 59.0%

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

   5. Applied egg-rr 59.0%

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

      1. clear-num 58.9%

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

      2. associate-/r/ 59.0%

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

      3. clear-num 59.1%

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

   7. Applied egg-rr 59.1%

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

   if -4.99999999999999986e-29 < (/.f64 z t) < 3.99999999999999984e-23

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 78.5%

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

   if 3.99999999999999984e-23 < (/.f64 z t)

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 85.7%

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

   3. Taylor expanded in y around inf 40.4%

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

      1. associate-*l/ 43.9%

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

      2. associate-/l* 48.8%

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

   5. Applied egg-rr 48.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+74} \lor \neg \left(y \leq 1.44 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e+74) (not (<= y 1.44e+85)))
   (/ y (/ t z))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e+74) || !(y <= 1.44e+85)) {
		tmp = y / (t / z);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.2d+74)) .or. (.not. (y <= 1.44d+85))) then
        tmp = y / (t / z)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e+74) || !(y <= 1.44e+85)) {
		tmp = y / (t / z);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e+74) or not (y <= 1.44e+85):
		tmp = y / (t / z)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e+74) || !(y <= 1.44e+85))
		tmp = Float64(y / Float64(t / z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.2e+74) || ~((y <= 1.44e+85)))
		tmp = y / (t / z);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e+74], N[Not[LessEqual[y, 1.44e+85]], $MachinePrecision]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e74 or 1.44e85 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 70.9%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. associate-*l/ 67.8%

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

      2. associate-/l* 73.0%

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

   5. Applied egg-rr 73.0%

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

   if -5.2000000000000001e74 < y < 1.44e85

   1. Initial program 96.5%

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

   2. Taylor expanded in z around -inf 95.3%

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

   3. Taylor expanded in x around inf 78.8%

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

      1. *-commutative 78.8%

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

      2. mul-1-neg 78.8%

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

      3. unsub-neg 78.8%

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

   5. Simplified 78.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+74} \lor \neg \left(y \leq 1.44 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 10: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+65} \lor \neg \left(y \leq 3.3 \cdot 10^{-27}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.3e+65) (not (<= y 3.3e-27))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.3e+65) || !(y <= 3.3e-27)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.3d+65)) .or. (.not. (y <= 3.3d-27))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.3e+65) || !(y <= 3.3e-27)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.3e+65) or not (y <= 3.3e-27):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.3e+65) || !(y <= 3.3e-27))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.3e+65) || ~((y <= 3.3e-27)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.3e+65], N[Not[LessEqual[y, 3.3e-27]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e65 or 3.29999999999999998e-27 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 69.5%

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

   3. Taylor expanded in y around inf 62.7%

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

   if -2.3e65 < y < 3.29999999999999998e-27

   1. Initial program 96.1%

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

   2. Taylor expanded in z around 0 48.5%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+65} \lor \neg \left(y \leq 3.3 \cdot 10^{-27}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. clear-num 96.9%

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

   2. un-div-inv 97.2%

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

3. Applied egg-rr 97.2%

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

4. Final simplification 97.2%

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

Alternative 12: 39.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in z around 0 37.4%

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

3. Final simplification 37.4%

   \[\leadsto x \]

Developer target: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t_1 < -1013646692435.8867:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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