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

Percentage Accurate: 97.4% → 97.7%

Time: 6.5s

Alternatives: 13

Speedup: 1.0×

• 25.0% 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: 97.4% 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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z t)))))
   (if (<= t_1 5e+301) t_1 (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = ((y - x) * 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / t))
    if (t_1 <= 5d+301) then
        tmp = t_1
    else
        tmp = ((y - x) * z) / t
    end if
    code = tmp
end function

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 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - x) * (z / t))
	tmp = 0
	if t_1 <= 5e+301:
		tmp = t_1
	else:
		tmp = ((y - x) * z) / t
	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 <= 5e+301)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	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 <= 5e+301)
		tmp = t_1;
	else
		tmp = ((y - x) * z) / t;
	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, 5e+301], t$95$1, N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < 5.0000000000000004e301

   1. Initial program 99.4%

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

   if 5.0000000000000004e301 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 87.2%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. sub-div 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l/ 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 2: 66.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1000:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))))
   (if (<= (/ z t) -2e+148)
     t_1
     (if (<= (/ z t) -1000.0)
       (* x (- (/ z t)))
       (if (<= (/ z t) 2e-7) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if ((z / t) <= -2e+148) {
		tmp = t_1;
	} else if ((z / t) <= -1000.0) {
		tmp = x * -(z / t);
	} else if ((z / t) <= 2e-7) {
		tmp = x;
	} 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 / (t / z)
    if ((z / t) <= (-2d+148)) then
        tmp = t_1
    else if ((z / t) <= (-1000.0d0)) then
        tmp = x * -(z / t)
    else if ((z / t) <= 2d-7) then
        tmp = 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 t_1 = y / (t / z);
	double tmp;
	if ((z / t) <= -2e+148) {
		tmp = t_1;
	} else if ((z / t) <= -1000.0) {
		tmp = x * -(z / t);
	} else if ((z / t) <= 2e-7) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	tmp = 0
	if (z / t) <= -2e+148:
		tmp = t_1
	elif (z / t) <= -1000.0:
		tmp = x * -(z / t)
	elif (z / t) <= 2e-7:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (Float64(z / t) <= -2e+148)
		tmp = t_1;
	elseif (Float64(z / t) <= -1000.0)
		tmp = Float64(x * Float64(-Float64(z / t)));
	elseif (Float64(z / t) <= 2e-7)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	tmp = 0.0;
	if ((z / t) <= -2e+148)
		tmp = t_1;
	elseif ((z / t) <= -1000.0)
		tmp = x * -(z / t);
	elseif ((z / t) <= 2e-7)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+148], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1000.0], N[(x * (-N[(z / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-7], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2.0000000000000001e148 or 1.9999999999999999e-7 < (/.f64 z t)

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 86.4%

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

   3. Taylor expanded in y around inf 57.9%

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

      1. *-commutative 57.9%

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

      2. associate-*l/ 58.7%

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

      3. associate-/l* 63.0%

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

   5. Applied egg-rr 63.0%

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

   if -2.0000000000000001e148 < (/.f64 z t) < -1e3

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   4. Simplified 67.4%

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

   5. Taylor expanded in z around inf 67.4%

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

      1. neg-mul-1 67.4%

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

      2. distribute-neg-frac 67.4%

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

   7. Simplified 67.4%

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

   if -1e3 < (/.f64 z t) < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 80.7%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+148}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq -1000:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+58}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -50000.0) (not (<= (/ z t) 2e+58)))
   (* 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) <= -50000.0) || !((z / t) <= 2e+58)) {
		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) <= (-50000.0d0)) .or. (.not. ((z / t) <= 2d+58))) 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) <= -50000.0) || !((z / t) <= 2e+58)) {
		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) <= -50000.0) or not ((z / t) <= 2e+58):
		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) <= -50000.0) || !(Float64(z / t) <= 2e+58))
		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) <= -50000.0) || ~(((z / t) <= 2e+58)))
		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], -50000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e+58]], $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) < -5e4 or 1.99999999999999989e58 < (/.f64 z t)

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 89.5%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. distribute-frac-neg 89.5%

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

      3. +-commutative 89.5%

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

      4. distribute-frac-neg 89.5%

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

      5. sub-neg 89.5%

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

      6. div-sub 94.2%

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

   5. Simplified 94.2%

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

   if -5e4 < (/.f64 z t) < 1.99999999999999989e58

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

   4. Simplified 79.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -50000 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{+58}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 4: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.0) (not (<= (/ z t) 2e-7)))
   (* (- y x) (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.0) || !((z / t) <= 2e-7)) {
		tmp = (y - x) * (z / 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) <= (-2.0d0)) .or. (.not. ((z / t) <= 2d-7))) then
        tmp = (y - x) * (z / 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) <= -2.0) || !((z / t) <= 2e-7)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2.0) or not ((z / t) <= 2e-7):
		tmp = (y - x) * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2.0) || !(Float64(z / t) <= 2e-7))
		tmp = Float64(Float64(y - x) * Float64(z / 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) <= -2.0) || ~(((z / t) <= 2e-7)))
		tmp = (y - x) * (z / 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], -2.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-7]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / 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) < -2 or 1.9999999999999999e-7 < (/.f64 z t)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 84.8%

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

      1. sub-div 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-/r/ 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. clear-num 96.1%

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

      2. associate-/r/ 95.3%

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

      3. clear-num 95.3%

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

   6. Applied egg-rr 95.3%

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

   if -2 < (/.f64 z t) < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. unsub-neg 82.1%

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

   4. Simplified 82.1%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 5: 96.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.0) (not (<= (/ z t) 2e-7)))
   (* (- y x) (/ z t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.0) || !((z / t) <= 2e-7)) {
		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) <= (-2.0d0)) .or. (.not. ((z / t) <= 2d-7))) 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) <= -2.0) || !((z / t) <= 2e-7)) {
		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) <= -2.0) or not ((z / t) <= 2e-7):
		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) <= -2.0) || !(Float64(z / t) <= 2e-7))
		tmp = Float64(Float64(y - x) * Float64(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) <= -2.0) || ~(((z / t) <= 2e-7)))
		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], -2.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-7]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / 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) < -2 or 1.9999999999999999e-7 < (/.f64 z t)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 84.8%

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

      1. sub-div 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-/r/ 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. clear-num 96.1%

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

      2. associate-/r/ 95.3%

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

      3. clear-num 95.3%

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

   6. Applied egg-rr 95.3%

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

   if -2 < (/.f64 z t) < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 93.4%

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

      1. associate-*r/ 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 0.01\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.0) (not (<= (/ z t) 0.01)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.0) || !((z / t) <= 0.01)) {
		tmp = (y - x) / (t / z);
	} 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) <= (-2.0d0)) .or. (.not. ((z / t) <= 0.01d0))) then
        tmp = (y - x) / (t / z)
    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) <= -2.0) || !((z / t) <= 0.01)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2.0) or not ((z / t) <= 0.01):
		tmp = (y - x) / (t / z)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2.0) || !(Float64(z / t) <= 0.01))
		tmp = Float64(Float64(y - x) / Float64(t / z));
	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) <= -2.0) || ~(((z / t) <= 0.01)))
		tmp = (y - x) / (t / z);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.01]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2 or 0.0100000000000000002 < (/.f64 z t)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 85.3%

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

      1. sub-div 89.7%

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

      2. *-commutative 89.7%

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

      3. associate-/r/ 96.2%

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

   4. Applied egg-rr 96.2%

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

   if -2 < (/.f64 z t) < 0.0100000000000000002

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 93.4%

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

      1. associate-*r/ 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 0.01\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 95.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2.0)
   (* (- y x) (/ z t))
   (if (<= (/ z t) 2e-7) (+ x (* y (/ z t))) (/ (* (- y x) z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2.0) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 2e-7) {
		tmp = x + (y * (z / t));
	} else {
		tmp = ((y - x) * 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) <= (-2.0d0)) then
        tmp = (y - x) * (z / t)
    else if ((z / t) <= 2d-7) then
        tmp = x + (y * (z / t))
    else
        tmp = ((y - x) * 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) <= -2.0) {
		tmp = (y - x) * (z / t);
	} else if ((z / t) <= 2e-7) {
		tmp = x + (y * (z / t));
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2.0:
		tmp = (y - x) * (z / t)
	elif (z / t) <= 2e-7:
		tmp = x + (y * (z / t))
	else:
		tmp = ((y - x) * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2.0)
		tmp = Float64(Float64(y - x) * Float64(z / t));
	elseif (Float64(z / t) <= 2e-7)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2.0)
		tmp = (y - x) * (z / t);
	elseif ((z / t) <= 2e-7)
		tmp = x + (y * (z / t));
	else
		tmp = ((y - x) * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2.0], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-7], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 86.6%

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

      1. sub-div 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-/r/ 97.1%

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

   4. Applied egg-rr 97.1%

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

      1. clear-num 96.9%

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

      2. associate-/r/ 96.7%

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

      3. clear-num 96.7%

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

   6. Applied egg-rr 96.7%

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

   if -2 < (/.f64 z t) < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 93.4%

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

      1. associate-*r/ 98.4%

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

   4. Simplified 98.4%

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

   if 1.9999999999999999e-7 < (/.f64 z t)

   1. Initial program 95.1%

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

   2. Taylor expanded in z around inf 83.4%

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

      1. sub-div 87.3%

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

      2. *-commutative 87.3%

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

      3. associate-*l/ 95.4%

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

   4. Applied egg-rr 95.4%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 8: 54.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-100} \lor \neg \left(z \leq 2.6 \cdot 10^{-85}\right) \land \left(z \leq 5.6 \cdot 10^{-32} \lor \neg \left(z \leq 1.7 \cdot 10^{+23}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e-100)
         (and (not (<= z 2.6e-85)) (or (<= z 5.6e-32) (not (<= z 1.7e+23)))))
   (* z (/ y t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e-100) || (!(z <= 2.6e-85) && ((z <= 5.6e-32) || !(z <= 1.7e+23)))) {
		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 ((z <= (-2.9d-100)) .or. (.not. (z <= 2.6d-85)) .and. (z <= 5.6d-32) .or. (.not. (z <= 1.7d+23))) 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 ((z <= -2.9e-100) || (!(z <= 2.6e-85) && ((z <= 5.6e-32) || !(z <= 1.7e+23)))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e-100) or (not (z <= 2.6e-85) and ((z <= 5.6e-32) or not (z <= 1.7e+23))):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e-100) || (!(z <= 2.6e-85) && ((z <= 5.6e-32) || !(z <= 1.7e+23))))
		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 ((z <= -2.9e-100) || (~((z <= 2.6e-85)) && ((z <= 5.6e-32) || ~((z <= 1.7e+23)))))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e-100], And[N[Not[LessEqual[z, 2.6e-85]], $MachinePrecision], Or[LessEqual[z, 5.6e-32], N[Not[LessEqual[z, 1.7e+23]], $MachinePrecision]]]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.89999999999999975e-100 or 2.60000000000000011e-85 < z < 5.5999999999999998e-32 or 1.69999999999999996e23 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 77.9%

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

   3. Taylor expanded in y around inf 52.3%

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

   if -2.89999999999999975e-100 < z < 2.60000000000000011e-85 or 5.5999999999999998e-32 < z < 1.69999999999999996e23

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 72.4%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-100} \lor \neg \left(z \leq 2.6 \cdot 10^{-85}\right) \land \left(z \leq 5.6 \cdot 10^{-32} \lor \neg \left(z \leq 1.7 \cdot 10^{+23}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.0) (not (<= (/ z t) 2e-7))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.0) || !((z / t) <= 2e-7)) {
		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) <= (-2.0d0)) .or. (.not. ((z / t) <= 2d-7))) 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) <= -2.0) || !((z / t) <= 2e-7)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2.0) or not ((z / t) <= 2e-7):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2.0) || !(Float64(z / t) <= 2e-7))
		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) <= -2.0) || ~(((z / t) <= 2e-7)))
		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], -2.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-7]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2 or 1.9999999999999999e-7 < (/.f64 z t)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 84.8%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. associate-*l/ 53.2%

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

      3. associate-/l* 58.1%

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

   5. Applied egg-rr 58.1%

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

   6. Taylor expanded in y around 0 53.2%

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

      1. *-commutative 53.2%

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

      2. associate-*l/ 57.8%

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

   8. Simplified 57.8%

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

   if -2 < (/.f64 z t) < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 81.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.0) (not (<= (/ z t) 2e-7))) (/ y (/ t z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.0) || !((z / t) <= 2e-7)) {
		tmp = y / (t / z);
	} 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) <= (-2.0d0)) .or. (.not. ((z / t) <= 2d-7))) then
        tmp = y / (t / z)
    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) <= -2.0) || !((z / t) <= 2e-7)) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2.0) or not ((z / t) <= 2e-7):
		tmp = y / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2.0) || !(Float64(z / t) <= 2e-7))
		tmp = Float64(y / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -2.0) || ~(((z / t) <= 2e-7)))
		tmp = y / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-7]], $MachinePrecision]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2 or 1.9999999999999999e-7 < (/.f64 z t)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 84.8%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

      2. associate-*l/ 53.2%

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

      3. associate-/l* 58.1%

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

   5. Applied egg-rr 58.1%

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

   if -2 < (/.f64 z t) < 1.9999999999999999e-7

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 81.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+140} \lor \neg \left(y \leq 4.2 \cdot 10^{+178}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e+140) (not (<= y 4.2e+178)))
   (* y (/ z t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e+140) || !(y <= 4.2e+178)) {
		tmp = y * (z / 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 ((y <= (-6d+140)) .or. (.not. (y <= 4.2d+178))) then
        tmp = y * (z / 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 ((y <= -6e+140) || !(y <= 4.2e+178)) {
		tmp = y * (z / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e+140) or not (y <= 4.2e+178):
		tmp = y * (z / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e+140) || !(y <= 4.2e+178))
		tmp = Float64(y * Float64(z / 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 ((y <= -6e+140) || ~((y <= 4.2e+178)))
		tmp = y * (z / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6e+140], N[Not[LessEqual[y, 4.2e+178]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999993e140 or 4.1999999999999997e178 < y

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 68.5%

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

   3. Taylor expanded in y around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 72.4%

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

      3. associate-/l* 80.5%

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

   5. Applied egg-rr 80.5%

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

   6. Taylor expanded in y around 0 72.4%

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

      1. *-commutative 72.4%

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

      2. associate-*l/ 80.6%

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

   8. Simplified 80.6%

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

   if -5.99999999999999993e140 < y < 4.1999999999999997e178

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

   4. Simplified 80.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+140} \lor \neg \left(y \leq 4.2 \cdot 10^{+178}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 12: 97.5% 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 97.6%

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

2. Taylor expanded in y around 0 88.9%

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

   1. +-commutative 88.9%

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

   2. mul-1-neg 88.9%

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

   3. sub-neg 88.9%

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

   4. associate-/l* 90.9%

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

   5. associate-/l* 92.3%

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

   6. div-sub 98.2%

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

4. Simplified 98.2%

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

5. Final simplification 98.2%

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

Alternative 13: 39.3% 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 97.6%

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

2. Taylor expanded in z around 0 37.5%

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

3. Final simplification 37.5%

   \[\leadsto x \]

Developer target: 97.2% 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 2023312 
(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))))