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

Percentage Accurate: 97.6% → 97.7%

Time: 7.9s

Alternatives: 8

Speedup: 1.0×

• 24.9% 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: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - x) * (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 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 97.3%

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

   1. clear-num 97.2%

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

   2. un-div-inv 97.6%

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

4. Applied egg-rr 97.6%

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

Alternative 2: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+15} \lor \neg \left(x \leq 2.6 \cdot 10^{+76}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.4e+15) (not (<= x 2.6e+76)))
   (* x (- 1.0 (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e+15) || !(x <= 2.6e+76)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (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 ((x <= (-3.4d+15)) .or. (.not. (x <= 2.6d+76))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.4e+15) || !(x <= 2.6e+76)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.4e+15) or not (x <= 2.6e+76):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.4e+15) || !(x <= 2.6e+76))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.4e+15) || ~((x <= 2.6e+76)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.4e+15], N[Not[LessEqual[x, 2.6e+76]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e15 or 2.5999999999999999e76 < 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 92.6%

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

      1. mul-1-neg 92.6%

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

      2. unsub-neg 92.6%

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

   5. Simplified 92.6%

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

   if -3.4e15 < x < 2.5999999999999999e76

   1. Initial program 95.7%

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

      1. clear-num 95.6%

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

      2. un-div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in y around inf 85.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+15} \lor \neg \left(x \leq 2.6 \cdot 10^{+76}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-32} \lor \neg \left(y \leq 1.8 \cdot 10^{-64}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e-32) (not (<= y 1.8e-64)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-32) || !(y <= 1.8e-64)) {
		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 <= (-3.2d-32)) .or. (.not. (y <= 1.8d-64))) 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 <= -3.2e-32) || !(y <= 1.8e-64)) {
		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 <= -3.2e-32) or not (y <= 1.8e-64):
		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 <= -3.2e-32) || !(y <= 1.8e-64))
		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 <= -3.2e-32) || ~((y <= 1.8e-64)))
		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, -3.2e-32], N[Not[LessEqual[y, 1.8e-64]], $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 < -3.2000000000000002e-32 or 1.7999999999999999e-64 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 86.2%

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

      1. associate-*r/ 89.3%

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

   5. Simplified 89.3%

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

   if -3.2000000000000002e-32 < y < 1.7999999999999999e-64

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-32} \lor \neg \left(y \leq 1.8 \cdot 10^{-64}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+15}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+76}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.5e+15)
   (- x (* x (/ z t)))
   (if (<= x 1.8e+76) (+ x (/ y (/ t z))) (* x (- 1.0 (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e+15) {
		tmp = x - (x * (z / t));
	} else if (x <= 1.8e+76) {
		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 (x <= (-2.5d+15)) then
        tmp = x - (x * (z / t))
    else if (x <= 1.8d+76) 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 (x <= -2.5e+15) {
		tmp = x - (x * (z / t));
	} else if (x <= 1.8e+76) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.5e+15:
		tmp = x - (x * (z / t))
	elif x <= 1.8e+76:
		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 (x <= -2.5e+15)
		tmp = Float64(x - Float64(x * Float64(z / t)));
	elseif (x <= 1.8e+76)
		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 (x <= -2.5e+15)
		tmp = x - (x * (z / t));
	elseif (x <= 1.8e+76)
		tmp = x + (y / (t / z));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.5e+15], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+76], 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 3 regimes

2. if x < -2.5e15

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 91.9%

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

      1. mul-1-neg 91.9%

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

      2. unsub-neg 91.9%

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

      3. distribute-lft-out-- 91.9%

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

      4. *-rgt-identity 91.9%

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

   7. Simplified 91.9%

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

   if -2.5e15 < x < 1.8000000000000001e76

   1. Initial program 95.7%

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

      1. clear-num 95.6%

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

      2. un-div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in y around inf 85.3%

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

   if 1.8000000000000001e76 < 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 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

   5. Simplified 93.4%

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

Alternative 5: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -13000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 0.031:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -13000000000.0) x (if (<= t 0.031) (/ (* z (- x)) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -13000000000.0) {
		tmp = x;
	} else if (t <= 0.031) {
		tmp = (z * -x) / 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 <= (-13000000000.0d0)) then
        tmp = x
    else if (t <= 0.031d0) then
        tmp = (z * -x) / 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 <= -13000000000.0) {
		tmp = x;
	} else if (t <= 0.031) {
		tmp = (z * -x) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -13000000000.0:
		tmp = x
	elif t <= 0.031:
		tmp = (z * -x) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -13000000000.0)
		tmp = x;
	elseif (t <= 0.031)
		tmp = Float64(Float64(z * Float64(-x)) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -13000000000.0)
		tmp = x;
	elseif (t <= 0.031)
		tmp = (z * -x) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -13000000000.0], x, If[LessEqual[t, 0.031], N[(N[(z * (-x)), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e10 or 0.031 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 60.6%

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

   if -1.3e10 < t < 0.031

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 49.7%

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

      1. mul-1-neg 49.7%

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

      2. associate-/l* 53.8%

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

      3. distribute-lft-neg-out 53.8%

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

      4. *-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in t around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. distribute-rgt-neg-out 49.0%

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

      3. +-commutative 49.0%

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

      4. *-commutative 49.0%

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

      5. distribute-lft-out 49.0%

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

   8. Simplified 49.0%

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

   9. Taylor expanded in t around 0 37.1%

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

       1. associate-*r* 37.1%

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

       2. neg-mul-1 37.1%

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

   11. Simplified 37.1%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -13000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 0.031:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.6% 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 97.3%

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

Alternative 7: 64.6% 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 97.3%

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

3. Taylor expanded in x around inf 62.7%

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

   1. mul-1-neg 62.7%

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

   2. unsub-neg 62.7%

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

5. Simplified 62.7%

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

Alternative 8: 38.4% 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 97.3%

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

3. Taylor expanded in z around 0 37.2%

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

Developer Target 1: 97.4% 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 2024145 
(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))))