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

Percentage Accurate: 97.8% → 97.9%

Time: 7.9s

Alternatives: 9

Speedup: 1.0×

• 25.4% 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: 97.8% 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: 97.9% 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. associate-*r/ 90.6%

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

   2. associate-/l* 97.5%

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

3. Applied egg-rr 97.5%

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

4. Final simplification 97.5%

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

Alternative 2: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-71} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.95e-71) (not (<= y 1.05e+66)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.95e-71) || !(y <= 1.05e+66)) {
		tmp = x + (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 <= (-2.95d-71)) .or. (.not. (y <= 1.05d+66))) then
        tmp = x + (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 <= -2.95e-71) || !(y <= 1.05e+66)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.95e-71) or not (y <= 1.05e+66):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.95e-71) || !(y <= 1.05e+66))
		tmp = Float64(x + 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 <= -2.95e-71) || ~((y <= 1.05e+66)))
		tmp = x + (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, -2.95e-71], N[Not[LessEqual[y, 1.05e+66]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.95000000000000001e-71 or 1.05000000000000003e66 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 92.1%

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

   4. Simplified 92.1%

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

   if -2.95000000000000001e-71 < y < 1.05000000000000003e66

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 89.2%

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

      1. mul-1-neg 89.2%

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

      2. unsub-neg 89.2%

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

   4. Simplified 89.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-71} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 3: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-68} \lor \neg \left(y \leq 1.15 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e-68) (not (<= y 1.15e+66)))
   (+ x (/ y (/ t z)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-68) || !(y <= 1.15e+66)) {
		tmp = x + (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 <= (-4.4d-68)) .or. (.not. (y <= 1.15d+66))) then
        tmp = x + (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 <= -4.4e-68) || !(y <= 1.15e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e-68) or not (y <= 1.15e+66):
		tmp = x + (y / (t / z))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e-68) || !(y <= 1.15e+66))
		tmp = Float64(x + 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 <= -4.4e-68) || ~((y <= 1.15e+66)))
		tmp = x + (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, -4.4e-68], N[Not[LessEqual[y, 1.15e+66]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000005e-68 or 1.15e66 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. associate-/l* 92.2%

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

      2. associate-/r/ 88.3%

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

   4. Simplified 88.3%

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

      1. associate-/r/ 92.2%

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

   6. Applied egg-rr 92.2%

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

   if -4.40000000000000005e-68 < y < 1.15e66

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 89.2%

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

      1. mul-1-neg 89.2%

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

      2. unsub-neg 89.2%

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

   4. Simplified 89.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-68} \lor \neg \left(y \leq 1.15 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 4: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-73} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e-73) (not (<= y 1.05e+66)))
   (+ x (/ y (/ t z)))
   (- x (* x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-73) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (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 ((y <= (-3d-73)) .or. (.not. (y <= 1.05d+66))) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (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 ((y <= -3e-73) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e-73) or not (y <= 1.05e+66):
		tmp = x + (y / (t / z))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e-73) || !(y <= 1.05e+66))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3e-73) || ~((y <= 1.05e+66)))
		tmp = x + (y / (t / z));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e-73], N[Not[LessEqual[y, 1.05e+66]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e-73 or 1.05000000000000003e66 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. associate-/l* 92.2%

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

      2. associate-/r/ 88.3%

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

   4. Simplified 88.3%

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

      1. associate-/r/ 92.2%

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

   6. Applied egg-rr 92.2%

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

   if -3e-73 < y < 1.05000000000000003e66

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 89.9%

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

      2. associate-*r/ 89.9%

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

      3. neg-mul-1 89.9%

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

   4. Simplified 89.9%

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

      1. distribute-frac-neg 89.9%

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

      2. unsub-neg 89.9%

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

      3. div-inv 89.2%

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

      4. clear-num 89.2%

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

   6. Applied egg-rr 89.2%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-73} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-69} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.9e-69) (not (<= y 1.05e+66)))
   (+ x (/ y (/ t z)))
   (- x (/ x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.9e-69) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (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 ((y <= (-6.9d-69)) .or. (.not. (y <= 1.05d+66))) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (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 ((y <= -6.9e-69) || !(y <= 1.05e+66)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.9e-69) or not (y <= 1.05e+66):
		tmp = x + (y / (t / z))
	else:
		tmp = x - (x / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.9e-69) || !(y <= 1.05e+66))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(x / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.9e-69) || ~((y <= 1.05e+66)))
		tmp = x + (y / (t / z));
	else
		tmp = x - (x / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.9e-69], N[Not[LessEqual[y, 1.05e+66]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8999999999999997e-69 or 1.05000000000000003e66 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. associate-/l* 92.2%

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

      2. associate-/r/ 88.3%

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

   4. Simplified 88.3%

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

      1. associate-/r/ 92.2%

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

   6. Applied egg-rr 92.2%

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

   if -6.8999999999999997e-69 < y < 1.05000000000000003e66

   1. Initial program 96.4%

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

   2. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 89.9%

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

      2. associate-*r/ 89.9%

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

      3. neg-mul-1 89.9%

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

   4. Simplified 89.9%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{-69} \lor \neg \left(y \leq 1.05 \cdot 10^{+66}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \end{array} \]

Alternative 6: 92.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in y around 0 85.2%

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

   1. associate-*r/ 85.2%

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

   2. associate-*r* 85.2%

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

   3. neg-mul-1 85.2%

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

   4. associate-*r/ 85.9%

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

   5. associate-*r/ 89.1%

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

   6. distribute-rgt-out 96.9%

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

   7. +-commutative 96.9%

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

   8. sub-neg 96.9%

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

   9. associate-*l/ 90.6%

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

   10. associate-*r/ 94.4%

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

4. Simplified 94.4%

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

5. Final simplification 94.4%

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

Alternative 7: 97.8% 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]

Derivation

1. Initial program 96.9%

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

2. Final simplification 96.9%

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

Alternative 8: 65.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (z / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in x around inf 66.3%

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

   1. mul-1-neg 66.3%

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

   2. unsub-neg 66.3%

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

4. Simplified 66.3%

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

5. Final simplification 66.3%

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

Alternative 9: 38.6% 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 40.8%

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

3. Final simplification 40.8%

   \[\leadsto x \]

Developer target: 97.7% 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 2023301 
(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))))