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

Percentage Accurate: 97.8% → 97.8%

Time: 8.2s

Alternatives: 10

Speedup: 1.1×

• 26.0% 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: 97.8% 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: 97.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 97.2

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

4. Applied rewrites 97.2%

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

5. Final simplification 97.2%

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

Alternative 2: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -100:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+18}:\\ \;\;\;\;\frac{z}{t} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -100.0)
   (* (/ z t) (- y x))
   (if (<= (/ z t) 4e+18) (+ (* (/ z t) y) x) (* (/ (- y x) t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -100.0) {
		tmp = (z / t) * (y - x);
	} else if ((z / t) <= 4e+18) {
		tmp = ((z / t) * y) + x;
	} else {
		tmp = ((y - x) / t) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-100.0d0)) then
        tmp = (z / t) * (y - x)
    else if ((z / t) <= 4d+18) then
        tmp = ((z / t) * y) + x
    else
        tmp = ((y - x) / t) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -100.0) {
		tmp = (z / t) * (y - x);
	} else if ((z / t) <= 4e+18) {
		tmp = ((z / t) * y) + x;
	} else {
		tmp = ((y - x) / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -100.0:
		tmp = (z / t) * (y - x)
	elif (z / t) <= 4e+18:
		tmp = ((z / t) * y) + x
	else:
		tmp = ((y - x) / t) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -100.0)
		tmp = Float64(Float64(z / t) * Float64(y - x));
	elseif (Float64(z / t) <= 4e+18)
		tmp = Float64(Float64(Float64(z / t) * y) + x);
	else
		tmp = Float64(Float64(Float64(y - x) / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -100.0)
		tmp = (z / t) * (y - x);
	elseif ((z / t) <= 4e+18)
		tmp = ((z / t) * y) + x;
	else
		tmp = ((y - x) / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -100.0], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 4e+18], N[(N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -100

   1. Initial program 96.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 96.8

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

   4. Applied rewrites 96.8%

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

   5. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 96.0

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

   7. Applied rewrites 96.0%

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

   if -100 < (/.f64 z t) < 4e18

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 95.9

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

   5. Applied rewrites 95.9%

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

   if 4e18 < (/.f64 z t)

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 93.4

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

   5. Applied rewrites 93.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -100:\\ \;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{z}{t} \leq 4 \cdot 10^{+18}:\\ \;\;\;\;\frac{z}{t} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Developer Target 1: 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 2024230 
(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))))