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

Percentage Accurate: 97.7% → 97.7%

Time: 6.6s

Alternatives: 11

Speedup: 1.0×

• 25.1% 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: 97.7% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, \frac{z}{t}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.9%

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

   1. +-commutative 98.9%

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

   2. fma-def 98.9%

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

3. Simplified 98.9%

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

4. Final simplification 98.9%

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

Alternative 2: 81.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+25} \lor \neg \left(\frac{z}{t} \leq -2 \cdot 10^{-163}\right) \land \left(\frac{z}{t} \leq -1 \cdot 10^{-253} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-10}\right)\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e+25)
         (and (not (<= (/ z t) -2e-163))
              (or (<= (/ z t) -1e-253) (not (<= (/ z t) 2e-10)))))
   (* z (/ (- y x) t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e+25) || (!((z / t) <= -2e-163) && (((z / t) <= -1e-253) || !((z / t) <= 2e-10)))) {
		tmp = z * ((y - x) / 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 (((z / t) <= (-2d+25)) .or. (.not. ((z / t) <= (-2d-163))) .and. ((z / t) <= (-1d-253)) .or. (.not. ((z / t) <= 2d-10))) then
        tmp = z * ((y - x) / 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 (((z / t) <= -2e+25) || (!((z / t) <= -2e-163) && (((z / t) <= -1e-253) || !((z / t) <= 2e-10)))) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e+25) or (not ((z / t) <= -2e-163) and (((z / t) <= -1e-253) or not ((z / t) <= 2e-10))):
		tmp = z * ((y - x) / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2e+25) || (!(Float64(z / t) <= -2e-163) && ((Float64(z / t) <= -1e-253) || !(Float64(z / t) <= 2e-10))))
		tmp = Float64(z * Float64(Float64(y - x) / 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 (((z / t) <= -2e+25) || (~(((z / t) <= -2e-163)) && (((z / t) <= -1e-253) || ~(((z / t) <= 2e-10)))))
		tmp = z * ((y - x) / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2e+25], And[N[Not[LessEqual[N[(z / t), $MachinePrecision], -2e-163]], $MachinePrecision], Or[LessEqual[N[(z / t), $MachinePrecision], -1e-253], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-10]], $MachinePrecision]]]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.00000000000000018e25 or -1.99999999999999985e-163 < (/.f64 z t) < -1.0000000000000001e-253 or 2.00000000000000007e-10 < (/.f64 z t)

   1. Initial program 98.3%

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

   2. Taylor expanded in z around -inf 89.8%

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

   3. Taylor expanded in t around 0 86.7%

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

      1. associate-*l/ 92.4%

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

   5. Applied egg-rr 92.4%

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

   if -2.00000000000000018e25 < (/.f64 z t) < -1.99999999999999985e-163 or -1.0000000000000001e-253 < (/.f64 z t) < 2.00000000000000007e-10

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. distribute-lft-out-- 74.0%

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

      5. *-rgt-identity 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in x around 0 74.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+25} \lor \neg \left(\frac{z}{t} \leq -2 \cdot 10^{-163}\right) \land \left(\frac{z}{t} \leq -1 \cdot 10^{-253} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-10}\right)\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 3: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+31} \lor \neg \left(x \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z t)))))
   (if (<= x -7.2e-49)
     t_1
     (if (<= x 4.7e-163)
       (/ y (/ t z))
       (if (or (<= x 2.85e+31) (not (<= x 7.8e+43))) t_1 (* z (/ y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -7.2e-49) {
		tmp = t_1;
	} else if (x <= 4.7e-163) {
		tmp = y / (t / z);
	} else if ((x <= 2.85e+31) || !(x <= 7.8e+43)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / t))
    if (x <= (-7.2d-49)) then
        tmp = t_1
    else if (x <= 4.7d-163) then
        tmp = y / (t / z)
    else if ((x <= 2.85d+31) .or. (.not. (x <= 7.8d+43))) then
        tmp = t_1
    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 t_1 = x * (1.0 - (z / t));
	double tmp;
	if (x <= -7.2e-49) {
		tmp = t_1;
	} else if (x <= 4.7e-163) {
		tmp = y / (t / z);
	} else if ((x <= 2.85e+31) || !(x <= 7.8e+43)) {
		tmp = t_1;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (z / t))
	tmp = 0
	if x <= -7.2e-49:
		tmp = t_1
	elif x <= 4.7e-163:
		tmp = y / (t / z)
	elif (x <= 2.85e+31) or not (x <= 7.8e+43):
		tmp = t_1
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (x <= -7.2e-49)
		tmp = t_1;
	elseif (x <= 4.7e-163)
		tmp = Float64(y / Float64(t / z));
	elseif ((x <= 2.85e+31) || !(x <= 7.8e+43))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (x <= -7.2e-49)
		tmp = t_1;
	elseif (x <= 4.7e-163)
		tmp = y / (t / z);
	elseif ((x <= 2.85e+31) || ~((x <= 7.8e+43)))
		tmp = t_1;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e-49], t$95$1, If[LessEqual[x, 4.7e-163], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.85e+31], N[Not[LessEqual[x, 7.8e+43]], $MachinePrecision]], t$95$1, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999939e-49 or 4.7e-163 < x < 2.85e31 or 7.8000000000000001e43 < x

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 81.9%

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

      1. *-commutative 81.9%

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

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

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

      4. distribute-lft-out-- 81.9%

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

      5. *-rgt-identity 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in x around 0 81.9%

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

   if -7.19999999999999939e-49 < x < 4.7e-163

   1. Initial program 98.1%

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

   2. Taylor expanded in z around -inf 92.4%

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

   3. Taylor expanded in t around 0 79.2%

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

      1. associate-*l/ 77.2%

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

   5. Applied egg-rr 77.2%

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

   6. Taylor expanded in y around inf 75.5%

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

      1. associate-/l* 79.7%

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

   8. Simplified 79.7%

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

   if 2.85e31 < x < 7.8000000000000001e43

   1. Initial program 99.7%

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

   2. Taylor expanded in z around -inf 99.7%

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

   3. Taylor expanded in t around 0 99.7%

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

      1. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 100.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+31} \lor \neg \left(x \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 94.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000 \lor \neg \left(\frac{z}{t} \leq 0.2\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2000000.0) (not (<= (/ z t) 0.2)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2000000.0) || !((z / t) <= 0.2)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-2000000.0d0)) .or. (.not. ((z / t) <= 0.2d0))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2000000.0) || !((z / t) <= 0.2)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2000000.0) or not ((z / t) <= 0.2):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2000000.0) || !(Float64(z / t) <= 0.2))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -2000000.0) || ~(((z / t) <= 0.2)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.2]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2e6 or 0.20000000000000001 < (/.f64 z t)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around -inf 89.7%

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

   3. Taylor expanded in t around 0 87.8%

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

      1. associate-*l/ 94.1%

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

   5. Applied egg-rr 94.1%

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

   if -2e6 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 93.4%

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

      1. associate-*r/ 97.9%

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

   4. Simplified 97.9%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000 \lor \neg \left(\frac{z}{t} \leq 0.2\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -2000000.0)
   (/ z (/ t (- y x)))
   (if (<= (/ z t) 0.2) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -2000000.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 0.2) {
		tmp = x + (y * (z / t));
	} else {
		tmp = 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 ((z / t) <= (-2000000.0d0)) then
        tmp = z / (t / (y - x))
    else if ((z / t) <= 0.2d0) then
        tmp = x + (y * (z / t))
    else
        tmp = 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 ((z / t) <= -2000000.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 0.2) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -2000000.0:
		tmp = z / (t / (y - x))
	elif (z / t) <= 0.2:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -2000000.0)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (Float64(z / t) <= 0.2)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -2000000.0)
		tmp = z / (t / (y - x));
	elseif ((z / t) <= 0.2)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -2000000.0], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.2], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2e6

   1. Initial program 96.1%

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

   2. Taylor expanded in z around -inf 90.7%

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

   3. Taylor expanded in t around 0 88.5%

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

      1. associate-*l/ 92.1%

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

   5. Applied egg-rr 92.1%

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

      1. *-commutative 92.1%

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

      2. clear-num 92.1%

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

      3. un-div-inv 92.2%

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

   7. Applied egg-rr 92.2%

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

   if -2e6 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 93.4%

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

      1. associate-*r/ 97.9%

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

   4. Simplified 97.9%

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

   if 0.20000000000000001 < (/.f64 z t)

   1. Initial program 99.7%

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

   2. Taylor expanded in z around -inf 88.9%

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

   3. Taylor expanded in t around 0 87.3%

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

      1. associate-*l/ 95.6%

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

   5. Applied egg-rr 95.6%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2000000:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 6: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+199)
   (* z (- (/ x t)))
   (if (<= z -1.1e-67) (* z (/ y t)) (if (<= z 1.6e-139) x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+199) {
		tmp = z * -(x / t);
	} else if (z <= -1.1e-67) {
		tmp = z * (y / t);
	} else if (z <= 1.6e-139) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-5d+199)) then
        tmp = z * -(x / t)
    else if (z <= (-1.1d-67)) then
        tmp = z * (y / t)
    else if (z <= 1.6d-139) then
        tmp = x
    else
        tmp = 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 (z <= -5e+199) {
		tmp = z * -(x / t);
	} else if (z <= -1.1e-67) {
		tmp = z * (y / t);
	} else if (z <= 1.6e-139) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e+199:
		tmp = z * -(x / t)
	elif z <= -1.1e-67:
		tmp = z * (y / t)
	elif z <= 1.6e-139:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+199)
		tmp = Float64(z * Float64(-Float64(x / t)));
	elseif (z <= -1.1e-67)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 1.6e-139)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e+199)
		tmp = z * -(x / t);
	elseif (z <= -1.1e-67)
		tmp = z * (y / t);
	elseif (z <= 1.6e-139)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+199], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, -1.1e-67], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-139], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9999999999999998e199

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf 73.2%

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

   3. Taylor expanded in t around 0 73.2%

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

      1. associate-*l/ 84.3%

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

   5. Applied egg-rr 84.3%

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

   6. Taylor expanded in y around 0 61.2%

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

      1. neg-mul-1 61.2%

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

      2. distribute-neg-frac 61.2%

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

   8. Simplified 61.2%

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

   if -4.9999999999999998e199 < z < -1.1000000000000001e-67

   1. Initial program 98.0%

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

   2. Taylor expanded in z around -inf 81.8%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. associate-*l/ 75.9%

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

   5. Applied egg-rr 75.9%

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

   6. Taylor expanded in y around inf 55.2%

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

   if -1.1000000000000001e-67 < z < 1.6e-139

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 66.2%

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

   if 1.6e-139 < z

   1. Initial program 98.7%

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

   2. Taylor expanded in z around -inf 87.3%

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

   3. Taylor expanded in t around 0 73.9%

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

      1. associate-*l/ 79.6%

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

   5. Applied egg-rr 79.6%

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

   6. Taylor expanded in y around inf 55.4%

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

      1. associate-/l* 65.5%

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

   8. Simplified 65.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+199}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 7: 52.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+200}:\\ \;\;\;\;\frac{z}{\frac{t}{-x}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+200)
   (/ z (/ t (- x)))
   (if (<= z -1.2e-68) (* z (/ y t)) (if (<= z 6e-138) x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+200) {
		tmp = z / (t / -x);
	} else if (z <= -1.2e-68) {
		tmp = z * (y / t);
	} else if (z <= 6e-138) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-2.3d+200)) then
        tmp = z / (t / -x)
    else if (z <= (-1.2d-68)) then
        tmp = z * (y / t)
    else if (z <= 6d-138) then
        tmp = x
    else
        tmp = 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 (z <= -2.3e+200) {
		tmp = z / (t / -x);
	} else if (z <= -1.2e-68) {
		tmp = z * (y / t);
	} else if (z <= 6e-138) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+200:
		tmp = z / (t / -x)
	elif z <= -1.2e-68:
		tmp = z * (y / t)
	elif z <= 6e-138:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+200)
		tmp = Float64(z / Float64(t / Float64(-x)));
	elseif (z <= -1.2e-68)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 6e-138)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+200)
		tmp = z / (t / -x);
	elseif (z <= -1.2e-68)
		tmp = z * (y / t);
	elseif (z <= 6e-138)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+200], N[(z / N[(t / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-68], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-138], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.30000000000000003e200

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf 73.2%

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

   3. Taylor expanded in t around 0 73.2%

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

      1. add-cube-cbrt 73.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\left(y - x\right) \cdot z} \cdot \sqrt[3]{\left(y - x\right) \cdot z}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot z}}}{t} \]

      2. pow3 73.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot z}\right)}^{3}}}{t} \]

   5. Applied egg-rr 73.2%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot z}\right)}^{3}}}{t} \]

   6. Taylor expanded in y around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. distribute-frac-neg 53.9%

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

      3. distribute-rgt-neg-out 53.9%

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

      4. associate-/l* 61.4%

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

   8. Simplified 61.4%

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

   if -2.30000000000000003e200 < z < -1.19999999999999996e-68

   1. Initial program 98.0%

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

   2. Taylor expanded in z around -inf 81.8%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. associate-*l/ 75.9%

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

   5. Applied egg-rr 75.9%

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

   6. Taylor expanded in y around inf 55.2%

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

   if -1.19999999999999996e-68 < z < 6.0000000000000001e-138

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 66.2%

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

   if 6.0000000000000001e-138 < z

   1. Initial program 98.7%

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

   2. Taylor expanded in z around -inf 87.3%

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

   3. Taylor expanded in t around 0 73.9%

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

      1. associate-*l/ 79.6%

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

   5. Applied egg-rr 79.6%

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

   6. Taylor expanded in y around inf 55.4%

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

      1. associate-/l* 65.5%

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

   8. Simplified 65.5%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+200}:\\ \;\;\;\;\frac{z}{\frac{t}{-x}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 8: 53.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-73} \lor \neg \left(z \leq 1.05 \cdot 10^{-136}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.5e-73) (not (<= z 1.05e-136))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e-73) || !(z <= 1.05e-136)) {
		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 ((z <= (-4.5d-73)) .or. (.not. (z <= 1.05d-136))) 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 ((z <= -4.5e-73) || !(z <= 1.05e-136)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.5e-73) or not (z <= 1.05e-136):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.5e-73) || !(z <= 1.05e-136))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.5e-73) || ~((z <= 1.05e-136)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.5e-73], N[Not[LessEqual[z, 1.05e-136]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e-73 or 1.0499999999999999e-136 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around -inf 83.3%

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

   3. Taylor expanded in t around 0 71.6%

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

      1. associate-*l/ 79.1%

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

   5. Applied egg-rr 79.1%

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

   6. Taylor expanded in y around inf 56.0%

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

   if -4.5e-73 < z < 1.0499999999999999e-136

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 66.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-73} \lor \neg \left(z \leq 1.05 \cdot 10^{-136}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-74} \lor \neg \left(z \leq 4 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.3e-74) (not (<= z 4e-137))) (/ y (/ t z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.3e-74) || !(z <= 4e-137)) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.3d-74)) .or. (.not. (z <= 4d-137))) then
        tmp = y / (t / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.3e-74) || !(z <= 4e-137)) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.3e-74) or not (z <= 4e-137):
		tmp = y / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.3e-74) || !(z <= 4e-137))
		tmp = Float64(y / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.3e-74) || ~((z <= 4e-137)))
		tmp = y / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.3e-74], N[Not[LessEqual[z, 4e-137]], $MachinePrecision]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999972e-74 or 3.99999999999999991e-137 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around -inf 83.3%

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

   3. Taylor expanded in t around 0 71.6%

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

      1. associate-*l/ 79.1%

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

   5. Applied egg-rr 79.1%

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

   6. Taylor expanded in y around inf 49.1%

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

      1. associate-/l* 57.8%

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

   8. Simplified 57.8%

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

   if -4.29999999999999972e-74 < z < 3.99999999999999991e-137

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 66.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-74} \lor \neg \left(z \leq 4 \cdot 10^{-137}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 97.7% 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 98.9%

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

2. Final simplification 98.9%

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

Alternative 11: 37.4% 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 98.9%

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

2. Taylor expanded in z around 0 36.9%

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

3. Final simplification 36.9%

   \[\leadsto x \]

Developer target: 97.5% 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 2023238 
(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))))