Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 85.0% → 98.3%

Time: 8.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

   1. +-commutative 86.7%

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

   2. associate-*r/ 99.2%

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

   3. fma-def 99.2%

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

3. Simplified 99.2%

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

   1. fma-udef 99.2%

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

5. Applied egg-rr 99.2%

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

6. Final simplification 99.2%

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

Alternative 2: 75.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-25}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 34:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e-73)
   (+ y x)
   (if (<= t 4.9e-92)
     (+ x (* y (/ z a)))
     (if (<= t 7e-25)
       (- x (* z (/ y t)))
       (if (<= t 34.0) (+ x (/ z (/ a y))) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e-73) {
		tmp = y + x;
	} else if (t <= 4.9e-92) {
		tmp = x + (y * (z / a));
	} else if (t <= 7e-25) {
		tmp = x - (z * (y / t));
	} else if (t <= 34.0) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.5d-73)) then
        tmp = y + x
    else if (t <= 4.9d-92) then
        tmp = x + (y * (z / a))
    else if (t <= 7d-25) then
        tmp = x - (z * (y / t))
    else if (t <= 34.0d0) then
        tmp = x + (z / (a / y))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e-73) {
		tmp = y + x;
	} else if (t <= 4.9e-92) {
		tmp = x + (y * (z / a));
	} else if (t <= 7e-25) {
		tmp = x - (z * (y / t));
	} else if (t <= 34.0) {
		tmp = x + (z / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e-73:
		tmp = y + x
	elif t <= 4.9e-92:
		tmp = x + (y * (z / a))
	elif t <= 7e-25:
		tmp = x - (z * (y / t))
	elif t <= 34.0:
		tmp = x + (z / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e-73)
		tmp = Float64(y + x);
	elseif (t <= 4.9e-92)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 7e-25)
		tmp = Float64(x - Float64(z * Float64(y / t)));
	elseif (t <= 34.0)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e-73)
		tmp = y + x;
	elseif (t <= 4.9e-92)
		tmp = x + (y * (z / a));
	elseif (t <= 7e-25)
		tmp = x - (z * (y / t));
	elseif (t <= 34.0)
		tmp = x + (z / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e-73], N[(y + x), $MachinePrecision], If[LessEqual[t, 4.9e-92], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-25], N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 34.0], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.5e-73 or 34 < t

   1. Initial program 78.7%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around inf 81.2%

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

   if -4.5e-73 < t < 4.9e-92

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*r/ 97.9%

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

      3. fma-def 97.9%

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

   3. Simplified 97.9%

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

      1. fma-udef 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in t around 0 86.7%

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

   if 4.9e-92 < t < 7.0000000000000004e-25

   1. Initial program 94.7%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around inf 66.5%

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

      1. associate-*l/ 71.5%

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

      2. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in a around 0 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. sub-neg 66.8%

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

      4. associate-*l/ 66.6%

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

      5. *-commutative 66.6%

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

   9. Simplified 66.6%

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

   if 7.0000000000000004e-25 < t < 34

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 99.7%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

   6. Simplified 99.7%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in a around inf 100.0%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-92}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-25}:\\ \;\;\;\;x - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 34:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 3: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+64} \lor \neg \left(t \leq 2.4 \cdot 10^{+146}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.5e+64) (not (<= t 2.4e+146)))
   (+ y x)
   (+ x (/ z (/ (- a t) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+64) || !(t <= 2.4e+146)) {
		tmp = y + x;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.5d+64)) .or. (.not. (t <= 2.4d+146))) then
        tmp = y + x
    else
        tmp = x + (z / ((a - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.5e+64) || !(t <= 2.4e+146)) {
		tmp = y + x;
	} else {
		tmp = x + (z / ((a - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.5e+64) or not (t <= 2.4e+146):
		tmp = y + x
	else:
		tmp = x + (z / ((a - t) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.5e+64) || !(t <= 2.4e+146))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.5e+64) || ~((t <= 2.4e+146)))
		tmp = y + x;
	else
		tmp = x + (z / ((a - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.5e+64], N[Not[LessEqual[t, 2.4e+146]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999999e64 or 2.4000000000000002e146 < t

   1. Initial program 73.3%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in t around inf 87.1%

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

   if -3.4999999999999999e64 < t < 2.4000000000000002e146

   1. Initial program 93.7%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 81.6%

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

      1. associate-*l/ 84.4%

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

      2. *-commutative 84.4%

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

   6. Simplified 84.4%

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

      1. clear-num 84.3%

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

      2. un-div-inv 84.8%

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

   8. Applied egg-rr 84.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+64} \lor \neg \left(t \leq 2.4 \cdot 10^{+146}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\ \end{array} \]

Alternative 4: 82.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-25} \lor \neg \left(t \leq 4.2 \cdot 10^{-93}\right):\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.2e-25) (not (<= t 4.2e-93)))
   (- (+ y x) (/ y (/ t z)))
   (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e-25) || !(t <= 4.2e-93)) {
		tmp = (y + x) - (y / (t / z));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.2d-25)) .or. (.not. (t <= 4.2d-93))) then
        tmp = (y + x) - (y / (t / z))
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.2e-25) || !(t <= 4.2e-93)) {
		tmp = (y + x) - (y / (t / z));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.2e-25) or not (t <= 4.2e-93):
		tmp = (y + x) - (y / (t / z))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.2e-25) || !(t <= 4.2e-93))
		tmp = Float64(Float64(y + x) - Float64(y / Float64(t / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.2e-25) || ~((t <= 4.2e-93)))
		tmp = (y + x) - (y / (t / z));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.2e-25], N[Not[LessEqual[t, 4.2e-93]], $MachinePrecision]], N[(N[(y + x), $MachinePrecision] - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000002e-25 or 4.2000000000000002e-93 < t

   1. Initial program 80.4%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around -inf 81.4%

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

      1. +-commutative 81.4%

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

      2. mul-1-neg 81.4%

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

      3. unsub-neg 81.4%

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

      4. *-commutative 81.4%

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

      5. distribute-lft-out-- 81.4%

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

      6. associate-/l* 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in z around inf 89.5%

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

   if -2.2000000000000002e-25 < t < 4.2000000000000002e-93

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-*r/ 98.0%

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

      3. fma-def 98.0%

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

   3. Simplified 98.0%

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

      1. fma-udef 98.0%

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

   5. Applied egg-rr 98.0%

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

   6. Taylor expanded in a around inf 90.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-25} \lor \neg \left(t \leq 4.2 \cdot 10^{-93}\right):\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 5: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+64}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+146}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.7e+64)
   (+ y x)
   (if (<= t 3e+146) (+ x (* z (/ y (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e+64) {
		tmp = y + x;
	} else if (t <= 3e+146) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.7d+64)) then
        tmp = y + x
    else if (t <= 3d+146) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e+64) {
		tmp = y + x;
	} else if (t <= 3e+146) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.7e+64:
		tmp = y + x
	elif t <= 3e+146:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.7e+64)
		tmp = Float64(y + x);
	elseif (t <= 3e+146)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.7e+64)
		tmp = y + x;
	elseif (t <= 3e+146)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.7e+64], N[(y + x), $MachinePrecision], If[LessEqual[t, 3e+146], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.70000000000000029e64 or 3.00000000000000002e146 < t

   1. Initial program 73.0%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in t around inf 88.0%

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

   if -4.70000000000000029e64 < t < 3.00000000000000002e146

   1. Initial program 93.7%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around inf 81.8%

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

      1. associate-*l/ 84.0%

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

      2. *-commutative 84.0%

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

   6. Simplified 84.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+64}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+146}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 6: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.45 \cdot 10^{+190}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.45e+190)
   (+ x (* (- z t) (/ y (- a t))))
   (- (+ y x) (/ y (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.45e+190) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = (y + x) - (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 2.45d+190) then
        tmp = x + ((z - t) * (y / (a - t)))
    else
        tmp = (y + x) - (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.45e+190) {
		tmp = x + ((z - t) * (y / (a - t)));
	} else {
		tmp = (y + x) - (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.45e+190:
		tmp = x + ((z - t) * (y / (a - t)))
	else:
		tmp = (y + x) - (y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.45e+190)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = Float64(Float64(y + x) - Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.45e+190)
		tmp = x + ((z - t) * (y / (a - t)));
	else
		tmp = (y + x) - (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.45e+190], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.4499999999999998e190

   1. Initial program 89.4%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   if 2.4499999999999998e190 < t

   1. Initial program 67.5%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around -inf 91.1%

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

      1. +-commutative 91.1%

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

      2. mul-1-neg 91.1%

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

      3. unsub-neg 91.1%

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

      4. *-commutative 91.1%

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

      5. distribute-lft-out-- 91.1%

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

      6. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around inf 100.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.45 \cdot 10^{+190}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + x\right) - \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 7: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-73} \lor \neg \left(t \leq 3.8 \cdot 10^{-90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.8e-73) (not (<= t 3.8e-90))) (+ y x) (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e-73) || !(t <= 3.8e-90)) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.8d-73)) .or. (.not. (t <= 3.8d-90))) then
        tmp = y + x
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.8e-73) || !(t <= 3.8e-90)) {
		tmp = y + x;
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.8e-73) or not (t <= 3.8e-90):
		tmp = y + x
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.8e-73) || !(t <= 3.8e-90))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.8e-73) || ~((t <= 3.8e-90)))
		tmp = y + x;
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.8e-73], N[Not[LessEqual[t, 3.8e-90]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.80000000000000011e-73 or 3.8e-90 < t

   1. Initial program 81.1%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around inf 77.7%

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

   if -4.80000000000000011e-73 < t < 3.8e-90

   1. Initial program 95.9%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around inf 89.4%

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

      1. associate-*l/ 89.2%

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

      2. *-commutative 89.2%

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

   6. Simplified 89.2%

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

      1. clear-num 89.2%

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

      2. un-div-inv 90.0%

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

   8. Applied egg-rr 90.0%

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

   9. Taylor expanded in a around inf 85.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-73} \lor \neg \left(t \leq 3.8 \cdot 10^{-90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-88}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.4e-74) (+ y x) (if (<= t 2.8e-88) (+ x (* z (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e-74) {
		tmp = y + x;
	} else if (t <= 2.8e-88) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.4d-74)) then
        tmp = y + x
    else if (t <= 2.8d-88) then
        tmp = x + (z * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.4e-74) {
		tmp = y + x;
	} else if (t <= 2.8e-88) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.4e-74:
		tmp = y + x
	elif t <= 2.8e-88:
		tmp = x + (z * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.4e-74)
		tmp = Float64(y + x);
	elseif (t <= 2.8e-88)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.4e-74)
		tmp = y + x;
	elseif (t <= 2.8e-88)
		tmp = x + (z * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.4e-74], N[(y + x), $MachinePrecision], If[LessEqual[t, 2.8e-88], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3999999999999999e-74 or 2.79999999999999976e-88 < t

   1. Initial program 81.1%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around inf 77.7%

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

   if -2.3999999999999999e-74 < t < 2.79999999999999976e-88

   1. Initial program 95.9%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around inf 89.4%

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

      1. associate-*l/ 89.2%

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

      2. *-commutative 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in a around inf 85.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-74}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-88}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 9: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.9e-73) (+ y x) (if (<= t 1.35e-90) (+ x (* y (/ z a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.9e-73) {
		tmp = y + x;
	} else if (t <= 1.35e-90) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.9d-73)) then
        tmp = y + x
    else if (t <= 1.35d-90) then
        tmp = x + (y * (z / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.9e-73) {
		tmp = y + x;
	} else if (t <= 1.35e-90) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.9e-73:
		tmp = y + x
	elif t <= 1.35e-90:
		tmp = x + (y * (z / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.9e-73)
		tmp = Float64(y + x);
	elseif (t <= 1.35e-90)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.9e-73)
		tmp = y + x;
	elseif (t <= 1.35e-90)
		tmp = x + (y * (z / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.9e-73], N[(y + x), $MachinePrecision], If[LessEqual[t, 1.35e-90], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.90000000000000028e-73 or 1.34999999999999998e-90 < t

   1. Initial program 81.1%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around inf 77.7%

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

   if -4.90000000000000028e-73 < t < 1.34999999999999998e-90

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*r/ 97.9%

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

      3. fma-def 97.9%

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

   3. Simplified 97.9%

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

      1. fma-udef 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in t around 0 85.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-73}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-90}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 10: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.7%

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

   1. associate-/l* 99.1%

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

3. Simplified 99.1%

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

4. Final simplification 99.1%

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

Alternative 11: 63.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-75}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e-75) (+ y x) (if (<= t 1e-88) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-75) {
		tmp = y + x;
	} else if (t <= 1e-88) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.15d-75)) then
        tmp = y + x
    else if (t <= 1d-88) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e-75) {
		tmp = y + x;
	} else if (t <= 1e-88) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e-75:
		tmp = y + x
	elif t <= 1e-88:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e-75)
		tmp = Float64(y + x);
	elseif (t <= 1e-88)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e-75)
		tmp = y + x;
	elseif (t <= 1e-88)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e-75], N[(y + x), $MachinePrecision], If[LessEqual[t, 1e-88], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e-75 or 9.99999999999999934e-89 < t

   1. Initial program 81.1%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around inf 77.7%

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

   if -1.15e-75 < t < 9.99999999999999934e-89

   1. Initial program 95.9%

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

      1. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 53.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-75}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]

Alternative 12: 50.7% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 86.7%

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

   1. associate-*l/ 93.8%

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

3. Simplified 93.8%

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

4. Taylor expanded in x around inf 51.1%

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

5. Final simplification 51.1%

   \[\leadsto x \]

Developer target: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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