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

Percentage Accurate: 67.6% → 86.5%

Time: 11.1s

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: 67.6% 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: 86.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-11} \lor \neg \left(t \leq 3 \cdot 10^{+144}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e-11) (not (<= t 3e+144)))
   (+ y (* (- y x) (/ (- a z) t)))
   (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 <= -1.15e-11) || !(t <= 3e+144)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} 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 <= -1.15e-11) || !(t <= 3e+144))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	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, -1.15e-11], N[Not[LessEqual[t, 3e+144]], $MachinePrecision]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $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 < -1.15000000000000007e-11 or 2.9999999999999999e144 < t

   1. Initial program 36.0%

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

   3. Taylor expanded in t around inf 63.0%

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

      1. associate--l+ 63.0%

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

      2. associate-*r/ 63.0%

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

      3. associate-*r/ 63.0%

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

      4. div-sub 63.0%

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

      5. distribute-lft-out-- 63.0%

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

      6. associate-*r/ 63.0%

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

      7. mul-1-neg 63.0%

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

      8. unsub-neg 63.0%

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

      9. distribute-rgt-out-- 63.1%

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

      10. associate-/l* 86.5%

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

   5. Simplified 86.5%

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

   if -1.15000000000000007e-11 < t < 2.9999999999999999e144

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. associate-/l* 94.1%

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

      3. fma-define 94.1%

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

   3. Simplified 94.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-11} \lor \neg \left(t \leq 3 \cdot 10^{+144}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq -2 \cdot 10^{-306}\right) \land \left(t\_1 \leq 0 \lor \neg \left(t\_1 \leq 2 \cdot 10^{+281}\right)\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (or (<= t_1 (- INFINITY))
           (and (not (<= t_1 -2e-306))
                (or (<= t_1 0.0) (not (<= t_1 2e+281)))))
     (+ y (* (- y x) (/ (- a 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 - t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || (!(t_1 <= -2e-306) && ((t_1 <= 0.0) || !(t_1 <= 2e+281)))) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || (!(t_1 <= -2e-306) && ((t_1 <= 0.0) || !(t_1 <= 2e+281)))) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -math.inf) or (not (t_1 <= -2e-306) and ((t_1 <= 0.0) or not (t_1 <= 2e+281))):
		tmp = y + ((y - x) * ((a - z) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || (!(t_1 <= -2e-306) && ((t_1 <= 0.0) || !(t_1 <= 2e+281))))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - 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 - t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || (~((t_1 <= -2e-306)) && ((t_1 <= 0.0) || ~((t_1 <= 2e+281)))))
		tmp = y + ((y - x) * ((a - 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[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], And[N[Not[LessEqual[t$95$1, -2e-306]], $MachinePrecision], Or[LessEqual[t$95$1, 0.0], N[Not[LessEqual[t$95$1, 2e+281]], $MachinePrecision]]]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or -2.00000000000000006e-306 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0 or 2.0000000000000001e281 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 31.5%

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

   3. Taylor expanded in t around inf 60.2%

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

      1. associate--l+ 60.2%

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

      2. associate-*r/ 60.2%

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

      3. associate-*r/ 60.2%

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

      4. div-sub 60.2%

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

      5. distribute-lft-out-- 60.2%

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

      6. associate-*r/ 60.2%

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

      7. mul-1-neg 60.2%

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

      8. unsub-neg 60.2%

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

      9. distribute-rgt-out-- 61.2%

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

      10. associate-/l* 81.1%

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

   5. Simplified 81.1%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000006e-306 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.0000000000000001e281

   1. Initial program 97.9%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-306}\right) \land \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0 \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2 \cdot 10^{+281}\right)\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-286}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.6e-7)
   y
   (if (<= t -3.15e-114)
     (* x (- 1.0 (/ z a)))
     (if (<= t 1.2e-286)
       (+ x (/ (* y z) a))
       (if (<= t 7e+132) (+ x (* z (/ y a))) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e-7) {
		tmp = y;
	} else if (t <= -3.15e-114) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.2e-286) {
		tmp = x + ((y * z) / a);
	} else if (t <= 7e+132) {
		tmp = x + (z * (y / 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 <= (-6.6d-7)) then
        tmp = y
    else if (t <= (-3.15d-114)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.2d-286) then
        tmp = x + ((y * z) / a)
    else if (t <= 7d+132) then
        tmp = x + (z * (y / 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 <= -6.6e-7) {
		tmp = y;
	} else if (t <= -3.15e-114) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.2e-286) {
		tmp = x + ((y * z) / a);
	} else if (t <= 7e+132) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e-7:
		tmp = y
	elif t <= -3.15e-114:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.2e-286:
		tmp = x + ((y * z) / a)
	elif t <= 7e+132:
		tmp = x + (z * (y / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e-7)
		tmp = y;
	elseif (t <= -3.15e-114)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.2e-286)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 7e+132)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.6e-7)
		tmp = y;
	elseif (t <= -3.15e-114)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.2e-286)
		tmp = x + ((y * z) / a);
	elseif (t <= 7e+132)
		tmp = x + (z * (y / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e-7], y, If[LessEqual[t, -3.15e-114], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-286], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+132], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.6000000000000003e-7 or 7.00000000000000041e132 < t

   1. Initial program 36.7%

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

   3. Taylor expanded in t around inf 57.2%

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

   if -6.6000000000000003e-7 < t < -3.15000000000000007e-114

   1. Initial program 76.2%

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

   3. Taylor expanded in t around 0 48.4%

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

      1. associate-/l* 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in x around inf 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   8. Simplified 51.3%

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

   if -3.15000000000000007e-114 < t < 1.19999999999999997e-286

   1. Initial program 96.1%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0 74.7%

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

   if 1.19999999999999997e-286 < t < 7.00000000000000041e132

   1. Initial program 84.3%

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

   3. Taylor expanded in t around 0 58.8%

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

      1. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

      1. clear-num 65.2%

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

      2. un-div-inv 65.2%

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

   7. Applied egg-rr 65.2%

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

   8. Taylor expanded in y around inf 54.6%

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

      1. associate-*l/ 58.8%

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

      2. *-commutative 58.8%

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

   10. Simplified 58.8%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.15 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-286}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-146}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+138}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))))
   (if (<= t -1.4e-56)
     t_1
     (if (<= t 4e-146)
       (+ x (* z (/ (- y x) a)))
       (if (<= t 4.8e+138) (+ x (* z (/ y (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double tmp;
	if (t <= -1.4e-56) {
		tmp = t_1;
	} else if (t <= 4e-146) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 4.8e+138) {
		tmp = x + (z * (y / (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 + (z * (x / t))
    if (t <= (-1.4d-56)) then
        tmp = t_1
    else if (t <= 4d-146) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 4.8d+138) then
        tmp = x + (z * (y / (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 + (z * (x / t));
	double tmp;
	if (t <= -1.4e-56) {
		tmp = t_1;
	} else if (t <= 4e-146) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 4.8e+138) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	tmp = 0
	if t <= -1.4e-56:
		tmp = t_1
	elif t <= 4e-146:
		tmp = x + (z * ((y - x) / a))
	elif t <= 4.8e+138:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -1.4e-56)
		tmp = t_1;
	elseif (t <= 4e-146)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 4.8e+138)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -1.4e-56)
		tmp = t_1;
	elseif (t <= 4e-146)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 4.8e+138)
		tmp = x + (z * (y / (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[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-56], t$95$1, If[LessEqual[t, 4e-146], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+138], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999997e-56 or 4.8000000000000002e138 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. associate-*r/ 64.2%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

      10. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in y around 0 57.5%

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

       1. associate-*r/ 57.5%

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

       2. *-commutative 57.5%

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

       3. neg-mul-1 57.5%

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

       4. distribute-rgt-neg-in 57.5%

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

       5. associate-/l* 66.5%

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

       6. distribute-neg-frac 66.5%

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

       7. distribute-neg-frac2 66.5%

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

   11. Simplified 66.5%

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

   if -1.39999999999999997e-56 < t < 4.0000000000000001e-146

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0 88.4%

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

      1. associate-/l* 91.1%

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

   5. Simplified 91.1%

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

   if 4.0000000000000001e-146 < t < 4.8000000000000002e138

   1. Initial program 80.5%

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

   3. Taylor expanded in z around inf 68.5%

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

      1. associate-/l* 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in y around inf 63.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-56}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-146}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+138}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -3.15 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))))
   (if (<= t -3.15e-56)
     t_1
     (if (<= t 1.55e-136)
       (+ x (/ z (/ a (- y x))))
       (if (<= t 7.8e+132) (+ x (* z (/ y (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double tmp;
	if (t <= -3.15e-56) {
		tmp = t_1;
	} else if (t <= 1.55e-136) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 7.8e+132) {
		tmp = x + (z * (y / (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 + (z * (x / t))
    if (t <= (-3.15d-56)) then
        tmp = t_1
    else if (t <= 1.55d-136) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 7.8d+132) then
        tmp = x + (z * (y / (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 + (z * (x / t));
	double tmp;
	if (t <= -3.15e-56) {
		tmp = t_1;
	} else if (t <= 1.55e-136) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 7.8e+132) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	tmp = 0
	if t <= -3.15e-56:
		tmp = t_1
	elif t <= 1.55e-136:
		tmp = x + (z / (a / (y - x)))
	elif t <= 7.8e+132:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -3.15e-56)
		tmp = t_1;
	elseif (t <= 1.55e-136)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 7.8e+132)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -3.15e-56)
		tmp = t_1;
	elseif (t <= 1.55e-136)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 7.8e+132)
		tmp = x + (z * (y / (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[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.15e-56], t$95$1, If[LessEqual[t, 1.55e-136], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+132], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.1499999999999999e-56 or 7.80000000000000002e132 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. associate-*r/ 64.2%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

      10. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in y around 0 57.5%

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

       1. associate-*r/ 57.5%

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

       2. *-commutative 57.5%

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

       3. neg-mul-1 57.5%

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

       4. distribute-rgt-neg-in 57.5%

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

       5. associate-/l* 66.5%

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

       6. distribute-neg-frac 66.5%

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

       7. distribute-neg-frac2 66.5%

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

   11. Simplified 66.5%

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

   if -3.1499999999999999e-56 < t < 1.55e-136

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 86.8%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

      1. clear-num 90.4%

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

      2. un-div-inv 90.4%

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

   7. Applied egg-rr 90.4%

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

   if 1.55e-136 < t < 7.80000000000000002e132

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 63.1%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= t -2e-56)
     t_1
     (if (<= t 1.9e-136)
       (+ x (/ z (/ a (- y x))))
       (if (<= t 8.6e+132) (+ x (* z (/ y (- a t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -2e-56) {
		tmp = t_1;
	} else if (t <= 1.9e-136) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 8.6e+132) {
		tmp = x + (z * (y / (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 + (z * ((x - y) / t))
    if (t <= (-2d-56)) then
        tmp = t_1
    else if (t <= 1.9d-136) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 8.6d+132) then
        tmp = x + (z * (y / (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 + (z * ((x - y) / t));
	double tmp;
	if (t <= -2e-56) {
		tmp = t_1;
	} else if (t <= 1.9e-136) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 8.6e+132) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * ((x - y) / t))
	tmp = 0
	if t <= -2e-56:
		tmp = t_1
	elif t <= 1.9e-136:
		tmp = x + (z / (a / (y - x)))
	elif t <= 8.6e+132:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -2e-56)
		tmp = t_1;
	elseif (t <= 1.9e-136)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 8.6e+132)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (t <= -2e-56)
		tmp = t_1;
	elseif (t <= 1.9e-136)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 8.6e+132)
		tmp = x + (z * (y / (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[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-56], t$95$1, If[LessEqual[t, 1.9e-136], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+132], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0000000000000001e-56 or 8.59999999999999964e132 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. associate-*r/ 64.2%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

      10. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   if -2.0000000000000001e-56 < t < 1.9000000000000001e-136

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 86.8%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

      1. clear-num 90.4%

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

      2. un-div-inv 90.4%

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

   7. Applied egg-rr 90.4%

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

   if 1.9000000000000001e-136 < t < 8.59999999999999964e132

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 63.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-56}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-58}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.35e-58)
   (+ y (/ z (/ t (- x y))))
   (if (<= t 1.7e-136)
     (+ x (/ z (/ a (- y x))))
     (if (<= t 7e+132) (+ x (* z (/ y (- a t)))) (+ y (* z (/ (- x y) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.35e-58) {
		tmp = y + (z / (t / (x - y)));
	} else if (t <= 1.7e-136) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 7e+132) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / 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 (t <= (-2.35d-58)) then
        tmp = y + (z / (t / (x - y)))
    else if (t <= 1.7d-136) then
        tmp = x + (z / (a / (y - x)))
    else if (t <= 7d+132) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = y + (z * ((x - y) / 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 (t <= -2.35e-58) {
		tmp = y + (z / (t / (x - y)));
	} else if (t <= 1.7e-136) {
		tmp = x + (z / (a / (y - x)));
	} else if (t <= 7e+132) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.35e-58:
		tmp = y + (z / (t / (x - y)))
	elif t <= 1.7e-136:
		tmp = x + (z / (a / (y - x)))
	elif t <= 7e+132:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.35e-58)
		tmp = Float64(y + Float64(z / Float64(t / Float64(x - y))));
	elseif (t <= 1.7e-136)
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	elseif (t <= 7e+132)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.35e-58)
		tmp = y + (z / (t / (x - y)));
	elseif (t <= 1.7e-136)
		tmp = x + (z / (a / (y - x)));
	elseif (t <= 7e+132)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.35e-58], N[(y + N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-136], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+132], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.34999999999999997e-58

   1. Initial program 52.4%

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

   3. Taylor expanded in t around inf 67.5%

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

      1. associate--l+ 67.5%

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

      2. associate-*r/ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. div-sub 67.5%

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

      5. distribute-lft-out-- 67.5%

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

      6. associate-*r/ 67.5%

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

      7. mul-1-neg 67.5%

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

      8. unsub-neg 67.5%

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

      9. distribute-rgt-out-- 67.5%

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

      10. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in z around inf 65.4%

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

      1. associate-/l* 72.8%

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

   8. Simplified 72.8%

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

      1. clear-num 72.7%

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

      2. un-div-inv 73.8%

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

   10. Applied egg-rr 73.8%

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

   if -2.34999999999999997e-58 < t < 1.7e-136

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0 86.8%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

      1. clear-num 90.4%

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

      2. un-div-inv 90.4%

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

   7. Applied egg-rr 90.4%

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

   if 1.7e-136 < t < 7.00000000000000041e132

   1. Initial program 80.8%

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

   3. Taylor expanded in z around inf 69.7%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 63.1%

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

   if 7.00000000000000041e132 < t

   1. Initial program 24.5%

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

   3. Taylor expanded in t around inf 58.9%

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

      1. associate--l+ 58.9%

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

      2. associate-*r/ 58.9%

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

      3. associate-*r/ 58.9%

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

      4. div-sub 58.9%

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

      5. distribute-lft-out-- 58.9%

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

      6. associate-*r/ 58.9%

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

      7. mul-1-neg 58.9%

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

      8. unsub-neg 58.9%

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

      9. distribute-rgt-out-- 59.1%

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

      10. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around inf 51.8%

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

      1. associate-/l* 79.7%

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

   8. Simplified 79.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-58}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 3.75 \cdot 10^{+133}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.15e-56) (not (<= t 3.75e+133)))
   (+ y (* (- y x) (/ (- a z) t)))
   (+ x (* z (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.15e-56) || !(t <= 3.75e+133)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x + (z * ((y - x) / (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 ((t <= (-3.15d-56)) .or. (.not. (t <= 3.75d+133))) then
        tmp = y + ((y - x) * ((a - z) / t))
    else
        tmp = x + (z * ((y - x) / (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 ((t <= -3.15e-56) || !(t <= 3.75e+133)) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else {
		tmp = x + (z * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.15e-56) or not (t <= 3.75e+133):
		tmp = y + ((y - x) * ((a - z) / t))
	else:
		tmp = x + (z * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.15e-56) || !(t <= 3.75e+133))
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.15e-56) || ~((t <= 3.75e+133)))
		tmp = y + ((y - x) * ((a - z) / t));
	else
		tmp = x + (z * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.15e-56], N[Not[LessEqual[t, 3.75e+133]], $MachinePrecision]], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1499999999999999e-56 or 3.74999999999999996e133 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. associate-*r/ 64.2%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

      10. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   if -3.1499999999999999e-56 < t < 3.74999999999999996e133

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf 82.4%

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

      1. associate-/l* 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 3.75 \cdot 10^{+133}\right):\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-7}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e-7)
   (+ y (/ z (/ t (- x y))))
   (if (<= t 7e+132)
     (+ x (* z (/ (- y x) (- a t))))
     (+ y (* z (/ (- x y) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e-7) {
		tmp = y + (z / (t / (x - y)));
	} else if (t <= 7e+132) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / 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 (t <= (-6d-7)) then
        tmp = y + (z / (t / (x - y)))
    else if (t <= 7d+132) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = y + (z * ((x - y) / 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 (t <= -6e-7) {
		tmp = y + (z / (t / (x - y)));
	} else if (t <= 7e+132) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y + (z * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e-7:
		tmp = y + (z / (t / (x - y)))
	elif t <= 7e+132:
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = y + (z * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e-7)
		tmp = Float64(y + Float64(z / Float64(t / Float64(x - y))));
	elseif (t <= 7e+132)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e-7)
		tmp = y + (z / (t / (x - y)));
	elseif (t <= 7e+132)
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = y + (z * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e-7], N[(y + N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+132], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.9999999999999997e-7

   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 t around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. associate-*r/ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

      6. associate-*r/ 67.0%

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

      7. mul-1-neg 67.0%

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

      8. unsub-neg 67.0%

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

      9. distribute-rgt-out-- 67.0%

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

      10. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in z around inf 68.0%

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

      1. associate-/l* 80.3%

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

   8. Simplified 80.3%

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

      1. clear-num 80.3%

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

      2. un-div-inv 80.3%

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

   10. Applied egg-rr 80.3%

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

   if -5.9999999999999997e-7 < t < 7.00000000000000041e132

   1. Initial program 86.5%

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

   3. Taylor expanded in z around inf 78.5%

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

      1. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   if 7.00000000000000041e132 < t

   1. Initial program 24.5%

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

   3. Taylor expanded in t around inf 58.9%

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

      1. associate--l+ 58.9%

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

      2. associate-*r/ 58.9%

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

      3. associate-*r/ 58.9%

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

      4. div-sub 58.9%

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

      5. distribute-lft-out-- 58.9%

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

      6. associate-*r/ 58.9%

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

      7. mul-1-neg 58.9%

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

      8. unsub-neg 58.9%

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

      9. distribute-rgt-out-- 59.1%

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

      10. associate-/l* 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around inf 51.8%

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

      1. associate-/l* 79.7%

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

   8. Simplified 79.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-7}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 5.7 \cdot 10^{+133}\right):\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.15e-56) (not (<= t 5.7e+133)))
   (+ y (* z (/ x t)))
   (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.15e-56) || !(t <= 5.7e+133)) {
		tmp = y + (z * (x / t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.15d-56)) .or. (.not. (t <= 5.7d+133))) then
        tmp = y + (z * (x / t))
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.15e-56) || !(t <= 5.7e+133)) {
		tmp = y + (z * (x / t));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.15e-56) or not (t <= 5.7e+133):
		tmp = y + (z * (x / t))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.15e-56) || !(t <= 5.7e+133))
		tmp = Float64(y + Float64(z * Float64(x / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.15e-56) || ~((t <= 5.7e+133)))
		tmp = y + (z * (x / t));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.15e-56], N[Not[LessEqual[t, 5.7e+133]], $MachinePrecision]], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1499999999999999e-56 or 5.69999999999999977e133 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. associate-*r/ 64.2%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

      10. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in y around 0 57.5%

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

       1. associate-*r/ 57.5%

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

       2. *-commutative 57.5%

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

       3. neg-mul-1 57.5%

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

       4. distribute-rgt-neg-in 57.5%

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

       5. associate-/l* 66.5%

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

       6. distribute-neg-frac 66.5%

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

       7. distribute-neg-frac2 66.5%

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

   11. Simplified 66.5%

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

   if -3.1499999999999999e-56 < t < 5.69999999999999977e133

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-/l* 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in a around inf 66.1%

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

      1. associate-/l* 71.0%

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

   8. Simplified 71.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 5.7 \cdot 10^{+133}\right):\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 7.8 \cdot 10^{+132}\right):\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.15e-56) (not (<= t 7.8e+132)))
   (- y (* z (/ y t)))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.15e-56) || !(t <= 7.8e+132)) {
		tmp = y - (z * (y / t));
	} else {
		tmp = x + (y * (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 ((t <= (-3.15d-56)) .or. (.not. (t <= 7.8d+132))) then
        tmp = y - (z * (y / t))
    else
        tmp = x + (y * (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 ((t <= -3.15e-56) || !(t <= 7.8e+132)) {
		tmp = y - (z * (y / t));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.15e-56) or not (t <= 7.8e+132):
		tmp = y - (z * (y / t))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.15e-56) || !(t <= 7.8e+132))
		tmp = Float64(y - Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.15e-56) || ~((t <= 7.8e+132)))
		tmp = y - (z * (y / t));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.15e-56], N[Not[LessEqual[t, 7.8e+132]], $MachinePrecision]], N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1499999999999999e-56 or 7.80000000000000002e132 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. associate-*r/ 64.2%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

      10. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in y around inf 60.0%

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

   if -3.1499999999999999e-56 < t < 7.80000000000000002e132

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-/l* 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in t around 0 61.7%

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

      1. +-commutative 61.7%

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

      2. associate-/l* 65.3%

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

   8. Simplified 65.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 7.8 \cdot 10^{+132}\right):\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 7 \cdot 10^{+132}\right):\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.15e-56) (not (<= t 7e+132)))
   (+ y (* z (/ x t)))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.15e-56) || !(t <= 7e+132)) {
		tmp = y + (z * (x / t));
	} else {
		tmp = x + (y * (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 ((t <= (-3.15d-56)) .or. (.not. (t <= 7d+132))) then
        tmp = y + (z * (x / t))
    else
        tmp = x + (y * (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 ((t <= -3.15e-56) || !(t <= 7e+132)) {
		tmp = y + (z * (x / t));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.15e-56) or not (t <= 7e+132):
		tmp = y + (z * (x / t))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.15e-56) || !(t <= 7e+132))
		tmp = Float64(y + Float64(z * Float64(x / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.15e-56) || ~((t <= 7e+132)))
		tmp = y + (z * (x / t));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.15e-56], N[Not[LessEqual[t, 7e+132]], $MachinePrecision]], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1499999999999999e-56 or 7.00000000000000041e132 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 64.2%

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

      1. associate--l+ 64.2%

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

      2. associate-*r/ 64.2%

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

      3. associate-*r/ 64.2%

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

      4. div-sub 64.2%

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

      5. distribute-lft-out-- 64.2%

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

      6. associate-*r/ 64.2%

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

      7. mul-1-neg 64.2%

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

      8. unsub-neg 64.2%

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

      9. distribute-rgt-out-- 64.3%

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

      10. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 75.4%

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

   8. Simplified 75.4%

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

   9. Taylor expanded in y around 0 57.5%

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

       1. associate-*r/ 57.5%

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

       2. *-commutative 57.5%

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

       3. neg-mul-1 57.5%

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

       4. distribute-rgt-neg-in 57.5%

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

       5. associate-/l* 66.5%

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

       6. distribute-neg-frac 66.5%

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

       7. distribute-neg-frac2 66.5%

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

   11. Simplified 66.5%

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

   if -3.1499999999999999e-56 < t < 7.00000000000000041e132

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-/l* 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in t around 0 61.7%

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

      1. +-commutative 61.7%

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

      2. associate-/l* 65.3%

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

   8. Simplified 65.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56} \lor \neg \left(t \leq 7 \cdot 10^{+132}\right):\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e-7) y (if (<= t 7.5e+132) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e-7) {
		tmp = y;
	} else if (t <= 7.5e+132) {
		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 <= (-3.4d-7)) then
        tmp = y
    else if (t <= 7.5d+132) 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 <= -3.4e-7) {
		tmp = y;
	} else if (t <= 7.5e+132) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e-7:
		tmp = y
	elif t <= 7.5e+132:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e-7)
		tmp = y;
	elseif (t <= 7.5e+132)
		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 <= -3.4e-7)
		tmp = y;
	elseif (t <= 7.5e+132)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e-7], y, If[LessEqual[t, 7.5e+132], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.39999999999999974e-7 or 7.50000000000000017e132 < t

   1. Initial program 36.7%

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

   3. Taylor expanded in t around inf 57.2%

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

   if -3.39999999999999974e-7 < t < 7.50000000000000017e132

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in x around inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. unsub-neg 52.4%

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

   8. Simplified 52.4%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+133}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e-7) y (if (<= t 3.75e+133) (+ x (* z (/ y a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e-7) {
		tmp = y;
	} else if (t <= 3.75e+133) {
		tmp = x + (z * (y / 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 <= (-6.5d-7)) then
        tmp = y
    else if (t <= 3.75d+133) then
        tmp = x + (z * (y / 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 <= -6.5e-7) {
		tmp = y;
	} else if (t <= 3.75e+133) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e-7:
		tmp = y
	elif t <= 3.75e+133:
		tmp = x + (z * (y / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e-7)
		tmp = y;
	elseif (t <= 3.75e+133)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e-7)
		tmp = y;
	elseif (t <= 3.75e+133)
		tmp = x + (z * (y / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e-7], y, If[LessEqual[t, 3.75e+133], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -6.50000000000000024e-7 or 3.74999999999999996e133 < t

   1. Initial program 36.7%

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

   3. Taylor expanded in t around inf 57.2%

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

   if -6.50000000000000024e-7 < t < 3.74999999999999996e133

   1. Initial program 86.5%

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

   3. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 70.7%

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

   5. Simplified 70.7%

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

      1. clear-num 70.7%

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

      2. un-div-inv 70.7%

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

   7. Applied egg-rr 70.7%

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

   8. Taylor expanded in y around inf 56.8%

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

      1. associate-*l/ 59.9%

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

      2. *-commutative 59.9%

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

   10. Simplified 59.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3.75 \cdot 10^{+133}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.6e-7) y (if (<= t 1.05e+133) (+ x (* y (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.6e-7) {
		tmp = y;
	} else if (t <= 1.05e+133) {
		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 <= (-6.6d-7)) then
        tmp = y
    else if (t <= 1.05d+133) 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 <= -6.6e-7) {
		tmp = y;
	} else if (t <= 1.05e+133) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.6e-7:
		tmp = y
	elif t <= 1.05e+133:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.6e-7)
		tmp = y;
	elseif (t <= 1.05e+133)
		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 <= -6.6e-7)
		tmp = y;
	elseif (t <= 1.05e+133)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.6e-7], y, If[LessEqual[t, 1.05e+133], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6000000000000003e-7 or 1.05e133 < t

   1. Initial program 36.7%

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

   3. Taylor expanded in t around inf 57.2%

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

   if -6.6000000000000003e-7 < t < 1.05e133

   1. Initial program 86.5%

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

   3. Taylor expanded in y around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-/l* 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in t around 0 56.8%

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

      1. +-commutative 56.8%

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

      2. associate-/l* 61.2%

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

   8. Simplified 61.2%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.15e-56) y (if (<= t 7e+132) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.15e-56) {
		tmp = y;
	} else if (t <= 7e+132) {
		tmp = x;
	} 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 <= (-3.15d-56)) then
        tmp = y
    else if (t <= 7d+132) then
        tmp = x
    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 <= -3.15e-56) {
		tmp = y;
	} else if (t <= 7e+132) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.15e-56:
		tmp = y
	elif t <= 7e+132:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.15e-56)
		tmp = y;
	elseif (t <= 7e+132)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.15e-56)
		tmp = y;
	elseif (t <= 7e+132)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.15e-56], y, If[LessEqual[t, 7e+132], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1499999999999999e-56 or 7.00000000000000041e132 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 51.2%

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

   if -3.1499999999999999e-56 < t < 7.00000000000000041e132

   1. Initial program 89.3%

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

   3. Taylor expanded in a around inf 38.5%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 25.7% 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 69.4%

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

3. Taylor expanded in a around inf 27.0%

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

4. Final simplification 27.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 86.6% 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 2024050 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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