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

Percentage Accurate: 97.8% → 98.5%

Time: 8.8s

Alternatives: 8

Speedup: 1.0×

• 24.7% 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: 98.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -inf.0

   1. Initial program 72.3%

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

      1. associate-*r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 z t)

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      2. fma-define 98.5%

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

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

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

Alternative 2: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot y}{t}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z y) t)))
   (if (<= t -2.9e+104)
     x
     (if (<= t -3.7e-180)
       t_1
       (if (<= t 2.2e-239) (* (/ z t) (- x)) (if (<= t 6.8e-19) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) / t;
	double tmp;
	if (t <= -2.9e+104) {
		tmp = x;
	} else if (t <= -3.7e-180) {
		tmp = t_1;
	} else if (t <= 2.2e-239) {
		tmp = (z / t) * -x;
	} else if (t <= 6.8e-19) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z * y) / t
    if (t <= (-2.9d+104)) then
        tmp = x
    else if (t <= (-3.7d-180)) then
        tmp = t_1
    else if (t <= 2.2d-239) then
        tmp = (z / t) * -x
    else if (t <= 6.8d-19) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * y) / t;
	double tmp;
	if (t <= -2.9e+104) {
		tmp = x;
	} else if (t <= -3.7e-180) {
		tmp = t_1;
	} else if (t <= 2.2e-239) {
		tmp = (z / t) * -x;
	} else if (t <= 6.8e-19) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) / t
	tmp = 0
	if t <= -2.9e+104:
		tmp = x
	elif t <= -3.7e-180:
		tmp = t_1
	elif t <= 2.2e-239:
		tmp = (z / t) * -x
	elif t <= 6.8e-19:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) / t)
	tmp = 0.0
	if (t <= -2.9e+104)
		tmp = x;
	elseif (t <= -3.7e-180)
		tmp = t_1;
	elseif (t <= 2.2e-239)
		tmp = Float64(Float64(z / t) * Float64(-x));
	elseif (t <= 6.8e-19)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) / t;
	tmp = 0.0;
	if (t <= -2.9e+104)
		tmp = x;
	elseif (t <= -3.7e-180)
		tmp = t_1;
	elseif (t <= 2.2e-239)
		tmp = (z / t) * -x;
	elseif (t <= 6.8e-19)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -2.9e+104], x, If[LessEqual[t, -3.7e-180], t$95$1, If[LessEqual[t, 2.2e-239], N[(N[(z / t), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[t, 6.8e-19], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8999999999999998e104 or 6.8000000000000004e-19 < t

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 64.6%

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

   if -2.8999999999999998e104 < t < -3.70000000000000016e-180 or 2.19999999999999983e-239 < t < 6.8000000000000004e-19

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-/l* 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in t around 0 74.0%

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

   7. Taylor expanded in t around 0 58.0%

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

      1. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if -3.70000000000000016e-180 < t < 2.19999999999999983e-239

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in z around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. distribute-frac-neg 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-180}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-19}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+160} \lor \neg \left(x \leq 7.2 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.55e+160) (not (<= x 7.2e+31)))
   (* x (- 1.0 (/ z t)))
   (+ x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.55e+160) || !(x <= 7.2e+31)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + ((z / t) * y);
	}
	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 ((x <= (-2.55d+160)) .or. (.not. (x <= 7.2d+31))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + ((z / t) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.55e+160) || !(x <= 7.2e+31)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + ((z / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.55e+160) or not (x <= 7.2e+31):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + ((z / t) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.55e+160) || !(x <= 7.2e+31))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(Float64(z / t) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.55e+160) || ~((x <= 7.2e+31)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + ((z / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.55e+160], N[Not[LessEqual[x, 7.2e+31]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5500000000000001e160 or 7.19999999999999992e31 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

   5. Simplified 94.1%

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

   if -2.5500000000000001e160 < x < 7.19999999999999992e31

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 81.4%

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

      1. associate-*r/ 84.3%

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

   5. Simplified 84.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+160} \lor \neg \left(x \leq 7.2 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-121} \lor \neg \left(x \leq 1.75 \cdot 10^{-155}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.25e-121) (not (<= x 1.75e-155)))
   (* x (- 1.0 (/ z t)))
   (/ (* z y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e-121) || !(x <= 1.75e-155)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (z * y) / 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 ((x <= (-1.25d-121)) .or. (.not. (x <= 1.75d-155))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = (z * y) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e-121) || !(x <= 1.75e-155)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (z * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.25e-121) or not (x <= 1.75e-155):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = (z * y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.25e-121) || !(x <= 1.75e-155))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(Float64(z * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.25e-121) || ~((x <= 1.75e-155)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = (z * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.25e-121], N[Not[LessEqual[x, 1.75e-155]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999997e-121 or 1.75000000000000008e-155 < x

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf 78.8%

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

      1. mul-1-neg 78.8%

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

      2. unsub-neg 78.8%

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

   5. Simplified 78.8%

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

   if -1.24999999999999997e-121 < x < 1.75000000000000008e-155

   1. Initial program 93.2%

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

   3. Taylor expanded in y around inf 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-/l* 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around 0 91.5%

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

   7. Taylor expanded in t around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-121} \lor \neg \left(x \leq 1.75 \cdot 10^{-155}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -inf.0

   1. Initial program 72.3%

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

      1. associate-*r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (/.f64 z t)

   1. Initial program 98.5%

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

4. Final simplification 98.6%

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

Alternative 6: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-19}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.9e+104) x (if (<= t 1.85e-19) (/ (* z y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.9e+104) {
		tmp = x;
	} else if (t <= 1.85e-19) {
		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 (t <= (-2.9d+104)) then
        tmp = x
    else if (t <= 1.85d-19) 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 (t <= -2.9e+104) {
		tmp = x;
	} else if (t <= 1.85e-19) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.9e+104:
		tmp = x
	elif t <= 1.85e-19:
		tmp = (z * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.9e+104)
		tmp = x;
	elseif (t <= 1.85e-19)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.9e+104)
		tmp = x;
	elseif (t <= 1.85e-19)
		tmp = (z * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.9e+104], x, If[LessEqual[t, 1.85e-19], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999998e104 or 1.85000000000000003e-19 < t

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 64.6%

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

   if -2.8999999999999998e104 < t < 1.85000000000000003e-19

   1. Initial program 96.0%

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

   3. Taylor expanded in y around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-/l* 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in t around 0 66.0%

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

   7. Taylor expanded in t around 0 52.0%

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

      1. *-commutative 52.0%

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

   9. Simplified 52.0%

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

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Final simplification 96.8%

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

Alternative 8: 38.8% 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 96.8%

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

3. Taylor expanded in z around 0 37.0%

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

Developer Target 1: 97.5% 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 2024136 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* (- y x) (/ z t)) -10136466924358867/10000) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z))))))

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