Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 68.0% → 88.6%

Time: 16.3s

Alternatives: 17

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+175} \lor \neg \left(t \leq 1.65 \cdot 10^{+224}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \left(\frac{1}{t} \cdot \left(a - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e+175) (not (<= t 1.65e+224)))
   (+ y (* (- y x) (* (/ 1.0 t) (- a z))))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e+175) || !(t <= 1.65e+224)) {
		tmp = y + ((y - x) * ((1.0 / t) * (a - z)));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e+175) || !(t <= 1.65e+224))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(1.0 / t) * Float64(a - z))));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e+175], N[Not[LessEqual[t, 1.65e+224]], $MachinePrecision]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(1.0 / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.80000000000000017e175 or 1.64999999999999998e224 < t

   1. Initial program 18.6%

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

      1. +-commutative 18.6%

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

      2. associate-/l* 43.2%

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

      3. fma-define 43.2%

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

   3. Simplified 43.2%

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

   5. Taylor expanded in t around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. associate-*r/ 72.7%

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

      3. associate-*r/ 72.7%

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

      4. mul-1-neg 72.7%

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

      5. div-sub 72.7%

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

      6. mul-1-neg 72.7%

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

      7. distribute-lft-out-- 72.7%

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

      8. associate-*r/ 72.7%

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

      9. mul-1-neg 72.7%

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

      10. unsub-neg 72.7%

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

      11. distribute-rgt-out-- 72.8%

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

   7. Simplified 72.8%

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

      1. div-inv 72.8%

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

   9. Applied egg-rr 72.8%

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

       1. associate-*l* 92.4%

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

   11. Simplified 92.4%

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

   if -1.80000000000000017e175 < t < 1.64999999999999998e224

   1. Initial program 75.7%

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

      1. +-commutative 75.7%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+175} \lor \neg \left(t \leq 1.65 \cdot 10^{+224}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \left(\frac{1}{t} \cdot \left(a - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(y - x\right) \cdot \left(\frac{1}{t} \cdot \left(a - z\right)\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- y x) (* (/ 1.0 t) (- a z))))))
   (if (<= t -1.55e+175)
     t_1
     (if (<= t -2.2e+70)
       (+ x (/ 1.0 (/ (/ (- a t) y) (- z t))))
       (if (<= t 1.22e+66) (+ x (/ (* (- y x) (- z t)) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((1.0 / t) * (a - z)));
	double tmp;
	if (t <= -1.55e+175) {
		tmp = t_1;
	} else if (t <= -2.2e+70) {
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	} else if (t <= 1.22e+66) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = y + ((y - x) * ((1.0d0 / t) * (a - z)))
    if (t <= (-1.55d+175)) then
        tmp = t_1
    else if (t <= (-2.2d+70)) then
        tmp = x + (1.0d0 / (((a - t) / y) / (z - t)))
    else if (t <= 1.22d+66) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((y - x) * ((1.0 / t) * (a - z)));
	double tmp;
	if (t <= -1.55e+175) {
		tmp = t_1;
	} else if (t <= -2.2e+70) {
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	} else if (t <= 1.22e+66) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((y - x) * ((1.0 / t) * (a - z)))
	tmp = 0
	if t <= -1.55e+175:
		tmp = t_1
	elif t <= -2.2e+70:
		tmp = x + (1.0 / (((a - t) / y) / (z - t)))
	elif t <= 1.22e+66:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(y - x) * Float64(Float64(1.0 / t) * Float64(a - z))))
	tmp = 0.0
	if (t <= -1.55e+175)
		tmp = t_1;
	elseif (t <= -2.2e+70)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - t) / y) / Float64(z - t))));
	elseif (t <= 1.22e+66)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((y - x) * ((1.0 / t) * (a - z)));
	tmp = 0.0;
	if (t <= -1.55e+175)
		tmp = t_1;
	elseif (t <= -2.2e+70)
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	elseif (t <= 1.22e+66)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(1.0 / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e+175], t$95$1, If[LessEqual[t, -2.2e+70], N[(x + N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+66], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.54999999999999992e175 or 1.21999999999999993e66 < t

   1. Initial program 26.6%

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

      1. +-commutative 26.6%

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

      2. associate-/l* 61.5%

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

      3. fma-define 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in t around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-*r/ 64.3%

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

      3. associate-*r/ 64.3%

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

      4. mul-1-neg 64.3%

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

      5. div-sub 64.3%

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

      6. mul-1-neg 64.3%

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

      7. distribute-lft-out-- 64.3%

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

      8. associate-*r/ 64.3%

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

      9. mul-1-neg 64.3%

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

      10. unsub-neg 64.3%

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

      11. distribute-rgt-out-- 64.5%

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

   7. Simplified 64.5%

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

      1. div-inv 64.5%

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

   9. Applied egg-rr 64.5%

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

       1. associate-*l* 85.4%

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

   11. Simplified 85.4%

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

   if -1.54999999999999992e175 < t < -2.20000000000000001e70

   1. Initial program 40.2%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. *-commutative 56.7%

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

   5. Simplified 56.7%

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

      1. clear-num 56.6%

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

      2. inv-pow 56.6%

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

      3. *-commutative 56.6%

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

   7. Applied egg-rr 56.6%

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

      1. unpow-1 56.6%

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

      2. associate-/r* 77.5%

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

   9. Simplified 77.5%

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

   if -2.20000000000000001e70 < t < 1.21999999999999993e66

   1. Initial program 88.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+175}:\\ \;\;\;\;y + \left(y - x\right) \cdot \left(\frac{1}{t} \cdot \left(a - z\right)\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \left(\frac{1}{t} \cdot \left(a - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (* (- y x) (- a z)) t))))
   (if (<= t -5.5e+198)
     t_1
     (if (<= t -2.15e+66)
       (+ x (/ 1.0 (/ (/ (- a t) y) (- z t))))
       (if (<= t 4.4e+84) (+ x (/ (* (- y x) (- z t)) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) * (a - z)) / t);
	double tmp;
	if (t <= -5.5e+198) {
		tmp = t_1;
	} else if (t <= -2.15e+66) {
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	} else if (t <= 4.4e+84) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = y + (((y - x) * (a - z)) / t)
    if (t <= (-5.5d+198)) then
        tmp = t_1
    else if (t <= (-2.15d+66)) then
        tmp = x + (1.0d0 / (((a - t) / y) / (z - t)))
    else if (t <= 4.4d+84) then
        tmp = x + (((y - x) * (z - t)) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) * (a - z)) / t);
	double tmp;
	if (t <= -5.5e+198) {
		tmp = t_1;
	} else if (t <= -2.15e+66) {
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	} else if (t <= 4.4e+84) {
		tmp = x + (((y - x) * (z - t)) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) * (a - z)) / t)
	tmp = 0
	if t <= -5.5e+198:
		tmp = t_1
	elif t <= -2.15e+66:
		tmp = x + (1.0 / (((a - t) / y) / (z - t)))
	elif t <= 4.4e+84:
		tmp = x + (((y - x) * (z - t)) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t))
	tmp = 0.0
	if (t <= -5.5e+198)
		tmp = t_1;
	elseif (t <= -2.15e+66)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - t) / y) / Float64(z - t))));
	elseif (t <= 4.4e+84)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) * (a - z)) / t);
	tmp = 0.0;
	if (t <= -5.5e+198)
		tmp = t_1;
	elseif (t <= -2.15e+66)
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	elseif (t <= 4.4e+84)
		tmp = x + (((y - x) * (z - t)) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+198], t$95$1, If[LessEqual[t, -2.15e+66], N[(x + N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+84], N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000004e198 or 4.3999999999999997e84 < t

   1. Initial program 27.9%

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

      1. +-commutative 27.9%

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

      2. associate-/l* 61.2%

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

      3. fma-define 61.2%

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

   3. Simplified 61.2%

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

   5. Taylor expanded in t around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. associate-*r/ 68.8%

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

      3. associate-*r/ 68.8%

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

      4. mul-1-neg 68.8%

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

      5. div-sub 68.8%

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

      6. mul-1-neg 68.8%

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

      7. distribute-lft-out-- 68.8%

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

      8. associate-*r/ 68.8%

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

      9. mul-1-neg 68.8%

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

      10. unsub-neg 68.8%

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

      11. distribute-rgt-out-- 69.2%

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

   7. Simplified 69.2%

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

   if -5.5000000000000004e198 < t < -2.15000000000000013e66

   1. Initial program 33.7%

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

   3. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

   5. Simplified 51.3%

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

      1. clear-num 51.2%

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

      2. inv-pow 51.2%

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

      3. *-commutative 51.2%

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

   7. Applied egg-rr 51.2%

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

      1. unpow-1 51.2%

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

      2. associate-/r* 71.7%

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

   9. Simplified 71.7%

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

   if -2.15000000000000013e66 < t < 4.3999999999999997e84

   1. Initial program 87.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+198}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+66}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-125}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ (- z t) a)))))
   (if (<= a -1.5e-36)
     t_1
     (if (<= a 1.45e-125)
       (+ y (/ (* (- y x) (- a z)) t))
       (if (<= a 3.5e-37) (+ x (/ 1.0 (/ (/ (- a t) y) (- z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) / a));
	double tmp;
	if (a <= -1.5e-36) {
		tmp = t_1;
	} else if (a <= 1.45e-125) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 3.5e-37) {
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * ((z - t) / a))
    if (a <= (-1.5d-36)) then
        tmp = t_1
    else if (a <= 1.45d-125) then
        tmp = y + (((y - x) * (a - z)) / t)
    else if (a <= 3.5d-37) then
        tmp = x + (1.0d0 / (((a - t) / y) / (z - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * ((z - t) / a));
	double tmp;
	if (a <= -1.5e-36) {
		tmp = t_1;
	} else if (a <= 1.45e-125) {
		tmp = y + (((y - x) * (a - z)) / t);
	} else if (a <= 3.5e-37) {
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * ((z - t) / a))
	tmp = 0
	if a <= -1.5e-36:
		tmp = t_1
	elif a <= 1.45e-125:
		tmp = y + (((y - x) * (a - z)) / t)
	elif a <= 3.5e-37:
		tmp = x + (1.0 / (((a - t) / y) / (z - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)))
	tmp = 0.0
	if (a <= -1.5e-36)
		tmp = t_1;
	elseif (a <= 1.45e-125)
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	elseif (a <= 3.5e-37)
		tmp = Float64(x + Float64(1.0 / Float64(Float64(Float64(a - t) / y) / Float64(z - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * ((z - t) / a));
	tmp = 0.0;
	if (a <= -1.5e-36)
		tmp = t_1;
	elseif (a <= 1.45e-125)
		tmp = y + (((y - x) * (a - z)) / t);
	elseif (a <= 3.5e-37)
		tmp = x + (1.0 / (((a - t) / y) / (z - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e-36], t$95$1, If[LessEqual[a, 1.45e-125], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-37], N[(x + N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5000000000000001e-36 or 3.5000000000000001e-37 < a

   1. Initial program 65.6%

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

   3. Taylor expanded in a around inf 60.9%

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

      1. associate-/l* 78.9%

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

   5. Simplified 78.9%

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

   if -1.5000000000000001e-36 < a < 1.4500000000000001e-125

   1. Initial program 66.3%

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

      1. +-commutative 66.3%

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

      2. associate-/l* 78.0%

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

      3. fma-define 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in t around inf 75.6%

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

      1. associate--l+ 75.6%

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

      2. associate-*r/ 75.6%

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

      3. associate-*r/ 75.6%

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

      4. mul-1-neg 75.6%

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

      5. div-sub 75.6%

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

      6. mul-1-neg 75.6%

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

      7. distribute-lft-out-- 75.6%

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

      8. associate-*r/ 75.6%

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

      9. mul-1-neg 75.6%

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

      10. unsub-neg 75.6%

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

      11. distribute-rgt-out-- 75.6%

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

   7. Simplified 75.6%

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

   if 1.4500000000000001e-125 < a < 3.5000000000000001e-37

   1. Initial program 83.2%

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

   3. Taylor expanded in y around inf 72.0%

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

      1. *-commutative 72.0%

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

   5. Simplified 72.0%

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

      1. clear-num 71.9%

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

      2. inv-pow 71.9%

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

      3. *-commutative 71.9%

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

   7. Applied egg-rr 71.9%

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

      1. unpow-1 71.9%

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

      2. associate-/r* 88.3%

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

   9. Simplified 88.3%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{y}}{z - t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-36}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-125}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{y}}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 42.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-222}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-53}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -1.6e-22)
     t_1
     (if (<= a -8.5e-222)
       y
       (if (<= a 7.8e-247) (* x (/ (- z a) t)) (if (<= a 3.9e-53) y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.6e-22) {
		tmp = t_1;
	} else if (a <= -8.5e-222) {
		tmp = y;
	} else if (a <= 7.8e-247) {
		tmp = x * ((z - a) / t);
	} else if (a <= 3.9e-53) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-1.6d-22)) then
        tmp = t_1
    else if (a <= (-8.5d-222)) then
        tmp = y
    else if (a <= 7.8d-247) then
        tmp = x * ((z - a) / t)
    else if (a <= 3.9d-53) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.6e-22) {
		tmp = t_1;
	} else if (a <= -8.5e-222) {
		tmp = y;
	} else if (a <= 7.8e-247) {
		tmp = x * ((z - a) / t);
	} else if (a <= 3.9e-53) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -1.6e-22:
		tmp = t_1
	elif a <= -8.5e-222:
		tmp = y
	elif a <= 7.8e-247:
		tmp = x * ((z - a) / t)
	elif a <= 3.9e-53:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -1.6e-22)
		tmp = t_1;
	elseif (a <= -8.5e-222)
		tmp = y;
	elseif (a <= 7.8e-247)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= 3.9e-53)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -1.6e-22)
		tmp = t_1;
	elseif (a <= -8.5e-222)
		tmp = y;
	elseif (a <= 7.8e-247)
		tmp = x * ((z - a) / t);
	elseif (a <= 3.9e-53)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e-22], t$95$1, If[LessEqual[a, -8.5e-222], y, If[LessEqual[a, 7.8e-247], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-53], y, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.59999999999999994e-22 or 3.9000000000000002e-53 < a

   1. Initial program 67.0%

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

   3. Taylor expanded in t around 0 62.4%

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

      1. associate-/l* 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in x around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   8. Simplified 57.1%

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

   if -1.59999999999999994e-22 < a < -8.5000000000000003e-222 or 7.8000000000000006e-247 < a < 3.9000000000000002e-53

   1. Initial program 68.6%

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

      1. +-commutative 68.6%

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

      2. associate-/l* 83.8%

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

      3. fma-define 83.8%

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

   3. Simplified 83.8%

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

      1. clear-num 83.7%

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

      2. inv-pow 83.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 83.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 83.7%

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

   8. Simplified 83.7%

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

   9. Taylor expanded in t around inf 49.3%

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

   if -8.5000000000000003e-222 < a < 7.8000000000000006e-247

   1. Initial program 61.8%

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

      1. +-commutative 61.8%

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

      2. associate-/l* 69.0%

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

      3. fma-define 69.0%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in t around inf 84.7%

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

      1. associate--l+ 84.7%

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

      2. associate-*r/ 84.7%

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

      3. associate-*r/ 84.7%

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

      4. mul-1-neg 84.7%

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

      5. div-sub 84.7%

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

      6. mul-1-neg 84.7%

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

      7. distribute-lft-out-- 84.7%

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

      8. associate-*r/ 84.7%

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

      9. mul-1-neg 84.7%

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

      10. unsub-neg 84.7%

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

      11. distribute-rgt-out-- 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in y around 0 57.9%

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

      1. associate-/l* 63.8%

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

   10. Simplified 63.8%

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

Alternative 6: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+175} \lor \neg \left(t \leq 5.5 \cdot 10^{+85}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \left(\frac{1}{t} \cdot \left(a - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e+175) (not (<= t 5.5e+85)))
   (+ y (* (- y x) (* (/ 1.0 t) (- a z))))
   (+ x (* (- z t) (* (- y x) (/ -1.0 (- t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+175) || !(t <= 5.5e+85)) {
		tmp = y + ((y - x) * ((1.0 / t) * (a - z)));
	} else {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (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 <= (-2.6d+175)) .or. (.not. (t <= 5.5d+85))) then
        tmp = y + ((y - x) * ((1.0d0 / t) * (a - z)))
    else
        tmp = x + ((z - t) * ((y - x) * ((-1.0d0) / (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 <= -2.6e+175) || !(t <= 5.5e+85)) {
		tmp = y + ((y - x) * ((1.0 / t) * (a - z)));
	} else {
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e+175) or not (t <= 5.5e+85):
		tmp = y + ((y - x) * ((1.0 / t) * (a - z)))
	else:
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e+175) || !(t <= 5.5e+85))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(1.0 / t) * Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) * Float64(-1.0 / Float64(t - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.6e+175) || ~((t <= 5.5e+85)))
		tmp = y + ((y - x) * ((1.0 / t) * (a - z)));
	else
		tmp = x + ((z - t) * ((y - x) * (-1.0 / (t - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e+175], N[Not[LessEqual[t, 5.5e+85]], $MachinePrecision]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(1.0 / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e175 or 5.50000000000000008e85 < t

   1. Initial program 26.1%

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

      1. +-commutative 26.1%

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

      2. associate-/l* 59.8%

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

      3. fma-define 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in t around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. associate-*r/ 66.9%

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

      3. associate-*r/ 66.9%

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

      4. mul-1-neg 66.9%

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

      5. div-sub 66.9%

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

      6. mul-1-neg 66.9%

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

      7. distribute-lft-out-- 66.9%

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

      8. associate-*r/ 66.9%

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

      9. mul-1-neg 66.9%

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

      10. unsub-neg 66.9%

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

      11. distribute-rgt-out-- 67.2%

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

   7. Simplified 67.2%

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

      1. div-inv 67.2%

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

   9. Applied egg-rr 67.2%

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

       1. associate-*l* 86.2%

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

   11. Simplified 86.2%

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

   if -2.6e175 < t < 5.50000000000000008e85

   1. Initial program 81.6%

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

      1. div-inv 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*l* 90.9%

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

   4. Applied egg-rr 90.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+175} \lor \neg \left(t \leq 5.5 \cdot 10^{+85}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \left(\frac{1}{t} \cdot \left(a - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t - a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-270}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))))
   (if (<= z -2.05e+43)
     t_1
     (if (<= z 2.2e-270)
       (- x (* t (/ y a)))
       (if (<= z 3.6e+76) (+ y x) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -2.05e+43) {
		tmp = t_1;
	} else if (z <= 2.2e-270) {
		tmp = x - (t * (y / a));
	} else if (z <= 3.6e+76) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    if (z <= (-2.05d+43)) then
        tmp = t_1
    else if (z <= 2.2d-270) then
        tmp = x - (t * (y / a))
    else if (z <= 3.6d+76) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double tmp;
	if (z <= -2.05e+43) {
		tmp = t_1;
	} else if (z <= 2.2e-270) {
		tmp = x - (t * (y / a));
	} else if (z <= 3.6e+76) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	tmp = 0
	if z <= -2.05e+43:
		tmp = t_1
	elif z <= 2.2e-270:
		tmp = x - (t * (y / a))
	elif z <= 3.6e+76:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (z <= -2.05e+43)
		tmp = t_1;
	elseif (z <= 2.2e-270)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (z <= 3.6e+76)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (z <= -2.05e+43)
		tmp = t_1;
	elseif (z <= 2.2e-270)
		tmp = x - (t * (y / a));
	elseif (z <= 3.6e+76)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+43], t$95$1, If[LessEqual[z, 2.2e-270], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+76], N[(y + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.05e43 or 3.6000000000000003e76 < z

   1. Initial program 61.7%

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

      1. +-commutative 61.7%

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

      2. associate-/l* 89.5%

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

      3. fma-define 89.5%

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

   3. Simplified 89.5%

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

      1. clear-num 89.4%

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

      2. inv-pow 89.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 89.4%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 89.4%

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

   8. Simplified 89.4%

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

   9. Taylor expanded in z around inf 72.4%

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

       1. div-sub 72.4%

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

   11. Simplified 72.4%

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

   if -2.05e43 < z < 2.1999999999999998e-270

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf 72.5%

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

      1. *-commutative 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in a around inf 60.4%

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

      1. associate-/l* 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in z around 0 52.6%

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

       1. mul-1-neg 52.6%

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

       2. unsub-neg 52.6%

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

       3. associate-/l* 57.8%

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

   11. Simplified 57.8%

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

   if 2.1999999999999998e-270 < z < 3.6000000000000003e76

   1. Initial program 66.9%

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

   3. Taylor expanded in y around inf 61.6%

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

      1. *-commutative 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in t around inf 52.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-270}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+76}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+198}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -19:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+198)
   y
   (if (<= t -19.0) (+ y x) (if (<= t 4.6e+84) (* x (- 1.0 (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+198) {
		tmp = y;
	} else if (t <= -19.0) {
		tmp = y + x;
	} else if (t <= 4.6e+84) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = 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 <= (-1.15d+198)) then
        tmp = y
    else if (t <= (-19.0d0)) then
        tmp = y + x
    else if (t <= 4.6d+84) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = 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 <= -1.15e+198) {
		tmp = y;
	} else if (t <= -19.0) {
		tmp = y + x;
	} else if (t <= 4.6e+84) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+198:
		tmp = y
	elif t <= -19.0:
		tmp = y + x
	elif t <= 4.6e+84:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+198)
		tmp = y;
	elseif (t <= -19.0)
		tmp = Float64(y + x);
	elseif (t <= 4.6e+84)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+198)
		tmp = y;
	elseif (t <= -19.0)
		tmp = y + x;
	elseif (t <= 4.6e+84)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+198], y, If[LessEqual[t, -19.0], N[(y + x), $MachinePrecision], If[LessEqual[t, 4.6e+84], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e198 or 4.5999999999999998e84 < t

   1. Initial program 27.9%

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

      1. +-commutative 27.9%

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

      2. associate-/l* 61.2%

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

      3. fma-define 61.2%

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

   3. Simplified 61.2%

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

      1. clear-num 61.2%

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

      2. inv-pow 61.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 61.2%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 61.2%

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

   8. Simplified 61.2%

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

   9. Taylor expanded in t around inf 59.5%

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

   if -1.15e198 < t < -19

   1. Initial program 47.3%

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

   3. Taylor expanded in y around inf 52.5%

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

      1. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in t around inf 43.4%

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

   if -19 < t < 4.5999999999999998e84

   1. Initial program 88.7%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. associate-/l* 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in x around inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   8. Simplified 53.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+198}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -19:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-36} \lor \neg \left(a \leq 7.5 \cdot 10^{-55}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.42e-36) (not (<= a 7.5e-55)))
   (+ x (* (- y x) (/ (- z t) a)))
   (+ y (/ (* (- y x) (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.42e-36) || !(a <= 7.5e-55)) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	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 ((a <= (-1.42d-36)) .or. (.not. (a <= 7.5d-55))) then
        tmp = x + ((y - x) * ((z - t) / a))
    else
        tmp = y + (((y - x) * (a - z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.42e-36) || !(a <= 7.5e-55)) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else {
		tmp = y + (((y - x) * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.42e-36) or not (a <= 7.5e-55):
		tmp = x + ((y - x) * ((z - t) / a))
	else:
		tmp = y + (((y - x) * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.42e-36) || !(a <= 7.5e-55))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(y + Float64(Float64(Float64(y - x) * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.42e-36) || ~((a <= 7.5e-55)))
		tmp = x + ((y - x) * ((z - t) / a));
	else
		tmp = y + (((y - x) * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.42e-36], N[Not[LessEqual[a, 7.5e-55]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(N[(y - x), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.41999999999999996e-36 or 7.50000000000000023e-55 < a

   1. Initial program 66.6%

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

   3. Taylor expanded in a around inf 61.3%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

   if -1.41999999999999996e-36 < a < 7.50000000000000023e-55

   1. Initial program 67.7%

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

      1. +-commutative 67.7%

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

      2. associate-/l* 80.6%

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

      3. fma-define 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in t around inf 73.1%

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

      1. associate--l+ 73.1%

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

      2. associate-*r/ 73.1%

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

      3. associate-*r/ 73.1%

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

      4. mul-1-neg 73.1%

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

      5. div-sub 73.1%

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

      6. mul-1-neg 73.1%

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

      7. distribute-lft-out-- 73.1%

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

      8. associate-*r/ 73.1%

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

      9. mul-1-neg 73.1%

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

      10. unsub-neg 73.1%

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

      11. distribute-rgt-out-- 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-36} \lor \neg \left(a \leq 7.5 \cdot 10^{-55}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-24} \lor \neg \left(a \leq 3.2 \cdot 10^{-37}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.65e-24) (not (<= a 3.2e-37)))
   (+ x (* (- y x) (/ (- z t) a)))
   (* (- z t) (/ y (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.65e-24) || !(a <= 3.2e-37)) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else {
		tmp = (z - t) * (y / (a - t));
	}
	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 ((a <= (-1.65d-24)) .or. (.not. (a <= 3.2d-37))) then
        tmp = x + ((y - x) * ((z - t) / a))
    else
        tmp = (z - t) * (y / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.65e-24) || !(a <= 3.2e-37)) {
		tmp = x + ((y - x) * ((z - t) / a));
	} else {
		tmp = (z - t) * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.65e-24) or not (a <= 3.2e-37):
		tmp = x + ((y - x) * ((z - t) / a))
	else:
		tmp = (z - t) * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.65e-24) || !(a <= 3.2e-37))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.65e-24) || ~((a <= 3.2e-37)))
		tmp = x + ((y - x) * ((z - t) / a));
	else
		tmp = (z - t) * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.65e-24], N[Not[LessEqual[a, 3.2e-37]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.64999999999999992e-24 or 3.1999999999999999e-37 < a

   1. Initial program 65.6%

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

   3. Taylor expanded in a around inf 60.7%

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

      1. associate-/l* 79.1%

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

   5. Simplified 79.1%

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

   if -1.64999999999999992e-24 < a < 3.1999999999999999e-37

   1. Initial program 68.8%

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

      1. +-commutative 68.8%

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

      2. associate-/l* 81.8%

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

      3. fma-define 81.8%

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

   3. Simplified 81.8%

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

      1. clear-num 81.7%

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

      2. inv-pow 81.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 81.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 81.7%

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

   8. Simplified 81.7%

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

   9. Taylor expanded in y around inf 70.6%

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

       1. div-sub 70.6%

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

       2. associate-*r/ 57.6%

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

       3. *-commutative 57.6%

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

       4. associate-*r/ 61.4%

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

   11. Simplified 61.4%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-24} \lor \neg \left(a \leq 3.2 \cdot 10^{-37}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00068 \lor \neg \left(a \leq 2.75 \cdot 10^{-37}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.00068) (not (<= a 2.75e-37)))
   (+ x (* z (/ (- y x) a)))
   (* (- z t) (/ y (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00068) || !(a <= 2.75e-37)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = (z - t) * (y / (a - t));
	}
	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 ((a <= (-0.00068d0)) .or. (.not. (a <= 2.75d-37))) then
        tmp = x + (z * ((y - x) / a))
    else
        tmp = (z - t) * (y / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -0.00068) || !(a <= 2.75e-37)) {
		tmp = x + (z * ((y - x) / a));
	} else {
		tmp = (z - t) * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -0.00068) or not (a <= 2.75e-37):
		tmp = x + (z * ((y - x) / a))
	else:
		tmp = (z - t) * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -0.00068) || !(a <= 2.75e-37))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	else
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -0.00068) || ~((a <= 2.75e-37)))
		tmp = x + (z * ((y - x) / a));
	else
		tmp = (z - t) * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -0.00068], N[Not[LessEqual[a, 2.75e-37]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.8e-4 or 2.7499999999999999e-37 < a

   1. Initial program 65.6%

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

   3. Taylor expanded in t around 0 62.1%

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

      1. associate-/l* 71.9%

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

   5. Simplified 71.9%

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

   if -6.8e-4 < a < 2.7499999999999999e-37

   1. Initial program 68.8%

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

      1. +-commutative 68.8%

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

      2. associate-/l* 81.4%

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

      3. fma-define 81.4%

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

   3. Simplified 81.4%

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

      1. clear-num 81.3%

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

      2. inv-pow 81.3%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 81.3%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in y around inf 70.5%

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

       1. div-sub 70.5%

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

       2. associate-*r/ 57.8%

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

       3. *-commutative 57.8%

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

       4. associate-*r/ 61.6%

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

   11. Simplified 61.6%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00068 \lor \neg \left(a \leq 2.75 \cdot 10^{-37}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-24} \lor \neg \left(a \leq 5 \cdot 10^{+65}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.6e-24) (not (<= a 5e+65)))
   (- x (* y (/ (- t z) a)))
   (* (- z t) (/ y (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.6e-24) || !(a <= 5e+65)) {
		tmp = x - (y * ((t - z) / a));
	} else {
		tmp = (z - t) * (y / (a - t));
	}
	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 ((a <= (-3.6d-24)) .or. (.not. (a <= 5d+65))) then
        tmp = x - (y * ((t - z) / a))
    else
        tmp = (z - t) * (y / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.6e-24) || !(a <= 5e+65)) {
		tmp = x - (y * ((t - z) / a));
	} else {
		tmp = (z - t) * (y / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.6e-24) or not (a <= 5e+65):
		tmp = x - (y * ((t - z) / a))
	else:
		tmp = (z - t) * (y / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.6e-24) || !(a <= 5e+65))
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.6e-24) || ~((a <= 5e+65)))
		tmp = x - (y * ((t - z) / a));
	else
		tmp = (z - t) * (y / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.6e-24], N[Not[LessEqual[a, 5e+65]], $MachinePrecision]], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6000000000000001e-24 or 4.99999999999999973e65 < a

   1. Initial program 65.5%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in a around inf 60.7%

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

      1. associate-/l* 72.3%

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

   8. Simplified 72.3%

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

   if -3.6000000000000001e-24 < a < 4.99999999999999973e65

   1. Initial program 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 81.9%

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

      3. fma-define 81.9%

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

   3. Simplified 81.9%

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

      1. clear-num 81.8%

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

      2. inv-pow 81.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 81.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 81.8%

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

   8. Simplified 81.8%

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

   9. Taylor expanded in y around inf 66.3%

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

       1. div-sub 66.3%

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

       2. associate-*r/ 53.3%

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

       3. *-commutative 53.3%

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

       4. associate-*r/ 57.4%

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

   11. Simplified 57.4%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-24} \lor \neg \left(a \leq 5 \cdot 10^{+65}\right):\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00042:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-37}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.00042)
   (+ x (/ z (/ a (- y x))))
   (if (<= a 2.65e-37) (* (- z t) (/ y (- a t))) (+ x (* z (/ (- y x) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00042) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 2.65e-37) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x + (z * ((y - x) / 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 (a <= (-0.00042d0)) then
        tmp = x + (z / (a / (y - x)))
    else if (a <= 2.65d-37) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = x + (z * ((y - x) / 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 (a <= -0.00042) {
		tmp = x + (z / (a / (y - x)));
	} else if (a <= 2.65e-37) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x + (z * ((y - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00042:
		tmp = x + (z / (a / (y - x)))
	elif a <= 2.65e-37:
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = x + (z * ((y - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00042)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (a <= 2.65e-37)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00042)
		tmp = x + (z / (a / (y - x)));
	elseif (a <= 2.65e-37)
		tmp = (z - t) * (y / (a - t));
	else
		tmp = x + (z * ((y - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00042], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e-37], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.2000000000000002e-4

   1. Initial program 68.5%

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

   3. Taylor expanded in t around 0 60.9%

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

      1. associate-/l* 73.1%

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

   5. Simplified 73.1%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.2%

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

   7. Applied egg-rr 73.2%

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

   if -4.2000000000000002e-4 < a < 2.64999999999999998e-37

   1. Initial program 68.8%

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

      1. +-commutative 68.8%

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

      2. associate-/l* 81.4%

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

      3. fma-define 81.4%

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

   3. Simplified 81.4%

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

      1. clear-num 81.3%

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

      2. inv-pow 81.3%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 81.3%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in y around inf 70.5%

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

       1. div-sub 70.5%

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

       2. associate-*r/ 57.8%

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

       3. *-commutative 57.8%

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

       4. associate-*r/ 61.6%

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

   11. Simplified 61.6%

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

   if 2.64999999999999998e-37 < a

   1. Initial program 62.6%

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

   3. Taylor expanded in t around 0 63.3%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

Alternative 14: 53.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00047:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-37}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.00047)
   (+ x (* y (/ z a)))
   (if (<= a 3.4e-37) (* (- z t) (/ y (- a t))) (* x (- 1.0 (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00047) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.4e-37) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x * (1.0 - (z / 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 (a <= (-0.00047d0)) then
        tmp = x + (y * (z / a))
    else if (a <= 3.4d-37) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = x * (1.0d0 - (z / 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 (a <= -0.00047) {
		tmp = x + (y * (z / a));
	} else if (a <= 3.4e-37) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00047:
		tmp = x + (y * (z / a))
	elif a <= 3.4e-37:
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00047)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (a <= 3.4e-37)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00047)
		tmp = x + (y * (z / a));
	elseif (a <= 3.4e-37)
		tmp = (z - t) * (y / (a - t));
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00047], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-37], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.69999999999999986e-4

   1. Initial program 68.5%

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

   3. Taylor expanded in y around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in t around 0 57.5%

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

      1. associate-/l* 65.6%

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

   8. Simplified 65.6%

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

   if -4.69999999999999986e-4 < a < 3.40000000000000018e-37

   1. Initial program 68.8%

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

      1. +-commutative 68.8%

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

      2. associate-/l* 81.4%

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

      3. fma-define 81.4%

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

   3. Simplified 81.4%

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

      1. clear-num 81.3%

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

      2. inv-pow 81.3%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 81.3%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 81.3%

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

   8. Simplified 81.3%

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

   9. Taylor expanded in y around inf 70.5%

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

       1. div-sub 70.5%

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

       2. associate-*r/ 57.8%

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

       3. *-commutative 57.8%

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

       4. associate-*r/ 61.6%

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

   11. Simplified 61.6%

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

   if 3.40000000000000018e-37 < a

   1. Initial program 62.6%

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

   3. Taylor expanded in t around 0 63.3%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in x around inf 58.4%

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

      1. mul-1-neg 58.4%

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

      2. unsub-neg 58.4%

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

   8. Simplified 58.4%

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

Alternative 15: 52.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+196}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+196) y (if (<= t 1.75e+51) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+196) {
		tmp = y;
	} else if (t <= 1.75e+51) {
		tmp = x + (y * (z / a));
	} else {
		tmp = 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 <= (-3.4d+196)) then
        tmp = y
    else if (t <= 1.75d+51) then
        tmp = x + (y * (z / a))
    else
        tmp = 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 <= -3.4e+196) {
		tmp = y;
	} else if (t <= 1.75e+51) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+196:
		tmp = y
	elif t <= 1.75e+51:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+196)
		tmp = y;
	elseif (t <= 1.75e+51)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+196)
		tmp = y;
	elseif (t <= 1.75e+51)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+196], y, If[LessEqual[t, 1.75e+51], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4e196 or 1.75e51 < t

   1. Initial program 29.5%

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

      1. +-commutative 29.5%

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

      2. associate-/l* 65.7%

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

      3. fma-define 65.7%

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

   3. Simplified 65.7%

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

      1. clear-num 65.6%

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

      2. inv-pow 65.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 65.6%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 65.6%

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

   8. Simplified 65.6%

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

   9. Taylor expanded in t around inf 56.7%

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

   if -3.4e196 < t < 1.75e51

   1. Initial program 81.1%

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

   3. Taylor expanded in y around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 53.2%

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

      1. associate-/l* 57.7%

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

   8. Simplified 57.7%

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

Alternative 16: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e-23) x (if (<= a 1.5e+60) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e-23) {
		tmp = x;
	} else if (a <= 1.5e+60) {
		tmp = y;
	} else {
		tmp = 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 (a <= (-2.3d-23)) then
        tmp = x
    else if (a <= 1.5d+60) then
        tmp = y
    else
        tmp = 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 (a <= -2.3e-23) {
		tmp = x;
	} else if (a <= 1.5e+60) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e-23:
		tmp = x
	elif a <= 1.5e+60:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e-23)
		tmp = x;
	elseif (a <= 1.5e+60)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e-23)
		tmp = x;
	elseif (a <= 1.5e+60)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e-23], x, If[LessEqual[a, 1.5e+60], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.3000000000000001e-23 or 1.4999999999999999e60 < a

   1. Initial program 65.5%

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

      1. +-commutative 65.5%

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

      2. associate-/l* 89.9%

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

      3. fma-define 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in a around inf 50.3%

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

   if -2.3000000000000001e-23 < a < 1.4999999999999999e60

   1. Initial program 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 81.9%

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

      3. fma-define 81.9%

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

   3. Simplified 81.9%

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

      1. clear-num 81.8%

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

      2. inv-pow 81.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]

   6. Applied egg-rr 81.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}}, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 81.8%

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

   8. Simplified 81.8%

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

   9. Taylor expanded in t around inf 41.2%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 24.9% accurate, 13.0× 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 67.0%

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

   1. +-commutative 67.0%

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

   2. associate-/l* 85.6%

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

   3. fma-define 85.7%

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

3. Simplified 85.7%

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

5. Taylor expanded in a around inf 28.6%

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

Developer Target 1: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -646122513817703/4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 1887201585041587/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))))))

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