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

Percentage Accurate: 97.8% → 98.5%

Time: 7.2s

Alternatives: 9

Speedup: 0.5×

• 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: 97.8% 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, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq -\infty:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (* (- y x) (/ z t))) (- INFINITY))
   (+ x (/ 1.0 (/ t (* (- y x) z))))
   (+ x (/ (- y x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + ((y - x) * (z / t))) <= -((double) INFINITY)) {
		tmp = x + (1.0 / (t / ((y - x) * z)));
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + ((y - x) * (z / t))) <= -Double.POSITIVE_INFINITY) {
		tmp = x + (1.0 / (t / ((y - x) * z)));
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + ((y - x) * (z / t))) <= -math.inf:
		tmp = x + (1.0 / (t / ((y - x) * z)))
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y - x) * Float64(z / t))) <= Float64(-Inf))
		tmp = Float64(x + Float64(1.0 / Float64(t / Float64(Float64(y - x) * z))));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + ((y - x) * (z / t))) <= -Inf)
		tmp = x + (1.0 / (t / ((y - x) * z)));
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < -inf.0

   1. Initial program 85.7%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 98.7%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.8%

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

   3. Applied egg-rr 98.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} \leq -\infty:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 2: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z t)))))
   (if (<= t_1 (- INFINITY)) (+ x (* z (/ (- y x) t))) t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - x) * (z / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - x) * (z / t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - x) * (z / t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (z * ((y - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < -inf.0

   1. Initial program 85.7%

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

   2. Taylor expanded in y around 0 92.3%

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

      1. +-commutative 92.3%

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

      2. mul-1-neg 92.3%

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

      3. sub-neg 92.3%

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

      4. associate-/l* 77.7%

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

      5. associate-/l* 74.3%

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

      6. div-sub 87.9%

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

      7. associate-/r/ 99.9%

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

      8. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 98.7%

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

4. Final simplification 98.9%

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

Alternative 3: 98.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t))) < -inf.0

   1. Initial program 85.7%

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

   2. Taylor expanded in y around 0 92.3%

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

      1. +-commutative 92.3%

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

      2. mul-1-neg 92.3%

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

      3. sub-neg 92.3%

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

      4. associate-/l* 77.7%

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

      5. associate-/l* 74.3%

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

      6. div-sub 87.9%

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

      7. associate-/r/ 99.9%

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

      8. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

   1. Initial program 98.7%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.8%

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

   3. Applied egg-rr 98.8%

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

4. Final simplification 98.9%

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

Alternative 4: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+26} \lor \neg \left(x \leq 1.25 \cdot 10^{+49}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.4e+26) (not (<= x 1.25e+49)))
   (- x (* x (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e+26) || !(x <= 1.25e+49)) {
		tmp = x - (x * (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 <= (-5.4d+26)) .or. (.not. (x <= 1.25d+49))) then
        tmp = x - (x * (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 <= -5.4e+26) || !(x <= 1.25e+49)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.4e+26) or not (x <= 1.25e+49):
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.4e+26) || !(x <= 1.25e+49))
		tmp = Float64(x - Float64(x * 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 <= -5.4e+26) || ~((x <= 1.25e+49)))
		tmp = x - (x * (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.4e+26], N[Not[LessEqual[x, 1.25e+49]], $MachinePrecision]], N[(x - N[(x * 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 < -5.4e26 or 1.2500000000000001e49 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.4%

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

      1. mul-1-neg 91.4%

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

      2. unsub-neg 91.4%

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

      3. distribute-lft-out-- 91.4%

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

      4. *-rgt-identity 91.4%

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

   4. Simplified 91.4%

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

   if -5.4e26 < x < 1.2500000000000001e49

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 75.3%

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

      1. associate-*r/ 84.1%

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

   4. Simplified 84.1%

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

      1. clear-num 84.0%

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

      2. div-inv 84.1%

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

   6. Applied egg-rr 84.1%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+26} \lor \neg \left(x \leq 1.25 \cdot 10^{+49}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.05e+25)
   (- x (/ x (/ t z)))
   (if (<= x 1.38e+50) (+ x (/ y (/ t z))) (- x (* x (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e+25) {
		tmp = x - (x / (t / z));
	} else if (x <= 1.38e+50) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.05d+25)) then
        tmp = x - (x / (t / z))
    else if (x <= 1.38d+50) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.05e+25) {
		tmp = x - (x / (t / z));
	} else if (x <= 1.38e+50) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.05e+25:
		tmp = x - (x / (t / z))
	elif x <= 1.38e+50:
		tmp = x + (y / (t / z))
	else:
		tmp = x - (x * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.05e+25)
		tmp = Float64(x - Float64(x / Float64(t / z)));
	elseif (x <= 1.38e+50)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.05e+25)
		tmp = x - (x / (t / z));
	elseif (x <= 1.38e+50)
		tmp = x + (y / (t / z));
	else
		tmp = x - (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.05e+25], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.38e+50], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e25

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. unsub-neg 91.5%

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

      3. distribute-lft-out-- 91.5%

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

      4. *-rgt-identity 91.5%

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

   4. Simplified 91.5%

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

      1. clear-num 91.6%

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

      2. div-inv 91.6%

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

   6. Applied egg-rr 91.6%

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

   if -1.05e25 < x < 1.3800000000000001e50

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 75.3%

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

      1. associate-*r/ 84.1%

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

   4. Simplified 84.1%

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

      1. clear-num 84.0%

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

      2. div-inv 84.1%

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

   6. Applied egg-rr 84.1%

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

   if 1.3800000000000001e50 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

      3. distribute-lft-out-- 91.3%

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

      4. *-rgt-identity 91.3%

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

   4. Simplified 91.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 1.38 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \end{array} \]

Alternative 6: 92.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.4e+50) (- x (/ x (/ t z))) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.4e+50) {
		tmp = x - (x / (t / z));
	} else {
		tmp = x + (z * ((y - x) / 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 <= (-7.4d+50)) then
        tmp = x - (x / (t / z))
    else
        tmp = x + (z * ((y - x) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.4e+50) {
		tmp = x - (x / (t / z));
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.4e+50:
		tmp = x - (x / (t / z))
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.4e+50)
		tmp = Float64(x - Float64(x / Float64(t / z)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.4e+50)
		tmp = x - (x / (t / z));
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.4e+50], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4000000000000001e50

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 92.5%

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

      1. mul-1-neg 92.5%

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

      2. unsub-neg 92.5%

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

      3. distribute-lft-out-- 92.5%

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

      4. *-rgt-identity 92.5%

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

   4. Simplified 92.5%

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

      1. clear-num 92.5%

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

      2. div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   if -7.4000000000000001e50 < x

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 86.3%

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

      1. +-commutative 86.3%

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

      2. mul-1-neg 86.3%

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

      3. sub-neg 86.3%

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

      4. associate-/l* 89.8%

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

      5. associate-/l* 90.3%

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

      6. div-sub 96.2%

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

      7. associate-/r/ 94.1%

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

      8. *-commutative 94.1%

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

   4. Simplified 94.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 7: 77.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

2. Taylor expanded in y around inf 69.7%

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

   1. associate-*r/ 75.3%

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

4. Simplified 75.3%

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

5. Final simplification 75.3%

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

Alternative 8: 77.6% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

2. Taylor expanded in y around inf 69.7%

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

   1. associate-*r/ 75.3%

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

4. Simplified 75.3%

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

   1. clear-num 75.3%

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

   2. div-inv 75.4%

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

6. Applied egg-rr 75.4%

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

7. Final simplification 75.4%

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

Alternative 9: 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 96.7%

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

2. Taylor expanded in z around 0 35.4%

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

3. Final simplification 35.4%

   \[\leadsto x \]

Developer target: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t_1 < -1013646692435.8867:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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