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

Percentage Accurate: 97.8% → 97.9%

Time: 8.7s

Alternatives: 8

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: 97.8% 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 97.7%

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

   1. clear-num 97.6%

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

   2. un-div-inv 98.1%

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

4. Applied egg-rr 98.1%

   \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
5. Add Preprocessing

Alternative 2: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -40000000000 \lor \neg \left(\frac{z}{t} \leq 0.05\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -40000000000.0) (not (<= (/ z t) 0.05)))
   (* x (/ z (- t)))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -40000000000.0) || !((z / t) <= 0.05)) {
		tmp = x * (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) <= (-40000000000.0d0)) .or. (.not. ((z / t) <= 0.05d0))) then
        tmp = x * (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) <= -40000000000.0) || !((z / t) <= 0.05)) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -40000000000.0) or not ((z / t) <= 0.05):
		tmp = x * (z / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -40000000000.0) || !(Float64(z / t) <= 0.05))
		tmp = Float64(x * Float64(z / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -40000000000.0) || ~(((z / t) <= 0.05)))
		tmp = x * (z / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -40000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.05]], $MachinePrecision]], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4e10 or 0.050000000000000003 < (/.f64 z t)

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. unsub-neg 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in z around inf 58.3%

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

      1. associate-*r/ 58.3%

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

      2. neg-mul-1 58.3%

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

   8. Simplified 58.3%

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

   if -4e10 < (/.f64 z t) < 0.050000000000000003

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 71.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -40000000000 \lor \neg \left(\frac{z}{t} \leq 0.05\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -40000000000:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.05:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -40000000000.0)
   (/ (- x) (/ t z))
   (if (<= (/ z t) 0.05) x (* x (/ z (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -40000000000.0) {
		tmp = -x / (t / z);
	} else if ((z / t) <= 0.05) {
		tmp = x;
	} else {
		tmp = 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) <= (-40000000000.0d0)) then
        tmp = -x / (t / z)
    else if ((z / t) <= 0.05d0) then
        tmp = x
    else
        tmp = 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) <= -40000000000.0) {
		tmp = -x / (t / z);
	} else if ((z / t) <= 0.05) {
		tmp = x;
	} else {
		tmp = x * (z / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -40000000000.0:
		tmp = -x / (t / z)
	elif (z / t) <= 0.05:
		tmp = x
	else:
		tmp = x * (z / -t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -40000000000.0)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (Float64(z / t) <= 0.05)
		tmp = x;
	else
		tmp = Float64(x * Float64(z / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -40000000000.0)
		tmp = -x / (t / z);
	elseif ((z / t) <= 0.05)
		tmp = x;
	else
		tmp = x * (z / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -40000000000.0], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.05], x, N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4e10

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. unsub-neg 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in z around inf 57.7%

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

      1. associate-*r/ 57.7%

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

      2. neg-mul-1 57.7%

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

   8. Simplified 57.7%

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

      1. distribute-frac-neg 57.7%

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

      2. distribute-rgt-neg-in 57.7%

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

      3. distribute-lft-neg-in 57.7%

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

      4. clear-num 57.7%

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

      5. un-div-inv 58.4%

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

   10. Applied egg-rr 58.4%

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

   if -4e10 < (/.f64 z t) < 0.050000000000000003

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 71.5%

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

   if 0.050000000000000003 < (/.f64 z t)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in z around inf 58.9%

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

      1. associate-*r/ 58.9%

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

      2. neg-mul-1 58.9%

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

   8. Simplified 58.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -40000000000:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.05:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 9.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -36.0) (not (<= y 9.2e-11)))
   (+ x (* y (/ z t)))
   (- x (* x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -36.0) || !(y <= 9.2e-11)) {
		tmp = x + (y * (z / t));
	} 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 <= (-36.0d0)) .or. (.not. (y <= 9.2d-11))) then
        tmp = x + (y * (z / t))
    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 <= -36.0) || !(y <= 9.2e-11)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -36.0) or not (y <= 9.2e-11):
		tmp = x + (y * (z / t))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -36.0) || !(y <= 9.2e-11))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	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 <= -36.0) || ~((y <= 9.2e-11)))
		tmp = x + (y * (z / t));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -36.0], N[Not[LessEqual[y, 9.2e-11]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -36 or 9.20000000000000054e-11 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. associate-*r/ 93.0%

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

   5. Simplified 93.0%

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

   if -36 < y < 9.20000000000000054e-11

   1. Initial program 97.1%

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

      1. associate-*r/ 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in y around 0 84.1%

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

      1. neg-mul-1 84.1%

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

   7. Simplified 84.1%

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

      1. div-inv 84.1%

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

      2. add-sqr-sqrt 41.0%

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

      3. sqrt-unprod 47.2%

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

      4. sqr-neg 47.2%

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

      5. sqrt-unprod 24.5%

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

      6. add-sqr-sqrt 50.5%

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

      7. remove-double-neg 50.5%

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

      8. distribute-lft-neg-out 50.5%

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

      9. cancel-sign-sub-inv 50.5%

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

      10. associate-*r* 53.3%

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

      11. div-inv 53.3%

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

      12. add-sqr-sqrt 26.0%

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

      13. sqrt-unprod 46.6%

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

      14. sqr-neg 46.6%

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

      15. sqrt-unprod 45.9%

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

      16. add-sqr-sqrt 87.7%

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

   9. Applied egg-rr 87.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 9.2 \cdot 10^{-11}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -100 \lor \neg \left(y \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -100.0) (not (<= y 1.35e-8)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -100.0) || !(y <= 1.35e-8)) {
		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 <= (-100.0d0)) .or. (.not. (y <= 1.35d-8))) 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 <= -100.0) || !(y <= 1.35e-8)) {
		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 <= -100.0) or not (y <= 1.35e-8):
		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 <= -100.0) || !(y <= 1.35e-8))
		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 <= -100.0) || ~((y <= 1.35e-8)))
		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, -100.0], N[Not[LessEqual[y, 1.35e-8]], $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 < -100 or 1.35000000000000001e-8 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 86.3%

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

      1. associate-*r/ 93.0%

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

   5. Simplified 93.0%

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

   if -100 < y < 1.35000000000000001e-8

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -100 \lor \neg \left(y \leq 1.35 \cdot 10^{-8}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 97.7%

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

Alternative 7: 65.3% 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 97.7%

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

3. Taylor expanded in x around inf 66.9%

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

   1. mul-1-neg 66.9%

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

   2. unsub-neg 66.9%

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

5. Simplified 66.9%

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

Alternative 8: 38.7% 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 97.7%

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

3. Taylor expanded in z around 0 41.8%

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

Developer target: 97.6% accurate, 0.3× 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 2024110 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (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))))